handbook of microstrip antennas

IEE ELECTROMAGNETIC WAVES SERIES 28 Series Editors: Professor P. J. B. Clarricoats Professor Y. Rahrnat-Samii Professor J. R. Wait

Handbook of

ANTENNAS

Other volumes in this series: Volume 1 Geometrical theory of diffraction for electromagnetic waves G. L. James Volume 2 Electromagneticwaves and CUN& structures L. Lewin, D. C. Chang and E. F. Kuester Volume 3 Microwave homodyne systems R. J. King Volume 4 Radio direction-finding P. J. D. Gething Volume 5 ELF communications antennas M. L. Burrows Volume 6 Waveguide tapers, transitions and couplers F. Sporleder and H. G. Unger Volume 7 Reflector antenna analysis and design P. J. Wood Volume 8 Effects of the troposphere on radio communications M. P. M. Hall Volume 9 Schumann resonances in the earth-ionosphere cavity P. V. Bliokh, A. P. Nikolaenko and Y. F. Flippov Volume 10 Aperture antennas and diffraction theory E. V. Jull Volume 11 Adaptive array principles J. E. Hudson Volume 12 Microstrip antenna theory and design J. R. James, P. S. Hall and C. Wood Volume 13 Energy in electromagnetism H. G. Booker Volume 14 Leaky feeders and subsurface radio communications P. Delogne Volume 15 The handbook of antenna design, Volume 1A. W. Rudge, K. Milne, A. D. Olver, P. Knight (Editors) Volume 16 The handbook of antenna design, Volume 2 A. W. Rudge, K. Milne. A. D. Olver. P. Kniaht (Editors) predichon P. Rohan e Volume 17 ~ u ~ e i l l & cradar Volume 18 Cormaated horns tor microwave antennas P. J. B. Clarricoats and A-D. Olver Volume 19 Microwave antenna theory and design S. Silver (Editor) Volume 20 Advances in radar techniques J. Clarke (Editor) Volume 21 Waveguide handbook N. Marcuvitz Volume 22 Target adaptive matched illumination radar D. T. Gjessing Volume 23 Ferrites at microwave frequencies A. J. Baden Fuller Volume 24 Propagation of short radio waves D. E. Kerr (Editor) Volume 25 Principles of microwave circuits C. G. Montgomery, R. H. Dicke, E. M. Purcell (Editors) Volume 26 Spherical near-field antenna measurements J. E. Hansen (Editor) Volume 27 Electromagnetic radiation from cylindrical structures J. R. Wait Volume 28 Handbook of microstrip antennas J. R. James and P. S. Hall (Editors) Volume 29 Satellite-to-ground radiowave propagation J. E. Allnutt Volume 30 Radiowave propagation M. P. M. Hall and L. W. Barclay . (Editors) Volume 31 Ionospheric radio K. Davies

Handbook of

ANTENNAS

Edited by

J R James & P s Hall

~

Peter Peregrinus Ltd, on behalf of the Institution of Electrical Engineers

Published by: Peter Peregrinus Ltd., London, United Kingdom

o 1989: Peter Peregrinus Ltd.

All rights resewed. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any meanselectronic, mechanical, photocopying, recording or otherwise-without the prior written permission of the publisher. While the authors and the publishers believe that the information and guidance given in this work are correct, all parties must rely upon their own skill and judgment when making use of them. Neither the authors nor the publishers assume any liability to anyone for any loss or damage caused by any error or omission in the work, whether such error or omission is the result of negligence o: any other cause. Any and aii such liability is disclaimed.

Contents

Volume 1

1

Foreword Preface List of contributors Introduction - J.R. James and P.S. Hall 1.I 1.2 1.3 1.4 1.5 1.6

British Library Cataloguing i n Publication Data Handbook of Microstrip Antennas 1. Microwave equipment: Microstrip antennas I. James, J. R. (James Roderick, 1933II. Hall, P. S. (Peter S) Ill. Institution of Electrical Engineers IV. Series 621.381'33

ISBN 0 86341 150 9

Printed in England by Short Run Press Ltd., Exeter

2

Historical development and future prospects Fundamental issues and design challenges Features of microstrip antenna technology 1.2.1 1.2.2 Fundamental problems The handbook and advances presented Glossary of printed antenna types Summary comments References

Analysis of circular microstrip antennas - L. Shafai and A.A. Kishk 2.1 2.2

2.3

2.4 2.5 2.6 2.7

Introduction Formulation of the problem 2.2.1 Matrix formulation 2.2.2 Excitation matrix 2.2.3 Radiation fields Application I: Circular patch antenna 2.3.1 Surface fields 2.3.2 Feed location Effect of the substrate permittivity 2.3.3 Effect of the substrate thickness 2.3.4 Effect of the ground-plane radius 2.3.5 Effect of the ground-plane thickness 2.3.6 2.3.7 Circular polarisation Effect of a central shorting pin 2.3.8 Application 2: Wraparound microstrip antenna Application 3: Reflector antenna feeds Concluding remarks References

xvii xix

xxi 1

Contents

vi Contents 3

Characteristics of microstrip patch antennas and some methods of improving frequency agility and bandwidth - K.F. Lee and J.S. Dahele Introduction Cavity model for analysing microstrip patch antennas 3.2.1 lntroduction 3.2.2 Feed modelling, resonant frequencies and internal fields 3.2.3 Radiation field 3.2.4 Losses in the cavity 3.2.5 Input impedance 3.2.6 VSWR bandwidth 3.2.7 Qualitative description of the results predicted by the model Basic characteristics of some common patches 3.3.1 The rectangular patch 3.3.2 The circular patch 3.3.3 The equitriangular patch 3.3.4 Annuiar-ring patch 3.3.5 Comparison of characteristics of rectangular, circular, equitriangular and annular-ring patches 3.3.6 Brief mention of other patches Some methods of improving the frequency agility and bandwidth of microstrip patch antennas 3.4.1 Introduction 3.4.2 Some methods of tuning MPAs 3.4.3 Dual-band structures 3.4.4 Electromagnetic-coupled patch antenna (EMCP) Summary Acknowledgments References

4

5

Microstrip dipoles - P.B. Katehi, D.R. Jackson and N.G. Alexopoulis Introduction Infinitesimal dipole 5.2.1 Analysis 5.2.2 Substrate effects 5.2.3 Superstrate effects Moment-method techniques for planar strip geometries 5.3.1 Basis functions 5.3.2 Reaction between basis functions 5.3.3 Plane-wave-spectrum method 5.3.4 Real-space integration method 5.3.5 Point-dipole approximation 5.3.6 Moment-method equations Centre-fed dipoles 5.4.1 Single dipole 5.4.2 Mutual impedance EMC dipoles 5.5.1 Methods of analysis 5.5.2 Single dipole 5.5.3 Multiple dipoles Finite array of EMC dipoles 5.6.1 Analysis 5.6.2 Calculation of coefficients 5.6.3 Array design Conclusions References

6

Multilayer and parasitic configurations - D.H. Schaubert 6.1 6.2

Circular polarisation and bandwidth - M. Haneishi and Y. Suzuki Various types of circularly polarised antenna 4.1.1 Microstrip patch antennas 4.1.2 Other types of circularly polarised printed antennas Simple design techniques for singly-fed circularly polarised microstrip antennas 4.2.1 Rectangular type 4.2.2 Circular type More exact treatment for singly-fed circularly polarised microstrip antennas 4.3.1 Analysis 4.3.2 Conditions for circularly polarised radiation 4.3.3 Example Some considerations on mutual coupling Wideband techniques 4.5.1 Design of wideband element 4.5.2 Technique using parasitic element 4.5.3 Technique using paired element References

6.3 6.4 6.5 6.6 7

Introduction Stacked elements for dual-frequency or dual polarisation operation Antennas with separate feeds for each function 6.2.1 Antennas for multiple frequencies and increased 6.2.2 bandwidth Two-sided aperture-coupled patch Parasitic elements on antenna substrate Summary References

Wideband flat dipole and short-circuit microstrip patch elements and arrays - G. Dubost 7.1 7.2 7.3

Flat dipole elements and arrays 7.1.1 Elementary sources Array designs: losses and efficiencies 7.1.2 Short-circuit microstrip patches and arrays 7.2.1 Elementary source 7.2.2 Array designs References

vii

viii

8

Contents Numerical analysis of microstrip patch antennas - J.R. Mosig, R.C. Hall and F.E. Gardiol Introduction 8.1.1 General description 8.1.2 The integral equation model Model based on the electric surface current 8.2.1 Geometry of the model and boundary conditions 8.2.2 Potentials for the diffracted fields 8.2.3 Green's functions 8.2.4 Mixed potential integral equation (MPIE) 8.2.5 Sketch of the proposed technique Horizontal electric dipole (HED) in microstrip 8.3.1 The vector potential 8.3.2 Scalar potential and the fields 8.3.3 Surface waves and spectral plane k 8.3.4 Far-field approximations 8.3.5 Radiation resistance and antenna efficiency Numerical techniques for Sommerfeld integrals 8.4.1 Numerical integration oii the real axis 8.4.2 Integrating oscillating functions over unbounded intervals Construction of the Green's functions Method of moments 8.6.1 Rooftop (subsectional) - basis functions 8.6.2 Entire domain basis functions Excitation and loading 8.7.1 Several microstrip-antenna excitations 8.7.2 Coaxial excitation and input impedance 8.7.3 Multiport analysis Single rectangular patch antenna 8.8.1 Entire-domain versus subdomain basis functions 8.8.2 Convergence using subsectional basis functions 8.8.3 Surface currents Microstrip arrays 8.9.1 Array modelling 8.9.2 Mutual coupling 8.9.3 Linear array of few patches Acknowledgments References

9

Contents Edge-admittance and mutual-coupling networks 9.4.1 Edge-admittance networks 9.4.2 Mutual-coupling network Analysis of multiport-network model 9.5.1 Segmentation method 9.5.2 Desegmentation method Examples of microstrip antenna structures analysed by multiportnetwork approach 9.6.1 Circularly polarised microstrip patches 9.6.2 Broadband multiresonator microstrip antennas Multiport microstrip patches and series-fed arrays 9.6.3 C A D of microstrip patch antennas and arrays Appendix: Green's functions for various planar configurations Acknowledgments References 10

Transmission-line model for rectangular microstrip antennas

- A. Van rle Capelle

Introduction Simple transmission-line model Description of the transmission line model 10.2.1 Expressions for G, and B, 10.2.2 Expressions for the line parameters 10.2.3 Improved transmission-line model Description of the improved transmission-line model 10.3.1 Expression for the self-susceptance B, 10.3.2 Expression for the self-conductance G, 10.3.3 Expression for the mutual conductance G, 10.3.4 Expression for the mutual susceptance B, 10.3.5 Expressions for the line parameters 10.3.6 Application of the improved transmission-line model Analysis and design of rectangular microstrip antennas 10.4.1 10.4.2 Comparison with other methods 10.4.3 Comparison with experimental results 10.4.4 Design application Transmission-line model for mutual coupling 10.5.1 Description of the model Calculation of the model parameters 10.5.2 10.5.3 Comparison with other methods Acknowledgements References

Multiport network approach for modelling and analysis of microstrip patch antennas and arrays - K.C. Gupta 455 11

9.1 9.2

9.3

Introduction Models for microstrip antennas 9.2.1 Transmission-line model 9.2.2 Cavity model 9.2.3 Multiport network model 2-matrix characterisation of planar segments 9.3.1 Green's functions 9.3.2 Evaluation of 2-matrix from Green's functions 9.3.3 2-matrices for segments of arbitrary shape

Design and technology of low-cost printed antennas E. Penard and C. Terret 11.1 11.2

11.3

- J.P. Daniel,

Introduction Analysis of simple patches and slots Rectangular and circular patches 11.2.1 11.2.2 Conical antennas 11.2.3 Linear and annular slots Design of planar printed arrays 1 1.3.1 Design parameters

ix

x

11.4

11.5

11.6 11.7 12

11.3.2 Cavity model analysis of mutual coupling 11.3.3 Linear series array of corner-fed square patches 113.4 Two-dimensional cross-fed arrays Synthesis methods for linear arrays 11.4.1 Relaxation methods 11.4.2 Simplex method 11.4.3 Experimental results New low-cost low-loss substrate 11.5.1 Substrate choice 11.5.2 Fabrication procedure 11.5.3 Electrical characteristics 11.5.4 Environmental tests 11.5.5 Examples of printed antennas on polypropylene substrate Concluding remarks References

Volume 2 14

14.3

Analysis and design considerations for printed phased-array antennas Pozar

12.3 12.4 12.5 12.6

Introduction Analysis of some canonical printed phased-array geometries 12.2.1 Some preliminaries 12.2.2 Infinite-planar-array solutions 12.2.3 Finite-array solutions Design considerations for printed phased arrays 12.3.1 Introduction 12.3.2 Array architectures Conclusion Acknowledgments References

Microstrip antenna feeds - R.P. Owens 14.1 14.2

14.4

- D.M. 12.1 12.2

13

Contents xi

Contents

14.5 14.6 14.7 15

Advances in substrate technology - G.R. Traut 15.1

Circularly polarised antenna arrays - K. Ito, T. Teshirogi and S. Nishimura 13.1

13.2

13.3

13.4

13.5

Various types of circularly polarised arrays 13.1.1 Arrays of patch radiators 13.1.2 Arrays of composite elements 13.1.3 Travelling-wave arrays 13.1.4 Other types of arrays Design of circularly polarised arrays 13.2.1 Arrays of patch radiators 13.2.2 Arrays of composite elements 13.2.3 Design of travelling-wave arrays Practical design problems 13.3.1 Mutual coupling 13.3.2 Unwanted radiation 13.3.3 Limitations and trade-offs 13.3.4 Non-planar scanning arrays Wideband circularly polarised arrays 13.4.1 Arrays of wideband elements 13.4.2 Arrays of dual-frequency stacked elements 13.4.3 Wideband-array techniques References

Introduction Coupling to microstrip patches 14.2.1 Co-planar coupling to a single patch 14.2.2 Series-array co-planar coupling 14.2.3 Probe coupling 14.2.4 Aperture coupling 14.2.5 Electromagnetic coupling Parallel and series feed systems 14.3.1 Parallel feeds for one and two dimensions 14.3.2 Series feed for one dimension 14.3.3 Combined feeds 14.3.4 Discontinuity arrays Direct-coupled stripline power dividers and combiners 4 . 4 Simple three-port power dividers 14.4.2 Isolated power dividers/combiners 14.4.3 Four-port direct-coupled power dividers Other feed systems 14.5.1 Alternative transmission tines 14.5.2 Multiple beam-forming networks Acknowledgments References

15.2

15.3

Considerations for substrate selection 15.1.1 Impact of properties of various substrate systems on microstrip antenna performance 15.1.2 Comparative list of available substrates 15.1.3 Selection of metal cladding for performance 15.1.4 Thermal characteristics of PTFE 15.1.5 Anisotropy of relative permittivity Measurement of substrate properties 15.2.1 Stripline-resonator test method 15.2.2 Microstrip-resonator test method 15.2.3 Full-sheet-resonance test method 15.2.4 Perturbation cavity method 15.2.5 Tabulated evaluation of methods for measuring relative permittivity and dissipation factor Processing laminates into antennas 15.3.1 Handline incoming copper-clad laminates 15.3.2 Handling prior to processing 15.3.3 Safetv considerations for PTFE-based substrates 15.3.4 ~ e d i c i the n ~ effects of etch strain relief 15.3.5 Machining of PTFE-based boards 15.3.6 Bending etched antenna boards 15.3.7 Bonded-board assemblies 15.3.8 Plating-through holes in' microstrip antenna boards

-

xii

15.4

15.5

15.6 16

Contents xiii

Contents

Device attachment on microstrip antenna substrates 15.3.9 Design considerations with selected materials Environmental effects o n antenna substrates 15.4.1 15.4.2 Conductor losses at millimetre-wave frequencies Multilayer circuit-board technology in microstrip 15.4.3 antennas Special features and new materials developments 15.5.1 Substrates clad on one side with thick metal 15.5.2 Low thermal coefficient of K' in fluoropolymer laminates 15.5.3 Microwave laminates with a resistive layer 15.5.4 Thermoset microwave materials 15.5.5 Low permittivity ceramic-PTFE laminates 15.5.6 Very-low-dielectric-constant substrates References

Special measurement techniques for printed antennas - E. Levine

17.3

17.4

Introduction Substrate properties Connector characterisation Measurements of printed lines and networks 16.4.1 Measurement of printed-line parameters 16.4.2 Measurement of printed networks Near-field probing Efficiency measurement Concluding remarks References 17

Computer-aided design of microstrip and triplate circuits - J.F. Ziircher and F.E. Gardiol 17.1

17.2

Introduction, definition of the structure 17.1.1 Outline 17.1.2 Microwaves 17.1.3 Transmission lines for microwaves 17.1.4 Balanced stripline or triplate 17.1.5 Microstrip 17.1.6 Adjustments 17.1.7 Multiple inhomogeneity 17.1.8 Measurement problems Basic relationships for uniform lines 17.2.1 Uniform lines 17.2.2 Conformal mapping 17.2.3 Schwartz-Christoffel transform 17.2.4 Zero-thickness balanced stripline 17.2.5 Finite-thickness balanced stripline 17.2.6 Equivalent homogeneous microstrip line 17.2.7 Characteristic impedance of microstrip 17.2.8 Finite-thickness homogeneous microstrip 17.2.9 Microstrip-line synthesis for b = 0 17.2.10 Dispersion in microstrip 17.2.11 Effect of an enclosure

17.5

17.2.12 Attenuation 17.2.13 Higher-order modes and radiation Discontinuities: bends and junctions 17.3.1 Definition 17.3.2 Models 17.3.3 TEM-line models 17.3.4 Variational techniques 17.3.5 Fourier transform 17.3.6 Dielectric Green's function 17.3.7 Integral equations for inductances Green's function and integral equation 17.3.8 17.3.9 Green's function and electrostatic-inductance computation 17.3.10 TLM (transmission-line-matrix) method 17.3.11 Waveguide model Technological realisation: Materials and manufacturing process 17.4.1 Introduction 17.4.2 Dielectric substrate i7.4.3 Comment 17.4.4 Inorganic substrates 17.4.5 Plastic substrates 17.4.6 Semiconductor substrates 17.4.7 Ferrimagnetic substrates 17.4.8 Metallisation 17.4.9 Circuit realisation 17.4.10 Etching 17.4.11 Metal deposition 17.4.12 Removal of photoresist 17.4.13 Under-etching 17.4.14 Thin and thick film Analysis and synthesis programs 17.5.1 Introduction EEsof: Touchstone CCC: The Supercompact Family CCC: CADEC Acline Thorn '6: Esope RCA: Midas LINMIC High Tech. Tournesol: Micpatch Spefco Software: CiAO Made-it-associates: Mama Ampsa: Multimatch Radar systems technology: Analop Microkop/Suspend Microwave software aoolications Planim DGS Associates: S/Filsyn Webb Laboratories: Transcad Layouts of circuits and cutting of masks 17.6.1 Description 17.6.2 CCC: Autoart 17.6.3 EFSOF: Micad

+

A

17.6

xiv

Contents xv

Contents

20.2.3 Feeding the patch 20.2.4 Theoretical design method 20.2.5 Patch design Dual patch element 20.3.1 Choice of design Location of patch phase centre 20.3.2 20.3.2 Design and optimisation Hybrid feeding network 20.4.1 Overview 20.4.2 Hybrid designs 20.4.3 90' bends 20.4.4 Minimum track distance 20.4.5 Feed-point terminations 20.4.6 Track lengths 20.4.7 Overall design Conical antenna array Substrate fabrication 20.6.1 Overview 20.6.2 Mask drawing and preparation 20.6.3 Etching 20.6.4 Substrate preparation 20.6.5 Triplate bonding Forming the antenna 20.7.1 Bending the substrates 20.7.2 Attachment of components 20.7.3 Final assembly Antenna performance 20.8.1 Grating-lobe suppression 20.8.2 Axial ratio 20.8.3 Antenna gain 20.8.4 Tracking slope Conclusions and future developments References

17.6.4 High Tech. Tournesol: Micros 17.6.5 British Telecom: Temcad 17.7 Insertion of components 17.7.1 Introduction 17.7.2 Discrete components 17.7.3 Mounting procedure Drilling holes in the dielectric substrate 17.7.4 17.7.5 Deposited components 17.8 Examples Design of a broadband amplifier 17.8.1 17.8.2 Bandpass filter design Design of a miniature Doppler radar 17.8.3 17.9 Conclusions 17.10 Acknowledgments 17.11 References 18

Resonant microstrip antenna elements and arrays for aerospace applications - A.G. Derneryd 18.1 18 2 18.3 18.4 18.5 18.6 18.7

19

Introduction Circular antenna element Dual-band circularly polarised antenna element Monopulse-array antenna Dual-polarised-array antenna Concluding remarks References

Applications in mobile and satellite systems -K. Fujimoto, T. Hori, S. Nishimura and K. Hirasawa Introduction Mobile systems 19.2.1 Design considerations 19.2.2 Base stations 19.2.3 Wheeled vehicles 19.2.4 Railways 19.2.5 Pedestrian 19.2.6 Radars Satellite system 19.3.1 Design considerations 19.3.2 Direct broadcasting reception 19.3.3 Earth stations 19.3.4 Satellite borne References

20

Conical conformal microstrip tracking antenna - P. Newham and G. Morris 20.1 20.2

Introduction Single patch element 20.2.1 Choice of array element 20.2.2 Choice of substrate

21

Microstrip field diagnostics - P.G.Frayne Introduction Surface analytical techniques Scanning-network probe Theory of the monopole probe Resonant microstrip discs Resonant microstrip triangles Open-circuited microstriplines Antenna diagnostics 21.8.1 The rectangular patch Linear element patch array Circularly polarised patch antenna Microstrip travelling-wave antenna Acknowledgments References

1155 1155 1158 1161 1161 1161 1162 1163 1163 1166 1168 1168 1171 1171 1172 1172 1175 1175 1175 1176 1176 1177 1177 1177 1178 1181 1181 1182 1185 1187 1188 1188 1191

xvi

22

Contents Microstrip antennas on a cylindrical surface - E.V. Sohtell 22.1 22.2 22.3

22.4

22.5 22.6 23

Introduction Theoretical models for a patch on a cylinder Cavity model of the patch 22.2.1 22.2.2 Surface-currentmodel Single patch application 22.3.1 Mechanical design 22.3.2 Measurements 22.3.3 Radiation-pattern comparisons Array application 22.4.1 General Theoretical treatment of finite and infinite arrays 22.4.2 Design of a phased array on C-band 22.4.3 22.4.4 Measured performance Summary References

Extensions and variations to tho microstrip antenna concept A. Henderson and J.R. James

Foreword

P.S. Hall, 1257

Introduction Radiation pattern control 23.2.1 Reflector feeds 23.2.2 Spherical dielectric overlays Wide-bandwidth techniques 23.3.1 Log-periodic structures 23.3.2 Dichroic dual-function apertures Millimetre-wave hybrid antenna Novel use of materials Foam substrates for large direct-broadcast-satellite 23.5.1 domestic receiving arrays 1288 23.5.2 Magnetic materials and beam scanning 1292 Use of very-high-permittivity substrates in hyperthermia 23.5.3 applicators 1293 Summary comment 1294 References 1295

The Handbook of Microstrip Antennas could not have been written even five years ago, for neither the technology nor the relevant analytical tools were sufficientlydeveloped. This text arrives when the field is at a rush of activity. Fundamental mathematical tools are on hand to solve a variety of the important problems, and practical engineering results are now finding applications. Potential future capabilities and applications now look more optimistic than at any time in the history of this young technology. This new text describes vast developments in theory and practice. In two volumes, and representing the work of over thirty authors, the text is presented with such authority that it is assured a role as a key reference tool for many years. Microstrip antennas are a new and exciting technology. Invented about twenty years ago for application as conformal antennas on missiles and aircraft, the microstrip antenna has found increasing use because it can be fabricated by lithographic techniques in monolithic circuits. Initially, microstrip patch antennas were used as individual radiators, but they soon found use in relatively large fixed beam (non scanning) arrays. More recently, they have progressed to arrays for scanning in one or two dimensions. The advantage of this technology at microwave frequencies is its compatability with large scale printed circuit fabrication. Boards are fabricated lithographically and devices mounted by robotics or automated production line techniques. Microstrip printed circuit arrays are seen as an essential key to affordable antenna technology. At millimeter wavelengths, the benefit of microstrip arrays are enormous and so revolutionary as to create an entirely new technology; the monolithic integrated antenna array. Such an array has transmission lines, amplifiers, phase shifters and radiating elements, all on semiconductor substrates. Beyond this, these monolithic subarrays will be compatible with the integration of various solid state technologies on wafer size substrates. At these integration levels, the antenna array design and monolithic integrated circuit design cannot be separated, for the antenna architecture will need to optimise radiation, solid state device integration, board layout and thermal design. And so is born the antenna system architect!

xviii Foreword

Against this backdrop of energy and creativity, this timely and important book is the first handbook entirely dedicated to presenting a detailed overview of microstrip antenna development and theory. The vast scope of the text does justice to the broad range of research and development being undertaken throughout the world that is addressing a wide variety of microstrip elements and arrays for radiating linearly and circularly polarised waves. The text presents the work of a number of the most prominent and knowledgeable authors and so documents the state of the art at many institutions and in several countries. This monumental handbook is a milestone in the development of microstrip antenna technology.

Preface

Robert J. Mailloux Within two decades Microstrip Antennas have evolved as a major innovative activity within the antenna field and for both of us it has indeed been a fascinating and challenging experience to play a part in this vibrant research. In so doing the opportunity to initiate this International Handbook has arisen and this again has been a stimulating, meaningful objective that has also enriched our personal experiences through contact with numerous colleagues worldwide. It was around 1985 when it was apparent to us that the topic had raced ahead so fast that our previous IEE book "Microstrip Antenna Theory and Design" published in 1981 would soon need up-dating. Such is the vigour in Microstrip Antenna research that neither of us felt that we could do justice to the topic, at least across all its frontiers in a reasonable time scale, and it was at this point that we conferred with colleagues worldwide and this multiauthored Handbook was conceived. As to the subject itself, it has been abundantly clear for years that it is system driven and indeed continues to be so, and that its alarming pace has promoted microstrip antennas from the ranks of a rather specialised technique to a major type of antenna technology in itself. Historically one has always associated low cost, low weight and low profile with Microstrip Antennas but this description is simplistic and inadequate in the industrial atmosphere today where many new systems owe their existence to these new radiators. In reality, the feasibility of a low profile printed radiator has inspired the system creators and there is an abundance of examples, not just in the Defence sector. For instance, we have new generations of printed paper antennas, adaptive conformal antennas sitting on the roofs of automobiles and printed antennas as true ground speed sensors in many transport scenarios. It is indeed a stimulating topic to be associated with and we hope that the Handbook will portray this. For the in-depth researcher, however, the frontiers to push forward carry the familiar headings of bandwidth extension techniques, pattern control, minimisation of losses etc. but the scene has moved on in a decade and industry is now thirsty for significant advances, all at low cost, to meet the demand for higher performance and competitive costs. Research thus

xx

Preface

addresses critical optimisation procedures and advances are hard won. The role of substrate technology is now well appreciated and major developments have taken place to design materials that withstand a wide range of operating constraints, yet are affordable. As to the main thrust in research, it centres around the continual quest for innovative electromagnetic printed structures that satisfy the expanding system demands coupled with the ability to manufacture them and it is in the latter area where computer aided design (CAD) forms the cutting edge. Whether the manufacture of microstrip arrays can be fully automated via CAD in the immediate future is an open question that echoes throughout the Handbook and at present, further research is necessary. In organising the Handbook we have attempted to address all these aspects giving a balanced viewpoint from both industry and research centres and the overlap between chapters is intended to be sufficient to allow meaningful comparisons between contributors to be made. The broad theme adopted is to take the reader through elements and arrays in the first volume followed by technology and applications in the second volume but as may be expected, many authors include material covering more than one aspect. Look-up charts relating items of interest to chapters and a Glossary of over one hundred different types of printed antennas form much of the Introduction to assist the reader to efficiently select those parts that are of immediate interest. Finally, we thank all authors for their creative contributions, splendid cooperation, careful preparation of manuscripts and fellowship in the collective aim to compile a worthy international text with many years9 useful life. In particular we thank Dr David Pozar and Dr Koichi Ito who helped us initially with communications in the USA and Japan respectively. We are also pleased to acknowledge the willing and professional cooperation of the publishers. On a personal note, we have enjoyed the project and in particular the sincere experience of making new friends and acquaintances worldwide. J. R. James P. S. Hall

List of contributors

N. G. Alexopoulos University of California USA A. R. Van de Capelle Katholieke Universiteit Leuven Belgium

J. S. Dahele Royal Military College of Science UK J. P. Daniel UniversitC de Rennes I France A. G. Derneryd Ericsson Radar Electronics Lab Sweden

G. Dubost UniversitC de Rennes I France

F. E. Gardiol Ecole Polytechnique FCdkrale de Lausanne Switzerland

K. C. Gupta University of Colorado USA P. S. Hall Royal Military College of Science UK R. C. Hall Ecole Polytechnique FCdCrale de Lausanne Switzerland

M. Haneishi Saitama University Japan

P. G. Frayne University of London UK

A. Henderson Royal Military College of Science UK

K. Fujimoto University of Tsukuba Japan

K. Hirasawa University of Tsukuba Japan

List of contributors xxiii

xxii List of contributors T. Hori Nippon Telegraph and Telephone Corporation Japan K. It0 Chiba University Japan

D. R. Jackson University of Houston USA J. R. James Royal Military College of Science UK P. B. Katehi University of Michigan USA A. H. Kishk University of Mississippi USA

K. F. Lee University of Toledo USA

E. Levine Weizmann Institute of Science Israel G. Moms Vega Cantley Instrument Co Ltd UK J. R. Mosig Ecole Polytechnique Fkdkrale de Lausanne Switzerland P. Newham Marconi Defence Systems UK

S. Nihimura University of Osaka Japan

R. P. Owens Thorn EM1 Electronics Ltd UK E. Penard Centre National D'Etudes de Elhmmunications France

D. M. Pozar University of Massachusetts USA D. H. Schaubert University of Massachusetts USA L. Shafai University of Manitoba Canada

E. V. SohteU Ericsson Radar Electronics Lab Sweden Y. Suzuki Toshiba Corporation Japan

C. Terret Centre National #Etudes de Elhmmunications France T. Teshirogi Radio Research Laboratories Ministry of Posts and Telecommunications Japan

G. R. Traut Rogers Corporation USA

J. E Zurcher Ecole Polytechnique Fkdkrale de Lausanne Switzerland

Chapter 1

Introduction J.R. James and P.S. Hall

1.1 Historical development and future prospects

The microstrip antenna is now an established type of antenna that is confidently prescribed by designers worldwide, particularly when low-profile radiators are demanded. The microstrip, or printed, antenna has now reached an age of maturity where many well tried techniques can be relied upon and there are few mysteries about its behaviour. The fact that you are now reading an historical review is interesting in itself because all this has happened in a relatively short time span of one or two decades; such is the rate of progress in contemporary antenna technology. To imply that the topic of microstrip antennas is now static would be grossly misleading because the opposite is true with the ever increasing output of research publications and intensifying industrial R and D. The quest now is for more and more innovative designs coupled with reliable manufacturing methods. The driving force is the thirst for lower-cost, less-weight, lowerprofile antennas for modern system requirements. Lower costs, however, rely on the ability of the designer to precisely control the manufacturing process, and this in turn usually demands that the prototype innovative structures can be adequately mathematically modelled and toleranced. It is in these latter respects that the challenge to the antenna expert originates, and the search for the more precise computer modelling of microstrip antennas is now the main preoccupation of designers and researchers alike, as is reflected in this handbook. The invention of the microstrip-antenna concept has been attributed to many sources and the earliest include Greig and Englemann [l] and Deschamp [2]. At that time the emission of unwanted radiation from the then new thin stripline circuits was well appreciated and subsequently the dimensions of the substrate and conducting strip were reduced to inhibit the radiation effects, thus creating 'microstrip'. Whether the advent of the transistor influenced the rapid development of these planar printed circuits is debatable and the main interest was likely to be the development of lower-cost microwave filters etc. Lewin [3] considered

2

Introduction

the nature of the radiation from stripline but there was apparently little or no interest in making use of the radiation loss. Apart from a few references [4, 5, 61 the antenna concept lay dormant until the early 1970s [7,8,9] when there was an immediate need for low-profile antennas on the emerging new generation of missiles. At this point in time, around 1970, the development of the microstrip-antenna concept started with earnest and the research publications, too numerous to itemise, started to flow. The period is perhaps most readily referenced by its workshops and major works. The most significant early workshop was held at Las Cruces, New Mexico, in 1979 [lo] and its proceedings were distilled into a major IEEE Transactions special edition [I I]. At that time two books were published by Bahl and Bhartia [I21 and James, Hall and Wood [I31 which remain in current use today. Another more specialised and innovative development was published as a research monograph by Dubost [14], and here the flat-plate antenna was approached from the standpoint of flat dipoles on subsiraies that generally only partially filled ihe available .;o!ume. The early 1980s were not only a focal point in publications but also a milestone in practical realism and ultimately manufacture. Substrate manufacturers tightened their specifications and offered wider ranges of products capable of working under extreme ambient conditions. Substrate costs were, however, to remain high. It was appreciated that analytical techniques for patch elements generally fell short of predicting the fine pattern detail of practical interest and the input-impedance characteristic to suficient accuracy. It was also appreciated that the connection of feeders to patch elements in a large array was fraught with problems and new approaches were necesary where the feeders and elements are regarded as a complete entity. More recently the term 'array architecture' has come into being as if to emphasise the importance of choice of array topology and the fact that feeders cannot necessarily be freely attached to printed elements, even if the latter are in themselves well optimised. Recent system demands are, as previously mentioned, a dominant factor in the development of printed antennas. Communication systems spanning wider bandwidths are continually emerging and techniques for increasing the bandwidth of microstrip antennas are a growth area. Controlling the polarisation properties of printed antennas is another area of activity arising largely out of the current awareness for making greater use of the polarisation properties of waves, particularly in radar. In defence applications, systems that have an electronic, as opposed to mechanical, beam-scanning facility are attracting much research effort and the concept of 'active-array architecture' is now with us where semiconductor packages and radiating elements are integrated into planar apertures. The cost of such an array is very high and the whole concept is state-of-the-art. This brings us to the present and how we see the immediate future of printed antennas. A seldom mentioned point is the fact that printed substrate technology is readily processed in University laboratories and continues to remain

Introduction

3

a rich source of complex electromagnetic problems; research publications will thus continue to abound, and in parallel with industrial development will most likely be dominated by two aspects: The search for mathematical models that will predict practical antennas more precisely and hence sharpen CAD techniques in manufacture. The creation of innovative antennas to match the demand for new systems. In this latter aspect it must be emphasised that a bulky conventional microwave antenna may well out-perform its thin conformal printed counterpart. Many new systems, however, particularly in aerospace, are only made feasible with the existence of the printed antenna concept, and here lies a major driving force where new systems arise solely from innovative antenna designs. As to the distant future, one can but extrapolate the present trends towards integrated electronically beam-scanned arrays. This leads to a vision of conformal antennas distributed over the surface of vehicles, aircraft, ships, missiles etc., thus replaciiig iiiary convcntional types of iadiatois, but the orgafiisatio:: and control of the radiation pattern co- and cross-polar characteristics is a complex control problem that cannot be solved by software alone and demands innovative physical concepts. Are we thus unconciously converging on the concept of distributed sensors, so common in the insect and animal world, where information is commonly gleaned in a variety of ways to best suit a particular situation? Taking the comparison a step forward, we would therefore expect the distributed conformal apertures to require a significant back-up from signalprocessing techniques, which amount to making use of temporal a priori information on signals and noise. Put this way these ideas are not so far-reaching because many of these adaptive concepts can be recognised in some of our new radar and communication systems, particularly for defence. In this light the printed-antenna concept would therefore appear as a gateway to system compatibility and optimal deployment of sensors, embracing the numerous facets of conformality, low costs, semiconductor integration, electronic radiation pattern control and an opportunity to exploit signal-processing techniques to the full using modern computing power. The prospects are indeed exciting and underline the importance of the microstrip-antenna concept, its continual evolution and impact on electronic systems design.

1.2 Fundamental issues and design challenges

A handbook of this type is intended as an all-embracing treatment that is both diverse and highly specialist. As such it is not possible to include comprehensive background information and we anticipate that readers wishing to recap on basic antenna theory, antenna mesurements and the rudiments of microstrip technology etc. will have no difficulty in obtaining relevant literature. It is our experience, however, that certain fundamental properties of printed antennas

4

lntroduction

lntroduction

have been central to their evolution and limitations, and therefore embody the design challenges of the future as follows. The microstrip antenna has many differences when compared with a conventional antenna. Most of these stem from the planar construction in which for a given substrate in the .uy plane there are only two degrees of freedom, allowing the very thin printed-conductor topology to take any shape within the confines of the .u and y co-ordinate directions. The first and most troublesome property is the issue of loss, principally in the thin conducting strip feeders connecting elements in large arrays. In some applications the loss in the radiating elements also creates dificulties. The radiating elements themselves have a restricted bandwidth arising from the intrinsic high-Q resonator action in the thin substrate. The generation of surface waves is equally important and cannot be avoided unless foam-type substrates are deployed allowing virtual air-spaced operation. The surface waves can corrupt radiation-pattern characteristics, particularly when low sidelobe and cross-polarisation levels are demanded. In many design specifications. problems can only be alleviated by compromising the manufacturing simplicity of the single coplanar printed assembly by employing overlaid element and feed concepts based on multilayer sandwich structures. Microstrip arrays generally require some sort of radome or weather shield, thus increasing the structure depth, but in some cases a degree of radiation-pattern enhancement is obtainable. Last but not least, mention must be made of the relatively high cost of substrates capable of providing the desired electrical and mechanical stability in operation. The substrate cost is often an inhibiting factor in what is otherwise a low-cost manufacturing process. These above issues are of a fundamental nature and we consider it important to highlight current understanding to identify aspects which may offer particular scope for future advancement. Before addressing this we list, for completion, some of the more commonly known properties of microstrip antennas in relation to both contemporary antenna-engineering and modern electronic-systems requirements. 1.2.1 Features of microstrip antenna technology The microstrip antenna is a newcomer to the world of antenna engineering and it is fitting to be reminded of features generally sought after when compiling an antenna specification. A typical checklist is given in Table 1.1 and it is appreciated that it is unlikely that all the performance factors are relevant or indeed critical in any given application. Equally demanding are operational and manufacturing considerations such as those listed in Table 1.2 and these are very dependent on the application in mind. The generation of thermal noise in a receiving antenna is insignificant for most conventional antennas and is clearly a new factor associated mainly with large lossy microstrip arrays. Likewise power-handling and material effects are particularly relevant for microstrip radiators, while the use of new materials such as carbon fibre necessitates careful evaluation of electrical loading, intermodulation effects etc.

5

Table 1.1 Antenna desi.qners' checklist of performance factors Input terminals matched to source feed Matching Main beam

Antenna gain and beamwidth properties

Sidelobes

Constrained to desired envelope

Polarisation

Cross-polar behaviour constrained to desired envelope

Circular polarisation

Constraints on ellipticity

Eficiency

Wastage of power in antenna structure

Aperture eficiency

Relates to illumination distribution, gain and pattern characteristics

Bandwidth

Frequency range over which all above parameters satisfy specification commonly based on input terminal impedance charactericstics

System demands

Size, weight, cost

The commonly upheld properties of microstrip antennas are listed in Table 1.3 and may be usefully compared with the general checklist of Tables 1.1 and 1.2 to ascertain the suitability of microstrip for various operational roles. However, it is important to appreciate that the interpretation of Table 1.3 is very dependent on the intended application. For instance, patch antennas on foam

Table 1.2

O~erationaland manufacturing considerations

Noise effects in receiving antennas Power handling in transmitting antennas Creation of hazards for personnel in near-field Robustness to lightning strikes Electrostatic charge effects in space applications Effects of wind, vibration, ice, snow, rain, hail Ambient conditions on temperature and humidity Exposure to sunlight Aerodynamic constraints, radomes and weather shields Metal corrosion and creep Mechanical and electrical stability of materials Mechanical and electrical tolerances in manufacture Sensitivitiy of design to manufacturing tolerances Generation of intermodulation effects in materials

6

introduction

Table 1.3 Some commonly acknowledged properties of microstrip antennas

Table 1 . 4 ~ Approximate performance trade-offs for a rectangular patch

Requirement

Advantages

Disadvantages

Thin profile

Low efficiency

Light weight

Small bandwidth

Simple to manufacture

Extraneous radiation from feeds, junctions and surface waves

Can be made conformal

Tolerance problems

Low cost

Require quality substrate and good temperature tolerance

Can be integrated with circuits

High-performance arrays require complex feed systems

Simp!e arrays created

Polarisation piiriiy difficuit ro achieve

readily

7

lntroduction

High radiation efficiency Low dielectric loss Low conductor loss Wide (impedance) bandwidth Low extraneous (surface wave) radiation Low cross polarisation Light weight Strong Low sensitivity to tolerances

Substrate height thick thin thick thick thin -

thin thick thick

Substrate relative nermittivitv low low

Patch width wide

-

-

low low

-

low low high low

wide

-

wide

Table 1.46 Approximate performance trade-offs for an array of circular patches

substrates may have a less desirable thick profile but good efficiency and reasonable bandwidth; in contrast a thin overlaid patch assembly with complex feed arrangements on a plastic substrate is likely to be more complicated to manufacture and not necessarily low cost. The modelling and subsequent engineering design of arrays for successful manufacture is often a factor that is originally overlooked and ultimately pushes up development costs. There are many other examples where the commonly quoted properties of Table 1.3 need qualifying, and recent experience from conferences and industrial contacts shows that academics have on occasions failed to convey a realistic impression to industry whereas industry itself has perhaps been too willing to implement the new technology without a sufficient design base that copes with the factors of Table 1.2. We have already stressed the need for advances in CAD techniques for manufacture and will specifically address this again later on, but now we return to the more general features of microstrip antennas such as the trade-offs listed in Table 1 . 4 for ~ rectangular patch antennas. These are very approximate and can be deduced from the basic patch equations [15]. An obvious deduction which is nevertheless significant is that the use of thick low-permittivity substrates, giving essentially air spacing, gives many benefits. When the behaviour of an array of patch elements (Table 1.4b) is considered, feeder radiation is seen to increase for thicker lower-permittivity substrates [16, 171. With this exception, any attempt to compact the antenna using a thin high-permittivity substrate will thus generally invoke all-round penalties in performance. These requirements are thus seen to be contrary to those for optimum operation of MICs, and this imposes restrictions on the integration of antennas and associated front-end circuitry. This perspective is valuable in emphasising the dominant characteris-

Requirement

Substrate height

Substrate relative permittivity

High efficiency Low feed radiation Wide (impedance) bandwith Low extraneous surfacewave radiation Low mutual coupling Low sensitivity to tolerances

thick thin thick thin

low high low low

thick thick

low low

tics of microstrip antennas and the fact that antenna volume-reduction benefits must manifest themselves as cost factors which in turn demand a high standard of engineering design to overcome. Finally we complete our discussion of general features with a list of applications in Table 1.5 that have attracted the use of printed-antenna technology. Almost without exception the employment of microstrip technology arises because of a system demand for thin low-profile radiators. Conventional antennas are clearly disadvantaged in such applications despite their often superior performance over microstrip antennas. In some cases the system has been created around the microstrip concept as mentioned earlier on. 1i2.2 Fundamental problems In our vision of the future we have singled out reliable CAD techniques in array manufacture and the system-led creation of innovative antennas as the major

8

Introduction

Introduction

'i

Table 1.5 Typical applications for printed-antenna technology

Table 1.7 Some generic types of bandwidth-extension techniques Increasing antenna volume by incorporating parasitic elements, stacked substrates, use of foam dielectrics

Aircrafr antennas

Communication .and navigation Altimeters Blind-landing systems

Missiles and telen?etr.y

Stick-on sensors Proximity fuzes Millimetre devices

Creation of multiple resonances in input response by addition of external passive networks and or internal resonant structures

Missile guidance

Seeker monopulse arrays Integral radome arrays

Incorporation of dissipative loading by adding lossy material or resistors

Adaptive arrays

Multi-target acquisition Semiconductor integrated array

Varactor and PIN dlode control grves a wlder effectrve bandwrdth and lrst

Batilefield communications and surveillilnce

Flush-mounted on vehicles

S ATCOMS

Domestic DBS receiver Vehicle-based antenna Switched-beam arrays

$1

I

Mobile radio

Pagers and hand telephones Manpack systems

Reflector feeds

Beam switching

Remote Sensing

Large lightweight apertures

Biomedical

Applicators in microwave cancer therapy

Covert antennas

Intruder alarms Personal communication

9

IS

not Included In the above

thrusts. The problem areas will however centre around the fundamental issues listed in Table 1.6. These issues are un~versallyacknowledged and we will review some of them as follows to emphasise certain aspects which in our opinion are worthy of clarification or perhaps need various points amplified, in particular to bridge the gap between academic research and industrial implementation. 1.2.2.1 Bandwidth extension: The search for new microstrip configurations with wider bandwith has been a dominant feature of the research literature and much effort continues to be expended. No other type of antenna has been so exhaustively treated as regards its bandwidth properties, yet the literature often portrays an incomplete picture by not defining what is meant by bandwidth [18]. The many factors involved are listed in Table 1.7. A common and generally realistic assumption is that the input-impedance characteristic of a resonant patch antenna behaves as a simple tuned circuit, in which case the 3 dB bandwidth B is approximately (100/Q) percent, where Q is the Q-factor of the equivalent tuned circuit. If the antenna is matched at the resonant frequency of the tuned circuit, then away from resonance the input impedance will be mismatched, creating a VSWR(> 1) of S, where

Table 1.6 Fundamental issues that will continue to be addressed Bandwidth extension techniques Control of radiation patterns involving sidelobes, beamshaping, cross-polarisation, circular polarisation, surface-wave and ground-plane effects Reducing loss and increasing radiation efficiency Optimal feeder systems (array architecture) Improved lower-cost substrates and radomes Tolerance control and operational factors

1

1

Use of a thicker and/or lower-permittivity substrate reduces Q and hence increases B. An examination of numerous examples shows that, irrespective of whether the permittivity or substrate thickness is changed, the main effect (Table 1.7) is that B increases with the volume of the antenna, i.e. the volume of substrate between the patch and ground plane. Some examples are shown in Fig. 1.1, which also includes curves of radiation efficiency with and without allowance for the power lost to surface waves. The first point of clarification is to note that there are numerous ways of increasing the volume of a patch element by employment of thicker substrate or stacking several substrates [19] or adding

10

Introduction

parasitic elements 1201, but they all belong to the same generic type of bandwidth extension technique. A second generic technique (Table 1.7) consists of introducing multiple

lntroduction

Table 1.8 Factors constraining the bandwidth of microstrip antenna elements and arrays

Element

Array

-

Fig. 1.I

Patch-antenna efficiency q and bandwidth B versus resonator volume for differen! permittivities (Reproduced from Fig. 2 of Reference 78) -x-x-x- is the radiation efficiency corrected for surface-wave action ( E , = 2 . 0 )

77

Input-impedance characteristic

Surface waves

Side-lobe level

Element mutual coupling

Cross-polarisation level

Feeder radiation

Circular polarisation (axial ratio)

Corporate feed and mismatch

Pattern shape (E- and H-plane symmetry)

Scanning loss

Element gain Efficiency Feeder radition

Fig. 1.2 Patch bandwidth extension using an external passive network a Antenna without network b Effect of matching network.

resonances in the input characteristic, as illustrated in Fig. 1.2 showing the inclusion of a passive network in the input port; the presence of the network invokes additional dissipative losses. The same bandwidth extension effects can be brought about by introducing multiple resonances within the antenna itself [I 81, which usually involves an increase in antenna thickness and hence volume. The important point to note is that a multiple resonance input response does not

obey the simple relationship of eqn. 1.1, and it is difficult to relate the various multiple resonance bandwidth extension techniques that are reported in the literature. Different researchers use different VSWR or insertion-loss criteria to define the bandwidth and the insertion-loss curve shapes are likewise very different. A third much less common technique (Table 1.7) is simply to add lossy material to the microstrip element. This technique would at first sight appear to lead to unacceptable loss, but the manufacturing simplicity has definite appeal and can outweight the other disadvantages. We summarise the above three generic bandwidth extension techniques in Table 1.7, but emphasise that from a system designers' standpoint the definition of bandwidth based on the input-impedance characteristic is just one of many factors listed in Table 1.8 that constrain the bandwidth of an antenna element or array. For instance, the designer may decide to use a rectangular patch accompanied by several parasitic elements to achieve an impedance bandwidth specification, but then finds that the configuration fails to achieve adequate cross-polarisation levels or perhaps E- and H-plane symmetry over the band. In another instance it may be straightforward to meet all the bandwidth criteria for a selected element only to find that, when the latter is connected in an array, the bandwidth specification is not achieved because of mutual coupling or perhaps feeder-line mismatches. Research workers seldom have the opportunity to address the totality of problems in a system design, and it is a natural consequence that they focus on the optimisation of a given property in isolation from other requirements. In contrast, the industrial designer has to optimise many parameters at the same time and bandwidth is a topic area where the gulf

72

Introduction

between isolated research and system design is at its widest. The challenge facing researchers and industrial designers alike is to establish reliable designs for elements and arrays that achieve bandwidth extension under a wide selection of contraints as listed in Table 1.8. It is also highly desirable that the performance of one type of element can be quantified in relation to the performance of any other type of new element; the fact that there are in reality few generic types of bandwidth-extension techniques (Table 1.7) [18] is an important guideline. 1.2.2.2 Pattern control: There is now ample evidence to show that the radiation-pattern control of printed radiators is an order more difficult than with reflector and aperture antennas. Even for modest performance levels of sidelobes and cross-polarisation the printed-conductor topology presents many variables to optimise for a given substrate thickness and permittivity. For sidelobe and cross-polarisation levels of about -20 dB extraneous radiation due to surface waves, feeder radiation and ground-plane edge effects is not insignificant and computer models lose their precision. Surface-wave effects decrease for lower-permittivity substrates but feeder radiation is then more prominent [17]. There is evidence in the literature that much lower levels can be achieved, but generally these are pattern cuts in certain preferred planes or pertain to arrays fitted with lossy material or other special effects. A consensus of opinion is that printed antennas are at present more fitted for applications with less demanding pattern specifications. The challenge for the future thus remains the lowering of the levels of extraneous radiation in printed arrays and improved computer modelling of the overall patterns. Some special mention needs to be made of circularly polarised elements and arrays because considerable progress has been made in this respect and it is likely to be an area for continued exploitation. It is well known that in principle a linearly polarised antenna can be converted to perfect circular polarisation by superimposing upon its radiation characteristics, those of its dual radiator having transposed E- and H-field sources. For instance, a wire dipole (electric source) would need to be combined with a wire loop (magnetic source), but in reality it is physically impossible to construct or feed such an arrangement precisely and compromises are made such as the employment of crossed-wire dipoles which yields circular polarisation in a limited region of the hemisphere and over restricted bandwidth. These and other techniques [21] are well established for conventional antennas, and the point we make here is that they are more difficult to translate to printed elements in view of the constrained planar geometry and feeder requirements. It is therefore inspiring to note the innovation that has been brought about whereby circular-polarisation characteristics have been enhanced by sequential rotation of elements [22], incorporation of finite substrate effects [23], novel feeder arrangements [24] and many more. Creating improved low-cost radiators that provide circular polarisation over wider bandwidths and larger sectors of the radiation-pattern hemisphere is a goal towards which much international effort will continue to be directed.

Introduction

73

1.2.2.3 Eficiency and feeder architecture: The outstanding advantage of microstrip - the simplicity of the printed conductor - is also the source of one of its major disadvantages, which is the relatively high transmission-line loss. The nature of the loss is well understood and arises from the high current density at the strip edge and substrate losses. It is a fact that no worthwhile reductions in transmission loss have been achieved since the inception of microstrip, and the simplicity of the structure offers little scope for innovation in this respect. For patch elements the loss is less significant, and with an appropriate low-loss substrate and strongly radiating patch, antenna efficiencies of 95% are achievable. A conventional wire dipole antenna would have a better efficiency than the patch but the order of loss of the latter is usually very small from a systems standpoint. The main problem arises in large arrays having microstrip or other forms of printed feeder lines because feeder losses limit the gain of the aperture; in fact, beyond a certain critical aperture size the gain will actually reduce. The beamwidth will, or course, also continue to narrow. The critical size is dependent on the feeder topology, substrate etc. and a maximum gain around 35 dB is not uncommon. Fig. 1.3 shows typical computed and measured results efficiency, % 100 50 j 0 /

I

gain

(dB)

u

O1

10 100 array size Dlho

Fig. 1.3 Patch-array gain 0 Calculated [17]; measured. with feed impedance + 100 a, x 120

A 200

[17] and indicates that at maximum gain an efficiency of about 10% can be expected. Travelling-wave antennas show some economy of feeder loss over corporate feeds but the frequency scanning loss for large travelling-wave apertures is then the dominant limitation. Once again the simplicity of a printed feeder system gives little scope for major design changes, and more recently hybrid feeder systems are being considered incorporating more conventional

14

lntroduction

Introduction

cables and waveguides for the longer feeder runs. We have already emphasised in Section 1.2.2.2 the limitations on pattern control enforced by extraneous feeder radiation and any breakthrough in feeder architecture will need to address the latter. However, for some applications the radiation-pattern specifications are less critical than loss of gain and any improvements in feeder loss would be a significant advance. The future challenge is to discover new feeder architectures giving less loss, and if possible less extraneous radiation, with the knowledge that the already simplistic printed configurations offer little scope for fundamental physical change. One possible avenue for advancement lies in the integrated antenna concept whereby transistors are embedded in the feed structure to facilitate beam scanning. This may circumvent the loss problem but exacerbate extraneous radiation effects, and of course escalate costs. 1.2.2.4 Substrate technology: Substrate technology and marketing has been, and will continue to be, a key factor in the acceptance by industry of the printed-antenna concept. Earlier microstrip antennas used plastic substrates or in some cases alumina, but in recent, years the use of lower-permittivity substrates is common. The substrate role thus appears to be mechanical, enabling the printed conductor to be suspended at a uniform height above the ground plane. The use of lower permittivities also reduces surface-wave effects but feeder radiation is then more difficult to suppress. Antenna designers thus require a wide range of substrates available having stable electrical and mechanical properties over the various ambient operating conditions. The major problem has been, and is likely to be in the foreseeable future, a matter of substrate cost because the world demand is relatively small compared with that of some other plastic products. This has encourage some companies to manufacture their own substrates while in other cases the substrate costs have made some large-array projects non-viable, and printed technology is then seen to be costly in contradiction to the commonly upheld properties of Table 1.3. It is also noted that many microstrip antennas will require some sort of weather shield or perhaps a radome, which again is a cost factor. Substrate technology thus offers a challenge to material manufacturers to create lower-cost high-performance stable substrates. Clearly this is a somewhat circular problem which appears to demand a higher-volume market to initiate an immediate advance; conversely such an advance would open up a larger-volume market. Such a situation is not uncommon, and with the considerable manufacturing interest in substrates that is building up (Table 1.9) antenna designers should be optimisitic about the way substrate technology is likely to develop in the next few years. 1.2.2.5 Manufacture and computer-aided design (CAD): The microstrip antenna has been widely mathematically modelled for many years and yet from the manufacturers' standpoint there is a dearth of ready-to-use design equations, and hence reliable CAD packages. This situation has arisen partly owing to the mathematical difficulties associated with practical geometries and partly

Table 1.9 E,

75

Representative substrate list

Material Aeroweb (honeycomb)

Supplier Ciba Geigy, Bonded Structures Div., Duxford, Cambridge, CB2 4QD

Eccofoam PP-4 (flexible low-loss plastic foam sheet)

Emerson & Cumming Inc, Canton, Massachusetts, USA (Colville Road, Acton, London. W3 8BU, UK)

Thermoset microwave foam material

Rogers Corp., Bo 700, Chandler, AZ 85224, USA. (Mektron Circuit Systems Ltd., 119 Kingston Road, Leatherhead, Surrey, UK)

RT Duroid 5880 (microfiber Teflon glass laminate)

Rogers Corp.

Polyguide 165 (polyolefin)

Electronized Chemical Corp., Burlington, MA 01803, USA

Fluorglas 60011 (PTFE impregnated glass cloth)

Atlantic Laminates, Oak Materials Group, 174 N. Main St., Franklin, M H 0323, USA. (Walmore Defence Components, Laser House, 1321140 Goswell Road, London, EClV 7LE)

Rexolite 200 (cross-linked styrene copolymer)

Atlantic Laminates

Schaefer Dielectric Material, PT (polystyrene with titania filler)

Marconi Electronic Devices Ltd., Radford Crescent, Billericay, Essex, CM12 ODN, U K

Kapton film (copper clad)

Dupont (Fortin Laminating Ltd., Unit 3, Brookfield Industrial Estate, Glossop, Derbyshire, UK)

Quartz (fuzed silica)

A & D Lee Co. Ltd., Unit 19, Marlissa Drive, Midland Oak Trading Estate, Lythalls Lane, Coventry, U K

76 Introduction

lntroduction

6.0

RT Duroid 6006 (ceramic-loaded PTFE)

Rogers Corp.,

9.9

Alumina

Omni Spectra Inc, 24600 Hallwood Ct. Farmington, Michigan, 48024, USA (Omni Spectra, 50 Milford Road, Reading, Berks, RGI 8LJ, UK)

10.2

RT Duroid 6010 (ceramic-loaded PTFE)

Rogers Corp.

II

Sapphire

Tyco Saphikin (A & D Lee Co Ltd., Unit 19, Marlissa Drive, Midland Oak Trading Estate, Lythalls Lane, Coventry, UK)

The brief details in the Table are intended to give readers an insight into the range and types of materials available. Mention of any particular product does not imply our endorsement. Likewise exclusion of a material does not imply adverse comment and we presume that some excellent products have been omitted.

17

making and convergence under the designers control. Such an approach has many merits since tolerance and operational effects can be added in gradually to create a reliable manufacturing tool. A disadvantage of the approach is that it must be re-established together with empirical data when a change is made in the design, and furthermore the experience is confined to the particular manufacturer. As we have mentioned already, some manufacturers have been surprised by the need to underpin printed-array manufacture with positive modelling in view of the commonly acknowledge property (Table 1.3) that the antennas are 'simple and low cost'. There is ample evidence, however, showing that the simplicity and low-cost properties are realisable once modelling has been accomplished, and the latter is a one-off development cost and perhaps no more than a few months of a printed-antenna specialist's time. The challenge for the immediate future thus lies in the evolution of reliable interactive CAD packages for printed-array manufacture that are capable of wider usage and of gaining universal acceptance. In the long term one might expect some advances in the rigorous analysis of microstrip-antenna geometries embodying practical features which in turn will translate into more precise manufacturing techniques.

1.3 The handboook and advances presented

to the many varieties of patch antennas and the fact that designs must conform to the vagaries of system requirements. Horn, wire and other conventional metal antennas can be modelled to a high accuracy with well established formulas and this is also true of electrically larger apertures such as the reflector antenna. In contrast to these homogeneous electromagnetic systems the modelling complexity arises largely from the presence of a finite-sized dielectric slab that gives rise to the factors noted in Table 1.8 and elsewhere. This complexity is compounded when the number of elements in an array increases and when the fine detail of patch feeding or complex feed networks is required. Mutual coupling, surfacewave effects and feed radiation manifest themselves as relatively small effects in a small array but they quickly take charge of sidelobe and cross-polarisation levels in the region of - 20 dB as the number of elements increase. When viewed in the light of increasingly tight requirements, modelling accuracy is seen to be the key parameter to successful implementation. As an example, the use of inaccurate CAD may well be more expensive for the manufacturer than design by hand in the long run. Likewise the range of applicability of the package needs to be understood if inherently good models are not to be brought to bear on the wrong problems. However, despite the unlikely possiblity of extending presentday numerical analysis to arrays of patches in the immediate future, the problem is not unsurmountable provided that a close liaison exists between the CAD and antenna designer. Indeed there is a trend for manufacturers to evolve their own CAD packages based on a mixture of simple closed-form expressions for the radiation mechanism backed up by empirical results for the particular array in question. Some degree of iteration is commonly included but with the decision

Many, if not most, of the international community of printed-antenna specialists have contributed to this handbook, which necessarily portrays the state-ofthe-art at the time of going to press. The contributions reflect the authors' specialisation which in some cases is fairly wide ranging. This has meant that it has not always been possible for the editors to maintain a full thematic flow throughout the handbook. However, the chapters have been generally ordered in the following way element analysis and design array aspects microstrip technology applications To assist the reader we have already listed in Table 1.5 the general application areas for microstrip antennas. In Table 1.10 the content of the Handbook is resolved in more detail to identify with the various topic areas within the subject of printed antennas. It can be seen that patch theory and design still concerns many researchers, with current emphasis being on basic characterisation and innovation for controlling in particular bandwidth and polarisation purity. The same applies to arrays, with additional topics such as mutual coupling in scanning arrays gaining more attention. Technology is addressed by several authors with contributions on substrates, connectors, radomes and computeraided design and manufacturing. However, little on environmental factors has

78

Introduction

I

.

Introduction

"I.

79

I

20

Introduction

1

Introduction

21

Table 1.11 Summary o f handbook chapters Element analysis and design

I

2 Shafai and Kishk: Analysis of circular microstrip antennas: An analysis is presented based on the equivalence principle involving both conducting and dielectric boundaries. This allows substrate edges to be accounted for. The method is used to optimise a circular disc on a finite-sized circular ground plane for low cross-polarisation and also a wrap around antenna. 3 Lee and Dahele: Characterisation of microstrip patch antennas and some methods of improving frequency agility and bandwidth: The basic characteristics of patches are reviewed here and conclusions on comparative performance are made. Bandwidth is identified as being- crucial and methods of overcoming the limitations by making the patches frequency agile are presented.

I

I I

4 Haneishi and Suzuki: Circular oolarisation and bandwidth: The methods of obtaining circular polarisation from patches are described in this chapler together with design techniques. Again, as in the previous chapter, bandidth-extension methods are noted and, in particular, element pairing which is described more fully in Chapter 13. 5 Katehi, Jackson and Alexopoulos: Microstrip dipoles: The analysis and design of narrow-strip microstrip dipoles is presented here. For electromagnetically coupled dipoles an improvement in feed radiation is noted together with methods for offsetting mutual coupling in arrays. Bandwidth and superstrate effects are also discussed. 6 Schaubert: Multilayer and parasitic confgurations: This chapter exhaustively reviews multilayer configurations and emphasises advances for wide bandwidth, multiple frequency and dual polarisation. Such structures increase the antenna thickness, and, as a contrast, antennas with coplanar parasitics are also described.

1

7 Dubost: Widebandflat dipole and short-circuit microstrip patch elements and arrays: Elements and arrays developed from the flat dipole concept are described in addition to short-circuited quarter-wavelength patch elements and arrays. The dipole work can perhaps be viewed as a parallel development with microstrip and has produced antennas whose performance is highly competitive. 8 Mosig, Hall and Gardiol: Numerical analysis of microstrip patch antennas: An integral-equation formulation is solved by the moments method to give solutions for arbitrary shaped wide patches, including input impedance, radiation patterns and surface-wave effects.

9 Gupta: Multiport network approach for modelling and analysis of microstrip patch antennas and arrays: Here patches possessing separable geometries in whole or part are analysed using a planar model involving impedance

22

Introduction

Table 1.11 (Cont) matrices. Radiation loading is included by means of edge admittances. The author presents several illustrative examples and discusses the extension of the work to CAD methods. Further progress in the application of analysis such as this and others in this handbook is expected in the near future.

10 Van de Cupelle: Transmission-line model for rectangular microstrip antennas: The application of the transmission-line model to patch analysis is described. Various improvements to the basic model are noted, such as connections for mutual coupling between the radiating edges, that enable good agreement with measurements to be obtained. However, the attraction here is the method's simplicity and easy adaption to CAD, an example of which is given.

Introduction

23

15 Traut: Advances in substrate technology: Microwave substrates are one of the important 'enabling technologies' in printed antennas. Advances in this area are presented which given the reader some insight into manufacturing and environmental factors that affect the antenna's progress from conception to use. Progress here is determined to some extent by the volume of production, and it is hoped that as the applications proliferate substrate technology will continue to imvrove.

Array Aspects

16 Levine: Special measurement techniques for printed antennas: Measurement characterisation of connectors, lines and discontinuities, together with analysis, form an important foundation to good antenna design. Such measurement characteristics are described here with particular emphasis on accuracy and applicability to design. Near-field probing can also form a useful diagnostic tool, and examples are given together with a novel method for efficiency measurement.

I1 Daniel, Penard and Terret: Design and technology of low-cost printed antennas: The design of elements and arrays with the emphasis on low-cost technology is important for successful application in many areas. Design and construction including array sythesis is described here. In addition, some technology and substrate innovations are included which can be compared to materials detailed in Chapter 15.

17 Zurcher and Gardiol: CAD of microstrip and triplate circuits: As noted above, computer-aided design is likely to be an increasingly important factor in printed antenna design. This Chapter is dedicated to CAD of microstrip and triplate systems and highlights some of the important aspects such as characterisation of components, materials, manufacturing, analysis and synthesis.

12 Pozar: Analysis and design considerations for printed phased-array antennas: The effects of scanning of printed phased arrays are derived using moments methods for both infinite and finite arrays of patches. Blind spots due to surface-wave effects are noted to be particularly severe where highdielectric-constant substrates are used for millimetric integrated arrays. Some alternative integration technologies are discussed that mitigate these and other problems.

Applications

18 Derneryd: Resonant microstrip antenna elements and arrays for aerospace applications: Four examples of resonant microstrip antennas and arrays are presented here for various requirements including dual frequency, monopulse radiation pattern and dual polarisation. Important design freatures are noted together with some environmental aspects.

13 Ito, Teshirogi and Nishimura: Circularly-polarised-array antennas; Various types of circularly polarised arrays are reviewed together with the possible feeding arrangements. Some practical problems are considered including pattern control and bandwidth. Some examples of practical arrays are also highlighted.

19 Fujimoto, Hori, Nishimura and Hirasawa: Applications in mobile and satellite systems: Mobile and satellite systems are an important area for lowcost low-profile printed antennas. Various examples of such antennas are given in this Chapter. It is likely that the explosive increase in information systems in the future will accelerate the development of antennas to meet these diverse needs.

Microstrip Technology

20 Newham and Morris: Conical conformal microstrip tracking antenna: A conical conformal microstrip tracking antenna is a severe requirement that involves difficult manufacturing and fundamental electromagnetic problems to be solved. Here the authors have described progress to date in this very challenging area that is likely to require much more research and innovation for some time to come.

14 Owens: Microstrip antenna feeds: Printed antenna feeds are sometimes given insufficientconsideration at the outset of an array design, thus degrading the array performance. Feed design is extensively reviewed here and comparative examples drawn from the literature are used to give engineering direction. Although considerable work has been done, further progress is expected as the importance of good feed design for printed antennas is more widely appreciated.

21 Frayne: Microstripfield diagnostics: The near-field probing technique noted in Chapter 16 is described here in some detail together with extensive results both for microstrip patches and patch arrays with feed networks.

24

22 SoizteN: Microstrip an~ennason a cylitirluiccrl .surfkce: Patch arrays on cylindrical bodies is likely to be an important future application of conformal concepts. Modifications to the basic patch-design expressions due to the curvature are presented here together with design and performance of a representative cylindrical array. 23 HUN, Henderson and Junzes: E.uretzsions and variations to the microstriptrntenncr concept: There are a wide variety of specialist applications that spawn innovative concepts in the use of microstrip antennas. This final Chapter highlights some of these, including applications where microstrip is combined with other radiating or transmission structures to form hybrid antennas. Operation over multi-octave bandwidths or at millimetric frequencies are also design challenges that are covered, together with applications involving very high and very low dielectric-constant materials. Such specialised requirements are likely to continue to lead antenna designers to further innovative progress in the microstrip field.

Relevant Chapter numbers are given together with References in brackets.

(a) Patches The generic microstrip patch is an area of metallisation supported above a ground plane and fed against the ground at an appropriate point or

Principal shapes The freedom in the xy plane gives rise to the possibility of a multiplicity of possible shapes. Only a few have been seriously examined such as the rectangular or square patch and disc [25], ellipse [26], equilateral[27],or rightangled isosceles [28] triangle, annular ring [29] and pentagon [30].

appeared in the literature and Chapter 15 contains one of the few appraisals of this area of printed technology. A diverse range of applications is also noted that mirror the list given in Table 1.5. In terms-of printed-antenna techniques microstrip is the predominant one discussed in the handbook although some contributions on printed dipoles and ground-plane slots are presented. Although both these elements are likely to have similar electromagnetic properties to microstrip radiators, the increased complexity involved in manufacture seems to have been the overriding factor that has influenced designers away from them. This is particularly true for slot antennas in triplate stripline where shorting pins or holes are needed to prevent parallel-plate mode excitation. It is thus clear that the conceptual simplicity of microstrip remains one of its most attractive features. As a final aid to the reader Table 1.1 1 highlights the advances described in each chapter with particular reference to the fundmental issues and challenges identified in Section 1.2.

1.4 Glossary of printed antenna types The various forms of printed elements and arrays are very numerous and it is useful for designers to have a check list at hand. With this in mind we have composed the glossary giving an outline sketch, some key references and a few supporting comments and an indication of which chapter in the handbook deals with each type. Although the glossary is by no means exhaustive, the 70 entries on radiating elements and the 37 on arrays reflect the wide range of flexibility and scope for innovation that microstrip offers.

25

Introduction

Introduction

2, 3, 4, 8,

9, 10, 11, 18, 21, 22

Characteristics of these principal shapes are generally similar [Chapter 31 with fundamental modes having broadside beam. Bandwidth and physical area vary between shapes. The annular ring gives increased bandwidth, gain and sidelobe levels for higher-order modes but becomes physically large.

a

l3ll

Patches can be short-circuited along a null voltage plane to form the shorted patch or hybrid microstrip antenna [31]. Impedance and resonant frequency remain the same as for a full-size patch but for low dielectric constant the bandwidth is increased.

7, 1 I , 20

26

Introduction

Introduction

Variants on principal shapes

Circularly polarised patches Single-point feeding gives circular polarisation with constructional simplicity. The feed excites two orthogonal degenerate modes [35]. The 90" excitation phase difference is obtained by detuning the two modes by a variety of geometrical distortions giving the following types: rectangular patch [36] notched square patch [37] slotted square patch [38] notched disc [39] truncated corner square [40] ellipse [26] penragon j3Fj

Single point feeds

Circular sector and annular-ring-sector [32] patches have been analysed using the cavity model. Expressions for impedance and resonant frequency, but no indication of likely bandwidths or pattern performance are given.

[331

Star microstrip patches have been theoretically investigated [33] as a radiator of higher-order modes with good symmetry. Rectangular-ring and H-shaped patches have been investigated by Palanisamy & Garg [34] and found to give performance similar to principle shapes.

Other possible shapes

27

4, 9

The input VSWR bandwidth is wider than that of an isolated mode but the axial-ratio bandwidth is much narrower with axial ratio rising to about 6 dB at the edge of the 2: 1 VSWR bandwidth. The above technique is shown for the fundamental mode. Use of internal slots in discs for higherorder modes has also been shown [41].

9

Many uninvestigated variants have been suggested [28]. They are expected to give performance similar to the principal shapes. A selection is given here. Multiple-point feed

135, 421

Circular polarisation can be produced using multiple-point feeding by: . Two offset rectangular patches [35], which is also used in arrays [42]. Here the offset phase centre leads to a more rapid degradation of axial ratio off boresight than the following

4, 1 I , 13, 18, 19, 21

Introduction

Introduction

28

- - - - - - -. 90' couplor -. -

-- -

-.

Single parches fed at two points [43, 44, 251

-,

[43, 44, 251

m

[ o...

4

5

1

[521

ZBZZZ

1531

Parasitics

110.

Short-circuit patches arranged to produce a crossed slot [46] which

270'

Patch shaping such as steps [521 or conical depression [53] also yields wide bandwidths

Shaped patches

Four-point feeding [45], which suppresses cross-polarisation generated by higher-order modes within the patch and this improves axial ratio

29

Multiple stacked patches with the upper patches acting as electromagnetically coupled parasitics can be designed for extended bandwidths. Examples using coaxial-probe feeding [54] and microstrip-line feeding [55] have been made with the latter designed for an alumina (E, = 10) base substrate.

3

Parasitics can also be mounted coplanar as thin resonators [56], as additional patches either gap or line coupled to square [57] or triangular patches [58]. Alternatively many thin parasitics [59] can be gap coupled to form a wideband patch. Some of these configurations exhibit variations in the radiation pattern with frequency.

3

1551 A patch in a corrugated ground plane [47], which also improves low-angle performance

\ \

.:-- -- -- _-- ----

/

0 0 0 n

I

'--_ - ,' _ [47] -

[561

Wideband patches Thick patches

Use of low-dielectric-constant (E, = 1.0), thick (h/& > 0.1) substrate results in bandwidths > 10% [48]. Alternatively patches on thinner substrates can be broadbanded (up to 30%) by e.uterna1 matching circuits [49]. Use of thick substrates leads to impedance-matching problems that can be overcome by use of matching gaps in the probe [SO] or patch [51].

2, 4, 6, 7, 11, 18

Short-circuited quarter-wavelength parasitic~have also been applied to square [60] or circular [61] patches. A band-width increase of 2 is obtained in the square-patch case. In the circular case cross-polarisation is substantially reduced.

30

Introduction

Introduction

Other wdeband forms

The m~crostripspiral [62] gives about 40% bandwidth with limited efficiency. The spiral 1s limited to less than one turn, as further turns give rise to radiation-pattern degradation.

p

p

* .

xledband patch notch

,

Dual-frequency patches Multiple layers

Multiple-layer patches having two- [I91 and three- [63] frequency operation use direct probe connection to the top patch and gap coupling to the lower ones. Direct connections to both patches in two-frequency designs [64, 651 have also been made. Tuning of the two frequencies is also possible by an adjustable-height upper patch using discs [66] and annular rings [67].

[731

2, 3, 4, 5, 6, 18,

[741 Other patch variants

'm. [761

Single-layer two-frequency patches with orthogonal polarisations [68] using two feed points. Use of shorting pins [69, 701 allows operation with the same polarisation. The use of tabs in rectangular [71] or circular [72] patches also permits dual-frequency operation.

3, 4, 6

1771

I /681

[69, 701

High-frequency patches have been located within low-frequency patches to give orthogonal polarisation [73] or same circular polarisation [74] using frequency-sensitive coupling stubs

19

751

Single layers

31

z

In the coplanar stripline patch [75] the input line is fed against the upper ground plane. The overall performance is similar to conventional patches with reduced cross-polarisation and mutual coupling. The electromagnetically coupled patch [76] allows reduction in feed radiation bv locating it closer to the -ground plane than the patch. The effect of dielectric covers (superstrates) is noted [77], where, in addition to element protection, enhanced gain can be obtained.

-

The use of superimposed dielectric spheres [78] on patches result in improved gain and reduced crosspolarisation.

patch resonator

23

32

Introduction

Introduction

The groundplane dot [79] fed by a microstrip line can be used as a bidirectional element or as a unidirectional one by the addition of a reflec tor.

ground plane

11n0

Outputs\

33

comparator ,ekments

grwnd plane

[791 Folded dipoles can be operated close to a ground plane by means of appropriate matching circuits [14]. Many variants are possible giving wide bandwidth and low cross-polarisation. Construction is more complex than the basic microstrip patch although, owing to the use of rr atching circuits, wider impedance bandwidths may be possible.

maon r~tlecto,

\

SUppMt

Microstrip patches and arrays can be combined with the reflector concept. Their use as feeds [80, 811 allows integration with microwave integrated circuits, but with lower bandwidth and cross-polarisation compared to conventional feeds.

substrate

Paiches have aiso been used in the reject array configuration [82] where beam scanning is achieved by varying the phase of the reflected wave by pin diodes. A single element is shown here. Phase shift in the circularly polarised system is obtained by varying the angle of the short-circuit plane.

2, 23 Conformal antennas

4°F ground plane

The flexibility of the microstrip concept allows use in conformal applications. Examples are: - Spiral slot [83]

2, 7, 19, 20, 22

34

Introduction

Introduction - Wrap-around antenna [84]: a single wide-quarter wavelength patch wrapped around a cylindrical body

(b) Arrays

Feed structures

- Cylindrical 185, 861 or spherical [87] patch arrays

Putch connection

Patch elements for arrays can be connected by through the substrate pin connections (through hole plating or via holes), to one or more layers [89] of feed circuits located behind the ground plane in microstrip or triplate. Mechanical simplification can be achieved by aperture coupling to a parallel [90] or a perpendicular [91] microstripline. Feeding can also be from a coplanar microstrip circuit [92] which involves pattern perturbation due to feed radiation. This can be reduced by electromagnetic coupling to overlaid patches [76]. Connector effects give rise to fundamental limits to array action [93] due to radiation from the discontinuity in the guiding structure. Pin connections to patches give rise to higher-order modes [94] that perturb the radiation pattern and increase cross-polarisation levels.

Feed circuits

Feed structures for many elements 4, 5, take various forms. Corporate feeds 7, I I, [95, 961 for either one- or 12, 13, two-dimensional arrays give wideband 14, 18, action, whilst series-fed arrays give - 19, 20, 22 narrow bandwidth with broadside beam when resonant or wide bandwidth with a scanning beam when travelling wave.

wide patch

P I corporate feed kcd

35

pomni

5, 6, I I, 12, 14, 16, 18, 19, 20, 22

--

Active patch

Active devices can be integrated into patches. An example with a Gunn diode [88] demonstrated the principle, but had high cross-polarisation and low patch efficiency.

LJ LJ LJ LJ [951

'4+"4-,-4'

36

lntroduction

Introduction

37

Dual polarisarion is obtained by dual series interconnection of patches [99]. Chain type structures for linear polarisation having rectangular [I001 and triangular or honeycomb shapes [loll. Both the series array of patches and chain arrays are resonant and thus have a narrow bandwidth.

Wideband squintless operation is obtained with the series-compensated feed [97] One-dimensional arrays: linear polarisation

feed oolnt

The cross-fed arrangement [98] gives narrowband action with a tapered distribution and hence low sidelobes with equal-width feed lines

Early microstrip antennas were series fed one-dimensional arrays of Gutton and Bassinot [4] and Dumanchin [I021 in 1955 and 1959, respectively. Since then many forms of series-fed array have been developed. Arrays can be formed using resonant elements or meandering microstrip lines, in which the radiation is determined by radius of curvature or line width. Examples of arrays using resonant elements are:

Sequentially rotated feeding [22] gives wide-bandwidth axial ratio and input VSWR for circularly polarised patch arrays

comb line [I031 parasitically coupled patch array [ 1041 series-connected patches [I051

-

-

Array structures Two-dimensional arrays

[921

Microstrip patch arrays can be fed by any of the feed structures noted above. A typical linearly polarised parch array [92] fed by a coplanar microstrip corporate feed is shown here.

7, 1I, 12, 13, 14, 18, 19, 20, 22

9, 10, I I, 13, 14, 18, 19

38

lntroduction

lntroduction

Other array forms

- - Pv X

i

*

Examples of arrays using meandering U06, 1071 microstrip lines are:

y

[I 061

Various other forms of series fed linear arrays exist: A A,/2 wide line can be made to radiate by feeding with an asymmetric step [I 131. Alternatively angled slots can also force the line to radiate.

serpent line 1106, 1071 triangle or tiapeioidi line 11061 rampart line [I081 chain line [I091 Franklin line [i l O]

A combination of strip dipoles and slots can be used to form a circularly polarised linear array [I 141. The high losses in long microstrip series arrays can be reduced by replacing the line by a dielectric rod [llj]; radiation occurs by coupling the line energy to microstrip patches.

An omni-directional array has been made by forming alternating resonators in the line and ground plane [I 161.

Circular polarisation is obtained from the rampart line [108], chain line [I 1I] and herringbone line [I 121.

Circular polarisation --.- r

I, F 0,

f- a,, hL2' (kqr)j,,(kqr')P~(cos9)P,"(cosO'), r'
45" and, in particular, for determining the cross-polarisation which, from Fig. 2.8, shows a peak at about - 25dB range. Here the cross-polarisation is computed in 4 = 45' plane, in which it maximizes. The results also show that increasing the substrate height generally increases the excitation efficiency of the other modes

Fig. 2.8

Analysis of circular microstrip antennas

Analysis of circular microstrip antennas

69

at = 0 . 7 5 ~Again, . their contributions are below the - 25 d B range. However. since the TM?, mode has a null along the z-axis, the contribution of the T M , , mode will cause a minor peak at this location. The results of Figs. 2.8 and 2.9 indicate that the resonance nature of a microstrip patch controls the excitation of the azimuthal modes, and the resonant modes can easily be excited significantly above the adjacent modes simply by selecting an appropriate location for the feed. With this type of excitation the contributions of the adjacent modes manifest themselves mainly in the cross-polarisation. They may be ignored if the antenna cross-polarisation is not the main concern. Also, the substrate permittivity seems to have a small effect on the mode excitation.

The effect of the feed position on the excitation efficiency of TM,, mode (Reproduced from Reference 74 @ 7986 IEEE)

The excitation efficiencies for a patch dominant a t the T M 2 , mode are shown in Fig. 2.9. The results are plotted for two different substrate permittivities, and show similar excitations. Again the dominant mode has the strongest excitation, but its peak radiation increases for Q, > 0 . 6 8 ~and decreases thereafter. The peak radiations of the other modes have more complex behaviour and minimise

Fig. 2.9

The effect of the position on the excitation efficiency of TM,, mode (Reproduced from Reference 14 @ 1986 lEEE)

We now present a few results for the radiation patterns. Fig. 2.10 shows the computed patterns for the T M , , mode and Fig. 2.1 1 for the TM,, mode. In both cases the feed location is selected to maximise the excitation of the dominant

70

Analysis of circular rnicrostrip antennas

Analysis of circular rnicrostrip antennas

mode. In Fig. 2.10, the T M , , mode is dominant and the radiation pattern is computed by including four modes, i.e. the T M , , mode along with adjacent TM,, , TM,, and TM,, modes. The radiation peak is in the broadside with a significant radiation level behind the ground plane, owing to its finite size. In Fig. 2.1 1 the TM,, mode is resonant and the radiation patterns are generated by including the first five modes, i.e. TM,, to TM,, modes. T o examine the accuracy of the computed results, sample calculations are also compared with experi-

77

2.3.3 Effect of the substrate permittivity Increasing the substrate permittivity reduces the patch size and consequently the size of the radiation zone. One therefore expects to see a broadening of the radiation pattern. This is shown in Figs. 2.14 and 2.15 for a T M , , mode patch and in both E and H-planes. Since the ground-plane sizes are all the same, the antennas have equal sizes. The results show that the broadening is taking place only in the E-plane. The H-plane patterns are independent of the substrate permittivity, but show an increase in the level of the back radiation, which is also evident in the E-plane patterns. Note that, for the selected antenna dimensions,

Fig. 2.10 The radiation patterns of a circular patch for the dominant mode excitation t = 0,021 Ground lane thickness = 0.01 1

ment. Figs. 2.12 and 2.13 show the comparison for the T M , , mode. The computed and experimental patterns are identical in the upper half plane and deviate slightly thereafter, owing to the coupling between the antenna and its support structure.

Fig. 2.11

The radiation patterns of a circular patch for the TM,, mode excitation; data same as Fig. 2.10

the small permittivity of E, = 2.32 gives nearly symmetric radiation patterns with small cross-polarisation, Since increasing e, broadens only the E-plane pattern, the pattern symmetry deterioriates by increasing the substrate permit-

72

Analysis of circular microstrip antennas

Analysis of circular microstrip antennas

-180.00

-135.00

-SB.00

-45.08

0.00

45.00

90.00

135.00

73

180

Angle, degrees Fig. 2.1 2

Measured and computed data in H-plane of a circular patch excited with a coaxial probe (Reproduced from Reference 1 4 @ 1986 IEEE) E, = 2.54, g = 4.5crn, h = 0.159cm, f = 3.2GH,, feed at edge -measured . . . . computed

Fig. 2.1 4

E-plane radiation patterns of a circular patch with different substrate permittivities (Reproduced from Reference 14 Q 1986 IEEE)

Fig. 2.15

H-plane and cross-polarisation patterns of Fig 2.14 (Reproduced from Reference 1 4 @ 1986 IEEE)

Angle, degrees Fig. 2.13

Measuredandcomputed data in E-plane of the case in Fig. 2.12 (Reproducedfrom Reference 14 @ 1986 IEEE) ---measured. data same as Fig. 2.1 2 ' ' ' ' computed

74

Analysis of circular microstrip antennas

Analysis of circular microstrip antennas

75

tivity. This means the antenna cross-polarisation will increase, which is evident from the results presented in Fig. 2.15. Here, the cross-polarisations are computed in the 4 = 45" plane, where it has the maximum magnitude.

--

-32

1

-(rh,

-- ---( ---(

-40

-180

=2.3:4A a, pi) ( h . a . f ,) h, a, pi) h . a . p,)

-135

-90

,

( = ( = ( = ( =

0.02. 0.04. 0.06. 0.10.

-45

0.1806. 0.1732. 0.1675. 0.1590. 0

8 Fig. 2.1 6

,

0.045 0.044 0.041 0.039 45

)A )A )A )A

E-plane

90

11

135

' 9 Fig. 2.17

H-plane and cross-polarisation patterns of Fig. 2.16 (Reproduced from Reference 14 @ 1986 IEEE)

180

E-plane radiation patterns of a circular patch with different substrate heights (Reproduced from Reference 14 @ 1986 IEEE)

2.3.4 Eflect of the substrate thickness The bandwidth of microstrip antennas increases by increasing the substrate height. It is therefore desirable to study its effect on the radiation patterns. For the TM,, mode patch, representative results are shown in Figs. 2.16 and 2.17. For h < 0.061 the beamwidth of the H-plane patterns decreases slightly by increasing h, but increases to some degree in the E-plane. The relationship reverses for h > 0.06 1. Consequently, the cross-polarisation increases initially with h, but tends to decrease afterwards. Also, it is interesting to note that the effect of the substrate may resemble a thinner one with a higher substrate permittivity, which, from Fig. 2.14 may affect the E-plane patterns significantly. However, the results of Fig. 2.16 show otherwise, where E-plane patterns are relatively independent of h. This can be understood by considering the effect of these two parameters. A higher permittivity reduces the patch size and the extent of the fringing fields. Consequently, the radiation is due to a narrow magnetic current ring around the patch periphery, which normally gives asymmetric radiation patterns. A thicker substrate, on the other hand, does not reduce the patch size significantly, but extends the zone of the fringing fields, thus resulting in a broad radiation ring.

Fig. 2.1 8 E-plane radiation patterns of a circular patch with different ground plane diameter for the dominant TM,, mode (Reproduced from Reference 14 @ 1986 IEEE)

76

Analysis of circular rnicrostrip antennas

Analysis of circular rnicrostrip antennas

77

2.3.5 Efect of the ground-plane r a d i u ~ Since the ground plane controls the back radiation, its size has a pronounced effect on the patch radiation pattern. For the T M , , mode case, sample computed patterns are shown in Figs. 2.18 and 2.19. Again, cross-polarisation are computed in the 4 = 45" plane. In the H-plane, shown in Fig. 2.19, pattern beamwidth decreases by increasing the ground-plane size. Consequently, the infinite ground plane has the most rapid pattern roll-off. In the E-plane, on the other hand, the beamwidth decreases initially by increasing the ground-plane radius g, but increases for g > 0.71. The infinite ground plane gives the broadest beam, which approaches -6 dB a t the horizontal plane. The crosspolarisation therefore increases rapidly by increasing the ground-plane size from its optimum radius. These results show that the assumption of an infinite ground plane in approximate analysis of microstrip antennas will have a serious effect on the correct prediction of the radiation patterns, particularly for angular ranges beyond 45' off the main beam. The prediction of the cross-polarisation will, in fact, be an impossible task.

Fig. 2.20 E-plane radiation patterns of a circular patch with different ground-plane diameter for the dominant TM,, mode (Reproduced from Reference 1 4 @ 1986 IEEE)

Fig. 2.19 H-plane and cross-polarisation patterns of Fig. 2 . 7 8 (Reproduced from Reference 14 @ 1986 IEEE)

For a TM2, mode excitation the corresponding computed results are shown in Figs. 2.20 and 2.21. The effect of the ground-plane size on the radiation patterns is similar to the T M , , mode case. The beamwidth in the H-plane decreases progressively with the ground-plane size, and for the infinite ground plane the pattern roll-off is the largest. The angle for the peak radiation, which is around 45O off the z-axis, is, however, almost independent of the ground plane. The E-plane patterns also show similar behaviour to those of the T M , ,

Fig. 2.21 H-plane and cross-polarisation radiation patterns of Fig. 2.20 (Reproduced from Reference 14 @ 1986 IEEE)

78

Analysis of circular microstrip antennas

Analysis of circular microstrip antennas

mode, and their beamwidth initially decreases by increasing g, but increases for larger ground planes. For an infinite ground plane the pattern remains relatively constant beyond the peak of the pattern at about 45'. It is therefore evident that the assumption of an infinite ground plane will not provide a meaningful pattern shape for the TM,, mode, where the main feature of the patterns manifest itself beyond the 45'.

Fig. 2.23 H-plane radiation patterns of the cases in Fig. 2.22

Fig. 2.22 E-plane radiation patterns of TM,,. T M , , and TM,, modes of a circular patch a = 0.1806 1. g = 0.31, Q, = 0.051, t = 0.021, E, = 2.32,and the ground plane thickness is zero.

The above results indicate that, the radiation characteristics of various modes can easily be controlled by the ground-plane size. So far, the total patterns are shown. It may be desirable to examine the effect of the ground-plane radius on the mode-excitation efficiencies. To investigate this, the case of the TM,, mode patch is selected and the mode patterns are computed for two ground-plane radii of 0.31 and 0.42. This range of ground-plane radius gives the most symmetric co-polar patterns, with minimum cross-polarisations. The computed patterns for the 0.32 antenna are shown in Figs. 2.22 - 2.24. The E-plane patterns in Fig. 2.22 are all in the 4 = 0 plane. The H-plane patterns are, however, in the H-plane of each mode, being 4 = 90" and 4 = 45' for the TMII and TM2, modes, respectively. The corresponding results for the 0.41 ground plane are shown in Figs. 2.25 - 2.27. These results indicate that the small ground plane, with g = 0.31, all non-resonant modes are well below the

Fig. 2.24

Total radiation patterns of the case in Fig. 2.22 -E-plane

--- H-plane cross-polarisation.

79

80

Analysis of circular rnicrostrip antennas

Analysis of circular rnicrostrip antennas

81

dominant T M , , mode and their peak amplitudes are less than - 30 dB. Increasing the ground-plane radius to 0.41 increases the excitation of both TM,, and TM,, modes, and their peak amplitudes approach - 17 dB range. The generated cross-polarisation is therefore larger in magnitude and increases from the - 25 dB level of 0.31 ground plane to more than - 20 dB for the 0.41 case.

0 Fig. 2.25 E-plane radiation patterns of TM,,, TM,,, TM,, and TM,, modes of a circularpatch a = 0.18061.g = 0.41.p, = 0.051.t = 0.021.6, = 2.32,and the ground plane th~cknessis zero

Fig. 2.27

Totalradiation patterns of the case in Fig. 2.25 -E-plane

---

H-plane Cross-polarisation

Fig. 2.26

H-plane radiation patterns of the cases in Fig. 2.25

2.3.6 Effect of the ground-plane thickness The results of the previous Section indicate that the size of the ground plane affects the excitation efficiency of non-resonant modes. In some applications such as reflector feeds, the ground plane may not be infinitesimally thin but may have a finite thickness. Since the thickness of the ground plane affects the reflection coefficients of various modes, at its terminal edge, it may also affect their excitation efficiency. This is investigated here for the TM,, excitation of the patch and a ground-plane radius of 0.4 1.The results are shown in Figs. 2.28 2.30. Again, each of the modes of the patterns are generated in their respective E- and H-planes. The overall patterns for the co-polarisation are in the q5 = 0" and 90' planes, the principal planes of the TM,, mode and the cross-polarisation are in the 45" plane. Comparing these results with those in Figs. 2.25 - 2.27 for zero ground-plane thickness, one notes that increasing the thickness of the ground plane to 0.05 1has reduced the excitation efficiencies of the higher TM2, and TM,, modes. The excitation of the TM,, mode, on the other hand, has

82

Analysis of circular microstrip antennas

I

I

Analysis of circular microstrip antennas

83

remained the same. One therefore concludes that the thickness of the ground plane can also be used to modify the mode excitation. In other words, in designing microstrip antennas with small ground plane and for a high degree of mode purity, one must optimise not only the resonant patch size but also the size and thickness of the ground plane. This is, of course, valid for a given location of the excitation source, which in practice is determined by the impedance requirements. However, as shown earlier, the feed location has its own effect on the mode excitation and can be used as a parameter if warranted.

B Fig. 2.28 Same as Fig. 2.25 with the ground-plane thickness of 0 . 0 5 1

2.3.7 Circular polarisation Many techniques have been proposed in the literature to generate circular polarisation with a microstrip patch antenna. In most methods a geometrical deformation is used to generate both symmetric and asymmetric modes to cause a circularly polarised radiation. These methods are convenient to generate circular polarisation when only one sense of polarisation is needed, and can be implemented by a single feed. However, when a polarisation diversity is required, one must use two separate feed arrangements. In such a case, a symmetric patch with two separate feed points and an appropriate phase switch will be sufficient. Also, to generate circularly polarised radiations with a low axial ratio, one needs an antenna with a nearly symmetric radiation pattern. The results of previous anlaysis indicated that the pattern symmetry can be controlled by

84

Fig. 2.31

Analysis of circular microstrip antennas

Radiation patterns of a circular patch fed by two dipoles for circular polarisation a = 0.18061, g = 0.4i.. e, = 0.051, t = 0.021, E, = 2.32, and the ground plane thickness of 0.1 1 ----- E-plane - - - H-plane

Analysis of circular microstrip antennas

85

modifying the ground-plane size and thickness. To investigate the quality of the circularly polarised radiation we present a few computed results for circular patches, fed at two locations, with a 90' phase difference. The antenna selected is resonant at the TM,, mode and has a ground-plane radius of 0.41. The circularly polarised E, and E4 components, and their difference as the cross-polarisation, are shown in Fig. 2.31. These principalplane electric vectors represent the envelopes of measurement data with a rotating linearly polarised test antenna. The actual right- and left-handed circular polarisation vectors are shown in Fig. 2.32. The peak of the left-hand vector, which is the cross-polarisation, is below - 20 dB level in the upper half plane, which is the main region of concern. Its pattern shape is identical to the difference pattern of Fig. 2.31 and indicates a fairly good circular polarisation. The computed data for the case of 0.3 1ground plane of zero thickness or for the 0.41 ground plane of 0.05 2 thickness are not shown here. However, their results can easily be determined from the co-polar and cross-polar patterns already. . provided. Since they have lower non-resonant mode excitations with reduced levels of cross-polarisation, their generated circular polarisations will also be more superior. Thus, the foregoing results indicate that, by a proper selection of the feed-point location or the size or thickness of the ground plane, circularly polarised patch antennas with extremely low axial ratio can be designed. One only needs to optimise the antenna dimensions properly.

Cross-polarisation.

2.3.8 Effects of a central shorting pin

So far the computed results were presented for a standard circular patch geometry. The patch dimension is therefore selected to resonate at a particular mode. However, it is reported in the literature that, by using a central pin to short the upper patch to the ground plane, one may improve the purity of the resonant mode. The previous results show that this may not be the case. Since, with a finite ground-plane size and thickness, the mode excitation can easily be controlled by modifying their dimensions. An addition of a shorting pin acts as an extra parameter to control the mode excitation. For a given antenna dimension, one can readily find a pin radius that minimised the non-resonant mode excitations. This can be done easily with the current method, provided that the pin does not destroy the rotational symmetry of the configuration. Since the introduction of the pin increases the resonance size of the patch, perhaps the most important property of the pin is to control the antenna gain by increasing the patch size. This may be a useful parameter to use in the design of higher-gain patch antennas.

2.4 Application 2: Wrap-around microstrip antenna 6' Fig. 2.32

Co-polar and cross-polar circularly polarised radiation patterns of the example of Fig. 2.37

The wrap-around antenna refers to a microstrip-ring conformal antenna that is embedded in a missile or cylinder body. Its various configurations are con-

,

86

Analysis of circular microstrip antennas

Analysis of circular microstrip antennas

sidered in literature and investigated [I 51, [3]. Analytic solutions, using cylindrical Green's functions, can be obtained [I61 by assuming that the cylinder length is infinite, so that boundary conditions on its surface can be satisfied. In practice, however, the missile shape and the location of the antenna on the body influence

87

mode number. Thus, when a particular mode must be excited, the exciting source must eliminate others, which can be achieved by the axial symmetry of multiple source excitations. For each excited mode, the radiation patterns then depend on the shape of the cylindrical surface. In most practical applications the zero-order mode is used and the present study will provide the computed data for its radiation patterns.

-B

-

Fig. 2.34 Rad~at~on patterns of wrap-around antennas for the zero and 4th order modes. Zero mode - - - 4th mode W, = 1,/4, L, = 4 11, Wd = 0.61. L, = 0.1 A, a = 30', 6, = 2 32, a = 0.2571, t = 0.021

Fig. 2.33

Cross-section geometry of wrap around antenna for missile geometry

the antenna radiation patterns. The accurate determination of the radiation patterns must again be determined numerically. Since the configuration is rotationally symmetric, it can be analysed readily by the current method. In this section, the radiation patterns for some of useful geometrical shapes are computed. We have selected this antenna because of its complex shape. Although it is a microstrip antenna, the conducting patch and the ground plane, i.e. the cylinder, are not planar and the mode configuration are different. Here, the modes under the patch form the azimuthal modes of the cylindrical zone and their excitation is dependent on the cylinder radius. In practice, for a single exciting source all modes are present, but their magnitudes decrease with the

Fig. 2.33 shows the cross-section of the antenna geometry that is investigated. It consists of a conducting ring conformal to the cylinder surface and is supported by a dielectric substrate, which is embedded in the cylinder. The radius of the cylinder is selected to be a = 0.257 1,which represents that of a typical small rocket. The excitation is due to four dipoles at the lower edge of the ring, which are angularly separated by 90". Since the cylinder radius is small, the selection of four excitations ensures that the azimuthal pattern is omnidirectional. The azimuthal symmetry of the excitation means that only 4Kn modes are allowed to be excited, where K is an integer. All intermediate modes cancel out. To investigate the mode excitation we select a geometry and compute the radiation patterns of the first two modes, i.e. K = 0 and 4. The results are shown in Fig. 2.34, where the dominant mode is for K = 0, the zero-order mode. The next mode for K = 4 is weakly excited and its contribution is below - 30 dB range. The next higher mode for K = 8 is far too weak to be shown on the plot. These

88

Analysis of circular microstrip antennas

results indicate that, for the selected radius of the cylinder, only the zero-order mode has a significant value and all other modes can be neglected. Also, since E, is zero for the zero-order mode, all radiation patterns in this section will show the plots of the E,, component only. Here, we present the dependance of E, o n the antenna parameters. Fig. 2.35 shows the computed patterns when the radiating ring is located at the base of the cone, i.e. L,, = 0. The computed patterns show the effect of the cone angle o n the radiation patterns, where cc is the halfcone angle and cc = 90' refers to the geometry of a finite cylinder. Since the patterns are all similar, they are progressively shifted down by 4 dB to improve the clarity. The results show that, although the antenna is located at the upper end of the cylinder, the main beam is in the backward direction and the radiation towards the cone tip is small. Also, for the selected cone angles, the effect of the cone is not significant. In this example, the substrate permittivity is 2.32 and the width of the ring is 0.51,; i.e. one half wavelength in the substrate. Other dimensional parameters are shown o n the Figure.

Analysis of circular microstrip antennas

89

same. This means that the separation distances of the antenna from the cylinder ends can be used to control the radiation intensities in the forward and backward directions. In the above examples the width of the ring was selected to be one half wavelength in the substrate. The effects of ring width on the radiation patterns are shown in Fig. 2.37, where the ring widths are 0.51,, 0.41, and 0.251,, respectively. Reducing the ring size reduces the broadside radiation.

e Fig. 2.35 Radiation patterns of wrap-around antennas with different nose angle a -a= 90" --- a = 60" a = 45" . . . . a = 30"

L, = 4.1 i, Wd = 0 . 6 L L,

=

0.0. W,, = 1 d / 2 ,E, = 2.32, a = 0.2571

For G( = 30°, Fig. 2.36 shows the effects of moving the antenna away from the cone tip and changing the cylinder length, by retaining all other parameters constant. It is evident that increasing the separation from the cone base improves the forward radiation. Also reducing the antenna separation from the cylinder base reduces the back-lobe level. Otherwise, the pattern shape stays the

6 Fig. 2.36 Radiation patterns of wrap-around antennas with different tail lengths From up to down: L, = 5.1 1. L, = 3.1 1 and L, = 2.1 1, respectively. W, = 0.61, L, = 0.1 1. W, = 1,/2, E, = 2.32, a = 0,2571. a = 30"

Here, patterns are normalised by the main beam peaks. The quarter-wavelenth ring is a n end-fire antenna and radiates mainly in the back direction. The effect of the substrate permittivity is shown in Fig. 2.38, where the width of the ring is again0.5 1,. Increasing the permittivity rapidly reduces the broadside radia-

90

Analysis of circular microstrip antennas

tion. Finally, Fig. 2.39 shows the effects of moving the antenna towards the cylinder base. It indicates that, by increasing the antenna separation from the cone, the forward radiation increases.

Analysis of circular microstrip antennas

97

symmetric and radiates mainly near the broadside direction, but the beam peak is around 70'. Increasing the cylinder radius moves the beam peak initially towards 90' and then towards the back direction. The effect of the substrate thickness is also studied and shown in Fig. 2.42. Decreasing the substrate thickness moves the beam peak towards the broadside and improves its symmetry. The effect of the substrate permittivity is shown in Fig. 2.43. Larger permittivities broaden the radiation pattern, which is partly . . due to the reduction of the effective ring width.

Fig. 2.38 Radiation patterns of wrap-around antennas with different dielectric constants

-E,

--- E, . E , =

Fig. 2.37 Radiation patterns of wrap-around antennas with different patch widths -w, = 1,/2 --- W, = 0.4 1, W, = 1,/4 L, = 4.1 1, a = 30'. E, = 2.32. a = 0.2571, t = 0.021

To complete this study, the radiation characteristics of the ring antenna on a dielectric-coated cylinder with the antenna located symmetrically from two ends. Fig. 2.41 shows the effect of the cylinder radius on the patterns. The exciation is again due to four dipoles. For a small cylinder radius the pattern is

=

4

= 2.32

-10

Since the analytic solution of wrap-around antennas on infinite cylinders is known, it is useful to generate their numerical solutions as well for comparison. To handle the problem, the image theory of infinite cylinders is applied to modify the originual geometry. Fig. 2.44 shows the original and equivalent problems. In the originual problem a ring antenna, excited by four dipoles, is supported on a dielectric-coated infinite cylinder. Applying the image theory one can determine the image of dipoles and the conducting ring inside the cylinder. The equivalent problem, in the cross-section of the cylinder, thus has eight dipoles and additional central ring representing the image of the original ring inside the cylinder. The two rings are separated by the dielectric substrate and excited by eight dipoles. The numerical solution is obtained for the finite geometry, i.e. a truncated cylinder of height 0.61, and the corresponding radiation patterns are shown in Fig. 2.45 for different dielectric permittivities. The

92

Analysis of circular microstrip antennas

Analysis of circular microstrip antennas

computed results agree well with the published analytical data [16]. The radiation is in the broadside direction, for the selected ring width of 0.5 l,, and the pattern broadens by increasing the permittivity. These results show that the

Fig. 2.40 Geometry of a wrap-around antenna on a finite dielectric-coated cylinder

e Fig. 2.39 Radiation patterns of wrap-around antennas with different L, and L, From up to down (L, = 2.1 1, L, = 3.21). (L, = 1.1 1, L, = 4.1 1 ) and (L, L, = 5.1 1 ) . respectively W d = 0 . 6 1 ,W p = 1 , / 2 . ~ , = 2 . 3 2 , a = 0 . 2 5 7 1 , a = 3 0 '

=

0.1 1,

numerical method presented here can also be used to investigate infinite structures and the accuracy of the generated results is satisfactory. The usefulness of the method, however, is in handling finite geometries where analytic methods fail.

Fig. 2.41 Effect of the radius on the radiation patterns = 0,451 -a a = 0.351 --- a = 0.25L. w, = 1,/2, t = 0.021

93

94

Analysis of circular rnicrostrip antennas

e Fig. 2.42

Effect of coating thickness on the radiation patterns -t = 0.051 . . . . . t = 0.031 - - - t = 0.021

Analysis of circular microstrip antennas

Fig. 2.44 Geometry of wrap-aroundantenna of an infinite cylinder Left cross-section indicates the original problem with four dipoles for excitation; right is the cross-section using the image theory.

8 Fig. 2.43 Effect of dielectric constant on the radiation patterns -a, = 10 ---- E, = 4

a,

=

2.32

w, = &I2 a = 0,251,t = 0.021

95

Fig. 2.45

Effect of the dielectric constant on the radiation patterns

a, = 2.32 --- a, = 4.0 -8, = 10 a = 0.2571,t = 0.021

96

Analysis of circular rnicrostrip antennas

2.5 Application 3: Reflector antenna feeds In high-gain applications microstrip antennas may be used as feeds for ryflector antennas [I7 - 201. The merits of microstrip feeds, however, depend oq the type of application. In symmetric prime focus systems, the feed nomrally blocks the central region of the aperture and causes reductions in aperture Jiiciency and gain factor, raises the sidelobe levels and causes undesirable diffraction effects. The rise of the antenna sidelobes also increases the antenna ~ o i s etemperature. Because the size of the feed depends on the operating frequc .,y and the reflector f / D , where f and D are the reflector focal length and diameter, the aperature blockage is most severe in small paraboloid reflectors. A larger feed blocks a larger portion of the reflector central region and also requires heavier support structures. The latter further blocks the aperture, reducing the reflector performance and limiting the cross-polarisation performance. A microstrip feed is normally smaller and reduces the central blockage and its subsequent degrading effects. Furthermore, it is low cost and light weight. which reduces the complexity of the supporting structure, and can be integrated readily with its associated electronics. The simplicity of microstrip elements also offers additional features with other reflector configurations. In offset paraboloids and dual reflector systems a small array can be used to control the reflector illumination and provides a limited scan capability with reduced sidelobes and coma lobe difficulties. Such arrays can also be used in non-paraboloidal reflectors, such as spherical reflectors, to improve the aperture efficiency and reduce the abberation. Their main advantage, however, is in the reduction of the system complexity. Microstrip feed arrays can be integrated readily with their associated circuitry and electronics, such as the power dividers, phase shifters and amplifiers. Here, we will only address the design approach and determine the performance levels for wideangle feeds that are used with symmetric paraboloids. The array designs and their associated problems are beyond the scope of this Chapter and are discussed in subsequent Chapters. In symmetric paraboloid reflectors the system performance is controlled primarily by the feed [21, 221. A desirable feed must illuminate the reflector efficiently and cause small spillover. This means that the feed pattern must be broad within the cone of the reflector and roll off rapidly thereafter. It should also have negligible back radiation. The shape of the feed pattern controls the reflector efficiency, but with a symmetric system does not affect the reflector cross-polarisation. Thus, for low cross-polarisation the feed must also have a good polarisation property. From Ludwig's third definition, for minimum cross-polarisation. the feed pattern must be symmetric and have a unique phase centre [23]. A circular patch antenna is a good candidate as a feed for a symmetric reflector. Its pattern shape can be controlled readily by the size and thickness of the ground plane. Fortunately, symmetric patterns are achievable with small

Analysis of circular microstrip antennas

97

ground planes, which reduces the blockage. There are, however, a few problems to be overcome. The back radiation of a microstrip antenna with a small ground plane is high and its bandwidth is normally narrow. The level of the back radiation can be reduced by incorporating peripheral chokes. Generally, adding a single quarter-wavelength choke on the periphery of a waveguide feed reduces its back radiation by about 10 dB [24]. Such a reduction of the back radiation in microstrip antennas is also expected. Additional chokes can further reduce the back-lobe level, but at the expense of increased aperture blockage. In microstrip feeds one should select one or perhaps two chockes, since a large number of chokes will increase the feed size. Microstrip antennas are small in size and peripheral chokes will increase their relative size considerably, thus eliminating one of their main advantages. The limitation in the microstrip antenna band-width can also be overcome by using any of the many methods which are avaiable in literature. However, broadening the bandwidth should not affect the pattern symmetry and shape.

8 Fig. 2.46 Radiation patterns of a circular rnicrostrip patch, covered by a dielectric thickness ofO.11 a = 0.171. g = 0.41, Q, = 0.17 1 and E, = 2.32 -E-plane --- H-plane - .- .- Cross-~ o l a r

Here, we present a design example. The previous results for a circular microstrip patch indicated that the ground-plane size and thickness can be used as parameters to equalize the E- and H-plane patterns. It was also shown that, for a ground plane radius around 0.4 1, the pattern symmetry is satisfactory. This

98

Analysis of circular microstrip antennas

Analysis of circular microstrip antennas

99

A

m

a

-180

e Fig. 2.47

Radiation patterns of a circular parch covered by a dielectric g = 0.31,other data same as Fig. 2.46 -E-plane --- H-plane Cross-polar

-135

-90

-45

0

45

BO

135

180

B Fig. 2.49

Radiation patterns of a covered circular patch with a conducting collar g = 0.31; other data same as Fig. 2.48 -E-plane --- H-plane Cross-polar

8 Fig. 2.48

Radiation patterns of a covered circular patch with a conducting collar Data same as Fig. 2.46 -E-plane --- H-plane Cross-polar

Fig. 2.50 Radiation patterns of a two-layer stacked rnicrostr~p(Reproduced from Reference 20 @ 1986 IEEE Diameters: 0.321.(up); 0,341(bottom; g = 0.4A)

100

Analysis of circular microstrip antennas

Analysis of circular microstrip antennas

results in a feed of diameter less than one wavelenth, which is considerably smaller than commonly used waveguide feeds with chokes. To retain the geometrical symmetry and to increase the bandwidth one may use a stacked patch configuration [25]. This means the resonant patch will be covered by another dielectric-substrate which will alter its resonance frequency and the radiation pattern. To investigate the latter we have shown the radiation patterns of the new structure for ground-plane radii of 0.4 and 0.3 i in Figs. 2.46 and 2.47. The symmetry of the patterns is satisfactory, but not perfect. To improve the geometrical rigidity we then incorporate a peripheral collar around the substrate and compute the new radiation patterns. They are shown in Figs. 2.48 and 2.49 for the previous configurations. The addition of the collar limits the radiation from the substrate termination and considerably improves the pattern symmetry. The cross-polarisation is thus improved. Finally, we add the upper patch to the configuration. The radiation patterns of the final design are shown in Figs. 2.50 and 2.51, respectively for 0.4 /1 and 0.3 1 ground planes. It is interest-

707

the ground-plane radius is 0.42 and compute the cross-polarisation of different modes. Fig. 2.52 shows the contribution of the first four modes,to the crosspolarisation. As expected, the TM,, and TM,, modes have the main contributions. However, since they have different azimuthal dependenmces their combined cross-polarisation is asymmetric. Note that the feed cross-polarisation is maximum in the 4 = 45" plane and all presented data are in this plane. Fig. 2.52 also shows that adding the contribution of the higher-order modes reduces the cross-polarisation of the TM,, and TM,, modes. The overall cross-polarisation is high at about - 24 dB, but within the small angular region of + 45" is below the - 30 dB range.

-56

-90

-45

0

45

90

0 Fig. 2.52 Effect of different modes on the cross-polarisation of antenna in Fig. 2.48. (Reproduced from Reference 20 @ 1986 IEEE) . . . TM, + TM,,

.

0 Fig. 2.51

Radiation patterns of a two-layer stacked microstrip (Reproduced from Reference 20 @ 1986 IEEE) g = 0.31;other data same as Fig. 2.50 -E-plane H-plane

---

Cross-polar

ing to note that the pattern characteristics remain unchanged and excellent pattern symmetries are found for both antenna geometries. The cross-polarisations for both cases are below - 24 dB, but the back radiations are high. The latter will be reduced later by incorporating chokes. For the present, we investigate the sources of the cross-polarisation. We select the case of Fig. 2.48 where

TMo, + TM,, + TM,, ---- TMol + TMl, TM,, + TM,,.

To reduce the back radiation we have used two different choke configurations. In Figs. 2.53 and 2.54 the antennas of Figs. 2.50 and 2.51 are incorporated with a choke behind the ground plane. Their pattern characteristics in the forward directions remain unchanged, but the back radiation decreases to around - 24 dB. This type of choke geometry is not as efficient as the peripheral chokes in reducing the back radiation, but does not increase the feed diameter. The results with a peripheral choke are shown in Fig. 2.55, where the back radiation decreases to about - 30 dB range. Adding a second choke behind the ground plane reduces the back lobe by an additional 2 dB. A second peripheral

102

Analysis of circular rnicrostrip antennas

Analysis of circular rnicrostrip antennas

-40 -180

-135

-90

0 Fig. 2.53 Radiation patterns of antenna in Fig. 2.51 with a 214 back choke (Reproduced for Reference 20 @ 7986 IEEE) -E-plane --- H-plane

Cross-polar

0

45

90

135

A

ID0

0 Fig. 2.55

Cross-~olar

Fig. 2.54 Radiation patterns of antenna in Fig. 2.50 with a 114 back choke (Reproduced for Reference 2 0 @ 7986 IEEE) --- E-plane --- H-plane

-45

103

Radiation patterns of antenna in Fig. 2.50 with a 114 side choke (Reproduced from Reference 2 0 @ 7986 IEEEJ -E-plane - - - H-plane Cross-polar

9 (degrees) Fig. 2.56

Measured patterns of feed shown in Fig. 2.55 -E-plane --- H-plane Cross-polarisation at 45" plane

104

Analysis of circular microstrip antennas

Analysis of circular microstrip antennas I

choke can also be incorporated, but may not be necessary since the back lobe is already low and a new choke will enlarge the feed size. The feed with the peripheral choke was also fabricated and tested. Its measured E- and H-plane patterns, as well as the cross-polarisation in the 4 = 45" plane shown in Fig. 2.56, which are at the band centre frequency of 4.6GHz. The principal plane patterns agree with the computed data, but the cross-polarisation is higher. The measured peak cross-polarisation is about - 21 dB, which is about 7 dB higher than the computed one. It also shows a central peak at the boresight, which indicates the misalignment of the test set up. Also, within a bandwidth of 500 MHz, i.e. 11%, the co-polar patterns remained nearly symmetric. We expect that, by improving the fabrication tolerances and a proper alignment of the test range the measured cross-polarisation should approach the computed ones. The return loss of the feed was also measured and is shown in Table 2.1. Further improvement of these return losses can be achieved by modifying the feed-point location.

Table 2.2a Feed characteristics at the resonant frequency f, Case of Fig.

Peak cross-pol. 0 < 0 < 900 (dB)

Gain (dB)

Beamwidths., dee '2

3 dB

10 dB

Table 2.1 Mearurpd return lower o f l e e d ~ Feed 2, Fig. 2.55

Feed 1, Fig. 2.51 Frequency, GHz

Return loss, dB

Frequency, GHz

Return loss, dB

4.10 4.15 4.20 4.25 4.30 4.35 4.40 4.45 4.50 4.55 4.60

9.5 11.0 13.0 14.0 17.0 18.0 16.0 15.5 14.0 11.0 9.0

4.30 4.35 4.40 4.45 4.50 4.55 4 60 4.65 4.70 4.75 4.80

10.0 11.0 11.5 12.0 12.5 12.5 12.5 12.5 12.0 11.5 10.0

Table 2.2 summarises the performance of the above antennas, where the beamwidths at 3 dB and 10 dB levels, as well as the peak cross-polarisation, are provided. To evaluate the performance of these feeds on a reflector antenna the data on the gain factor, spill-over efficiency and the corresponding aperture angles must be known. They are calculated and shown in Table 2.3. It shows that the aperture angle varies from 60" to 71° and the gain factor rises from 72.5% to 74.24%. The feed performance is therefore reasonable. The computed gain factors are somewhat smaller than those of waveguide feeds with a corrugated flange. However, their aperture blockage is small owing to their small size. Thus, when used on small reflectors, they should provide comparable performance. These microstrip feeds are, on the other hand, light weight and easy to fabricate and can readily be integrated with receiving electronics.

Table 2.2b Data of Table 2.2 at f = 1.05f, Case of

Peak cross-pol.

Gain

Beamwidths. deg

Table 2 . 2 ~Data of Table 2.2 at f = 0.95f, Case of Fig.

Peak cross-pol. 0 < 0 < 90' (dB)

Gain (dB)

Beamwidths, den3 dB

10 dB

105

106

Analysis of circular microstrip antennas

Analysis of circular microstrip antennas

Table 2.3 also shows the location of the phase centre of each antenna calculated over its aperture angle, given in column 2 [26]. Their location is measured from the ground plane, i.e. z = 0, and are all positive, indicating that the phase centres are above the ground plane. However, it is interesting to compare

Table 2.3a Reflector aperture angles, gain factors, spill-over eficiencies and phase-centre locations above the ground plane for various feeds, f = f , Case of Fig. Aperture angle, Gain factor, Spill-over efficiency,phase centre, O h Yo I deg 2.46 68 72.93 85.43 0.075 2.47 71 73.85 86.70 0.0675 2.48 66 73.14 85.23 0.1 127 2.49 71 73.37 85.50 0.1167 2.50 66 72.86 84.16 0.1202 2.51 71 73.47 85.48 0.1212 24 66 74.29 86.24 0 1186 2.55 60 73.83 84.67 0.1827

Table 2.3b Data of Table 2.3 a t f = 1.05f, Case of Fig. Aperture angle, Gain factor, Spill-over efficiency, phase centre, deg Yo % I 2.46 67 72.1 84.9 0.08 2.47 71 73.9 88.1 0.09 2.48 67 72.3 86.6 0.144 2.49 71 73.50 85.5 0.121 2.54 71 73.0 87.0 0.142 2.55 60 73.83 84.67 0.174

Table 2 . 3 ~Data of Table 2.3 at f = 0.95 f, Case of Fig. Aperture angle, Gain factor, Spill-over efficiency, phase centre, % % I deg 2.46 69 73.2 85.8 0.065 2.47 71 74.1 86.2 0.068 2.48 68 73.34 87.1 0.085 2.49 71 73.53 85.6 0.071 2.54 66 74.34 86.8 0.1 14 2.55 66 71.2 83.9 0.416 the cases of Figs. 2.46 and 2.47 with the remaining ones, which have the peripheral conducting collar. In the former cases the phase-centre location is just above the ground plane. Since the total thickness of the dielectric is 0.1 1,

707

the phase centres are inside the dielectric and under the lower patch. In the remaining cases, all phase centres are outside the dielectric. From these results the following important conclusion can be drawn: In microstrip antennas, in Figs. 2.46 and 2.47, the radiation is mostly from the aperture between the patch and the ground plane. Incorporating the side collar raises the radiation zone to the periphery around the upper patch. The performance of the above antennas listed in Tables 2.2a and 2.3a is also studied as a function of frequency. Within 5% frequency variation the computed results are shown in Tables 2.26, 2 . 2 ~ and 2.36,2.3c. An examination of these results reveals that the feed performance remains relatively constant within the band, in the magnitude of the peak cross-polarisation and the reflector gain factor. The feed gain, however, decreases to some degree, regardless of increasing or decreasing the frequency. This is primarily due to the increased excitation of the modes adjacent to the TM,, mode.

2.6 Concluding remarks

In this Chapter a general numerical method has been presented that enables one to solve antenna problems involving conductors and dielectrics. While the formulation is applicable to arbitrary antenna shapes, the matrix formulation was provided only for axisymmetric configurations. The method was then used to investigate the radiation properties of three distinctly different antenna types. The circular microstrip patch antenna was selected to study the radiation mechanism of a typical microstrip antenna element. The wraparound antenna was chosen to show that the method can be used to design or analyse complex antenna candidates. The last example, i.e. the reflector feed, was included to show the design steps involving high-precision antennas, with stringent amplitude and phase-pattern requirements. The circular patch antenna was studied in some detail to show the effect of various material and dimensional parameters on its radiation patterns. For instance, the results showed that the ground-plane size has a significant influence on the radiation patterns beyond 45' off the symmetric axis. In addition, it was shown that, by selecting an appropriate ground-plane size, nearly symmetric radiation pattern with very low cross-polarisation can be obtained. On the other hand, the feed-point location was shown to influence the excitation of nonresonant modes, which also contribute to the cross-polarisation. The information provided in this Chapter is intended to help the reader in understanding the radiation mechanism of microstrip antennas and use of various parameters to control them. While the results are computed for circular patch antennas, they can also be used for square-patch configurations, and with judicious qualifications, for other patch geometries as well. Also, the results are valid only for single, i.e. isolated microstrip antennas. When antenna elements in a practical array environment are considered, their radiation characteristics will be affected

708

Analysis of circular microstrip antennas

by their mutual coupling and the element location within the array. The main effect of the mutual coupling will manifest itself in the mode excitation, which is considered in a later chapter. The element location within the array affects its ground-plane size, and thus its radiation patterns. For large arrays the ground plane is large and its effect can be neglected. For small arrays the peripheral elements will 'see' a smaller ground plane than the central ones and their radiation patterns will be affected accordingly. However, the ground-plane effect in array applications becomes significant mainly in phased arrays, where the beam must be scanned for low elevation angles.

2.7 References I 2 3 4 5 6 7 8 9

10 11

12

13 14

15 16

17

JAMES, J.R.. HALL, P.S., and WOOD, C.: 'Microstrip antenna, theory and design' (Peter Peregrinus, 1981) BAHL, I.J., and BHARTIA, P.: 'Microstr~pantennas' (Artech House, 1980. Dedham, Mass.) JOHNSON. R.C., and JASIK, H. (Eds.): 'Antenna engineering handbook' (McGraw-Hill, NY, 1984) 2nd edn., chap. 7 HUANG, J.: 'Finite ground plane effect on microstrip antenna radiation patterns,' IEEE Trans., 1983, AP-31, 649-653 LIER, E.: 'Rectangular microstrip patch antennas.' Ph.D. Dissertation, University of Trondheim, Norway, June 1982 MAUTZ, J.R., and Harnngton, R.F.: 'Boundary formulation for aperture coupling problem,' Archivfur Elekronik & Ubertrangungstechnik, 1980, 34, pp. 377-384 MEDGYESI-MITSCHANG, L.N., and PUTNAM, J.M.: 'Electromagnetic scattering from axially inhomogeneous bodies of revolution,' IEEE Trans., 1984, AP-32, pp. 797-806 HARRINGTON, R.F.: 'Time harmonic electromagnetic fields' (McGraw-Hill, NY, 1961) Sec. 3-5 MAUTZ, J.R., and HARRINGTON, R.F.: 'H-field, E-field and combined field solutions for conducting bodies of revolution,' Archiv fur Elekrronik & ubertragungstecltnik, 1978, 32, pp. 175-164 MAUTZ, J.R., and HARRINGTON, R.F.: 'Electromagnetic scattering from a homogeneous material body of revolution, Archiv fur Elektronik & Ubertragungstechnik, 1979,33, pp. 71-80 ISKANDER, K.A., SHAFAI, L., FRADSEN, A., and HANSEN, J.E.: 'Application of impedance boundary conditions to numerical solution of corrugated circular horns,' IEEE trans., 1982, AP-30, pp. 366-372 KISHK, A.A.: 'Different integral equations for numerical solution of problems involving conducting or dielectric objects and their combination.' Ph.D., Dissertation, University of Manitoba, Winnipeg, Canada, I986 YAGHJIAN, A.D.: 'Augmented electric and magnetic-field integral equations,' Radio Science, 1981, 16, pp. 987-1001 KISHK, A.A., and SHAFAI, L.: 'The effect of various parameters of circular microstrip antennas on their radiation efficiency and the mode excitation,' IEEE Trans., 1986 AP-34, pp. 969-977 MUNSON, R.E.: 'Conformal microstrip antennas and microstrip phase arrays,' IEEE Trans., 1974. AP-22, pp. 74-78 FONSECA, S.B.A., and GIAROLA, A.J.: 'Pattern coverage of microstrip wraparound antennas.' Int. Conf. on Antennas and Propag., ICAP 83, Norwich, England, P. 1, 1983, pp. 300-304 KERR, J.L.: 'Microstrip antenna developments,' Proc. Workshop on Prmted Circuit Antenna Technology, New Mexico State University, USA, Oct. 1979, pp. 3.1-3.20

Analysis of circular microstrip antennas

709

18 HALL, P.S., and PRIOR, C.J.: 'Wide bandwidth microstrip reflector feed element.' 15th European Microwave Conference, Paris, 1985, pp. 1029-1044 19 PRIOR, C.J., and HALL, P.S.: 'Microstrip disc antenna with short circuit annular ring,' Electron. Lett. 1985, 21, pp. 719-721 20 KISHK, A.A., and SHAFAI, L.: 'Radiation characteristics of a circular microstrip feed,' Conference on Antennas and Comm., Montech 86, Montreal, Canada, 1986, pp. 89-92 21 CLARRICOATS, P.J.B., and OLVER, A.D.: 'Corrugated horns for microwave antennas.' IEE Electromagnetic Wave Series 18 (Peter Peregrinus, 1984) 22 RUDGE, A.W., MILNE, K., OLVER, A.D., and KNIGHT, P., (Eds.): 'The hand-book of antenna design' Vol. 1. IEE Electromagnetic Wave Series 15 (Peter Peregrinus, 1982) 23 LUDWIG, A.C.: 'The definition of cross-polarisation,' IEEE Trans., 1973, AP-21, pp. 116119 24 SHAFAI, L., and KISHK, A.A.: 'Coaxial waveguides as primary feeds for reflector antennas and their comparison with circular waveguides,' Archiv Fur EIektronik & Ubertragungstchnik, 1985, 39, pp. 8-15 25 OLTMAN, H.G.: 'Electromagnetically coupled microstrip dipole antenna,' IEEE Trans., 1986, AP-34, pp. 467-50 26 SHAFAI, L., and KISHK, A.A.: 'Phase centre of small primary feeds and its effect on the feed performance,' IEE Proc., 1985, 132, pp. 207-214

Chapter 3

Characteristics of microstrip patch antennas and some methods of improving frequency agility and bandwidth K.F. Lee and J.S. Dahele

3.1 Introduction

The develuptnerit of microstrip antennas arose from the idea of utilising printedcircuit technology not only for the circuit components and transmission lines but also for the radiating elements of an electronic system. The basic geometry of a microstrip patch antenna (MPA) is shown in Fig. 3.1. A conducting patch is printed on the top of a grounded substrate. The shape of the patch can in principle be arbitrary. In practice, the rectangular, the circular, the equitriangular and the annular ring are common shapes. The feed can be either a coaxial cable (Fig. 3.la) or a strip line (Fig. 3.lb), which guides the electromagnetic energy from the source to the region under the patch. Some of this energy crosses the boundary of the patch and radiates into space. The MPA is a relatively new form of radiator. In addition to compatibility with integratedcircuit technology, it offers other advantages such as thin profile, light weight, low cost and conformability to a shaped surface. The main disadvantage is its inherent narrow bandwidth (typically a few percent) arising from the fact that the region under the patch is basically a resonant cavity with a high quality factor. The MPA was first proposed by Deschamps in 1953 [I]. However, it was only in the past 15 years or so that extensive research was devoted to this type of antennas. This was motivated by the advantages mentioned above, which make the microstrip antenna an attractive candidate for use in high-speed moving vehicles such as aircraft, missiles, rockets and communication satellites. By 1981, two textbooks [2, 31 and a special journal issue [4] containing two review articles [ 5 , 61 were devoted to the subject. A wealth of information is now available about the microstrip patch antenna as a radiating element, primarily for the case when the substrate thickness is much smaller than a wavelength. This Chapter attempts to present some of this information, including some developments since 1981. The plan of the Chapter is as follows. In Section 3.2, the cavity model method of analysing MPAs is described. The basic characteristics of common patch

7 72

I

i

Characteristics of microstrip patch antennas

shapes are presented in Section 3.3. Some methods of improving frequency agility and bandwidth are discussed in Section 3.4. Section 3.5 contains concluding remarks. i

3.2.1 Introducrion Let us consider the basic geometry of a microstrip patch antenna shown in Fig. 3.1, where the z-axis is perpendicular to the plane of the patch. Electromagnetic waves are first guided along the coaxial or stripline and then spread out under the patch. When they reach the boundary of the patch, some are reflected and some radiate into open space. There are two lines of approach to deduce the radiation fields. One is to find the current distributions along the antenna structure and then obtain the radiation fields from these current sources. The other is to find the fields at the exit region. These fields act as equivalent sources, from which the radiation fields are obtained.

I

-

113

results accurate enough for many engineering purposes. Our discussion will be restricted to the thin-substrate case. At the time of writing, the extension of the model to thick substrates is still in the early stage of exploration.

3.2 Cavity model for analysing microstrip patch antennas

A

Characteristics of microstrip patch antennas

I

3.2.2 Feed modelling, resonant frequencies and internal fields The simplicity of the cavity model can be traced to the assumption that the thickness of the substrate is much less than a wavelength, i.e. t < A. The following observations then follow from this assumption:

(i) The electric field E has only the z component and the magnetic field H has only the transverse components in the region bounded by the conducting patch and the ground plane. (ii) The fields in the aforementioned region do not vary with z. (iii) Since the electric current in the microstrip must not have a component normal to the edge, it follows from Maxwell's equations that the tangential component of H along the edge is negligible. As a result of (i)-(iii), the region between the patch and the ground plane can be considered as a cavity bounded by electric walls on the top and bottom, and by a magnetic wall on the side. The fact that assumption (i) does not hold near the edge because of the existence of fringing fields is taken into account by extending the edge slightly. This model has long been used in the analysis of microstrip resonators. However, the application to microstrip patch antenna appears to be due to Lo et al. (71, Richards e t al. [8] and Derneryd [9, 101. Writing Maxwell's equations for the region under the patch, we have

conductma

ground biane feed

a Fig. 3.1

Microstrip patch antenna with (a) coaxial feed and (b) stripline feed

Under the two approaches mentioned above, a number of methods of analysis have been developed. The main ones are the transmission-line model, the cavity model and the integral equation method. The transmission-line model in its original form is limited to rectangular or square patches; however, extension to other shapes is possible. The integral-equation method is perhaps the most general: it can treat arbitrary patch shapes as well as thick substrates. However, it requires considerable computational effort and provides little physical insight. Both the transmission-line model and the integral-equation method are treated elsewhere in this Handbook. In this section, we shall introduce the cavity model. Most of the results obtained using this model are for electrically thin substrates. For this case, the cavity model offers both simplicity and physical insight. It also appears to yield I

E in eqns. 3.2 and 3.3 is the permittivity of the substrate, the permeabtlity of whlch is assumed to be p,. The current density J in eqn. 3.2 is due to the feed, which is usually in the form of a coaxial cable or a stripline. The advantages of the coaxial feed are that the desired impedance characteristic can be obtained by proper location of the Inner conductor (see Section 3.3) and that the cable can be placed under the ground plane to minimise coupling between the feed and the antenna patch. The disadvantage is that the structure is not completely monolithic and becomes more difficult to produce. This advantage is avoided in a stripline feed, which, however, introduces some radiation of its own and offers less flexibility in obtainmg the proper impedance. Usually, a quarter-wave line with a proper characteristic impedance 1s necessary to transform the antenna impedance to that of the stripline. It is appropriate at this point to discuss the modelling of a feed current which

174

Characteristics of microstrip patch antennas

has been used in the development of the cavity model. Consider first a coaxialline feed. It can be represented by a cylindrical band of electric current flowing from the ground plane to the patch, plus an annular ring of magnetic current at the coaxial opening in the ground plane [ l 11. The latter can be neglected with little error, and the former can be idealised by assuming that it is equivalent to a uniform current of some effective angular width 2w, centered on the feed axis. For example, for a circular patch fed at a distance d from the centre, it is illustrated in Fig. 3.2 and described by

I

1

Characteristics of microstrip patch antennas

115

be modelled by a :-directed equivalent current source of some effective width 2w. For the circular patch, it is of the same form as eqn. 3.5 except that d is replaced by the patch radius a. In both the coaxial and the stripline feed, the z-directed current is assumed to be independent of z on account of the thinness of the dielectric region. Hence V .J = -jwe = 0 and eqn. 3.3 reduces to V.E = 0

(3.7)

From eqns. 3.1, 3.2, 3.7 and 3.4, we obtain where is the wavenumber in the dielectric. The electric-wall conwhere k , = dition is automatically satisfied since E = Ezfwhile the magnetic-wall condition implies that

on the sides of the cavity. To solve eqn. 3.8 subject to the boundary conditions, we first find the eigen functions of the homogeneous wave equation

I

subject to the same boundary conditions. Let the eigen functions of eqn. 3.10 be $I,, and the eigen values of k , be km,. Assuming the eigen functions to be orthogonal, the solution to eqn. 3.8 is

where

, Fig. 3.2

Modelling of a coaxial feed by a current ribbon for a circular patch

The effective angular width 2w is a parameter chosen so that good agreement between the theoretical and experimental impedances is obtained. Usually, the arc length 2wd is several times the physical dimension of the inner conductor. If the feed is a stripline, it can be replaced by an equivalent current source obtainable from the transverse fields in the plane where the stripline connects the patch [12]. From uniqueness concepts, only the tangential magnetic field H backed by a perfect magnetic conductor is needed. Hence the stripline feed can

* denotes complex conjugate and

In eqns. 3.12 and 3.13, integration is over the domain of the patch. The resonant frequencies are obtained from setting k: - k i n = 0 and are given by

fmn =

kmn/2dZ.

(3.14)

3.2.3 Radiation field To calculate the radiation field, consider a closed surface S shown in Fig. 3.3. The top face of S lies just outside the patch and the bottom face lies just outside the ground plane. The vertical face of S coincides with the magnetic wall of the

7 76

Characteristics of microstrip patch antennas

cavity. The fields exterior to S c a n be calculated from the equivalent sources on Sand their images; the latter is necessary to account for the ground plane, which is assumed to be infinite in extent for the purpose of analysis. Since the tangential electric fields on the top and bottom faces, as well as the tangential magnetic field on the vertical surface, are zero, the only contribution to the equivalent sources are the tangential electric field E, on the vertical surface of the cavity. Together with its image, the total equivalent magnetic current is

Characteristics of microstrip patch antennas

1

1

7 17

given by Wood [I41 is more quantitative: t / l o < 0.07 for E, = 2.3 and t / l o < 0.023 for E, = 10 if the antenna is to launch no more than 25% of the total radiated power as surface waves. More recent work by Fonseca et al. [I51 showed that the size of the patch is also a parameter. For simplicity, we shall use Wood's criterion and assume that it is satisfied in subsequent discussions. The dielectric loss P, and the conductor loss P, are calculated from the electric field under the cavlty, while the radiation loss P, is calculated from the far-zone electromagnetic field. They are given by

where ri is the unit outward normal.

P, =

gro;nd

1

lo loIEI2 ? sin OdO d 9 2n

n

The quantity 6 In eqn. 3.20 is the loss tangent of the dielectric and R, in eqn. 3.21 is the surface resistivity of the conductors. The radiation or antenna efficiency is the ratio of radiated power to input power:

plane

coax feed

Fig. 3.3 Application of the equivalence principle to calculafe the radiation from a microstrip patch antenna

If the substrate thickness t is much less than the wavelength 1,its effect on the radiation field is small and M can be assumed to radiate in free space. Using the free-space Green's function, the electric potential F a t a point r is given by

In calculating the losses, it is usual to make use of the resonance approx~mation [8].This arises from the observation that, if the frequency is close to the resonant frequency of a particular mode, the factor l/(k: - k i n )in eqn. 3.11 is very large and the contribution to Ez, and hence to the radiation field E, is due mainly to the resonant-mode term. The electric energy stored at resonance is

where integration is over the perimeter of the patch. The fields in the far-zone are given by

and the total stored energy at resonance is

H(r) =

-joF(r)

E d r ) = IoHd(r) =

where

io=

The effective loss tangent of the cavity, taking into account the three losses P,, PCand P,, is given by

- IoHdr)

a.

8,

3.2.4 Losses in the cavity The losses in the cavity under the patch comprise dielectric loss P,, conductor loss PC,radiation loss P, and surface-wave loss James et al. [I31 estimated that surface-wave excitation is not important if t / & < 0.09 for E , = 2.3 and t/& < 0.03 for E , 10, where lois the free-space wavelength. The criterion

-

e,,..

= P T / ( ~ ~ T )

(3.26)

where PT = Pd

+ PC + P,.

(3.27)

A number of quality Q factors are defined as follows: Dielectric Q: Q, = o WT/Pd = 116

(3.28)

118

Characteristics of microstrip patch antennas

Characteristics of microstrip patch antennas

Conductor Q: Q,

=

wW,/P,

Radiation Q: Q,

=

w WT/P,

(3.30)

=

wWT/P, = 1/6,8

(3.31)

Total Q: QT

=

e

t

(3.29)

In eqn. 3.29, a is the conductivity of the patch and the ground plane. 3.2.5 Input impedance The input impedance at the feed of the antenna is given by Z = R

+ jX

=

V/I

=

E,t/I

119

specific standard. In the case of the microstrip patch antenna which is basically a strongly resonant device, it is usually the variation of impedance, rather than pattern, which limits the standard of performance. If the antenna impedance is matched to the transmission line at resonance, the mismatch off resonance is related to the VSWR. The value of VSWR which can be tolerated then defines the bandwidth of the antenna. If this value is to be less than S, the usable bandwidth of the antenna is related to the total Q-factor by [I I] Bandwidth (BW)

(3.32)

-

=

%

(s 2

1)

QT$

where E, is the average value of the electric field at the feed point and I is the total current. For example, if the feed is modelled by eqn. 3.5, we have

and I = -J(2wd)

(3.34)

Unlike the calculations of 6@, it was found that non-resonant modes must be included in the calculation of input impedance if good agreement between theory and experiment was to be obtained. The appropriate equation for EZis therefore eqn. 3.1 1, which contains the factor I/(k: - kin). To keep this term finite at resonance, the permittivity of the dielectric must be considered complex. If only the dielectric loss is considered, we have E

k:

=

E ~ E , (I j6)

= a 2 & & = k$z,(1 - js),

(3.35) (3.36)

However, Richards et al. [16] found that better agreement with experiment was obtained if, instead of the loss tangent of the dielectric, the effective loss tangent is used. Thus, in calculating the input impedance, eqn. 3.1 1 is modified to read

Fig. 3.4

Typical impedance characteristics around the resonant frequency of a mode

For S = 2, which is a common standard, the above equation reduces to

where

A typical impedance versus frequency curve is illustrated in Fig. 3.4. There is usually some reactance at the resonant frequency of a mode due to the contributions from the non-resonant modes. 3.2.6 VSWR bandwidth The bandwidth of an antenna is the range of frequencies within which the performance of the antenna, with respect to some characteristic, conforms to a

While eqn. 3.39 is the most commonly used definition for bandwidth and is the one we use in this Chapter, it should be pointed out that this is not a universal definition. For example, some authors define the bandwidth as l/Q,. 3.2.7 Qualitative description of the results predicted by the model

In Section 3.3, the equations presented above will be used to obtain the specific results for a number of microstrip patch antennas. It is perhaps instructive to describe here the qualitative features which are common to MPAs. These features follow naturally from viewing the MPA as a leaky cavity.

720

Characteristics of microstrip patch antennas

Characteristics o f microstrip patch antennas

(i) There are an infinite number of resonant modes, each characterised by a resonant frequency. (ii) Because of fringing fields at the edge of the patch, the patch behaves as if it has a slightly larger dimension. Semi-empirical factors are usually introduced to obtain these effective dimensions. These factors vary from patch to patch. (iii) Each resonant mode has its own characteristic radiation pattern. The lowest mode usually radiates strongest in the broadside direction. The pattern of this mode is broad, with half-power beamwidths of the order of 100". (iv) For coaxial-fed antennas, the input impedance is dependent on the feed position. The variation of input resistance at resonance with feed position essentially follows that of the cavity field. For the lowest mode, it is usually large when the feed is near the edge of the patch and decreases as the feed moves inside the patch. Its magnitude can vary from tens to hundreds of ohms. By choosing the feed position properly, an effective match between the antenna and the transmission line can be obtained. jvj Since the cavity under the patch is basicaily a resonaror, the rorai Q and the impedance bandwidth are dependent on the thickness of the substrate t and its permittivity E . For low values of E,, the bandwidth generally increases with increasing t and decreases with increasing E,. This is presumably due to the fact that the stored energy W, decreases with t and increases with E, while the total loss P, is insensitive to these changes. However, detailed analysis (Section 3.3) shows that the bandwidth and Q are complicated functions of frequency, substrate thickness and the permittivity. (vi) For thin substrates, the impedance bandwidth varies from less than one to several percent.

121

width b. The electric field of a resonant mode in the cavity under the patch is given by (3.41) Er = E,,cos (mnxla) cos (nnylb) where m, n = 0, 1, 2 . . . The resonant frequency is where

In the next Section, the results obtained by applying the formulas of this Section to rectangular, circular, equitriangular and annular-ring patches will be presented.

3.3 Basic characteristics of some common patches Fig. 3.5

Geometry for the rectangular patch

-c47

A number of canonical patch shapes can be analysed by straightforward application of the cavity model. Of these, the rectangular, the circular, the equitriangular and the annular ring are the common shapes used in practice. They will be considered in detail in this Section. An example comparing the characteristics of these patches will be given in Section 3.4, while other patch shapes will be briefly mentioned in Section 3.5.

Eqn. 3.42 is based on the assumption of a perfect magnetic wall. To account for the fringing fields at the perimeter of the patch, the following empirical formula can be used for the effective dimensions [7]:

3.3.1 The rectangular patch

b, = A more accurate but lengthy formula, suggested by James et al. [3] is

3.3.1.1 Introduction: The rectangular patch (Fig. 3.5) is probably the most commonly used microstrip antenna. It is characterised by the length a and the

+ 112 b + 112

a, = a

(3.44) (3.45)

122

Characteristics of microstrip patch antennas

Characteristics of microstrip patch antennas

123

where

where f, is the resonant frequency given by eqn. 3.42. Eqn. 3.46 is found to yield resonant frequencies which are within 3% of experimental values, while the perfect magnetic-wall model gives errors up to 20%. The far-field, losses and Q, and input impedance can be calculated by applying the equations of Section 3.2. Since for the rectangular patch they are well documented [ 3 , 7 , 8 ] ,they will not be reproduced here. In what follows, we shall present numerical results based on these equations to illustrate the basic characteristics of the rectangular patch. Experimental results will also be given.

TMol mode

3.3.1.2 Illustrative results: We present in this Section numerical, and in some cases experimental, results illustrating the basic characteristics of the rectangular patch antenna. (a) Magnetic-current distribution The electric-field and magnetic-surface-current distributions on the side wall for TM,,, TM,, and TM, modes are illustrated in Fig. 3.6. For the TM,, mode, the magnetic currents along b are constant and in phase while those along a vary sinusoidally and are out of phase. For this reason, the b edge is known as the radiating edge since it contributes predominantly to the radiation. The a edge is known as the non-radiating edge. Similarly, for the TM,, mode, the magnetic currents are constant and in phase along a and are out of phase and vary sinusoidally along b. The a edge is thus the radiating edge for the TM,, mode. (b) Radiation patterns The modes of the greatest interest are TM,, and TM,, . However, the TM,, mode has also received some attention. These three modes all have broadside radiation patterns. The computed patterns for a = 1.56 and two values of E, are shown in Figs. 3 . 7 ~ - fIn . the principal planes, the TM,, and TM,, modes have similar polarisations while that of the TM,, mode is orthogonal to the other two. As will be discussed in Section 3.4.3.2,the TM,, and TM,, modes can be utilised to operate the rectangular patch as a dual-frequency antenna. The patterns do not appear to be sensitive to alb or t. However, they change appreciably with E,

.

TMIO mode b

TMZO mode

Fig. 3.6 Electric field and magnetic-surface-current distributions in walls for several modes of a rectangular microstrip parch antenna a TM,, mode b TM,, mode c TM,, mode

124

Characteristics of rnicrostrip patch antennas

Characteristics of rnicrostrip patch antennas -9

OdB

,

L,

,

, ,J,or

-80' -30 -90'

OdB

-10

-20

-30

-30

-20

b

-8

l Eel

-10

OdB

-10

-20

-30

-30

-20

-10

OdB

125

126

Characteristics of rnicrostrip patch antennas

Characteristics of microstrip patch antennas

127

a = 1.5b. For E, = 2.32 and E , = 9.8, the results for three thicknesses are given. In general, the efficiency increases with the thickness of the substrate and decreases with increasing E, . In using these curves, the criterion given by Wood for the avoidance of excessive surface-wave excitation mentioned in Section 3.2.4 should be kept in mind. For E, = 2.32 and E, = 9.8, the cut-off frequencies (below which the surface wave is less than 25% of total radiated power) are 21/t and 6.9/t GHz, respectively, where t is in millimetres. These correspond to 6.60 GHz for E, =

OdB

Fig. 3.7

-10

-20

-30

-30

-20

-10

OdB

Helatlve fleld patterns for a rectangular patch with alb = 1.5, f,, = 1 GHz, and (I) 2.32, t = 0.318, 0.159, 0,0795cm; (ii) E, = 9.8, t = 0.127, 0.0635, 0.0254 cm ( a ) TM,,. 4 = O' ( b ) TM,,. = 90" ( c ) TMOl , 4 = 90" ( d ) T M , , . 4 = 0" ( e ) TM,,, 4 = 90' ( f ) TM,,.4 = 0" ( g ) TM,, , 6, = 2.32

E, =

+

The patterns of most of the other modes have maxima off broadside. For example, those of the T M , , mode are illustrated in Fig. 7g. Fig. 3.8 shows the computed and measured radiation patterns of the TM,, and TM,, modes obtained by Lo et al. [7] for a rectangular patch with a = 11.43cm, b = 7.6cm, E, = 2.62 and t = 0.159 cm. Both Eo and E4 were measured in each of the two cuts, q5 = 0" and q5 = 90". It was found that one component of polarisation was negligible when compared to the other in each case and is not shown. (c) Radiation eficiency Let us first obtain some idea of the relative magnitudes of the power dissipated in the metal, the power dissipated in the dielectric, and the antenna radiation efficiency. These are described by the quantities P,/P,, P,/P, and P,/P,, respectively. The cases of (i) a = 1,5b, E, = 2.32, t = 0.159 cm and (ii) a = 1.56, E, = 9.8, t = 0.0635cm are illustrated in Fig. 3.9 for the TM,, mode. It is seen that, for both E, = 9.8 and E, = 2.32, the loss due to the conductor is larger than the loss due to the dielectric. The ratio P,/P, decreases rapidly as frequency increases. The radiation efficiency e = P,/P, of the TM,,, TM,, and TM,, modes as a function of resonant frequent is shown in Figs. 3.10~-c for a patch with

Fig. 3.8 Theoretical (x) and measured (solid or dashed line) radiation patterns in 4 = 0' and C $ = 90' planes of a rectangular patch antenna with a = 17.43 cm, b = 7.6 cm, E, = 2.62, t = 0.159 cm. (Reproduced from Reference 7 p. 140 @ 1979 IEEE) ( a ) and ( 6 ) at resonant frequency 8 0 4 MHz of (1, 0 ) mode ( c ) and ( d ) at resonant frequency 1187 MHz of (0, 1) mode

2.32, t = 0.318cm and 5.43GHz for E, = 9.8, r = 0.127cm. For the other cases, the cut-off frequencies occur beyond 10 GHz. (d) Directivity and gain The directivity D of an antenna is defined as the ratio of power density in the main beam to the average power density while the gain G = eD. For a rectangular patch with a = 1.5b, the directivities as a function of resonant frequency

128

Characteristics of microstrip patch antennas

Characteristics of microstrip patch antennas

129

for the three broadside modes are illustrated in Fig. 3.1 1. The directivity of the TM,, mode is largest and that of the TM,, mode the smallest. It is not sensitive to substrate thickness and resonant frequency. The gain, on the other hand, increases with resonant frequency in the manner shown in Figs. 3.12L~-c.

"., resonant frequency (GHz)

a

resonant frequency (GHz)

F i g . 3.9

Metallic (P,), dielectric (P,) and radiation (P,) losses for the TM,, mode as a function of resonant frequency for (a) a = 1.56. c, = 2.32,t = 0.159cm and (6) a = 1.56, e, = 9.8, t = 0.0635cm

(e) Total Q and bandwidth For the three broadside modes, the variation of total Q with resonant frequency is shown in Figs. 3.13~-c for the case a = 1.56. The bandwidth, as defined by eqn. 3.43, is shown in Figs. 3.14~-c.It is seen that the TM,, mode has the lowest Q and therefore the largest bandwidth compared to the other two modes. For E, = 2.32, the bandwidth for a given mode increases with substrate thickness except for frequencies below about 0.7 GHz. The behaviour is more complicated for E, = 9.8. For this case, there appears to be a range of frequencies for which a thinner substrate actually yields a larger bandwidth. (f) Input impedance Richards et al. [8] have reported calculated and measured values of the input impedance of a coaxial-fed rectangular patch with e, = 2.62 and t = 0.159cm. The Smith chart plot for the TM,, mode is shown in Fig. 3.15 for three feed positions. The variation of the input resistances at resonance of the TM,, and TM,, modes is shown in Fig. 3.16. It is seen that the input resistance is largest

resonont frequency (GHz)

Fig. 3.10 Radiation efficiency as a function of resonant frequency for a rectangular patch witho = 5 . 8 x 107S/m,6 = 0.0005, a = 1.5band(i) e, = 2.32,t = 0.318.0.159, 0.0795 cm; (ii) 8, = 9.8, t = 0,127, 0,0635, 0,0254 cm

130

Characteristics of rnicrostrip patch antennas T"03

Characteristics of rnicrostrip patch antennas

137

a-1 5 b

resonant frequency (GHz) C

when fed at the edge of the patch, but it can attain the convenient value of 50 R when the feed position is chosen properly. More detailed theoretical results for the input resistance at resonance are shown in Figs. 3.17~-c for the TM,,, TM,, and TM,, modes for E , = 2.32, t = 0.159cm and a/b = 1.5. The resistances are plotted as a function of feed position parametric in the resonant frequencies. It is seen that the values vary somewhat with the resonant frequency. It should also be noted that, for the TM,, mode, the variation with feed position is not a monotonically decreasing function, which is the case for the TM,, and TM,, modes. It is clear from these illustrations that, for a coaxial feed, matching the antenna impedance to the transmission-line impedance can be accomplished simply by putting the feed at the proper location. There is less flexibility in the case of a stripline feed. In this case, a quarter-wave transformer may be added to effect matching. Alternatively, an insert into the patch can be made. To conclude this Section, we point out that a rectangular patch with a single feed produces linearly polarised radiation. If circular polarisation is desired, the most direct approach is to use two feeds located geometrically 90' apart and with a relative phase shift of 90". This arrangement excites two orthogonal modes, each providing a linearly polarised wave at right angles to each other and at phase quadrature. Circular polarisation can also be produced by a nearly square patch, where one pair of sides resonates at a slightly higher frequency than the other pair. If the phase difference at the centre frequency between the pairs of sides is 4 2 , circular polarisation results. Lo and Richards [17, 181 have shown that the sides

0

2

L

6

8

10

resonant frequency (GHz)

Fig. 3.11 Directivities (absolute value) of the TM,,, TM,, and TM,, modes as a function of resonant frequency for a rectangular patch with a = 7.56 and (ii) 6, = 2.32, t = 0,318, 0.159, 0.0795crn; (ii) E, = 9.8, t = 0.127, 0.0635, 0,0254 cm

a and b must satisfy a/b = 1 + l/Q and the feed must be located along the line y = f bxla. The plus and minus signs produce left-hand and right-hand circular polarisations, respectively, in the direction normal to the patch.

Characteristics of microstrip patch antennas

Characteristics of microstrip patch antennas

I

133

a11.5b

T"l~

resonant frequency (GHz) a

resonant frequency

(GHz)

C

Fig. 3.12

Gain (absolute value) as a function of resonant frequency for a rectangular patch witho = 5.8 x 1O7Slm.6= 0.0005.a = 1.5band(i)c, = 2.32, t = 0~318.0.159, 0.0795cm; (ii) c, = 9.8, t = 0.127. 0,0635, 0.0254cm (a) TM,, ( 6 ) TMo, ( c ) TMo3

resonant frequency

b

(GHz)

134

Characteristics of microstrip patch antennas

Characteristics of microstrip patch antennas T"03

resonant frequency (GHz)

735

a=1.5b

resonant frequency (GHz)

a Fig. 3.13

Total Q factor as a function of resonant frequency for a rectangular patch with x 107Slrn, S = 0.0005, a = 1.56 and (i) E, = 2.32, t = 0.318, 0.159, 0.0795cm; (ii) E, = 9.8, t = 0.1 17, 0.0635, 0,0254crn ( a ) TWO ( b ) TMOI ( c ) TM03

rr = 5.8

3.3.2 The circular patch

0.318 crn

3.3.2.1 Introduction: The geometry of the circular patch or disc (Fig. 3.18) is characterised by a single parameter, namely, its radius a. In this respect, it is perhaps the simplest geometry since other shapes require more than one parameter to describe them. The mathematical analysis, however, involves Bessel functions. The electric field of a resonant TM, mode in the cavity under the circular patch is given by

E, = E,,J, (k,, Q)cos n$ resonant frequency (GHz) b

(3.49)

where Q and I) are the radial and azimuthul co-ordinates, respectively. E, is an arbitrary constant, J, is the Bessel function of the first kind of order n and

k,

= Xm/a

(3.50)

136

Characteristics of microstrip patch antennas

Characteristics of microstrip patch antennas

resonant frequency (GHz)

resonant frequency (GHz) C

a

30

TMOI

137

a:l

Fig. 3.14 Bandwidth as a function of resonant frequency for a rectangular patch with a = 5 . 8 x 107Slm. 6 = 0,0005. a = 7.56 and (i) E, = 2.32, t = 0.378, 0.759, 0.0795cm; (ii) E, = 9.8, t = 0.1 17, 0.0635, 0,0254 cm ( a ) TMto ( b ) TMo, ( c ) TMo3

5b

In eqn. 3.50, &, are the roots of the equation where differentiation is with respect to x. The first five non-zero roots of eqn. 3.51 are shown in Table 3.1. The resonant frequency of a TM,,, mode is given by

where c is the velocity of light in free space. Eqn. 3.52 is based on the assumption of a perfect magnetic wall and neglects the fringing fields at the open-end edge of the microstrip patch. To account for these fringing fields, an effective radius a,, which is slightly larger than the physical radius a, is introduced [19]:

10 resonant frequency (GHz)

b

10

138

Characteristics of rnicrostrip patch antennas

Characteristics of microstrip patch antennas

Eqn. 3.53 is obtained by considering the radius of an ideal circular parallel-plate capacitor which would yield the same static capacitance after fringing is taken into account. Although the result is borrowed from the static case, it appears to yield theoretical resonant frequencies which are within 2.5% of measured values.

3.3.2.2 Illustrative results: In this Section, we present graphical illustrations of the circular microstrip patch antenna. They include the magnetic-current distribution, radiation patterns, efficiency, directivity and gain, bandwidth and Q,and input impedance.

x

T6

739

x measurement

- theory feed polnts

w

-

N

C

rectangular microstrip antenna substrate rexolite 2200 1116"nominal th~ckness

o measured locus x computed locus x increment: 5 M H z (increasmg frequency is clockwise)

o

0

0.2

0.3

0.4

0.5

y'lb for x'=5.33cm for (0.1) mode x'lb for y'=3.81 cm for (1.0) mode (x'y') IS location of feed point

b

a

0.1

Fig. 3.15 Impedance of the TM,, mode of a rectangular patch antenna of a = 1743cm. b = 7.6 cm, 6, = 2.62, t = 0.759 cm. (Reproduced from Reference 8 p. 3 9 @ 198 1 IEEE) a Feed placement for impedance measurements b Comparison of measured (0) and computed (x) impedance loci

Table 3.1 The first five non-zero roots of J, ( x ) = 0

Fig. 3.1 6

As with the rectangular patch, the expressions for the far field, losses and Q, input impedance etc. are well documented [2] for the circular patch and will not be reproduced here. The characteristics obtained from these equations will be illustrated in the next Section.

Variation of resonant resistance with feed position of the TM,, and TM,,, mode in a rectangular patch antenna with a = 17.43cm. b = 7.62cm. &, = 2.62, t = 0.159cm. (Reproduced from Reference 8 p. 42 @ 1987 IEEE)

(i) Magnetic current distribution The magnetic-current distribution around the edge of the disc for the nmth mode is proportional to cosn($ - a).This is illustrated in Fig. 3.19 for n = 0, 1, 2 and 3. It is independent of I(/ for modes with n = 0 and undergoes three sinusoidal periods for modes with n = 3.

140

Fig. 3.1 7

Characteristics of microstrip patch antennas

Characteristics of microstrip patch antennas

74 1

Variation of resonant resistance with resonant frequency for a rectangular patch antenna with alb = 7.5,E, = 2.32,t = 0.159cm ( a ) TMlo ( b ) TMoi

( c ) TM03 y'lb

(ii) Radiation patterns Lo and co-workers [7] were among the first to obtain theoretical and experimental radiation patterns of the circular disc. Some of their results are shown below. In their experiment, a disc with a radius of 6.7cm and a dielectric thickness of 1.5 mm was used. The relative permittivity was 2.62. For this disc, the first resonance, i.e. that of the TM,, mode, was at 794MHz. The second

resonance, i.e. that of the TM,, mode, was at 1324MHz. The calculated and measured radiation patterns in the Q, = 0" and Q, = 90" planes are shown in Fig. 3.20. Qualitatively, the calculated and measured results showed reasonable agreement. No attempt was made to take into account the effects of a finite

142

Characteristics of microstrip patch antennas

Characteristics of microstrip patch antennas

143

(iv) Directivity and gain The directivity versus resonant frequency is plotted in Fig. 3.22. A circular patch on an alumina substrate has a directivity of about 3.5, which is almost independent of substrate thickness and resonant frequency. If the substrate is Duroid, it has a maximum directivity of about 5.3, which decreases with increasing resonant frequency and dielectric thickness. The gain of the lowest mode is illustrated in Fig. 3.23.

Fig. 3.18

Geometry of the circular patch antenna

ground plane in the theory, which was about 12 wavelengths on a side for frequencies near 794 MHz. The radiation patterns of the higher-order modes (0,2) and (3,O) also exhibit nulls in the broadside direction. Since the higher-order modes are seldom used in practice, only the characteristics of the lowest mode will be illustrated in subsequent sections.

(v) Total Q and bandwidth The variation of total Q with resonant frequency for the lowest mode is shown in Fig. 3.24. The bandwidth, as defined by eqn. 3.40, is shown in Fig. 3.25. Its dependences on substrate thickness and E, are similar to the rectangular patch.

(iii) Eflciency The radiation efficiency for the lowest mode TM,, as a function of resonant frequency for various dielectric substrate is shown in Fig. 3.21. It is seen that the efficiency increases with increasing substrate thickness and decreasing dielectric constant.

(vi) Input impedance Richards et al. have reported calculated and measured values of the input impedance of a coaxially fed circular patch as a function of radial feed position. This is shown in Fig. 3.26 for the TM,, mode. It is seen that the input resistance is largest when fed at the edge of the patch, but it can attain the convenient value of 50R when the feed location is chosen properly.

744

I

Characteristics of microstrip patch antennas

Characteristics of microstrip patch antennas

745

Dahele and Lee [20] have studied experimentally the effect of substrate thickness on the input im~edanceof a coaxially fed circular patch. Their results are shown in Fig. 3.27.

Fig. 3.20

Theorettcal (x) and measured radtatlon patterns tn the q5 = 0' and q5 = 90' planes of a circular patch w ~ t radius h a = 6 . 7 5 ~ 1E,, = 2.32 (Reproducedfrom Reference 7 p. 141 @ 1979 IEEE) (a) and ( b ) At 794 MHz of mode ( 1 . 1 ) ( c ) and ( d ) At 1324 M H z if mode ( 2 , l )

Fig. 3.21

Radiatton efficiency versus resonant frequency for the TM,, mode of the ctrcular patch with g = 5.8 x 1O7Slm, 6 = 0.0005 and (I) E, = 2.32, t = 0.318, 0.159, 0.0795cm; (;I) c, = 9.8, t = 0.127, 0.0635, 0.0254cm

Fig. 3.19 Surface magnetic-current distribution of the nmth mode in the circular patch antenna resonant frequency (GHz)

TO conclude this Section, We point out that, as in the case of the rectangular patch, feeding the circular patch at a single point results in linearly polarised radiation. Circular polarisation on boresight can be obtained using two feeds at

i

146

Characteristics of rnicrostrip patch antennas

Characteristics o f rnicrostrip patch antennas

147

1

resonant frequency (GHzI

Fig. 3.22 Directivity versus resonant frequency for the TM,, mode of the circular patch: (i) e, = 2.32, t = 0~318,0~759,0~0795cm;(ii) e, = 9.8, t = 0~127,0~0635,0~0254cm

0.1

Fig. 3.24

resonant frequency ( G H ~ )

Total Q versus resonant frequency for the TM,, mode of the circular patch with a = 5.8 x 107S/m, 6 = 0.0005 and (i) E, = 2.32, t = 0.318, 0.759, 0.0795cm; (ii) e, = 9.8, t = 0.727, 0.0635, 0.0254cm

0.1 01

10

resonant frequency (GHzl

1 resonant frequency (GHz)

Fig. 3.23 Gain versus resonant frequency for the TM,, mode of the circular patch with a = 5 8 x 707S/m, 6 = 0,0005 and (i) E, = 2.32, t = 0,318, 0.159, 0,0795cm; (ii) 6, = 9.8, t = 0.127, 0,0635, 0.0254cm

Fig. 3.25 Bandwidth versus resonant frequency for the TM,, mode of the circular patch with a = 5.8 x 107S/m,6 = 0.0005 and (ii) E, = 2.32, t = 0.318, 0.159, 0~0795cm: (ii) e, = 9.8, t = 0.127, 0.0635, O.0254cm

748

Characteristics of microstrip patch antennas

-

Characteristics of microstrip patch antennas

749

+

x x computed p a n t 2 5 M H z Increment measured locus 5.0 MHz Increme

(1, = t+b, and (1,, 90' and excited in phase quadrature. Alternatively, a slightly elliptical patch with the right amount of ellipticity and fed at theappropriate location can produce circularly polarised waves. This will be discussed further in Section 3.3.6.

u computed polnt Increment 5 OMHr

260r 2~0.

0

measured

P

+ Calculated 220 -

--

200 -

/

/

C 180-

-

-,a5

i

P

120-

/ /

loo-

/

0

; 8060

-

/

d

/

,

,

,

,

6 radlal source locat1on.d

Fig. 3.26

,

,

Fig. 3.27

8 ial8

(a) Calculated and measured TM,, mode input impedance loci for several radial feed locations. (6) Variation of TM,, resonant input resistance with radial feed position for a circular patch with a = 6.7~171 on Rexolite 2200 substrate (E, = 2.62) of thickness O.159cm (Reproduced from Reference 8 p. 41, @ 1987, IEEE)

Measured real part (R) and imaginary part (X) of input impedance as function of frequency for the TM,, mode of a circular patch with a = 6.8cm. 8, = 2.32 and three dielectric thicknesses. The feed is at d = 6.5 cm (Reproduced from Reference 20 p. 359 @ 1983 IEEE)

3.3.3 The Equitriangular patch Several triangular patch shapes are amendable to analysis by the cavity model. These include the 45"-45"-90°, 30'-60"-90°, and the 60"-60"-60" equitriangular

150

151

Characteristics of microstrip patch antennas

Characteristics of microstrip patch antennas

(equilateral triangular) patches. However, unlike the rectangular and circular patches which have been studied extensively, there are only a handful of investigation on the triangular patches [2, 21-24]. In this Section, the equitriangular patch is treated in detail. The geometry, for the case of a coaxial feed, is shown in Fig. 3.28. The presentation follows closely that of Luk et al. [24].

There were two suggestions for accounting for non-perfect magnetic wall effects. Helszain and James [I71 suggested that the side length a in eqn. 3.55 be replaced by the effective value a, = a

+ t(~,)-'"

(3.56)

On the other hand, Bahl and Bhartia [2] proposed that, in addition to a, replacing a in eqn. 3.55, E, should also be replaced by the effective value

-x

top vlew

z patch,

Fig. 3.28

t

Geometry of the equitriangular patch antenna

3.3.3.1 Formulas based on the cavity model: The solutions for the fields in an equitriangular waveguide with perfect electric walls have been described by Schelkunoff 1251. It follows from the duality principle of electromagnetism that the TM modes with perfect magnetic walls are the same as those of TE modes with perfect electric walls. Starting with the solutions given in Schelkunoff, we obtain the following results for the equitriangular patch antenna.

The question of which suggestion is appropriate can only be determined by comparison with experiment. It was shown by Dahele and Lee [23] that the suggestion of Helszajn and James [21] yielded much better agreement, and consequently, in the cavity-model theory of the equitriangular patch, the side length a will be replaced by its effective value a, but E, will not be replaced by E,. This is similar to the correction used in circular patch antennas. (ii) Internal and radiation fields of the coaxial-fed antenna In this Section, we present the formulas for the internal and radiation fields of the coaxial-fed equitriangular patch antenna. These take the form of doubleinfinite series comprising the various modes excited. If the characteristics of a particular resonant mode are desired, they can be obtained by examining the term corresponding to this mode. Let the coaxial feed be located on the bisector line at a distance d from the tip of the triangle (Fig. 3.28). The x and y co-ordinates of the tip are - a/,and 0, respectively. Following usual practice, the feed is modelled by a uniform current ribbon of some effective width 2w along the x-axis:

where

The internal field for TM modes inside the cavity is assumed to be z-directed and is given by m

E, = jog

m

"=om="

(i) Resonant frequencies The formula for the resonant frequencies of z-independent TM modes satisfying the perfect magnetic wall boundary condition is

X COS

2nIx' cos ,acos

[

1 1 C,,,,,

2n(n - 1)y 3a

2n(m - n)y 3a

2nmx' + cos $0

I

2nnx' 2741 - m)y + cos COS 3a

where the integers rn, n and I satisfy

a,

(3.60)

752

Characteristics of microstrip patch antennas

Characteristics of microstrip patch antennas

753

and x' = x

+ a/$ 4a 3a

k,,

= - (m2

+ mn + n2)'l2

(3.63b)

sin

C",, =

I

1

ifm=n=O

6

if ( m = 0 and n # 0 ) or ( m # 0 and n = 0 ) or ( m = n # 0 )

-

+ cos

3

3

""I 111 -

12 i f m # n # O (3.65~)

jo(x) = sin x/x

(3.656)

In eqn. 3.60, the conditions on the indices m , n are m > n 3 0 because the eigen functions ,$ = $, . The far-zone electric field at a point P(r, 0, 4 ) is given by Eo =

-jw(,(FX cos 0 cos 4

E,

-jwl;,(-FXsin4

=

+ Fycos 0 sin 4 )

(3.66a)

+ Fycos$)

(3.666)

where F, and Fy are the electric potential components given by

+ cos

J X ~

+jfi(a/2)z2

,pi(/- m)2b2(1 - m)b sin 2(1 - m)n + cos 3 3

+ COS

3

3

&%/2)x2

+ cos 2(m 3x

T[

( m - n)b

n)nl 11 -

sin

-

2(m - n)n 3

JXZ

~fi(012)~~

$[(m - n)2b2-

+ cos

3

x:]

754

Characteristics of microstrip patch antennas

X

( m - n)n (m - n ) sin ---cos ( 7 4 3 ) - v 3 ( m - n)n (- 1)"3a COS sin (nv/3) + 3 n[(n - 1)' - vZ]

-

I

(n x

Characteristics of microstrip patch antennas

-

(n - I)n I ) sin --- cos ( 7 4 3 ) - v 3

I

( n - I)n . cos ----- sin (nv/3) 3

1)"3a + n[(l (- m)* - v2]

I cos (nv/3) - v (I - m ) sin ( 3 x cos -----(' - m)n sin (nv/3)]}]

(3.68)

3

In eqns. 3.67 and 3.68,

XI

= kosin 0(cos $

+ sin $/$)

x2

=

kosin O(cos $

- sin dl$)

(3.73)

(iii) Input impedance The input impedance seen by the coaxial feed located at a distance d from the tip of the triangle is given by Z = R+jX=

+ cos

-jwhCC- 4

[

' cos ( 2n l d ) lo , ( . R ; ) fia

rzd)(T) (z) (%)I jo

where deA.is the effective loss tangent.

27a2

+ cos

jo

755

3.3.3.2 Illustrative results (i) Radiation patterns The radiation patterns are not sensitive to the resonant frequency or the size of the patch. The results to be presented are obtained using sidelength a = 10cm. For this length, the resonant frequencies of the first five modes for E, = 2.32, t = 0.159 cm and E, = 9.8, t = 0.635 mm are shown in Table 3.2. The fieldstrength patterns are shown in Figs. 3.29~-j.Notice that, in the $ = 0" plane, only the component E, is present. In the 95 = 90" plane, however, both the Ee and the E+ components are present, except in the broadside direction (0 = 0"). This feature is different from the circular and the rectangular patches, for which the principal-plane patterns contain only either E, or E+, but not both.

Characteristics of microstrip patch antennas

Characteristics of microstrip patch antennas

-0

OdB -10 -20

-20

-10

OdB

OdB -10

-20

-10

OdB

-20

157

158

Characteristics of microstrip patch antennas

Characteristics of rnicrostrip patch antennas

-e

159

For the TM,, and TM,, modes, radiation is strongest .in the ,broadside. Although there is a slight dip at the broadside for the TM,, mode, the radiation is still very strong in this direction. For convenience, we shall refer all three modes as broadside modes. Reference to the Figures shows that the polarisations of the three modes are the same at 6 = 0". This suggests that the equitrian-

Table 3.2

Theoretical resonant frequencies of an equitriangular patch with sidelength a = 10 crn

fm,GHz (W n) (1, 0) (1, 1) (2, 0) (2, 1) (3, 0)

Fig. 3.29 Radiation patterns of the equitriangular patch at,,,f t = O.159crn; (ii) e, = 9.8, t = 0.0635crn (a) TM,,. d = 0' (b) TM,,, 9 = 90' ( c ) TMii, d = 0' ( d ) TM,,,+ = 90' (e) TM ., d = 0' ( f ) TM, = 90' (9)TMa d = 0' ( h ) TM,, , 9 = 90' ( i ) TM, 4 = 0' ( j ) TM,. d = 90'

=

1GHz and (i)

E, =

E, =

2.32, t = 0.159cm 1.3 1.84 2.6 3.44 3.9

E, =

9.8, t = 0.0635cm 0.64 0.90 1.28 1.66 1.91

2.32.

2

4

6

resonant frequency

8

10

(GHz)

a

Fig. 3.30 Radiation efficiency versus resonant frequency for an equitriangular patch with 0 = 5.8 x 1O7S/rn,d = 0.0005 and (i) E, = 2.32, t = 0.318, 0.159, 0.0795crn; (ii) E, = 9.8, t = 0.127, 0.0635, 0,0254crn (a) TMlo (b) ( c ) TM21

Characteristics of microstrip patch antennas

Characteristics of microstrip patch antennas

-.,

-g

761

4-

-

t -1.275rnrn. 0.635rnrn.0.254rnrn

?

er:9.8

U

u

321-

7

0

2

4

6

8

10

resonant frequency (GHz)

resonant frequency (GHz)

b

resonant frequency (GHz)

Fig. 3.31

l

I

'

2

"

'

"

4

b

t

6

8

resonant frequency (GHz) C

10

Directivity versus resonant frequency for an equitriangular patch with: (i) E, = 2.32, t = 0,318, 0.159. 0,0795cm; (ii) E, = 9.8, t = 0.127. 0,0635, 0,0254cm ( a ) TWO ( b ) TM,o ( C ) TMz

162

Characteristics of microstrip patch antennas

Characteristics of microstrip patch antennas

Tho 31

0

2

6 6 8 1 resonant frequency (GHz)

0 0 0.1

C

1 resonant frequency (GHz)

b

0 0.1.

1

10

resonant frequency (GHz)

Fig. 3.32 Gain versus resonant frequency for an equitriangular patch with a = 5.8 x lo7 Slm. 6 = 0.0005 and (i) e, = 2.32,t = 0.318, 0.159, 0.0795cm; (ii) E, = 9.8, t = 0.127. 0.0635, 0.0254cm ( a ) TM,, ( b ) TMm ( c ) TMn

resonant frequency (GHz) C

10

163

164

Characteristics of microstrip patch antennas

Characteristics of microstrip patch antennas

TMZO

I

gular patch can be operated at the resonant frequencies of the three broadside modes with similar pattern and polarisation characteristics. We shall further show in the next Section that it is possible to find a position for a coaxial feed such that the input impedance of all three modes are in the range of 50-100 R. (ii) Radiation eficiency, directivity, gain, total Q and bandwidth The radiation efficiency, directivity, gain, total Q and bandwidth as a function of resonant frequency for the three lowest broadside modes, i.e. TM,,, TM,,, and TM,, are shown in Figs. 3.30-3.34. The results of e, Q,and BWare similar. However, the directivities and gains are significantly different.

resonant frequency (GHz) b 1'421

6,.9.8

0'

resonant frequency

(GHz)

6,-2.32 1 59 mrn

3.18 mrn

Fig. 3.33 Total 0 factor versus resonant frequency for an equitriangular patch with o = 5 . 8 x 107Slm. S = 0.0005 and (i) 8, = 2.32, t = 0.318, 0.159. 0,0795cm; (ii) E, = 9.8, t = 0.127, 0,0635, 0.0254cm ( a ) TMlo ( 6 ) TM*, ( c ) TM21

10

"

'2

k

"

j

m6

m

8

resonant frequency (GHz)

10

165

166

Characteristics of microstrip patch antennas

Characteristics of microstrip patch antennas

Compared to the rectangular and the circular patches, major differences are found in the Q, and B W curves. While these parameters depend on E,, t and f in a complicated manner for the rectangular and circular patches, their behaviour for the equitriangular patch is simple: Q , decreases (BW increases) with decreasing E, and increasing t irrespective of frequency. (iii) Input impedances and their variations with feed position The input impedances and their variations with feed positions are important characteristics of patch antennas. In the cavity-model theory for the equitriangular patch, the coaxial is modelled by a current ribbon of effective width 2w along the x-axis. Usually this is several times the physical diameter of the coaxial inner conductor and the input impedance is not a sensitive function of 2w. For a patch with a = IOcm, E, = 2.32 and t = 0.159cm, the input impedances of the three broadside modes, TM,,, TM2, and TM2, are shown in Fig. 3.35. The value of 2w used in the computation is 6 mm.

2

8 4 6 resonant frequency (GHz)

resonant frequency G H z ) a

Fig. 3.34

Bandwidth versus resonant frequency for an equitriangular patch with a = 5.8 (ii) e, = 9.8, 107S/m,6 = 0.0005 and (i) &, = 2.32, t = 0~318,0~159,0~0795cm; t = 0.127, 0,0635, 04254cm ( a ) TMlo (b) W o ( c ) TMz1

c (GHz) resonant frequency

10

167

168

Characteristics of microstrip patch antennas

Characteristics of microstrip patch antennas

169

The variations of R and X at resonance with feed position d a r e shown in Fig. 3.36. It is seen that R decreases with increasing d only up to a certain value of d. The distance d can be chosen so that, for a particular mode, it assumes the value necessary to match the characteristic impedance of the feed. If the antenna is to be used for more than one mode, it is desirable that the input impedances for these modes are not too different, in addition to having the same polarisation and similar radiation patterns. In this connection, it is interesting to point out that, by placing the feed at an appropriate location, the input resistances at

Fig. 3.36 Resonant resistance versus feed position of the three broadside modes of the equitriangular patch with sidelength a = 10cm. 6, = 2.32,t = 0.159crn I 0

8

0 0

u

0

,;I

..-.

r

0

0

u

resonance of the three broadside modes can be made to fall in the range of 50-100R. For example, if d is equal to 4,7cm, we obtain R = 100,50 and 60R for modes TM,,, TM,, and TM,,, respectively. Comparison of theory and experiment for the equilateral triangular patch is relatively scarce in the literature. In Reference 24, a comparison was made on resonant frequencies and input impedances, and reasonable agreements were obtained.

3.3.4 Annular-ring parch 3.3.4.1 Introductory remarks: While the rectangular and the circular patches are probably the most extensively studied patch shapes, the annular ring has also received considerable attention [26-341. There are several interesting features associated with this patch. First, for a given frequency, the size is substantially smaller than that of the circular patch when both are operated in the lowest mode (see example in Section 3.3.5). In application to arrays, this allows the

7 70

I

Characteristics of microstrip patch antennas

Characteristics of rnicrostrip patch antennas

777

I

elements to be more densely situated, thereby reducing the grating-lobe problem. Secondly, it is possible to combine the annular ring with a second microstrip element, such as a circular disc within its aperture, to form a compact dual-band antenna system [26]. Thirdly, the separation of the modes can be controlled by the ratio of outer to inner radii. Finally, it has been found that, by operating in one of the higher-order broadside modes, i.e. TM,,, the impedance bandwidth is several times larger than is achievable in other patches of comparable dielectric thickness. The annular ring has been analysed using the cavity model [2, 26, 301, the spectral-domain technique in Fourier-Hankel transform domain [28] and the

3.3.4.2 Cavity-model theory (i) Resonant frequencies, internal and radiation jields Consider an annular ring patch with outer radius b and inner radius a, as shown in Fig. 3.37. Assuming that only TM modes exist, the resonant frequencies are determined by

where k,,,, are the roots of the characteristic equation

J:, ( k b )Y', ( k a ) - J:, ( k a )Y:,( k b ) = 0 I

I I

(3.77)

In eqn. 3.77, J,,(x) and Y,(x) are Bessel functions of the first and second kind, order n, respect~vely,and the prime denotes derivatives with respect to x. Letting C = hla, eqn. 3.77 takes the form

1y:,(4,",1 - J:,(Kt",1Y'(c&,,,, 1 =

J:, (c4,,,,

0

(3.78)

where

X,",

=

k,,d

(3.79)

For the case C = 2, the roots of eqn. 3.78 are given in Table 3.3.

Table 3.3 Roots of the characteristic equation J',,(X,,C)Y,(X,,) (X,,)Y',,(X,,,C) = 0,where C = bla = 2 m

1

2

3

4

- J',,

5

s ~ d evlew

eed

Fig. 3.37

The cases when n = 1 and n = 2 are also of particular interest. The roots are shown in Figs. 3.38 and 3.39. Note that the spacings between the roots are dependent on alb. This parameter can therefore be used to control the frequency separation of the modes. For the general equation 3.77, solutions presented in the form of a mode chart are given in Reference 33. To account for the fact that a small fraction of the field exists outside the dielectric, it is customary to use an effective permittivity E, in place of F, in eqn.

Geometry of the annular-ring patch antenna

use of the method of matched asymptotic expansion [27].In what follows, the results obtained using the cavity model will be presented, together with some comparisons with experiment. V

7 72

Characteristics of microstrip patch antennas

Characteristics of microstrip patch antennas

3.76. The formula for E, as given by Schneider [31] is

173

To account for the fringing fields along the curved edges of the ring, it has been suggested that the outer and inner radii be modified according to

where W = (b

-

a)

where

po is the permeability and zo is the quasi-static characteristic impedance of a microstrip line of width W. A pair of empirical formulas for the modified radii, sufficient for many engineering purposes, are given by [33] C Fig. 3.38

The roots X, of eqn. 3.78, for n = 7, as a function of

C

= bla

For the glven values of a and b, a, and b, are calculated. Then the characteristic equation is solved by replacing a and b by a, and b,. After solving the characteristic equation for k,,,, the resonant frequencies are determined from

It should be pointed out that the correction to the resonant-frequency formula involves both the effective permittivity and the effective radii. This is somewhat different from the cases of the circular, the rectangular, and the equitriangular patches, which involve the effective dimensions only. Lee and Dahele [30] had shown that, in the case of the annular ring, good agreement between theory and experiment can be obtained only if both effective quantities are used. The electric field under the patch is given by I

Fig. 3.39

The roots, X, of eqn. 3.78, for n = 2, as a function of C = bla

The far-zone electric field is

776

Characteristics of microstrip patch antennas

Characteristics of microstrip patch antennas

7 77

The effective loss tangent, comprising the three kinds of losses, is given by

The total Q factor is the inverse of the effective loss tangent.

(iii) Coaxial-fed annular ring For an annular ring fed by a coaxial line at a distance d from the centre, which we modelled by a uniform current ribbon of effective width 2w (eqn. 3.9, the expression for E in the cavity is

where Rum =

and

Fig. 3.41 Sketches of the rad~at~on patterns of the TM,, and TM,, modes of the annular-r~ng patch antenna w ~ t hbla = 2 ( a ) 9 = 0' ( b ) lp = 90'

where the quantity I, is the integral: =

jo

~ 1 2n2cos20

J,,(koasin 0) - J,,(kob sin 0) J',(k,,,,, a) a

E,,

~ Z sin X (2nw) cos nn[J,(k,d)Y',(k,,a)

=

- Jk (k,a)

Y,(knmd)]

1 forn # 0 2 for n = 0

The 0 and C$ components of the far-zone electric field are E,

= j"+l

e-Ikor 2tk0up,, J X

r

n

m

cosnd knm

J,(koa sin 0) - J',(k0 b sin 0) -T--Jn (k,,rnb) E4 = -j""--- 2twp0J e-jkorcos e x r sin 8

.,

(3.101)

knm sinn)

-I

J,,(koa sin 8) - J,,(kob sin 8) J',,(k,,a) b J'"(k",b)

(3.102)

7 78

Characteristics of microstrip patch antennas

Characteristics of microstrip patch antennas

The input impedance is

7 79

addition to larger bandwidth, the TM,, mode also has a larger directivity. Similar results were obtained in Reference 35. The input impedance and bandwidth of the annular ring patch antenna have also been determined by modelling the antenna as a section of radial line loaded with wall admittances [36]. The results are in qualitative agreement with the other methods mentioned above.

where

3.3.4.3 Broadside modes T M , ,and TM,,: The most interesting finding for the annual ring patch is perhaps the relatively wide-band property of the TM,, mode. This was first predicted theoretically by Chew [27] and by Ali et al. [28] using the matched asymptotic expansion technique and the vector Hankel transform, respectively. Experimental verification of the theoretical prediction was first reported by Dahele and Lee [29]. Lee and Dahele [30] also obtain this theoretically within the framework of the cavity model, i.e. using the formulas of Section 3.3.4.2. For an annular ring patch with bla = 2, a = 3.5cm, E, = 2.32, t = 0.159cm, the variation of input impedance with frequency of the TM,, and TM,, modes is illustrated in Figs. 3.42 and 3.43 for two feed positions, one near the inner edge (d/a = 1.05 and the other near the outer edge (dl a) = 1.95. It is seen that, for the TM,, mode, the impedance is not sensitive to the feed position and the impedance bandwidth is very narrow ( < 1%). On the other hand, the input impedance of the TM,, mode is very sensitive to the feed position. With the feed near the outer edge, the value at resonance is only about 20R. With the feed near the inner edge, it attains the convenient value of about 60R at resonance. The bandwidth is about 4%, which is several times that of the TM,, mode. This is also larger than the bandwidth achievable with the rectangular, the circular, or the equitriangular patches with the same dielectric constant and thickness, as reference to the corresponding Figures in Sections 3.3.1-3.3.3 shows. The theoretical results agree with the conclusion of Chew [27], and Ali et al. 2][! who analysed the problem using considerably more complicated methods. ~ x ~ e r i r n e n tthe ~ l above ~ , predictions had been verified by Dahele and Lee [29] and Lee and Dahele [30]. Detailed theoretical results based on the cavity model for the characteristics of the TM,, and TM,, modes are shown in Figs. 3.44-3.48. Note that, in

-5001

590

600

610

620

630

640

650

f (MHz)

Fig. 3.42

Theoretical input impedance of the TM,, mode of an annular-ring patch with b = 7.0cm. a = 3.5cm. 8, = 2.32,t = 0.159cm. fed at two radial locations

3.3.5 Comparison of characteristics of the rectangular, circular, equitriangular and annular ring patches It is instructive at this point to present an example comparing the characteristics of the rectangular, the circular, the equitriangular and the annular ring patches. Let us take the operating frequency to be 2 GHz and fabricate the patches on a substrate material of thickness t = 1.59 mm and E, = 2.32. If the patches are designed to operate in the lowest mode, a rectangular patch with an aspect ratio 1.5 has dimensions b = 3.28 cm, a = 4.92 cm; a circular patch has radius 4.92cm; an equitriangular patch has side length 6.57cm; and an annular ring

180

Characteristics of rnicrostrip patch antennas

Characteristics of rnicrostrip patch antennas

with b / a = 2 has b = 1.84 cm, a = 0.92 cm. The characteristics of the lowest mode for the four patches are shown in Table 3.4. It is seen that all are broadside modes. The circular patch has the smallest beamwidth in both planes. The annular ring patch has the smallest physical area. The circular patch has the largest physical area but it also has the largest bandwidth, efficiency and gain.

I

I

a -0

a

2 -0 -%op

G a w

X

-30~7'5~'

"

a

2800 '

*

a

'

2850 ' 4

2900

f (MHz)

Fig. 3.43

Theoretical input impedance of the TM,, mode of an annular-ring patch with b = 7.0cm. a = 3.5crn. e, = 2.32, t = 0.159cm. fed at two radial locations

The picture changes somewhat if the annular ring with b = 2a is designed to operate in the TM,, mode. This is shown in the last column in Table 3.4. The beamwidth is much narrower while both the gain and the bandwidth are considerably larger. However, these improvements are achieved at the expense of increasing the size of the patch. For the TM,, mode to resonate at 2 GHz,

181

782

Characteristics of microstrip patch antennas

Characteristics of microstrip patch antennas

783

b = 8.9 cm and a = 4.45cm, yielding an area of 249cm2. This turns out to be a specific example of a general principle: increase in bandwidth can only be achieved at the expense of increasing the volume of the resonator.

resonant frequency ( G H z )

a

0

2

4

6

8

10

resonant frequency ( G H z ) Fig. 3.45 D~rect~v~ties of the T M , , and TM,, modes for the annular-rlng patch wlth b = 2a. (i) E, = 2.32, t = 0.318cm, 0.159 cm, 0.0795 cm, (ii) 8, = 9.8, t = 0.127 cm, 0,0635 em, 0.0254cm

0L 0.1

1

10

resonant frequency ( G H z ) b

Fig. 3.44

Radiation efficiency versus resonant frequency for the annular-ring patch with E, = 2.32, t = O.318cm. O.l59cm, 0.0795cm (ii) 6, = 9.8, t = 0.727 cm, 0,0635 cm, 0.0254 cm ( a ) TMll ( 6 ) TM12

b = 2a: (i)

3.3.6 Brief mention of other patches Besides the rectangular, circular, equitriangular and the annular ring, a number of other patch shapes have been studied in the literature. They include the right-angled isosceles triangular patch [2, 7, 371, the annular sector [7, 371, the circular sector [37], the rectangular ring [38], the H-shaped patch [38] and the elliptical patch [38-411. The analysis of the rectangular ring and the H-shaped patch requires the segmentation method, while the other patches mentioned above can be analysed using the simple cavity model. However, except for the elliptical patch which offers the'possibility of generating circularly bolarised waves using a single feed, the other shapes do not appear to contain any features which are not obtainable from the rectangular, circular, equitriangular or annular ring patches. For this reason, only the elliptical patch will be briefly discussed below. The geometry of the elliptical patch is shown in Fig. 3.49. Experimental study

184

Characteristics of microstrip patch antennas

0

'

~

~

~

~

Characteristics of microstrip patch antennas

~

6

;

~

h

l

185

b

resonant frequency (GHz) 0

resonant frequency (GHz)

2

6

3'

10

resonant frequency ( G H z )

resonant frequency (GHz)

b

Fig. 3.46

Gain versusresonant frequency for the annular-ring patch with b = 2a. a = 5.8 x 707Slm. d = 0,0005, and (i) E, = 2.32, t = 0.318em. 0.759 cm, 0,0795 cm, (ii) E, = 9.8, t = 0.727 cm, 0.0635 cm, 0.0254 cm ( a ) TMl, ( b ) TM12

Fig. 3.47

Total O factor versus resonant frequency for the annular-ring patch with b = 2a. a = 5.8 x 107Slm,6 = 0,0005and (i) E, = 2.32, t = 0.318cm. 0.159cm. 0,0795 em, (ii) E, = 9.8, t = 0.127em. 0.0635cm. 0.0254cm

(a) TMll ( 6 ) TM12

-

Characteristics of microstrip patch antennas

Characteristics of microstrip patch antennas

187

of this antenna was reported by Yu [39] and later by Long et al. [41]. Theoretical studies were carried out by Shen [40] using the cavity model, by LovandRichards [I81 using a perturbation method, and by Despande and Bailey [42] using moment method. The main conclusions of these studies are summarised as follows: (a) The radiation in the direction perpendicular to the patch is in general elliptically polarised. However, with proper selection of both the feed position and the eccentricity of the ellipse, circular polarisation can be obtained. (b) The desired circular polarisation is best achieved by limiting the eccentricity of the ellipse to a range of 10-20%. This corresponds to a (semi-major axis) and b (semi-minor axis) differing by only a few percent. The perturbation method of Lo et al. [18] yields the formulas

1

0.1 0.1

1.0

10

semimajor axis a semlmlnar axbs b

resonant frequency (GHz) a TMIZ

foci : x = bs2a

t

c

c=(a2-b21' eccentricity e,:+

Fig. 3.49

Geometry of the elliptical patch

where the quality factor Q can be assumed to be that of the circular patch of radius a or b. For example, if Q = 46.35, b/a = 0.976. (c) The feed point should be on a radial line making 45' relative to the semimajor axis, i.e. 4, = 45". The positive sign yields left-hand while the negative sign yields right-hand circular polarisation. ( d ) To achieve an operating frequencyf, the semi-major axis should be chosen to be

+ I

0.10.1

1.0

10

resonant frequency (GHz)

Fig. 3.48

Bandwidth versus resonant frequency for the annular-ring patch with b = 2a. o = 5 . 8 x 107Slm,6 = 0.0005 and (i) E, = 2.32, t = 0.318cm, 0.159cm, 0.0795cm. (ii) E, = 9.8, t = 0.127cm. 0.0635cm. 0.0254cm ( a ) TM,, ( b ) TM,,

where p is a constant ranging from 0.27 to 0.29.

188

Characteristics of microstrip patch antennas

Characteristics of microstrip patch antennas

( e ) To achieve an impedance of 50R, the feed point should be at a distance from the centre on the 4, = +45" line, where Q, 2. 0 . 2 8 ~ .

frequency agility of MPAs. One line of approach is to consider methods whereby the operating frequency of the antenna can be tuned over a range of values so that the same antenna can be used for several adjacent channels. This is the single-band tunable case illustrated in Fig. 3.50d. In another scheme, dualfrequency antennas with resonant frequencies separated by a certain range have

Q,

3.4 Some methods for improving the frequency agility and bandwidth of microstrip patch antennas 3.4.I Introduction As mentioned in Section 3.1, the microstrip patch antenna (MPA), being basically a leaky cavity, is inherently narrow band. The pattern bandwidth is usually many times larger than the impedance bandwidth, which therefore is the parameter controlling the frequency response of the antenna. For this reason, our subsequent discussion on bandwidth will refer to impedance. For a single patch operating at the lowest mode, typical bandwidth is from less than 1% to 2.3 several percent for thin substrates satisfying the criteria t / l , < 0.07 for E, and t l l , < 0.023 for E , 2: 10. When these inequalities are satisfied, the effect of surface wave is assumed to be unimportant. For comparison purposes, a halfwave dipole with a radiusllength ratio equal to 0.01 has a bandwidth of about 16%, while a medium-length helix operating in the axial mode has a bandwidth of about 70%. One way of obtaining a relatively wide bandwidth is to use an annular ring patch and operate it in the TM,, mode, as the results of Section 3.3.4 indicate. The price one has to pay is that the size of the patch is considerably larger than that of the rectangular, circular, equitriangular or the annular ring operated in the lowest mode. In this Section, we discuss a number of other methods which have been developed for overcoming the bandwidth problem. Let us illustrate our discussion of bandwidth with a series of frequency response characteristics depicted in Fig. 3.50. Let the response in (a) represent the ideal characteristics, in which the input resistance is constant over a wide range of frequencies. A typical MPA response, however, is that shown in (b). Since this is not satisfactory for most purposes, a great deal of attention has been devoted in recent years to improving the bandwidth characteristics of MPAs. One line of attack is to widen the absolute bandwidth of the antenna as much as possible, as illustrated in (c). This in principle can be achieved simply by increasing the thickness of the substrate. However, this introduces several problems. First, a thick substrate supports surface waves, which will produce undesirable effects on the radiation pattern as well as reducing the radiation efficiency of the antenna. Secondly, as the thickness of the substrate increases, problems associated with the feeding of the antenna arise. Thirdly, higher-order cavity modes with fields depending on z may develop, introducing further distortions in the pattern and impedance characteristics. It is therefore of interest to develop more sophisticated methods of improving the absolute bandwidth of MPAs, and a great deal of research has been devoted to this effort. There has also been a substantial amount of effort devoted to increasing the

789

1

j

\

a

deal

b

typ~cal MPA response

C

increased absolute bandw~dth

f

-

f

Rl

f

,,!7p '\

.'

f

d single band, tunable

n n

c

dual band non -tunable

f

dual band tunable

Fig. 3.50 Illustrating the various frequency-response characteristics

been developed (Fig. 3.50e). These duaLfrequency structures are useful in situations where the antenna is required to operate in two distinct frequencies which may be too far apart for a single antenna to perform efficiently at both frequencies. Related to this is the dual-band tunable configuration, in which one or both of the resonances are tunable. The case for which only the upper resonance is tunable is illustrated in Fig. 3.505

190

Characteristics of microstrip patch antennas

In the next two Sections, some of the methods that have been developed to provide the characteristics illustrated in Fig. 3.50 will be described.

3.4.2 Some methods of tuning MPAs We shall describe four methods of tuning the resonant frequencies of MPAs. These utilise (i) varactor diodes, (ii) shorting pins, (iii) optically controlled pin diodes and (iv) adjustable air gap. The advantages and disadvantages of these methods will be discussed.

Characteristics of microstrip patch antennas

the ground plane. These shorting posts present an inductance, and therefore alter the effective permittivity of the substrate. In the context ,of microstrip antennas, the method was first introduced by Schaubert et al. [44] in 1981. It is illustrated in Fig. 3.53. Using two posts, the experimental results obtained are shown in Fig. 3.54. It is seen that the resonant frequency is dependent on the separation of the two posts and a tuning range of some 18% is obtained as the separation varies between 0 and the whole width of the patch.

9l

Fig. 3.51

191

alpha D V H 6733-168-001 varactors

Illustrating the use of varactor diodes for tuning

3.4.2.1 Varactor diodes: For a given set of patch dimensions, the resonant frequency is primarily governed by the value of the relative permittivity E, of the substrate. If some means is available to alter E,, the resonant frequency will change. One method of achieving this is to introduce varactor diodes between the patch and the ground plane, as shown in Fig. 3.51. The diodes are provided with a bias voltage, which controls the varactor capacitance and hence the effective permittivity of the substrate. Bhartia and Bahl [43] performed an experiment on this method and the results are shown in Fig. 3.52. The resonant frequency f , of the lowest mode of the rectangular patch increases with the bias voltage, owing to the increase of the diode capacitance. It is seen that, in this experiment, a tuning range of some 20% was achieved with a 10V bias. The range increased to about 30% with a 30 V bias. Note that the curve ofj; versus bias voltage is not a linear one. Since the paper by Bhartia and Bahl [43], there appeared to be no further reports in the literature on this method, either experimentally or theoretically.

3.4.2.2 Tuning using shorting posts (pins): The value of E, can also be changed by introducing shorting posts (pins) at various points between the patch and

b ~ a svoltage ( V )

Fig. 3.52 Resonant frequency versus bias voltage for a varactor-loaded rectangular patch antenna (Reproduced from Reference 43 p. 306 @ IEEE 1982)

Schaubert et al. [44] developed a theory of shorting pins based on the transmission-line model, and the predictions (shown in Fig. 3.54) agree reasonably well with experimental data. However, because the transmission line model is not capable of predicting the variations in the inductive component of a load as its position is varied within the element, it fails to predict certain trends in the resonant frequency of a short-loaded patch as the shorting pin approaches the patch edge. This model also cannot predict the impedance of the element very accurately because the field distribution between the ground plane and the patch of a loaded element is much too complicated to be adequately represented by a single-mode transmission-line model. It should be noted, however, that the transmission-line model has been further developed for rectangular as well as for circular patches with shorting pins by Sengupta and co-workers [45, 461.

192

Characteristics of microstrip patch antennas

Characteristics of microstrip patch antennas

193

Lo and coworkers [47] have developed the cavity model for MPAs with lumped linear loads in general and shorting pins in particular. They have also applied the shorting-pin method to design dual-frequency structures. This will be discussed in Section 3.4.3.2. led

Fig. 3.55

Fig. 3.53

Illustrating the use of shorting posts for tuning the resonant frequency of a patch antenna

Tuning using optically controlled pin diode

3.4.2.3 Optically tuned patch antenna: A method of tuning the resonant frequencies of patch antennas utilising optically controlled pin diodes was recently reported [48]. The scheme is illustrated in Fig. 3.55. A stub is connected to the patch by means of an optically controlled pin diode. When the diode is reversed biased, it acts as an open circuit and the patch resonates at the frequency for which it is designed, say f,. When the diode is forward biased, it acts as a short circuit and the resonant frequency becomes that of the patch and the stub, i.e. f, - AJ In the experiment, f, was 10.285 GHz and f, - Af was 10.207GHz. These are the limits in the range of tuning. By illuminating the diode with light, the diode impedance can be varied from a high value to a low value. As a result, the resonant frequency is optically tuned. It was found in their experiment that an illumination of 1 w/cmZ resulted in a 15 MHz downward shift in the frequency. This method clearly needs further development as the range of tuning reported was extremely limited. Discussion: The three methods described so far suffer from the following disadvantages:

Fig. 3.54 Resonant frequency versus separation of posts for a 6 . 2 x 9.0 cm rectangular patch antenna with E, = 2.55,t = 1.6mrn (Reproducedfrom Reference 44p. 7 19 @ IEEE 79811

(i) The design of the patches is complicated by the added components such as varactor diodes, optically controlled pin diodes and their associated biasing circuit. In the case of shorting pins, their precise positions are also important. (ii) For high frequencies (say > IOGHz), the patch sizes are small and it is difficult to accommodate the diodes and shorting posts underneath each patch. (iii) The added complications in design multiply for an array consisting of a large number of elements.

194

Characteristics of microstrip patch antennas

The potential advantage of the three methods is the possibility of electronic tuning. For example, there were suggestions that the shorting pins could take the form of switching diodes so that the frequency can be changed by electronically switching the diodes on and off. However, to the authors' knowledge, a real demonstration of such electronic switching applied to MPAs has yet to be reported in the literature. In Section 3.4.2.4, we describe a somewhat different method of tuning the resonant frequency of an MPA, i.e. utilising an adjustable air gap between the substrate and the ground plane.

195

Characteristics of microstrip patch antennas

Experimental results: The first configuration studied by Dahele and Lee was the circular patch. The radius of the patch was 5cm fabricated on Duroid material of thickness 0.159 cm and relative permittivity 2.32. The width of the air gap is controlled by using spacers between the substrate and the ground plane. In the experiment, spacers of 0.5 mm and 1.Omm were used. The antenna was provided with a coaxial feed near the edge of the disc at a distance d = 4.75 cm from the centre. This feed position is chosen as it is well known that it yields a larger resistance at resonance compared to a feed which is closer to the centre. The

3.4.2.4 Tuning using an adjustable air gap Introduction: By introducting an air gap between the substrate and the ground plane in a microstrip patch antenna the effective permittivity of the cavity will change. This can be used to tune the resonant frequency of a microstrip patch antenna as discussed below.

substrace

I

I

conductma ~ a t c h

I

I A airgap

spacer

;;50'

I

II

/-coaxial

Fig. 3.57

1350

1400

Measured input impedance of the T M , , mode of a 5 c m circular-disc microstrip antenna for three values of air-gap width A. E, = 2.32,t = 0.159cm (After Reference 51 pp. 455-460)

feed

Table 3.5 Fig. 3.56

' 1300 '

'

f (MHz)

T ground'plane

'

Geometry of a microstrip patch antenna with air gap

Measured resonant frequencies and impedance bandwidths of the first few modes of a 5cm-radius circular-disc microstrip antenna for three values of the air-gap width --

The geometry of a microstrip antenna with an airgap is shown in Fig. 3.56. Consider the cavity under the conducting patch. It is made of two layers: a substrate of thickness t and an air region of thickness A. Compared to the case with no air gap the effective permittivity of the cavity is evidently smaller. As a result the resonant frequencies of the various modes will increase. Since the, effective permittivity decreases as A increases, tending towards the free-space value E,, as A -+ a,it follows that the resonant frequencies can be tuned by adjusting the air-gap width A. As a by product the bandwidth will also increase partly due to the increase in the height of the dielectric medium and partly because the effective permittivity is smaller. Based on the above idea, Dahele and Lee [49-521 have carried out a series of experimental and theoretical studies on the microstrip antenna with air gaps. Some of their results are presented below.

TM,, TM,, TM,, E,

fm

% BW

1128MHz 1879MHz 2596MHz

0.89 0.85 0.77

f,,,, 1286MHz 2136MHz 2951MHz

%BW 1.48 2.15 1.63

f,,

% BW

1350MHz 2256MHz 3106MHz

2.07 2.61 2.02

= 2.32, t = 0.159~111; fed at 4.75cm from the centre

measured resonant frequencies are shown in Table 3.5. For the lowest mode TM,,, there is a tuning range of about 20% in frequency and a more than twofold increase in the bandwidth as A goes from 0 to 1.0mm. Similar behaviour is recorded for the other modes. The measured input impedances of the TM,, mode as a function of frequency are shown in Fig. 3.57. The upward shift in the resonant frequency and the widening of the bandwidth are clearly seen.

196

Characteristics of microstrip patch antennas

Characteristics of microstrip patch antennas

As for the radiation pattern it was found that the air gap did not have a significant effect on the pattern. Another antenna studied was the annular-ring patch. The effect of an air gap on the two broadside modes TM,, and TM,, are shown in Table 3.6 for an annular ring of outer radius 7.0 cm and inner radius 3.5 cm fabricated on Duroid material of thickness 0.159cm and E, = 2.32. As in the circular patch there is an upward shift in the resonant frequencies and a widening of the bandwidths. It is significant that, for the TM,, mode, the bandwidth attains a value of 8.6% when A is equal to 1.0 mm. Table 3.6

Measured resonant frequencies and impedance bandwidths of the TM,, and TM,, modes of an annular-ring microstrip antenna for three values of the air-gap width A

A = 0 TM,, TM,,

626MHz 2757MHz

A 0.6 4.0

=

720MHz 3040MHz

Inner radius a = 3.5cm. outer radiur b = 7,0cm, 6, d/a = 1.05 where d is the distance from the centre

A

0.5mm

=

0.7 8.0 2.32, r

=

=

l.Omm

778MHz 3240MHz

0.8 8.6

197

effective permittivity of the two-layered medium:

Eqns. 3.108 and 3.109 are valid for any patch shape. Note that, as the air gap width A increases, E," decreases and the resonant frequency increases. The dependence ofJ;,,,(A) on A, however, is not a linear one.

Discussion:As in the other methods the adjustable air gap as a means of tuning the resonant frequencies has advantages and disadvantages. The advantages are: (i) No costly components are added. (ii) It can be applied to patches of any shape. There is no need to know the details of the fields in the cavity. (iii) The method is particularly attractive for an array made up of a great number of elements as illustrated in Fig. 3.58. If the elements are fed by striplines, the resonant frequencies of all the elements, and therefore of the array, can be tuned by a single adjustment of the air gap width A.

0.159cm. The feed is placed a t

Theory: Lee and Dahele has developed the theory of the two-layered microstrip antenna using the cavity model. The original assumptions of the model are modified to account for the two layers as follows: (i) Owing to the close proximity between the conducting patch and the ground plane only transverse magnetic (TM) modes are assumed to exist. The z-component of the electric field, however, is a function of z since the cavity is two-layered. (ii) The cavity is assumed to be bounded by perfect electric walls on the top and on the bottom and by a perfect magnetic wall along the edge. (iii) Across the dielectric-air interface the tangential electric field and the normal electric flux density are continuous. Based on the above assumptions detailed analysis for the circular and annularring patch were carried out and good agreement between theory and experiment was obtained. In the interest of brevity, except for the resonant frequencies, the theoretical formulas will not be included here. The formula for the resonant frequency, however, is a very simple one and is given by

where Jrf;,,(0)is the resonant frequency when there is no air gap and

is the

spacer alr gap

Fig. 3.58

Tuning a microstrip antenna array by using an adjustable airgap

Stripline feeds are assumed

The disadvantages are: (i) The width of the air gap has to be changed mechanically. Electronic tuning appears to be difficult. (ii) The antenna is slightly thicker. This however is compensated for by an increase of the bandwidth.

198

Characteristics of microstrip patch antennas

Characteristics of microstrip patch antennas

199

To end this Section we point out that it is possible to alter the resonant frequency by inserting a piece of dielectric in the air region, as illustrated in Fig. 3.59. The relative permittivity of the inserted dielectric can be either the same as that of the substrate or different. Both the thickness and the permittivity of the inserted dielectric will determine the resultant resonant frequency. ,conduct~ng

patch

s u b s t r a t e -spacer

resonant frequency cdn be tuned by Inserting a piece of dielectric In alr region (plug In u n ~ t )

Fig. 3.59 Altering the resonant frequency by inserting a piece of dielectric in the air gap

' . I 20, - 3 78cm

3.4.3 Dual-band structures There has been considerable interest in the development of dual-frequency microstrip antennas. The characteristics of this class of antennas is illustrated in Fig. 3.50e. They are useful when the antenna is required to operate in two distinct frequencies which are too far apart for a single antenna to perform efficiently at both frequencies while the behaviour of the antenna in the range of intermediate frequencies is of little or no concern. Several methods of obtaining the dual-frequency characteristics have been developed. We begin with the method of simply stacking two patches together. \ d l

Kconducting

1.0

,

3.2

frequency (GHz)

patch

?/

frequency ( (

Fig. 3.60 Non-tunable dual-frequency stacked microstrip antenna

3.4.3.1 Stacked circular-disc antenna: The first experimental report on a dual-frequency structure using two stacked circular patches was that of Long and Walton [53]. The geometry is shown in Fig. 3.60. The discs were photo-etched on separate substrates and aligsxd so that their centres were along the same

Fig. 3.61 Real and imaginary parts of impedance of stacked circular patches etched on a dielectric with E, = 2.47 ( a ) 2a, = 3.70ci-n ( b ) 2a, = 3.78cm ( c ) 2a, = 3.85 cm (Reproduced from Reference 53 p. 271 @ lEEE 1 9 7 9 )

200

Characteristics of microstrip patch antennas

Characteristics of rnicrostrip patch antennas

line. The sizes of the two discs and their spacings were varied and the resultant behaviour of the antenna characteristics measured. The antenna was fed by means of a coaxial line. The centre conductor passed through a clearance hole in the lower disc and is connected electrically to the upper disc. If one considers the two regions under the patch' as two resonant cavities it is clear that the system behaves as a pair of coupled cavities. Since the fringing fields are different for the upper and lower cavities, two resonant frequencies are expected even if the diameters of the two discs are the same. While the qualitative explanation is relatively simple the quantitative theory for this structure is still lacking. In what follows the experimental results of Long and Walton are described.

I

I

207

Walton which showed that they were similar to the radiation pattern of the lowest mode for the single circular patch. While the results of Long and Walton [53] showed that it is possible to design for the separation of the resonant frequencies by choosing the diameters of the upper and lower discs, this is not very convenient in practice because of the lack of formulas to predict the frequencies. Also once they are designed and etched, it is not possible to alter or tune the separation of the two resonant frequencies. The configuration as presented by Long and Walton was therefore a dual-band non-tunable antenna of the type illustrated in Fig. 3.50e.

-

I

conduct~ngpatch

!

ground 'plane

--I -I Fig. 3.63 Tunable dual-frequency stacked microstrip antenna utilising the air-gap idea

upper d~scdlameter 2al (mm)

Fig. 3.62 Resonant frequencies versus upper disc diameter of stacked circular patches etched on a dielectric with E, = 2.47, 2a2 = 3.78~171,t, = t, = 0.75mm. (Reproduced from Reference 53 p. 271 @ IEEE 1979)

Fig. 3.61 shows the real and imaginary parts of the input impedance for ?a, = 3.78 cm, t , = t2 = 0.075 cm and three values of 2a,. The resonant frequencies as a function of the upper disc diameter are shown in Fig. 3.62. Also shown is the resonant frequency of the lowest mode for a single disc of diameter 2a and substrate thickness t = 0.075cm, taking into account the fringing field through the effective diameter. It is seen that the lower resonant frequency is relatively constant, remaining near the value of a single disc with 2a = 3.78 cm and d = 0.075 cm. The upper resonance, on the other hand, is highly dependent on the size of the upper disc. Radiation patterns were also taken by Long and

Dahele and Lee 1541 have applied the air gap idea to study dual-frequency stacked discs. The geometry is shown in Fig. 3.63 in which air gaps between the lower substrate and the ground plane and/or between the two substrates are introduced. Either of the air gap widths can be set to zero. Their experimental results performed with two stacked discs of 7 cm radii, each etched on substrates with E, = 2.32 and thickness 0.159cm are shown in Fig. 3.64 and 3.65. In Fig. 3.64, with the lower air gap set to zero the upper air gap is seen to increase the resonant frequency of the upper resonance. In Fig. 3.65 the upper air gap is set to zero and the effect of the lower air gap is studied. It is seen that the effect is more complicated since it shifts not only the lower but also the upper resonance. In both cases the bandwidth of the lower resonance is substantially broadened. Dahele and Lee [55] have also studied a structure consisting of two stacked annular ring patches as shown in Fig. 3.66. This structure was also found to exhibit dual-frequency behaviour. As in the case of circular discs an upper air gap was found to be a convenient method of altering the separation of the frequency bands. 3.4.3.2 Single-element dual-frequency microstrip untenna: It is possible for a single-element microstrip antenna to operate at many frequencies correspond-

202

Characteristics of microstrip patch antennas

Characteristics of microstrip patch antennas

ing to the various resonant modes pertaining to the structure. However, for most applications it is required that the radiation pattern, the polarization and the impedance be similar if not identical in all the frequency bands of operation. T M l r mode; d-6.5cm; A1=O 400

-R

I

substrate

Fig. 3.64 Measured input impedances of the TM,, mode of a pair of stacked circular discs of 7 c m radius for three values of the upper air gap: d = 6.5cm. A, = 0, e, = 2.32, t = 0.159cm (After Reference 57 pp. 455-460)

Fig. 3.65

kb ground plane

conducting patches

,

Ill 11

/-coaxial

Fig. 3.66

feed

Geometry of the stacked annular-ring antenna

Measured input impedances of the TM,, mode of the stacked circular discs of Fig. 3.63 for two values of the lower air-gap. d = 6 5 c m . A, = 0, e, = 2.32, t = 0.759cm (After Reference 57 pp. 455-460)

This immediately rules out many modes. Furthermore, for a given geometry all the resonant frequencies are related in fixed ratios, providing no flexibility for the designer.

Fig. 3.67 Geometry of a rectangular patch antenna with six possible shorting pins anda short matching stub. (After Reference 56 pp. 298-300) All dimensions in centlmetres

204

Characteristics of microstrip patch antennas

If for a particular patch shape two modes can be found which produce similar radiation patterns with the same polarisation, dual frequency is possible with a single patch. For the rectangular patch the two modes (0, 1) and (0, 3) satisfy this requirement. However, their resonant frequencies are related by a fixed ratio of approximately 3, the exact value being dependent on the edge effect. Suppose now shorting pins are placed on the nodal lines of the (0,3) model field, there will be little effect on the (0, 3) mode but a strong effect on the (0, I) mode. This offers a way of altering the separation of the two frequency bands. The insertion of pins at proper locations can also be used to tune the input impedance for the (0, I) mode while the feed location is chosen first for the desired impedance for the (0, 3) mode. The above idea has been successfully demonstrated experimentally by Zhong and Lo [56]. A multiport-cavity-model theory has also been developed by Lo and coworkers which appears to predict the effects of shorting pins on frequency and impedance well. We limit here to a summary of the experimental results of Zhong and Lo.

Characteristics of microstrip patch antennas

205

directivities of the two modes are quite different. By increasing the number of pins the two frequencies can be brought to a ratio of about 1.8. If a smaller ratio is desired it is found that it can be achieved by introducing slots in the patch. This, however, makes the fabrication of the patch somewhat complicated.

H - plane

Table 3.7 Resonant frequencies for (0, 1 ) and (0, 3 ) modes against shorting pins used (After Reference 56)

E - plane -70"

-80"

80'

90'

-90"

---- low-band. f - 8 8 3 M H z -hlgh-band;f: 1848 MHz Fig. 3.68

The geometry of the rectangular patch in their experiment is shown in Fig. 3.67. It is made of 118 in copper-cladded Rexolite 2200 with six shorting-pin positions. The effects of successively adding more and more pins (each approxmately 0.05 cm in diameter) at the positions indicated in Fig. 3.67 are shown in Table 3.7. It is seen that the ratio of the two operating frequenciesf,,/f,, can be varied approximately from 3 to 2. Since all these pins are located on the (0, 3) nodal lines f,, remain constant at approximately 1865 MHz whilef,, is varied from 613 to 891 MHz. In order for the impedances of the two bands to be close to 50R at resonance it is necessary to attach a short capacitive stub of 0.6cm x 2.1 cm. With the stub added, the bandwidth with reference to 3:l VSWR is about 2% for the low band and almost 8% for the high band. Typical low- and high-band patterns in both E and H planes are shown in Figs. 3.68. It is seen that, while the two modes radiate strongest in the broadside, the

Typical radiation patterns in H- and E-planes for antennas shown in Fig. 3.67with six pins inserted (After Reference 56 pp. 298-300)

The rectangular patch is not the only geometry capable of providing dualfrequency operation. In Section 3.3.3, it was shown that the TM,,, TM,, and TM,, modes of the equitriangular patch are all broadside modes with similar polarisations in the broadside direction. Moreover, by choosing the location of the feed properly, the impedances of these modes do not vary greatly. It thus appears that it is possible to utilise the equitriangular patch for dual- or even triple-frequency operation. 3.4.3.3 Dual-band microstrip antennas with reactive loading: A dualfrequency microstrip antenna can also be obtained simply by loading it with a reactive load. If the reactive load takes the form of a short-circuited length of microstrip transmission line the low-profile characteristic of a microstrip patch

206

Characteristics of microstrip patch antennas

-

antenna is retained. Such a structure was suggested by Davidson et al. [57] and was demonstrated to work experimentally. Fig. 3.69 shows the dual-band rectangular microstrip patch antenna with a monolithic load studied in the experiment of Davidson et al. The patch was of

sut

Characteristics of microstrip patch antennas

The separation of the resonances can be varied by (i) changing the length of the microstrip line and (ii) introducing an inset dimension S with an accompanied gap spacing G between the line and the radiator, as shown in Fig. 3.71. The results for the resonant frequencies are shown in Table 3.8.

ground 'plane

str rate

Fig. 3.69 Dual-frequency rectangular patch antenna with monolithic reactive loading (After

Fig. 3.71 Geometry incorporating an insert dimension S and a gap spacing G (After Re-

Reference 57 p. 936-937)

ference 5 7 pp. 936-937)

Table 3.8 W cm 0.33 0.33 0.33 0.33 0.33

-501

2200

207

2400 2600 frequency ( M H z )

Fig. 3.70 impedance of edge-loaded, 4

2800

6cm patch antenna with 1 = 4,Ocm. W = 0.33 cm, E, = 2.77, t = 0.079 cm; coaxially fed near the edge and at the centre of the 6cm side (After Reference 5 7 pp. 936-937) x

dimension 6cm x 4cm etched on a substrate with E, = 2.17 and thickness 0.079 cm. It is coaxially fed near the edge and at the centre of the 6cm side. For a line length of L = 4.0cm and width w = 0.33 cm, the impedance characteristics is shown in Fig. 3.70. Good pattern performance was observed at each of the resonant frequencies (2.275 GHz and 2.666 GHz, respectively).

Resonant frequencies of monolithic microstrip elements (after Reference 57)

L cm 4.0 4.0 8.4 4.0 4.0

G cm 1.O 0 0 0.7 0.3

S

f~

fu

cm 1.5 0 0 1.5 1.5

GHz 2.356 2.275 2.339 2.437 2.47 1

GHz 2.494 2.666 2.628 2.494 2.514

Discussion: In summary three methods of obtaining dual-frequency characteristics for microstrip patch antennas have been described. The method using shorting pins use two different modes. As such the radiation patterns, while similar in the broad sense, do vary in detail as well as in directivity. The separation of the resonances can be controlled by the number of pins, but it is difficult to have them close together unless additional features such as slots are introduced in the patch. These additional design features appear to be difficult to accommodate at high frequencies where the patch size is small. The advantage of using shorting pins to realise dual-frequency characteristics and to control the frequency separation is that it is a single-patch geometry,

208

Characteristics of microstrip patch antennas

thereby retaining the low profile characteristic of microstrip antennas. This advantage is also shared by the monolithic reactive-loading method. In the reactive-loading method the two frequencies are separated by 10-20%. The separation can be controlled by several parameters associated with the reactive load. However, once a design is etched it is not possible to tune the antenna. For the case when the separation is in the range of 10-20% it appears that the stacked geometry discussed in Section 3.4.3.1 offers the advantages of operating in the same mode and the flexibility of tuning the separation by means of an air gap. This structure, however, is thicker than the single patch and the low-profile characteristics of the microstrip antenna is slightly compromised. 3.4.4 Electromagnetic-coupled patch antenna ( E M C P ) 3.4.4.1 Introduction: As mentioned in Section 3.4.1, a great deal of research has been devoted to increasing the absolute bandwidth of MPAs. The methods fall into three categories: electromagnetic-coupled patches (EMCP), use of parasiticelements and log-periodic arrangement of an array of patches. We shall discuss in this Section only the EMCP since it is related to the tunable stacked geometry of Section 3.4.3.1. The use of parasitic elements and log-periodic arrangement are covered in other Chapters of the Handbook. As mentioned in Section 3.4.1 it is possible to increase the absolute bandwidth of MPAs by simply using thicker substrates. This, however, introduces several problems. The first is the excitation of surface waves, which distorts the normal radiation pattern and introduces additional loss; the second is the excitation of higher-order modes with z dependence, which introduces further distortions on the pattern and impedance characteristics. The third is that the application of common feeding techniques, i.e. direct feeding by either a coplanar microstrip line or a perpendicular coaxial line, becomes increasingly difficult for the following reasons. Consider first a coaxial feed. Since the probe (extension of inner conductor of the coaxial line) introduces a series reactance almost proportional to the substrate thickness, the lead inductance will become significant with respect to the antenna radiation resistance for thick substrates and will therefore prevent proper matching. Consider next a patch which is edge-fed by a coplanar microstrip line. For a fixed impedance level the line width is almost propo~tional to the dielectric thickness. Since the patch dimensions for a fixed resonant frequency are only weakly dependent on the dielectric thickness (through the fringing field) the width of the feed line will become non-negligible as the substrate reaches a certain thickness. As a result the radiation pattern of the antenna will be disturbed partly due to the covering of the radiating patch edge by the line and partly due to increased radiation from the feed line. In view of the above problems, electromagnetic coupling (instead of direct coupling) has been studied as a possible feed technique for electrically thick MPAs. In particular, promising results have been obtained for the stacked dual-patch geometry which we now discuss.

Characteristics of microstrip patch antennas

209

3.4.4.2 Stacked dual-patch geometry: The basic geometry of the ,stacked dual-patch electromagnetic-coupled microstrip antenna is shown in Fig. 3.72. Each conducting patch is fabricated on an electrically thin substrate and separated by a region of air or foam with E, 2: 1. The structure looks similar to the tunable dual-frequency antenna of Section 3.4.3.1, but is different in two aspects. First, the thickness of the air region is several times the substrate thickness, while in the tunable version discussed earlier, it is a fraction of the substrate thickness. Secondly, rather than being fed directly by a transmission line, the top element is excited via electromagnetic coupling from the lower element, which is located closer to the ground plane and is connected directly to a feed line. The top and bottom patches are referred to as the radiating and the feeding patches, respectively.

radlatlng patch

spacer----A

I

O L r reg10nt

e

e

d

l

n

g patch

ground plane

Fig. 3.72

Electromagnetic-coupled patch antenna

When the air region is small two resonances are expected, as in the case discussed in Section 3.4.3.1. Experimental studies showed that, as the air region exceeds a certain thickness, the lower resonance disappears and only one resonance remains. The single resonance condition can also be obtained by designing the diameter of the radiating element to be larger than the feeding element. Electromagnetic-coupled patches appeared to be first discussed by Sabban [60]. Circular, annular-ring, rectangular and square patches in the S band (2-4GHz), etched with substrates about 0.01 1 thick, were reported to yield bandwidths ranging from 9% to 15%. His paper contained very little information on the air-gap width and the relative sizes of the elements, other than the statement that the radiating element was larger than the feeding element and that the antennas exhibited a single resonance rather than dual resonances. A more detailed experimental study was carried by Bhatnagar et al. [61]. The elements were triangular patches operating in the S band, and foam material with E , = 1 was introduced as the air gap between the dielectric layers (Fig. 3.73). The side lengths of both the top and bottom equitriangular patches were 37 mm fabricated on a substrate of thickness 1.6 mm and relative permittivity 2.55. The lower patch was provided with a coaxial feed at a distance

Characteristics of microstrip patch antennas

Characteristics of microstrip patch antennas

270

F, = 13.5 mm. The width A of the air gap is controlled by using foam material of uniform thickness. The functional behaviour of the impedance characteristics is given in Table 3.9. The results for A = 3 mm showed an increase in the bandwidth at lower resonance and a sizable radiation resistance at the second resonance. so that the structure may be operated as a dual-frequency antenna. Separation of the resonances was about 12% at A = 0 and 18% at A = 1.5 mm. For A > 3 mm the first resonance disappears. The second resonant frequency increased and the real and imaginary parts of the impedance increased with A. At t = 5mm the bandwidth was 595MHz, which was about 17.5% at the centre frequency of 3.407 GHz.

-,

27 7

and 20dB in the E-plane. It is interesting to note that the directivity of the antenna was larger than that of an ordinary microstrip patch, the beamwidth of which was greater than 85'-90'. The configurations of EMCP studied by Sabban and Bhatnagar et al. can be

p a r a s i t ~ cpatch

Fig. 3.73 Geometry of electromagnetic-coupled triangular patch antenna (After Reference 67 pp. 864-865)

Table 3.9

Characteristics of the stacked triangular patch antenna (after Reference 61)

First resonance

Second resonance

A

f

% BW

Maximum resistance

f

% BW

Maximum resistance

mm 0 1.5 3 4 5 6 9

GHZ 3.1 3.12 3.135

a 3.5 4.8 6.4

150 150 75

-

-

-

GHZ 3.54 3.8 1 3.77 3.72 3.61 3.56 3.45

2.5 3.1 3.2 10.5 17.46 14.8 8.6

90 55 48 52 55 62.5 105

-

a

The radiation patterns in both the E-plane and the H-plane at various frequencies within the impedance bandwidth are shown in Fig. 3.74 and Fig. 3.75, respectively. The beamwidth varied from 75" to 85" in the H-plane and 55" to 65" in the E-plane. The cross-polar level was better than 16 dB in the H-plane

angle (degree)

Fig. 3.74 E-plane radiation patterns of the antenna of Fig. 3.73 with L = 37mm. t , = t, = 7.6mm. A = 5 m m andF, = 73.5mm (After References 67 pp. 864-865) -3.1 GHz --- 3.3 GHz 3.5GHz 3.7 GHz

212

Characteristics of microstrip patch antennas

Characteristics of microstrip patch antennas

2 73

described as the 'normal' type. If the upper patch is fabricated on the underside of the substrate an 'inverted' configuration is cobtained. Fig. 3.76 illustrates these two types of configurations. The advantage of the inverted type is that there is a protective dielectric cover for the upper conducting patch. It has been studied by Chen et al. [62] and by Dahele et al. [63]. Further studies of the EMCP antenna were carried out by Lee et al. [64], using rectangular patches etched on Cuflon substrates ( E , = 2.17). Exciting the TM,, mode at about IOGHz, they recorded the variation of pattern shape, 3dB beamwidth and bandwidth with the separation A, for A between 0 and 0.37 1,. This is beyond the range studied by previous authors. It was found that, depending on A, the characteristics of the antenna can be separated into three

radlatlng patch

coax probe normal conf~guratlon 0

Fig. 3.76

angle (degree)

Fig. 3.75

H-plane radiation patterns of the antenna of Fig. 3.73 with L = 37mm. t , = t, = 1.6mm. A = 5mm and F, = 73.5mm (After Reference 61 pp. 864-865)

-3.1 G H z --- 3.3 G H z

3.5G H z 3.7 G H z

~ n v e r t e dconflguratlon

b

Normaland inverted configurations of the electromagnetic-coupledpatch antenna

regions. Region 1 is associated with bandwidths exceeding 10%; region 2 has abnormal radiation characteristics and region 3 is associated with narrow beamwidth and high gain. The value of A separating these regions depends on the dielectric material between the two layers. The gain in region 3 is 9-1 0 dB, compared to 5.3 dB for the single patch. It begins at A = 0.3 1 2, for air dielectric and at A = 0.21 1, for Teflon. The bandwidth in region 3, however, is only about 1.3% for air and 0.85% for Teflon. It is evident from the experimental results of the authors cited above that, by operating in region 1, the EMCP offers a promising way of achieving bandwidths in excess of lo%, while reducing the problems encountered by simply increasing the substrate thickness. If high gain rather than large bandwidth is desired, the EMCP can be operated in region 3. Although analytical methods are available [65], little work has been done to apply them to this interesting antenna. As such, the experimental results described above have not been quantitatively explained, nor are there formulas available which would aid the design in terms of resonant frequency, impedance, bandwidth and gain. Such theoretical research is urgently needed.

214

Characteristics of microstrip patch antennas

Characteristics of microstrip patch antennas

3.5 Summary

II

This Chapter begins with introducing the simple cavity model for analysing microstrip patch antennas with thin substrates. The formulas obtained from this model for rectangular, circular, equitriangular and annular-ring patches are then presented. The radiation pattern, efficiency, directivity, gain, quality factor and imvedance of these. antennas are illustrated. mainlv for the broadside modes. Experimental results are included or referenced where available. After a brief mention of some other geometries, notably the elliptical patch, the Chapter proceeds to discuss some methods of improving the frequency agility of microstrip patch antennas. They include the use of varactor diodes, shorting pins, optically controlled diodes, adjustable air gap, stacked geometries and reactive loading. The advantages and disadvantages of these methods are discussed. Finally, the method of increasing the absolute bandwidth by electromagnetic coupling of a fed and a parasitic patch in a stacked geometry is discussed.

12

13 14 15 16 17 18 19 20 21

3.6 Acknowledgments The authors wish to acknowledge the assistances of Dr. K.M. Luk and Mr. T. Huynh. Dr. Luk provided the numerical data for the majority of illustrations for the rectangular, equitriangular and annular-ring patches, while T. Huynh contributed to some of the computations for the rectangular and circular patches.

22 23 24

25 26

3.7 References 1 DESCHAMPS, G. A.: 'Microstrip microwave antennas'. Presented at the 3rd USAR Symposium on Antennas, 1953 2 BAHL, I. J., and BHARTIA, P.: 'Microstrip antennas' (Artech House, Mass., 1980) 3 JAMES, J. R., HALL, P. S., and WOOD, C.: 'Microstrip antenna theory and design' (Peter Peregrinus, 1981) 4 IEEE Trans., Jan. 1981, AP-29 5 CARVER, K. R., and MINK, J. W.: 'Microstrip antenna technology', IEEE Trans., 1981, AP-29, pp. 2-24 6 MAILLOUX, R. J., McILEVENNA, J. F., and KERNWEIS, N. P.: 'Microstrip array technology', IEEE Trans., 1981, AP-29, pp. 25-39 7 LO. Y. T., SOLOMON, D., and RICHARDS, W. F.: 'Theory and experiment on microstrip antennas', IEEE Trans., 1979, AP-27, pp. 137-145 8 RICHARDS, W. F., LO, Y. T., and HARRISON, D. D.: 'An improved theory for microstrip antennas and applications', IEEE Trans., 1981, AP-29, pp. 38-46 9 DERNERYD, A. G.: 'Analysis of the microstrip disk antenna element', IEEE Trans., 1979, AP-27, pp. 660-664 10 DERNERYD, A. G.: 'Extended analysis of rectangular microstrip resonator antenna', IEEE Trans., 1979, AP-27, pp. 846-849

27 28 29 30 31 32 33 34 35 36 37

2 15

DERNERYD. A. G.: 'Microstrio. array. antenna'. Proc. 6th European Microwave Conference, 1976, pp. 339-343 RICHARDS, W. F., LO, Y. T., and SOLOMON, D.: 'Theory and application for microstrip antennas'. Proc. Workshop on Printed Circuit Antenna Technology', New Mexico University, Las Cruces, 1979, pp. 8.1-8.23 JAMES, J. R., and HENDERSON, A,: 'High-frequency behaviour of microstrip open-circuit terminations', IEE J Microwaves, Optics & Acoustics, 1979, 3, pp. 205-218 WOOD, C.: 'Analysis of microstrip circular patch antennas', IEE Proc., 1981 128H. pp. 69-76 FONSECA, S. B. A,, and GIAROLA, A. J.: 'Microstrip disk antennas. Pt. I: Efficiency of space wave launching', IEEE Trans., 1984, AP-32, pp. 561-567 RICHARDS, W. F., LO, Y. T., and HARRISON, D. D.: 'Improved theory of microstrip antennas', Electron. Lett., 1979, 15, pp. 42-44 RICHARDS, W. F., LO, Y. T., and SIMON, P.: 'Design and theory of circularly polarized microstrip antennas'. IEEE AP-S International Symposium Digest, June 1979, pp. 117-120 LO, Y. T., and RICHARDS, W. F.: 'Perturbation approach to design of circularly polarized microstrip antennas'. Electron. Lett., 1981, 17, pp. 383-385 SHEN, L. C., LONG, S. A,, ALLERDING, M. R., and WALTON, M. D.: 'Resonant frequency of a circular disc, printed-circuit antenna', IEEE Trans., 1977, AP-25, pp. 595-596 DAHELE, J. S., and LEE, K. F.: 'Effect of substrate thickness on the performance of a circular-disk microstrip antenna', IEEE Trans., 1983, AP-31, pp. 358-360 HELSZAJN, J., and JAMES, D. S.: 'Planar triangular resonators with magnetic walls', IEEE Trans., 1978, MlT-26, pp. 95-100 KEUSTER, E. F., and CHANG, D. C.: 'A geometrical theory for the resonant frequencies and Q factors of some triangular microstrip patch antennas', IEEE Trans.,1983, AP-31,27-34 DAHELE, J. S., and LEE, K. F.: 'Experimental study of the triangular microstrip antenna'. IEEE AP-S International Symposium Digest, 1984, pp. 283-286 LUK, K. M., LEE, K. F., and DAHELE, J. S.: 'Theory and experiment on the equilateral triangular microstrip antenna'. Proc. 16th European Microwave Conference, 1986, pp. 661666 SCHELKUNOFF, S. A,: 'Electromagnetic waves' (Van Nostrand, New York, 1943) Chap. 10 MINK, J. W., 'Circular ring microstrip antenna elements'. IEEE AP-S Int. Symp. Digest, June 1980, pp. 605-608 CHEW, W. C.: 'A broad-band annular-ring microstrip antenna', IEEE Trans., 1982, AP-30, pp. 918-922 ALI, S. M., CHEW, W. C., and KONG, J. A,: 'Vector Hankel transform analysis of annularring microstrip antenna'. IEEE Trans., 1982, AP-30, pp. 637-644 DAHELE, J. S., and LEE, K. F.: 'Characteristics of annular-ring microstrip antenna', Electron. Lett., 1982, 28, pp. 1051-1052 LEE, K. F., and DAHELE, J. S.: 'Theory and experiment on the annular-ring microstrip antenna', Ann. des Telecomm., 1985, 40, pp. 508-515 SCHNEIDER, M. V.: 'Microstrip lines for microwave integrated circuits', Bell Syst. Tech. J., 1969.48, pp. 1421-1444 OWENS, R. P.: 'Curvature effect in microstrip ring resonators', Electron. Lett., 1976, 12, pp. 356-357 WU, Y. S., and ROSENBAUM, F. J.: 'Mode chart for microstrip ring resonators', lEEE Trans., 1973, MlT-21, pp. 487-489 DAS, A., DAS, S. K., and MATHUR, S. P.: 'Radiation characteristics of higher-order modes in microstrip ring antenna', IEE Proc., 1984, 131, pp. 102-106 EL-KHAMY, S. E., EL-AWADI, R. M., and EL-SHARRAWY, E-B. A,: 'Simple analysis and design of annular ring microstrip antennas', IEE Proc., 1986, 133H. pp. 198-202 BHA'ITACHARYYA, A. K., and GARG, R.: 'Input impedance of annular ring microstrip antenna using circuit theory approach', IEEE Trans., 1985, AP-33, pp. 369-374 RICHARDS, W. F., OU, J. D., and LONG, S. A,: 'A theoretical and experimental investiga-

2 76

Characteristics of microstrip patch antennas

tmn of annular, annular sector, and circular sector microstrip antennas', IEEE Trans., 1984. AP-12, pp. 864-866 PALANISAMY, V., and GARG, R.: 'Rectangular ring and H-shaped mlcrostrip antennas Alternatives to rectangular patch antenna', Electron. Lett., 1985, 21, pp. 874-876 YU. I. P.: 'Low profile circularly polarized antenna', NASA Report N78-15332, 1978 SHEN, L. C.: 'The elhptical microstrip antenna with circular polarization', IEEE Trans., 1981, AP-29, pp. 90-94 LONG, S. A., SHEN, L. C., SCHAUBERT, D. H., and FARRAR, F. G.: 'An experimental study of the circular-polarized elliptical printed circuit antenna', IEEE Trans., 1981, AP-29, pp. 95-99 BAILEY, M. C., and DESHPANDE, M. D.: 'Analysis of elliptical and circular microstrip antennas using moment method', IEEE Trans., 1985, AP-33, pp. 954-959 BHARTIA, P., and BAHL, I.: 'A frequency agile microstrip antenna', IEEE AP-S Int. Symp. Digest, 1982, pp. 304-307 SCHAUBERT, D. H., FARRAR, F. G., SINDORIS, A. R., and HAYES, S. T.: 'Microstrip antennas with frequency agility and polarization diversity', IEEE Trans., 1981, AP-29, pp. 118-123 SENGUPTA, D. L.: 'Resonant frequency of a tunable rectangular patch antenna', Electron. Lett., 1984, 20, pp. 614-615 LAN, G. L., and SENGUPTA, D. L.: 'Tunable circular patch antennas', Electron. Lett., 1985, 21, pp. 1022-1023 LO, Y. T., and RICHARDS, W. F.: 'Theoretical and experimental investigations of a microstrip radiator with multiple linear lumped loads', Electromagnetics, 1983, 3, pp. 371-385 DARYOUSH, A. S., BONTZOS, K., and HERCSFELD, P. R.: 'Optically tuned patch antenna for phased array applications'. IEEE AP-S Int. Syrn. Digest, 1986, pp. 361-364 DAHELE, J. S., LEE, K. F., and HO, K. Y.: 'Mode characteristics of annular-ring and circular disc microstrip antennas with and without airgaps'. IEEE AP-S Int. Sym. Digest, 1983, pp. 55-58 LEE, K. F., HO, K. Y., and DAHELE, J. S.: 'Circular-disk microstrip antenna with an air gap', IEEE Trans., 1984, AP-32, pp. 880-884 DAHELE, J. S., and LEE, K. F.: 'Theory and experiment on microstrip antennas with airgaps', IEE Proc., 1985, 132H, pp. 455460 LEE, K. F., and DAHELE, J. S.: 'The two-layered annular ring microstrip antenna', Int. J. Electronics, 1986, 61, pp. 207-217 LONG, S. A., and WALTON, W. D.: 'A dual frequency stacked circular disc antenna', IEEE Trans., 1979, AP-27, pp. 270-273 DAHELE, J. S., and LEE, K. F.: 'A dual-frequency stacked microstrip antenna'. IEEE AP-S Int. Sym. Digest, 1982, pp. 308-31 1 DAHELE, J. S., LEE, K. F., and WONG, D. P.: 'Dual-frequency stacked annular-ring microstrip antenna', IEEE Trans., 1987, AP-35 ZHONG, S. S., and LO, Y. T.: 'Single-element rectangular microstrip antenna for dualfrequency operation', Electron. Let?., 1983, 19, pp. 298-300 DAVIDSON, S. E., LONG, S. A., and RICHARDS, W. F.: 'Dual-band microstrip antennas with monolithic reactive loading', Electron. Lett., 1985, 21, pp. 936-937 DAHELE, J. S., and LEE, K. F.: 'Top-loaded single and coupled microstrip monopoles'. IEEE AP-S Int. Sym. Digest, 1983, pp. 47-50 MclLVENNA. J., and KERNWEIS, N.: 'Modified circular microstrip antenna elements', Electron. Lett., 1979, 15, pp. 207-208 SABBAN, A.: 'A new broadband stacked two-layer microstrip antenna'. IEEE AP-S Int. Sym. Digest, 1983, pp. 63-66 BHATNAGAR, P. S.. DANIEL, J.-P., MAHDJOUBI, K., and TERRET, C.: 'Experimental study on stacked triangular microstrip antennas', Electron. Lett., 1986, 22, pp. 864-865

Characteristics of microstrip patch antennas

2 17

62 CHEN, C. H., TULINTSEFF, A,, and SORBELLO, R. M.: 'Broadband two-layer microstrip antenna'. IEEE AP-S Int. Symp. Digest, 1984, pp. 251-254 63 DAHELE. J. S., TUNG, S. H.. and LEE, K. F.: 'Normal and inverted configurations of the broadband electromagnetic coupled microstrip antenna'. IEEE AP-S Int. Sym. Digest, 1986, pp. 841-844 64 LEE, R. Q., LEE, K. F., and BOBINCHAK, J.: 'Characteristics of a two-layer electromagnetically coupled rectangular patch antenna', Electron. Lett.. 1987, 23, pp. 1070-1072; also IEEE AP-S Int. Sym. Digest, 1988, pp. 948-951 65 RIVERA, J., and ITOH, T.: 'Analysis of an electromagneticallycoupled patch antenna'. IEEE AP-S Int. Sym. Digest, 1983, pp. 170-173

Chapter 4

Circular polarisation and bandwidth M. Haneishi and Y. Suzuki

Microstrip antennas are widely used as an efficient radiator inmany communication systems [I]. One of the most interesting applications is their use for transmitting or receiving systems ,required for circular polarisation [2-51. A circularly polarised microstrip antenna can be classified into two categories, e.g. single- or dual-fed types. The classification of an antenna is based upon the number of feeding points required for circularly polarised waves. The singly-fed antenna is useful, because it can excite circular polarisation without using an external polariser. Therefore, it is important to understand the radiation mechanism of the antenna. However, one of the most serious problem in such an antenna is the considerable narrowness of the bandwidth compared to ordinary microwave antennas. This is a serious problem for the practical application of this antenna. For this reason, it is also important to study some wideband techniques. In this Chapter, the various types of circularly polarised antennas are first briefly introduced in Section 4.1. In Section 4.2, a simple design method for a singly-fed antenna is described together with some useful design data. This method is useful in understanding its radiation mechanism and to roughly design it. However, if the general radiation mechanism and an accurate design method are required, then the more exact treatment, developed in Section 4.3, is necessary. In Section 4.4, some considerations of mutual coupling are described. Finally, three kinds of wideband techniques are introduced in Section 4.5.

4.1 Various types of circularly polarised antennas There are many types of circularly polarised (CP) printed antennas, which are widely used as efficient radiators in many communication systems. Fig. 4.1 shows basic arrangements for various types of CP-wave printed antennas. In this Section, we describe briefly techniques for designing such CP printed antennas.

220

Circular polarisation and bandwidth

4.1.1 Microstrip patch antennas A microstrip antenna is one of the most effective radiators for exciting circular polarisation. A circularly polarised microstrip antenna is categorised into two types by its feeding systems: one is a dual-feed CP antenna with an external polariser such as 3dB hybrid, and the other is a singly-fed one without a polariser. The classification of antennas is based upon the number of feeding point required for CP excitation.

Circular polarisation and bandwidth

221

both the input VSWR and ellipticity bandwidth are broad, since a 3 dB hybrid, in general, has a broadband nature. The other category is the offset-feeding CP antenna. Here, offset feeding lines, with one quarter wavelength longer than the other, are set at the edges of the patch, as shown in Fig. 4 . 2 ~One . of the most serious disadvantages of this type of antenna is the narrow bandwidth, since the frequency dependency of an offset-feeding line is greater than that of the usual hybrid.

(a-1) Dual fed patch

(a-2) Singly fed patch

hybrid

-

8

-

RHCP LHCP

RHCP LHCP

RHCP ( d l Microstrip printed slot

( a ) Dual f e d CP patches Fig. 4.1

( b ) Singly f e d CP p a t c h e s

Various types of circularly polarised printed antennas

Fig. 4.2

(a) Dual-fed CP patch antenna: The fundamental configurations of a dualfed CP patch antenna are shown in both Fig. 4.1 (a-1) and Fig. 4.2 (a). The patches are fed with equal amplitude and 90' out of phase by using an external polariser. As shown in the Figure, these antennas are also divided into two categories by the shape of an external polariser: one is the 3 dB hybrid type and the other is an offset-feeding one. As is well known, a 3 dB hybrid such as a branch-line coupler produces fields of equal amplitude but 90' out of phase at its centre frequency. Therefore, setting the outputs of such a hybrid to the edges of the patch, the antenna acts as a CP radiator. It is necessary to note that each input terminal of a hybrid, however, gives an opposite sense of circular polarisation. In the present case,

Typical arrangements for circularly polarised microstrip antennas LHCP: Left-hand circular polarisation RHCP: Right-hand circular polarisation

(b) Singly-jed CP patch antenna: A singly-fed CP antenna may be regarded as one of the simplest radiators for exciting circular polarisation. The typical configurations of this antenna are shown in Fig. 4.2b. It is important to note that the generated mode in this case is usually excited in an electrically thin cavity region of the microstrip antenna. Accordingly, the operational principle of this antenna is based on the fact that the generated mode can be separated into two orthogonal modes by the effect of a perturbation segment such as a slot or other truncated segment [6-7,10-1 I]. Consequently, by setting the perturbation segment to the edge of the patch, the generated mode is separated into two

222

Circular polarisation and bandwidth

orthogonal modes 1 and 2. The typical amplitude and phase diagrams after perturbation are shown in Fig. 4.3, together with typical samples of antennas. The radiated fields excited by these two modes are, in general, perpendicular to each other, and orthogonally polarised in the boresight direction. When the amount of perturbation segment is adjusted to the optimum value, modes 1 and 2 are excited in equal amplitude and 90' out of phase at the centre frequency, as shown in the Figure. This enables the antenna to act as a CP radiator in spite of single feeding. This antenna has several advantages compared to dual-fed ones and can excite CP radiation without using an external polariser. Design techniques will be described in detail in Sections 4.2 and 4.3.

Circular polarisation and bandwidth

223

the present case, on setting the radiating elements such as the strip and the slot to the maximum positions of V, and I,,these radiating elements radiate transverse and longitudinal electric fields E,, and E,,, respectively, in the boresight direction. The fields E,, and E,, can be excited in equal amplitude and at 90° out

-

input

microstrip l i n e M :

;C%+

l1

(a) Radiating element for composite-type circularly polarised printed antennaI81

( polarity)

input

E

matched

input i-----

i

Frequency Fig. 4.3 Amplitude andphase diagrams for singly-fed circularly polarisedmicrostripantennas

E

matched

input

4.1.2 Other types of circularly polarised printed antennas In this section, we describe briefly the fundamental design procedures for others types of CP antennas.

Fig. 4.4

( a ) Composite type of CP printed antenna: Fig. 4 . 4 shows ~ the fundamental configuration of a composite-type CP antenna [8]. The antenna is composed of the combination of a half-wavelength-long strip conductor and a slot in the ground plane. If the microstrip feeding line is short-circuited at 1 = 0, a standing-wave voltage V, and current I, occurs along the microstrip feeding line. In

of phase, if the strip and the slot are spaced one-quarter wavelength apart and the coupling between the radiating element and feeder is controlled to be identical in value. Therefore, this type of antenna acts as CP radiator without using any external polariser. Details of design techniques for this antenna will be discussed in Chapter 13.

(b) Various arrangements of rampart line antennas[6] Typical arrangements for travelling-wave-type printed antennas

224

Circular polarisation a n d bandwidth

Circular polarisation a n d bandwidth

(b) Discontinuity type of C P printed antenna: A rampart-line antenna is a typical radiator for the discontinuity type [6,9]. Fig. 4.4b shows typical rampart line antennas that act as CP and LP radiators. Each radiator consists of a microstrip meander line having a series of corner bends. The antenna also has a matched load at the open end of the meander line. In this system, radiation occurs mainly from the discontinuity section of the meander line such as a corner bend. Therefore, both C P and LP rampart line antennas can be easily fabricated by controlling the length L, width Wand period P of the meander line. If L, Wand P a r e adjusted to 412, 3$/4 and ,Ig, respectively, for a unit cell of the meander line (As is the wavelength of the travelling wave along the meander line), the antenna acts as a CP radiator. When L = 2A8/3, W = 413 and P = 2Ag/3, the antenna radiates horizontal polarisation, while L = W = 414, P = 1,/2 excites vertical polarisation, as shown in Fig. 4.46. Details of the design procedure will be discussed in Chapter 13.

225

equations. while a perfect magnetic wall is assumed as a boundary condition at the antenna peripheries (x = fa/2,y = 4 b/2); 4" = V, sin k x

4h = VOsin k y where Vo = $/a and k = z/a. The eigen function 4, is concerned with the field distribution of TM,, mode, and 4, with that of TMo,, mode. By setting the perturbation segment As at an appropriate position of the antenna, as shown in Fig. 4.5, two orthogonally polarised modes are excited in a cavity region of the antenna.

4.2 Simple design techniques for singly-fed circularly polarised microstrip antennas

This Section gives a brief description of design techniques for singly-fed radiators together with some useful experimental results. The approach is based on the variational method, and is useful for understanding the mechanism of CP radiation from such singly-fed radiators.

( a ) Standard patch

4.2.I Recfangular type In general, microstrip antennas are divided into two types by the shape of radiating element: rectangular type and circular type. However, since the rectangular patch antenna is considered to be a fundamental device for exciting CP radiation, the design techniques for this type are discussed first. (a) Fundamental configuration of rectangular CP-wave antenna: The fundamental configurations of the antenna and its co-ordinate system are shown in Fig. 4.5. In type A, the feeding point F is placed on the x- or y-axis, whereas in type B, F is placed on the diagonal axis. In both cases, the perturbation segment As is set at an appropriate location in the patch element to excite CP radiation. Here, we describe briefly the sense of direction for the CP-wave. Right-hand or left-hand CP radiation can be achieved by setting feeding points at appropriate locations such as F(f Q,, 0) and F(0, -+eo), as shown in Fig. 4.6. (b) EfSecf of perturbation segment: The effect of perturbation segment As for the type-A antenna is described first, since this type of radiator is a basic device for exciting CP radiation. The eigen functions 4 , and &,, which are excited in an electrically thin cavity region of the square patch, are generally given mathematically by the following

(b) Singly fed circularly polarised patch Fig. 4.5

Fundamental configurations of singly-fed rectangular patches (From Reference I I )

The new eigen function 4' and the new eigen value k', after perturbation by the segment, are determined by the following equations [I 1, 12, 151:

4'

=

P4, + Q 4 b

I

where P and Q are unknown expansion coefficients of the new eigen function 4'.

226

Circular polarisation and bandwidth

Circular polarisation and bandwidth

The new eigen value k' of the antenna can be derived by employing the following matrix, since eqn. 4.2 is a variational-expression form: det

I

k2

+ 41 - k 2 ( 1 + P I )

q12 - K2PI,

+ 92

- kf2(1 + PI)

q12 - V2 P i 2

In case of the type-A antenna, the parameters in eqn 4.3, such a s p , , p2, q , , q,, p , , and q,,, are expressed by the following equations [I I]:

227

The eigen values used in eqn. 4.6 are assumed to be k,' = k,,' = k by means of first-order approximation. Furthermore, the turn ratios N,' and Nb', which correspond to the energy distribution ratios for both the 4,' and 4,' modes after perturbation, are defined as [I I]

Nb

=

($?/a)(sin kx - sin ky)

Nb = (@/a)(sin kx

(4.7)

+ sin ky)

In the case of the type-B antenna shown in Fig. 4.5, the eigen functions & ,

$6 and other parameters can also be derived by similar calculations employed for type A. The equations obtained by these calculations are as follows: Substituting eqn. 4.4 into eqn. 4.3, the new eigen values k,' and k,' for type A are given as

where k,' and k,' correspond to the eigenvalues of the new orthogonal eigen functions, 4,' and 4,', respectively. modes are Using eqn. 4.5, new sets of resonant frequencies for the 4,' and easily obtained as follows: f, =

for + Af: = h , ( l - 2 W S ) f b = hr + AfL. = A,

wheref,, is the resonant frequency for a normal square patch before perturbation, and Af,' and Afb' are the shifts of resonant frequencies for the 4,' and 4,' modes after perturbation. Normalising the new eigen functions for the 4,' and 4,' modes, the unknown expansion coefficients P and Q are determined as follows [I I, 121: For 4,' mode,

P,

=

(I/$)

(1 - 2As/S)

Qa = ( - 1 1 4 ) ( I

For

-

2As/S)

2.

(I/$)

2.

(-I/$)

4,' mode P,

=

Q,

=

where V, = I/a and k = nla. Using eqns. 4.1-4.7, we can derive the equivalent circuit for the type-A antenna. Furthermore, the equivalent circuit of the type-B antenna after perturbation can also be derived using the relations given in eqns. 4.8. The circuit for both the types of antennas is shown in Fig. 4.7. In this circuit, T', and T', represent ideal transformers having turn ratios Nb and &, and is input voltage applied to the 1-1' terminal.

5

(%'5)

Finally, using eqns. 4.1, 4.2 and the expansion coefficient, the new eigen functions 4,' and 4,' are given in a closed form by

(c) Condition requiredfor CP-wave radiation: In this Section, conditions for exciting CP-wave radiation are determined by use of the preceding equivalent circuit. As is well known, the equivalent conductances Gh and Gb in the circuit are expressed as the sum of the radiation, dielectric and copper losses. However, in normal patches having adequate radiation efficiency above 90%, radiation loss is dominant compared with the other losses.

228

Circular polarisation and bandwidth

Circular polarisation and bandwidth

Consequently, the equivalent conductances Gb and G ; are mainly caused by the radiated fields resulting from the patch antenna. In other words, the induced voltages and generated on G:, and Gb can be assumed to correspond to the radiated fields caused by the orthogonal 4: and 4; modes.

c,

(Ijblt,) = + j is satisfied. Accordingly, these antennas act as a CP radiator by setting the relative amplitude and phase between the two orthogonal modes at I &/?,I = I and arg ( & I t ) = f90°, respectively. Applying the above conditions to eqn. 4.9, turns ratios are required to satisfy the relation INf,/N:,I = 1. In addition, when this restriction is applied to the type-A antenna, it is necessary to place the feeding point F on the x-axis for (Nb/N:,) = 1. Contrariwise, the feeding point F is required to be placed on the y-axis by another restriction (N',/K)= - 1. 1

( b l LHCP Fig. 4.6

229

Nb:l

dA- mode

(1r.l ~ a / 2 1

Feeding locations required for circular polarisation RHCP: Right-hand circular polarisation LHCP: Left-hand circular polarisation eo = feed location

1-;

L(1-1

%=-2.ds t,,

~'=Klsinkx -sin kyl sink* + i n k K=fi/a

*)N;=l/:!

(4.75)

(P)

Fig. 4.24 Relationship between 0,.6,. Po and input VSWR (From Reference 29)

Next, the relation between the resonant frequency, the dimension of the patch radiator, and the thickness and dielectric constant of the substrate used is derived. Let S be the physical area of the patch radiator and t be the substrate, thickness. Now, if @ / t is introduced as a parameter, the product of the can generally be expressed as a function of f i t resonant frequencyf (') and and the substrate dielectric constant 8,. Fig. 4.25 shows the relations between f@' @ and @/Iwith E, as a parameter for a circular microstrip antenna. The dots in the Figure show the measured results. On the other hand, if the radiation conductance can be regarded as a domi-

4

256

Circular polarisation and bandwidth

Circular polarisation and bandwidth

nant factor compared with the other conductance components, the unloaded Q denoted by Q, can also be approximated as a function of E, and f i t . Fig. 4.26 shows the relation between Q, and f i / t with E, as a parameter, for the circular microstrip antenna. In this Figure the dots show the measured results.

257

In eqn. 4.77, the second-order mode (TM,,,) is chosen as a dominant mode. From Fig. 4.24, the product of the maximum bandwidth and Q,, when Q = 2.0, is QoBr

=

0.75

(4.79)

From the above equation and eqn. 4.78, it is found that Q, necessary for this antenna is Qo = 8.6

(4.80)

It follows from Fig. 4.26 that when a substrate of E,

Fig. 4.25

t/S

Relations between ff2) and @t antenna (From Reference 29)

= 1.21

(4.81)

with E, as a parameter, for circular microstrip

Although only one example of a circular microstrip antenna is given here, the relationships shown in Figs. 4.25 and 4.26 are typical, and the above approach is applicable to any shape of antenna including rectangular and triangular microstrip. ( b ) Design example (291: In this Section, the specific design procedure is given for the example of a wideband circular microstrip antenna. Let us assume the following requirements for the frequency range and input VSWR: Frequency range: 1530-1670 MHz Input VSWR: less than 2.0 In this case, the centre or resonant frequency and the relative bandwidth are f'2' = 1600MHz (4.77)

Fig. 4.26 Relations between unloaded 0 and $ I t with E, as a parameter for circular microstrip antenna (From Reference 29)

is used, the &?/t

f i r value necessary to get the Q, value of eqn. 4.80 is = 5.84

Accordingly, in the case of a circular microstrip antenna whose equal to the above, it can be seen from Fig. 4.25 that

fly2' =

114.86

(4.82) fi/t

value is (4.83)

258

Circular polarisation and bandwidth

Circular polarisation and bandwidth

Eqns. 4.77 and 4.83 show that

fl

=

71.79mm

and the radius of the patch radiator is 40.5 mm. From the above result and eqn. 4.82, the thickness of the substrate to be used is calculated as In summary, the circular microstrip antenna to meet the proposed requirements has the following specifications: Dielectric constant of substrate: 1.21 Thickness of substrate:

12.3mm

Patch radius:

40.5 mm

-

259

mode, and their influence may become a serious problem, when the bandwidth is expanded without careful consideration. In this Section, the influence of lowering the quality factor is described. For example, the antenna shown in Fig. 4.27 is a fairly wideband antenna whose relative bandwidth is 8.75%, and the influence of the unwanted modes can no longer be ignored. The mode closest to the wanted one is the TM,,, mode in this case. The influence of the TM,,, mode may be most prominent when the antenna is used as a circularly polarised one with dual feeds. In that case, the TM,,, mode gives rise to some coupling between two terminals. The measured results for this coupling are shown, together with the calculated ones, in Fig. 4.29, where the solid line shows the measured results and the broken line shows the calculated ones. Also the chain-dotted line shows as a reference measured results for an antenna having a fairly high quality factor. In this Figure, the coupling is less

Such a microstrip antenna can be made using paper honeycomb materials as a substrate. Fig. 4.27 shows a circular microstrip antenna manufactured according to the above specification. Also, Fig. 4.28 shows the return-loss characteristics for this antenna, where the calculated and measured results are indicated by the solid and broken lines, respectively. Both results show the wideband performance of about 8.75% for VSWR 5 2.0, which agrees well with the requirement in eqn. 4.78. Circu l o r disk

Frequency

I/ V

I/

(

GHz )

Fig. 4.28 Return-loss characteristicsfor circular microstrip antenna shown in Fig. 4.27 (From Reference 29) a = 40.5 mm, t = 12.3mm, and E, = 1.21 Paper honeycomb core

C o a x i a l probes

Epoxy fiberglass skins Fig. 4.27 Structure of circular microstrip antenna consisting of epoxy Fiberglass skins and paper honeycomb core (From Reference 29)

( c ) Injhences of unwanted modes and countermeasures against them [28]: The bandwidth of a microstrip antenna can be increased by employing a

thick substrate with low dielectric constant, as shown in Fig. 4.28. However, it is expected that some unwanted modes will be generated as well as the wanted

than - 50 dB at the resonant frequency, which is small enough for the antenna with a high quality factor, and the coupling increases to about - 28 dB for an antenna with a low quality factor. These results suggest that the axial ratio may be degraded owing to the influence of this coupling when the latter antenna is used as a dual-fed circularly polarised antenna, although it is fed by a perfect 90' hybrid. Fig. 4.30 illustrates the axial-ratio characteristics for such an antenna, where the solid line shows the calculated results and the dots show the measured ones. This Figure shows that the best axial ratio is only of the order of 1.3 dB. In order to improve the axial ratio it is necessary to investigate the mechanism of the degradation. When a microstrip antenna has a low quality factor, the

260

Circular polarisation and bandwidth

Circular polarisation and bandwidth

261

Frequency (MHz) Fig. 4.29

Coupling characteristics between orthogonal ports for circular microstrip antenna with dual feeds (From Reference 28)

Frequency ( M H z ) Fig. 4.30 Axial-ratio characteristicsfor dual-fed circularly polarised circular microstrip antenna a = 40.5 mm, t = 12.3 mm, and E, = 1.21

Fig. 4.31 Equivalent circuit for dual-fed circular microstrip antenna having low-quality factor and the corresponding inner-surface current flows on the patch radiator a Equivalent circuit b Current flows (e signs denote the feed point)

equivalent circuit can be approximated by Fig. 4.31~.This Figure implies that the coupling may arise between two orthogonal terminals through the 4th resonant circuit, in which the current due to the unwanted mode flows. Therefore, the current flowing in the 4th resonant circuit must somehow be ,suppressed. Fig. 4.32 shows one method of cancelling out such a current by adding more two terminals to the original two, and feeding from four terminals 90" out of phase with equal amplitude. Fig. 4.33 shows the axial-ratio characteristics with such a method of feeding, where the solid line represents the calculated results and the broken line the measured ones. As expected, the axial ratio is improved remarkably compared with Fig. 4.30 for the case of the antenna fed from only two terminals. The above is particularly useful when the antenna is used only as a single element. When it is used as an element comprising an array antenna, it is also possible to cancel out the cross-polarised component radiated from each element at any observation point in free space. For convenience, let us consider a two-element array radiating elliptically polarised waves from each element, as shown in Fig. 4.34. If they are both RHCP and the excitation ratio is l : ~ e ' the ~, total electric field radiated from them can be determined from Fig. 4.34 as E = {a,

+ ydA(/?,C O S ~+ j/?,sinS)}f

262

Circular polarisation and bandwidth

Circular polarisation and bandwidth 1

& , =

1

5 [@I

- a21

263

+ yBAe-j6(8l - PI)]

(4.89)

with E, denoting the RHCP component. Therefore, in order to make the reverse polarised components cancel out on the boresight direction, the following complex excitation condition between two elements must be satisfied:

* Fig. 4.32 Actual feeding methods for circularly polarised circular microstrip antenna with four feed point (From Reference 28) a Right-hand circular polarisation b Left-hand circular polarisation

-

-:1.c 0 .+ "a. .-0

Fig. 4.34

d

-

2

Col.

I

f 30

1550

1600 Frequency

1650

1700

(MHz)

Two kinds of elliptically polarised waves radiated from two-element array a Polarisation ellipse of no. 1 element b Polarisation ellipse of no. 2 element

LHCP: left-hand circular polarisation RHCP: right-hand circular polarisation

Fig. 4.33 Axial-ratio characteristics improved by feeding from four terminals as shown in Fig. 4.32a (From Reference 28) a = 40.5rnrn, t = 1 2 . 3 rnrn, and e, = 1.21

on the boresight direction, where 6 indicates the physical rotation angle of the polarisation ellipse of the no. 2 element against that of the no. 1 element on an XY plane as shown in Fig. 4.34. Dividing the above field into the two components of co-polarisation and cross-polarisation, it can be expressed as

E where

= U

f

-

+ E,,,df + 9)

Frequency

(4.87)

[MHz)

Fig. 4.35 Axial-ratio characteristicsimprovedby employingpairedelemenrs (From Reference 28) a = 40.5 mm, t = 12.3 mrn, and

E, =

1.21

264

Circular polarisation and bandwidth

Circular polarisation and bandwidth

I

Since an ordinary array antenna consists of the same elements, the above relationship can be reduced to

265

tions, using an impedance matrix known as a matrix Green's function, as follows:

because it can be assumed that a, = p, and a, = B,. The radiation field for the RHCP, being a co-polarised component in this case, can be expressed as Em

=

ER

=

- j(a,

+ a,)d6sin6

(4.92)

parostic element

The above equation implies that the co-polarised component takes the maximum value

IEmI

=

lERl

=

la! +

(4.93)

when the following condition is satisfied for the rotation angle 6: 6

=

90"

(4.94)

On the other hand, the excitation condition for LHCP, instead of RHCP as above, can be similarly derived and is given by y p = - e-jd = &("-6) (4.95)

?(a)

when a , = p, and a, = B,. The resultant LHCP component is represented as a function of 6, as in the case of RHCP. So the same maximum value as in RHCP case can be obtained, when the same condition (eqn. 4.94) is satisfied for 6. It is concluded from the above discussion that the axial ratio may be improved, in case of an array antenna, by arranging for the paired elements to have a rotation angle 6 = 90". Fig. 4.35 shows the measured results for the axialratio characteristics of such paired elements. As expected, the resultant axial ratio is improved remarkably compared with the results of Fig. 4.30, and is of the same order as that obtained by the previous four terminal-fed cases. 4.5.2 Technique using parasitic element [34] The bandwidth of a microstrip antenna can also be increased by employing a parasitic element [25, 30-321. In this Section, the type shown in Fig. 4 . 3 6 ~is analysed using the Hankel-transformed domain-analysis method [33], and it is shown from theory and experiment to achieve an increase in the bandwidth. In this Figure, the two substrates are stacked so that they are parallel and the two circular etched disc conductors are concentric. The upper one is used as a parasitic element. (a) Characteristic equation in the Hankel-transformed domain: In general, Green's function in the real domain is a very complicated convolutional integral or summation form, as shown in eqn. 4.14. However, it is known that Green's function becomes of simple algebraic form if it is expressed in the Hankel-transformed domain. In this domain, it can be deduced from Reference 33 that the electric fields on the boundary are related to the corresponding current distribu-

air

short for E- wove

for H- wove

(b) Fig. 4.36

Circular microstrip antenna with parasitic element and its spectral-domain equivalent circuit (From Reference 34) a Structure of analytical model and co-ordinate system b Equivalent circuit for E- and H-waves

where the sub-vectors [E(a)],,, and [i(cc)],,, consist of two elements, respectively, and are

266

Circular polarisation a n d bandwidth

Circular polarisation a n d bandwidth

The tilde means the quantities in the Hankel-transformed domain, and each element is defined from its tangential components, which consists of both E-wave and H-wave, as

with F,(r) and F6(r) being the tangential components and J,,,(x) being the Bessel function of the first kind with (n + 1) or (n - I) th order. Also the subscripts 1 and 2, being the order of elements in each sub-matrix of eqn. 4.97, are referred to the lower and upper conductors. The sub-matrices in eqn. 4.96 can be represented by

for 1

= e

for 1

=

267

(E-wave)

h (H-wave)

for I

= e

for I

=

(E-wave)

h (H-wave)

These elements can be derived from the spectral-domain equivalent circuit shown in Fig. 4.366. Next, the unknown current distributions are expanded on each circular conductor in the real domain as follows:

where the matrices [Z(a)], and [Z(a)], denote the impedance matrices for E-wave and H-wave, respectively, and are written as where A, and B, are expansion coefficients with i = 1 and 2 being referred to the lower and upper conductors, whilef,,(r) and &(r) are basis functions. In this case, the Hankel-transformed current distribution $*)(a) in eqn. 4.976 is expressed as They can be easily determined from the corresponding admittance matrices, which consist of the following elements:

(4.101~)

- Ysin (pd) sin ( r t ) ]

Y:2(a)

=

Y:! (a) =

-jYY1 Ycos (pd) sin (B't) Y'cos (p't) sin (pd)

where [A,] and [B,] are unknown vectors with A;, and B,,, and [x(a)],,, and [&(a)](+, are the transformed basis function vectors with x!:)(a) and &'(a). Substituting eqn. 4.104 into eqn. 4.976 and then substituting the resulting equation and eqn. 4 . 9 7 ~into eqn. 4.96, the following matrix equation can be obtained:

+

[ A ~ l [ h f a ) l ( ++) j[~11[.?41fa)I(+)

(4.1016)

[A2l[X2fa)l1+, + i[~21[342fa)lc+) [ A l l [ ~ l f a ) l ( -) j[~~l&~fa)l(-)

- Y' sin (pd) sin (Pt)]

with I

=

(4.101~)

EJ-I (a)

[A21[.f,2fa)l(-) - j [ ~ ~ l t f 4 ~ f a ) l ~ - )

e or h and

p = ,/8. = J W ~ ~ , E , E ,

- a2

Taking inner products of eqn. 4.105 with all the transformed basis functions fi;)(a) and]$:'(a) according to Galerkin's method, the left-hand sides of all the resulting equations vanish owing to the boundary conditions. Thus it is possible

268

Circular polarisation and bandwidth

269

Circular polarisation and bandwidth

to choose the following combinations in order to avoid divergence of integrals appearing in the characteristic equation:

to exist. Therefore, the characteristic equation for this problem can be written as Q(w)

=

det[P] = 0

(4.1 12)

where w is the complex resonant angular frequency whose real and imaginary parts correspond to the resonant angular frequencies and the damping factors, respectively. where a bracket ( . ) in the above equations is employed for the following infinite integral:

Finally, eqn. 4.106 can be rewritten in a matrix form and is given by

p111

0.0

where the matrix [PI is defined as follows:

0.85

0.90

0.95

real port

Fig. 4.37

and the elements of the sub-matrices [P!]

I 0.80

through [ P a ] with i

=

1 or 2 and

j = I or 2 are given by

with

From eqn. 4.108, the determinant of [PI must vanish for a non-trivial solution

1 .OO

1.05

Dr

Contour of complex resonant frequencies of circular microstrip antenna with parasitic element (From Reference 34) t = 1.6 mm and E, = 2.55.b = w/wo = b, + jh,

( b ) Electrical characteristics: In this case, two basis functions for each current component provide satisfactory accuracy, so that the characteristic equation results in a form of determinant of size 8 x 8. Fig. 4.37 shows numerical results for the complex resonant frequencies solved from eqn. 4.1 12, where the thickness and dielectric constant for the substrate used are t = 1-6mm and E, = 2.55, respectively. The Figure shows the contour map for the real and imaginary parts of normarised complex resonant frequencies with a,/a, and d/al as parameters. From this Figure, it is found that two dominant resonant modes, which exhibit a double-tuned characteristic, exist in this antenna. So the input VSWR characteristics can be calculated by considering a double-tuned performance. In this case, two resonant resistances R, and R, can be determined uniquely as follows:

270

Circular polarisation and bandwidth

Circular polarisation and bandwidth

because

277

in some special applications [36]. In this Section, we briefly describe design procedure of such a paired element. Fig. 4 . 3 9 ~shows the fundamental arrangement of a microstrip paired-element unit. The patch elements are rotated orthogonally on the coplanar plane and are fed in uniform amplitude but 90' out of phase through the sequentially rotated feeding points F, and F,. w0 = 1441c in Fig. 4.37

(-n12) phase shifter

a,

where w,, and w,, are resonant angular frequencies for two dominant modes and cis the velocity of light in vacuum. Fig. 4.38 shows the calculated and measured input VSWR characteristics for the antenna with d = IOmm, a , = 20+3mm, a, = 21.0 mm, t = 1.6 mm, and 6, = 2.55. In this Figure, the results for the antenna without a parasitic element are also shown as a reference, and it is seen that the effect of the parasitic element is considerable.

( a ) Paired element

EY

>

1.1

I

2.4

2.5

2.6

2.7

2.8

frequency ( G H r )

Fig. 4.38

Calculated and measured VSW R characteristics for circular microstrip antenna with parasitic element (From Reference 34) d = 1 0 m m , a, = 2 0 . 8 m m . a , = 2 1 . 0 m m . t = 1.6rnm. a n d & , = 2.55

4.5.3 Technique using paired element Circularly polarised microstrip antennas including single-fed patches are widely used as effective radiators in many communication systems [6, 101. However, the most serious problem with such antennas is the narrowness of the ellipticity and impedance bandwidth compared with ordinary microwave antennas. Several techniques for the expansion of bandwidth have been reported in the literature [29-341. However, most of these broadband techniques, including double-stacked CP patches, are applicable to isolated CP patch antennas. Hence, other wideband techniques using sequential arrangements of antenna elements have been developed in recent years [26,35]. The simplest device for such a sequential array is a paired element, and it is used as an effective radiator

( b ) Principle of wideband

Fig. 4.39 Paired element and its polarisation pattern

A sub-array composed of such paired elements demonstrates the broadband nature in spite of using narrow-band patch elements [26]. In order to evaluate the performance, the polarisation pattern of an antenna is briefly described. In general, individual elements of a pair show elliptical patterns of polarisation, as shown in Fig. 4.396. The polarisation ellipses marked A and B correspond to those of each element of a pair, while the Ex- and E,-axes correspond to the horizontal and vertical components of the radiated electric field. The polarisation ellipses for an individual CP patch vary rapidly with change of frequency. However, if the CP patch of a pair is arranged orthogonally and is fed uniformly in amplitude but 90' out of phase, the resultant polarisation pattern due to the pair can be shown as a trace of perfectly circular polarisation over a wide frequency range, as shown in the figure.

272

Circular polarisation and bandwidth

In order to verify the performance, a 2 x 2 element sub-array unit having two pairs was constructed and tested at X-band. With regards the feeding system, the input impedance for each element of the pairs was matched to that of the main feeder M, by means of A,/4 impedance transformers, T,, T,,T, and T,, where 1, is the wavelength in stripline. Fig. 4.406 shows the typical measured ellipticity bandwidth for the sub-array unit. The ellipticity bandwidth for an isolated CP-patch antenna is also shown for comparison in the Figure. It is shown that the sub-array unit using the paired element contributes enormously to the improvement of the ellipticity bandwidth compared with a single CPpatch element. The 3 dB ellipticity bandwidth obtained by this sub-array unit is about five times the value obtained by an ordinary CP-patch element, as shown in the figure. A more detailed description of the sequential array is given in Chapter 13.

Circular polarisation and bandwidth 2

3 4 5 6 7 8 9 10 I1 12 13 14

15 16 17 18 19 20 21 22

23 24 Fig. 4.40 Sub-array unit and its ellipticity bandwidth

25

4.6 References 1 MAILLOUX, R. J., McILVENNA, J. F., and KERNWEIS, N. P.: 'Microstrip array technology', IEEE Trans., 1981, AP-29, pp. 25-37

26

27

273

WEINSCHEL, H. D.: 'A cylindrical array of circularly polarized microstrip antennas'. In!. Syn7p. Dig. Antennas Propagat. Soc., June 1975, pp. 177-180 SHEN, L. C.: 'The elliptical microstrip antenna with circular polarization', IEEE Trans., 1981, AP-29, pp. 90-94 RICHARDS, W. F., LO, Y. T., and HARRISON, D. D.: 'An improved theory for microstrip antennas and applications', IEEE Trans., 1981, AP-29, pp. 38-46 KERR. J. L.: 'Microstrip polarization techniques'. Proc. Antenna Applications Symp., Allerton Park, IL, Sept. 1978 JAMES, J. R., HALL, P. S., and WOOD, C.: 'Microstrip antenna'. (Peter Peregrinus, 1981) chap. 7 HANEISHI, M., NAMBARA, T., and YOSHIDA, S.: 'Study on elliptical properties of singly-fed circularly polarised microstrip antennas', Electron Lett., 1982, 18, pp. 191-193 ITOH, K.: 'Circularly polarised printed array composed of strip dipole and slot', Microwave J., April 1987, pp. 143-153 JAMES, J. R., HALL, P. S., WOOD, C., and HENDERSON, A,: 'Some recent developments in microstrip antenna design', IEEE Trans., 1981, AP-29, pp. 124-128 CARVER, K. R., and MINK, J. R.: 'Microstrip antenna technology*,IEEE Trans., Antennas & Piopagi., :98:, AP-29, pp. 2-24 HANEISHI, M., and YOSHIDA, S.: 'A design method of circularly polarised rectangular microstrip antenna by one-point feed', Electron & Commun in Japan, 1981, 54, pp. 46-54 OKOSHI, T., and MIYOSHI, T.: 'Planar circuits', (Ohm Publishing (in Japanese), 1973) SUZUKI, Y., MIYANO, N., and CHIBA, Y.: 'Circularly polarised radiation from singly-fed equilateral-triangular microstrip antenna', IEE Proc. 1987, 134, pp. 194-198 SCHAUBERT, D. H., FARRAR, F. G., SINDORIS, A,, and HAYES, S. T.: 'Microstrip antennas with frequency agility and polarization diversity', IEEE Trans., 1981, AP-29, pp. 118-123 OKOSHI, T., and MIYOSHI, T.: 'The planar circuits - An approach to microwave integrated circuitry', IEEE Trans., 1972, MlT-20, pp. 245-252 CARVER, K. R.: 'A modal expansion theory for the microstrip antenna', Int. Symp. Dig. Antennas Propagal. Soc., June 1979, pp. 101-104 SUZUKI, Y., and CHIBA, T.: 'Computer analysis method for arbitrarily shaped microstrip antenna with multi-terminals', IEEE Trans., 1984, AP-32, pp. 585-590 SUZUKI, Y., and CHIBA, T.: 'Improved theory for a singly-fed circularly polarized microstrip antenna', Trans. IECE Japan, 1985, E68, pp. 76-82 For example, NEWMAN, E. H., and TULYATHAN, P.: 'Analysis of microstrip antennas using moment methods', IEEE Trans., 1981, AP-29, pp. 47-53 MORSE, P. M., and FESHBACH, H.: 'Methods of theoretical physics: Pt. 11. (McGraw-Hill, NY, 1953). pp. 1112-1 119 CARVER, K. R.: 'Input impedance to probe fed microstrip antennas', In!. Symp. Dig. Antennas Propagat. Soc., June 1980, pp. 617-620 HANEISHI, M., YOSHIDA, S., and TABETA, M.: 'A design of back-feed type circularly polarised microstrip antenna having symmetrical perturbation segment', Electron & Commun. in Japan, 1981, 2, pp. 52-60 POZAR, D. M.: 'Input impedance and mutual coupling of rectangular microstrip antennas', IEEE Trans., 1982, AP-30, pp. 1191-1 197 DERNERYD, A. G., and LIND, A. G.: 'Extended analysis of rectangular microstrip resonator antennas', IEEE Trans., 1979, AP-27, pp. 846-849 ITAMI, H., and HORI, T.: 'Broad band circular polarized microstrip antenna'. In!. Conv. Rec. lECE (in Japanese), 1982, p. 642 HANEISHI, M., YOSHIDA, S., and GOTO, N.: 'A broadland microstrip array composed of single-feed type circularly polarized microstrip antennas', in In!. Symp. Dig. Antennas Propagal. Soc., May 1982, pp. 160-163 MURPHY, L.: 'SEASAT and SIR-A microstrip antennas', Proc. Workshop on Printed Circuit Antenna Technology, Oct. 1979, paper 18

274

Circular polarisation a n d bandwidth

28 CHIBA, T., SUZUKI, Y., MIYANO, N., MIURA, S., and OHMORI, S.: 'A phased array antenna using microstrip patch antennas', 12th European Microwave Conference, Sept. 1982, pp. 472-477 29 SUZUKI, Y.,and CHIBA, T.: 'Designing method of microstrip antenna considering the bandwidth', Trans. IECE Japan, 1984, E67, pp. 488-493 30 WOOD, C.: 'Improved bandwidth of microstrip antennas using parasitic elements', IEE Proc., 1980, 127, pp. 23 1-234 31 LONG, S. A., and WALTON, M. D.: 'A dual-frequency stacked circular disc antenna', Int. Symp. Dig. Antennas Propagat. Soc., June 1978, pp. 260-263 32 SANFORD, G. G.: 'Multiple resonance radio frequency microstrip antenna structure', US Patent 4070676, Jan. 1978 33 ARAKI, K., and ITOH, T.: 'Hankel transform domain analysis of open circular microstrip radiating structures', IEEE Trans., 1981 AP-29, pp. 84-89 34 ARAKI, K., UEDA, H., and TAKAHASHI, M.: 'Numerical analysis of circular disk microstrip antennas with parasitic elements', IEEE Trans., 1986, AP-34, pp. 1390-1394 35 TESHIROGI, T., TANAKA, M., and CHUJO, W.: 'Wideband circularly polarised array antennas with sequential rotations and phase shift of elements'. Proc. Int. Symp. on Antennas & Propagt., Japan, Vol. 1, Aug. 1985, pp. 117-120 36 HANEISHI, M., HAKURA, Y., SAITO, S . , and HASEGAWA, T.: 'A low-profile antenna for DBS reception'. Int. Symp. Dig. Antennas Propagat. Soc., June 1987, pp. 914-917 37 SUZUKI, Y.: 'Analysis of microstrip antennas based on the planar circuit theory and its applictions (in Japanese)'. Doctoral dissertation, Tokyo Inst. Technol., Nov. 1984

Chapter 5

Microstrip dipoles P.B. Katehi, D.R. Jackson and

N.G. Alexopoulos

5.1 Introduction

Microstrip dipoles have been studied extensively during the last 20 years. Tlley are planar elements which consist of a pair of collinear thin-strip conductcrs printed on the surface of a dielectric slab (Fig. 5.1). They resemble the free-space cylindrical dipoles in the sense that radiation results from a harmonically varying dipole moment. Microstrip dipoles are attractive elements owing to their desirable properties such as simplicity, small size and linear polarisation.

1

I

I

1

Coaxial Excitation

Fig. 5.1 Excitation mechanisms for a microstrip dipole

They are well suited for higher frequencies in particular, where the substrate may be electrically thick. In this case the bandwidth of the dipoles may be quite significant. For thicker substrates it is also possible to alter the radiation properties by the use of a superstrate layer, making dipoles a possible candidate in a substrate-superstrate geometry. When designing microstrip dipoles, the choice of feed mechanism is very

276

Microstrip dipoles

Microstrip dipoles

important and should be made taking into consideration the following two factors: theoretical modelling and practical implementation. Fig. 5.1 shows the most commonly used mechanisms: the coaxial feed, the twin-line feed and the coupled-line feed (EMC dipole). In the twin-line feed a voltage is applied directly to the arms of the dipole. In the coaxial feed the two dipole arms are shorted together, with the dipole becoming essentially a narrow patch antenna with a probe feed. The EMC dipole excitation is realised through electromagnetic coupling to the feed line, with no direct contact. Because of its simplicity, the EMC feed represents the most desirable way to feed a dipole from a microstrip line. Even if practical excitation mechanisms are employed in the design of microstrip dipoles, more ideal ones may be considered for their analysis. The reason lies in the fact that most of their radiation properties are independent of the excitation (i.e. bandwidth, efficiency, radiation pattern etc.). Throughout this Chapter the iiiiciosirip dip& is siiidied extensiveiy as a single radiator as well as an array element. Furthermore, infinitesimally small, centre-fed and EMC dipoles are presented separately, and the dependence of their properties on the electric characteristics of the dielectric layers is discussed. The study of microstrip dipoles is concluded by presenting a design technique for a n array of EMC dipoles which accounts for the mutual interactions between dipole elements.

277

complicated functions of 1, z, z', and are given in Reference 2. The time dependence is ef'"", and is suppressed here. The functionsf and g are of the form

where a and b are analytic functions of 1except for the branch-type singularity due to the wavenumber k

112

=

(G -2)

which appears in the expressions [2]. The functions D,(1) and Dm@)have zeros on the real axis at A,, producing poles in the integrand. The zeros of D,(1) are

5.2 Infinitesimal dipole The simplest dipole structure which can be studied is the infinitesimal dipole. An analysis of the infinitesimal dipole is important because all the radiation characteristics of full-size dipoles may be obtained simply from this solution. Only for near-field (impedance) calculations is it essential to analyse the full-size dipole with a moment-method technique.

5.2.1 Analysis A horizontal electric dipole (HED) is shown in Fig. 5.2. In general, the dipole may be embedded within an arbitrary number of layers, although two layers are sufficient to cover most cases of practical interest, including microstrip dipoles with a protective top (superstrate) layer, or EMC dipoles with a transmission line at the interface (z = b). In the classical Sommerfeld solution, components of the magnetic vector potential at x, y, z due to a source at x', y', z' are written as

with

Q,

q5 describing cylindrical coordinates [I]. The functions f and g are

Fig. 5.2 Substrate-superstrate geometry with horizontal electric dipole (HED) embedded

the TE-mode surface-wave propagation constants, while those of D,(1) correspond to the TM-mode surface waves. These poles are in the region where k, = max (k,, k,). The path of integration goes k, < A, < k,, around the poles, as shown by contour C in Fig. 5.3. By using symmetry properties [I] the integrations may be extended to (- co, + co) and the path deformed to an integral around the branch cut (contour C b ) plus integrals around the poles in the right-half plane. The potentials may then be written as

Microstrip dipoles

279

with P,a, and P,, the radiated and total surface-wave powers, respectively. 5.2.2 Substrate effects The effect of substrate thickness on the efficiency of an infinitesimal dipole on top of a single layer is shown plotted against the electrical substrate thickness b / A d (where Ad = A,/JE,) in Fig. 5.4 for various substrates. Note that the efficiencydecreases for increasing substrate thickness, and is lower for higher E , .

Fig. 5.3 Contours of integration

The residue contributions at the poles give the surface-wave fields. A steepestdescent method may be used to find the far-zone radiation field, although a reciprocity method is simpler [2]. The Poynting vector from the far-zone radiation field may be integrated over a hemisphere to find the radiated power. This reduces to a one-dimensional numerical integration [2]. The surface-wave Poynting vector may be integrated over a large cylinder to find a closed-form expression for the power in a surface wave. The surface waves are orthogonal with each other and with the radiation field in the lossless case [3], so the total power is simply the sum of all the powers. The radiation efficiency is defined in the lossless case as

Fig. 5.4 Efficiency of HED versus substrate thickness for dipole on top of single substrate layer

The efficiency approaches 1.0 for thin substrates, but the radiated power of the dipole then becomes very low, as seen from Fig. 5.5. This points toward one of the practical limitations of using resonant-length dipoles on thin substrates, namely low input resistance. A patch antenna does not have this disadvantage since the resonant resistance is fairly independent of substrate thickness [4].

280

Microstrip dipoles

,& Tad

Microstrip dipoles

Normalized by 10 ' 1 1%

281

Another limitation of resonant-length dipoles on thin substrates is a very small bandwidth -much lower than that of a patch (this is discussed in Section 5.4.2). Because of these limitations, dipoles find best application for thicker substrates where bandwidth and resistance are no longer serious limitations, and where the patch antenna becomes non-resonant [5]. 5.2.3 Superstrate effects

It is interesting to note that a superstrate (cover) layer on top of a microstrip dipole may significantly influence the radiation properties. For example, if the substrate is thin enough, a superstrate layer may be used to eliminate surfacewave excitation, resulting in an efficiency of 100% [2]. An example of this is shown in Fig. 5.6 for a GaAs superstrate over a Teflon substrate. In a different application, a substrate-superstrate geometry may be used to produce 'radiation into the horizon', a phenomenon in which the far-zone radiation field

-E-PLANE

PATTERN

blXd

Fig.

Radiated power of HED (Watts) versus substrate thickness for unit-strength dipole on top of single substrate layer

Fig. 5.7 Radiation pattern of HED demonstrating the radiation into the horizon effect (Reproduced from Reference 6,@ 1985 IEEE) The dipole is embedded within a single substrate layer here

Fig. 5.6 Efficiency of HED versus superstrate thickness, showing 100% efficiency at tlL, = 0.233 (Reproduced from Reference, 2, @ 1984 IEEE) The dipole is at the interface (z, = b )

remains non-zero down to the layer surface. One result is the possibility of producing very nearly omnidirectional patterns [6].An example of this is shown in Fig. 5.7 for a dipole embedded within a single substrate layer of thickness b (or, equivalently, the superstrate material is the same as the substrate). A third application of a superstrate layer is in the production of high-gain patterns about any desired angle 0, in space. By using one or more superstrate layers of the proper thickness, narrow-beam patterns may be produced as the superstrate E , ~becomes large [7].An example of this for 0, = 45" is shown in

282

Microstrip dipoles

Microstrip dipoles

Fig. 5.8 using a superstrate with E,, = 100. This narrow-beam effect is produced by weakly attenuated leaky waves which exist on the structure [a]. All the above effects pertain to any type of microstrip element in a substratesuperstrate geometry. However, except for the first effect (increased efficiency), these methods all require electrically thick layers, making dipoles an attractive candidate.

283

domain piecewise-sinusoidal basis functions of the form Bky)

= J,

= ~ 0 1 5(x) )

lyl < w / 2

(5.8)

1x1 < d where

E-PIANE PATTERN

Fig. 5.8 Radiation pattern of HED demonstrating the high-gain effect (Reproduced from Reference 7, @ 1985 IEEE) The dipole is embedded within the substrate with a superstrate layer on top

5.3 Moment-method techniques for planar strip geometries The analysis of geometries comprising dipoles and transmission lines involves strips which are usually narrow compared to a wavelength ( w 4 4). The geometry of a strip is shown in Fig. 5.9. Because the strip is narrow, current may be assumed in the f direction only. The narrow-strip assumption also allows for certain techniques to improve the computational efficiency of the analysis. In this Section methods for analysing strip structures are discussed. 5.3.1 Basis Functions For the moment-method solution of strip geometries, including dipoles and transmission lines, the current on the strips may be represented using sub-

Fig. 5.9 Planar strip in a layered geometry, divided into subsections. Also shown is the basis function variation in x

Three useful choices for the transverse variation are the pulse function, the modified Maxwell function [9] and the Maxwell function:

284

Microstrip dipoles

The normalisation constants here are chosen to give a unit current at x = 0. The Maxwell function more closely represents the true current on a narrow strip. The modified Maxwell function is similar to the Maxwell function except near the edges. Because it lacks the singular behaviour at the edges, the Fourier transform of the modified Maxwell function decays faster for large values of the transform variable, which makes it computationally more efficient for spectraldomain analysis techniques. 5.3.2 Reaction between basis functions The fundamental step in a Galerkin moment-method solution of strip problems is the computation of reaction between two basis functions:

Microstrip dipoles

285

5.3.3 Plane-wave spectrum method Two distinct methods have been used in the literature for the calculation of reaction: the Fourier transform (plane-wave spectrum) method and the realspace integration technique. In the spectral method, eqns. 5.1 and 5.2 are first transformed into rectangular (Fourier) transform form, and substituted into eqns. 5.12 - 5.14. The resulting integrations in x, y, x', y' result in Fourier transforms of the current [10,1I]. The result is

- z:

(I,, A,) cos &A,) cos

(44) d1d4

(5.15)

where

with and with S, and S, the basis-function surfaces. G,, is the f f component of the dyadic Green's function for E,(x, y, 2,) due to a source at x', y', z,. This is given by

a2n + 2. a2n + -+ ax axa~

ag A1 az h(1, z,, z,) = -

G,, = k Z n x

If more than one strip is involved in the problem under consideration, it is convenient to choose the x-axis offset between strips as an integral multiple of the subsection length d, so that the impedance submatrices will all be Toeplitz. Depending on the particular problem, d is typically in the range 0.01 A, < d < 0.05 A,. In this case 5(x) is close to a piecewise linear function, and the value of k, in eqn. 5.8 is not critical. The choice of transverse distribution ~ ( y has ) some influence in the reaction values obtained, especially for the self-term (no offset between basis functions). Experience has shown, however, that the current amplitudes, obtained from the moment-method matrix solution, are fairly independent of the choice of qb). For the solution of the strip problems, the starting point is the calculation of arrays Z,(m) where the mth element is reaction between basis functions separated by (m-l)d between centres in the %direction. The index i refers to the particular submatrix in the Galerkin impedance matrix, corresponding to basis functions on different strips. The y-directed offset may be different for each submatrix if the strips have transverse offset. z, and z, may be different for each submatrix as well.

The separation between basis-function centres is denoted as Ax, Ay here. For the basis function choices (eqns. 5.9 - 5.1 1) the transforms may be evaluated in closed form [lo]. The integral on (0, co) in eqn. 5.15 is along the Sommerfeld contour C in Fig. 5.3. A pole-extraction technique may be used to account for the poles on the real axis [I 11. A simpler way is just to deform the contour to go around the poles as shown by contour C, in Fig. 5.3 [12]. An advantage of the spectral approach is that self-term problems are avoided. However, the convergence of the Sommerfeld integral in eqn. 5.15 becomes worse as the separations Ax, Ay become large compared to the respective basis function dimensions, for the case z, = z,. This is because the functions f and h tend to constants as 1 + co in this case, resulting in a rapidly oscillating, slowly converging integral. For z, f z,, as is possible for the reaction between currents on different strips, the termsf and h decay exponentially in 1, and there is relatively little trouble for most values of Ax, Ay. T o speed up the computation for the case z, = z, = z, several numerical techniques may be employed. The first is the use of a Filon integration method to account for the oscillatory cosine terms [13]. A second technique is to subtract from the integrand a limiting-beha.viour term with constantsflco, z , z), h(co, z, z), so that the integral converges much faster. The integral of the extracted term may be evaluated by identifying

286

Microstrip dipoles

it as the reaction between currents in a grounded homogeneous half-space of effective wave number k, [14]. This reaction may be evaluated using a free-space Green's function with a real-space integration. In this case the pulse choice of q b ) (eqn. 5.9) is most convenient, since the resulting real-space reaction integral reduces to a one-dimensional integral [14]. Another type of extraction may be employed for the case z = z, = z, when z is sufficiently far from a layer boundary, as for a strip embedded within a layer. In this case, a term corresponding to the incident field in a grounded homogeneous space of wave number k, is extracted [15], where k, is the wave number of the layer. The resulting integrand then decays exponentially. The reaction in the grounded homogeneous half-space is computed as before. This extraction fails for a strip at the interface of different media, and is therefore of more limited use than the first type of extraction. Another method for improving the convergence of eqn. 5.15 is to asymptotically approximate the transform Jxfor large 2 in a sufficiently simple form so that the tail integral over ( A , co) may be performed analytically, for some large number A. This is the most straightforward technique, but the tail integral must be reformulated for each specific choice of qb). Finally, as an alternative to trying to accelerate the convergence of eqn. 5.15 for large separation between basis functions, the reaction may be computed by a different technique, as discussed in Sections 5.3.4 and 5.3.5. 5.3.4 Real-space integration method

The reaction Z,, may also be computed by integrating the electric field directly in the spatial variables. To avoid a prohibitive amount of calculation, a 6-function testing procedure is used at the strip centre instead of a Galerkin method, so that impedance elements are defined as

A technique due to Katehi and Alexopoulos [16,17] computes this impedance term by directly applying the electric-field operator (eqn. 5.14) to the Sommerfeld form of potentials (eqns. 5.1 and 5.2). An integration by parts is used to shift the derivatives to the current function J,, (x', y'), and various algebraic manipulations are employed, including an analytical tail integral evaluation. The resulting expression involves a single Sommerfeld-type integral of a rapidly converging series. This formulation does not suffer from convergence difficulties to the same degree that eqn. 5.15 does. Although a comprehensive comparison of computational efficiency has not been performed, it is felt that the real-space method is somewhat comparable to the spectral method when one of the accelerating techniques mentioned previously is used. Both methods have been used to generate the results of this Chaptei.

Microstrip dipoles

287

5.3.5 Point-dipole approximation The reaction between widely separated basis functions may often need to be computed, especially for mutual-impedance problems. In this case, the most efficient technique is to approximate the currents as point dipoles located at the basis-function centres. Computing reaction is then equivalent to finding the Ex field of an I-directed point source, which may be obtained efficiently. One way to perform this calculation is by directly applying the electric-field operator (eqn. 5.14) to eqns. 5.1 and 5.2. It is well known that the resulting Sommerfeld integrals are nonconvergent when z = z', however, and therefore cannot be evaluated directly. One technique for overcoming this difficulty is to extract terms from the integrand to give convergence [18]. Another way is to extend the integration contour to ( - co, + co) and deform around the branch cut, as described in Section 5.2.1. The numerical integration around the branch cut converges very rapidly for large radial separation @ between dipoles, owing to the exponmtia! decay of the Hankel functions in eqns. 5.5 and 5.6 along the imaginary axis. For separations larger than 0.25& this is usually the most efficient of the two methods.

5.3.6 Moment-method equations Consider an arbitrary set of x-directed strips having a 1V &gap voltage source at some point on one of the strips. Let the basis functions be numbered 1, ...N with the source at the centre of basis-function numbers, at x = x,. The current representation is then

with BJx, y) = B(x - x,, y - y,). Because q k ) in eqns. 5.9 - 5.11 is normalised, I,, represents the current in amperes at x = x,. Enforcing Ex = 6 (x - x,) on the strips by applying Galerkin's method using eqn. 5.17 results in the set of equations

which is then solved to find the currents on the strips. 5.4 Centre-fed dipoles

5.4.1 Single dipole The analysis described in Section 5.3.6 may be applied to find the current distribution for a centre-fed dipole, shown in Fig. 5.10. A variational expression for the input impedance is [I91

288

Microstrip dipoles

Z,

=

-

1

- j3Js, 4;

Microstrip dipoles CENTER

J,(i) G, (i,7 )Jr(?') dsds' .

-

289

FED DIPOLES

w = .05

LO

Using eqn. 5.17 this reduces to

z,

=

I -xz 1; ,""

4--

I I

mn

PATCH RESONATOR WITH Er= 2.45

"

/

\

\

which, in view of eqn. 5.18, reduces further to simply Z,"

Fig. 5.10

=

1 I",

-.

Centre-fed strip dipole

This simple formula for input impedance is thus accurate to second order owing to the relation between Galerkin's method and the variational method [20]. From input impedance, the resonant length and bandwidth may be determined. Approximate formulas for resonant dipoles may also be used [lo]. A dipole on a substrate layer has a resonant length

provided h 9 w and w 4 1,. At resonance the resistance is Fig. 5.11

where P, is the total power (watts) produced by a unit-strength point dipole on the substrate. Owing to the behavior of P, (see Fig. 5.5) R, is very small for thin substrates.

Bandwidth (%) of centre-fed dipole versus substrate thickness for two different substrates. The dashed lines indicate that no frequency is found for which X , = 0. In this case f, was chosen to minimise )Xj,,I, with X , (f,) then subtracted from all values. A patch resonator is shown for comparison for h l l , < 0.1

290

Microstrip dipoles

Microstrip dipoles

29 1

The substrate thickness has a dominant effect on bandwidth. The bandwidth for different substrates with a dipole width of 0.05 1, is shown in Fig. 5.11. Here the bandwidth is defined as

Fig. 5.12a

Real part of the input impedance of a centre-fed strip dipole with e, = 2.45 and h = 0.21,

with f, the resonant frequency ( X , = 0) and f,, f, the frequencies at which SWR = 2.0 on a feed line having a match at fa.The maximum bandwidth occurs for h/& z 0.30, and increases for larger E , . For substrates thinner than this, the bandwidth is relatively independent of E, for a given physical thickness h/&. For comparison, the bandwidth of a microstrip patch resonator is shown for the E, = 2.45 case. The patch has a much higher bandwidth for thin substrates, a conclusion reached previously by Pozar [5]. The effect of dipole width is seen in Figs. 5.12a, and b for a substrate with E, = 245. The resonant input resistance is insensitive to width, as is the resonant length. The slope dXi,,/dL a t f , is lower for wider dipoles, indicating a greater bandwidth. However, the slope is not extremely sensitive to width. Only when the substrate becomes thin does the width have a dramatic effect on bandwidth, owing to the cavity-resonator effect. 5.4.2 Mutual impedance

Mutual impedance between centre-fed dipoles may be calculated in different ways. In the moment method, dipole no. 1 is excited with no. 2 short-circuited. After solving eqn. 5.18 for the currents, the formula [lo] Xln

(Ohms) 800

.

- - 0.0002 w

1,

with may be employed. Alternatively, the classical reciprocity formula [21]

Fig. 5.1 2b

Imaginary part of the input impedance of a centre-fed strip dipole with e, = 2.45 and h = 0.2 1,

-1 Z,, = Jx2 ds Il(O)I*(0) J-s2 may be used, with piecewise-sinusoidal currents assumed on the dipoles. The reaction may be evaluated using eqn. 5.15. For narrow strips, the dipoles may be assumed filamentary and the integral (eqn. 5.26) evaluated directly using the real-space technique, or by using the point-dipole approximation to find Ex (Section 5.3.5). Results for filamentary dipoles obtained in this way are shown in Figs. 5.13a,b for broadside and endfire dipoles on a substrate with E, = 10. The slow decay of Z12in the endfire case is due to the dominant TMo mode, which is strongest at 4 = 0 [22].

292

Microstrip dipoles

Microstrip dipoles

2.0

I

(Ohms)

1.5

1.5

1.0 (Ohms)

1.0

.5

.5

0 0

-. 5

-.5

I

I

0

0.2

I

0.4

I

0.6

I

I

I

I

I

I

0.8

1.0

1.2

1.4

1.6

1.8

s IX, Y

Fig. 5.1 3a

Mutual impedance versus separation for resonant-length filamentary dipoles in broadside configuration with E, = 10.0 (Reproduced from Reference 10, @ 1986 IEEE)

-1.0

Fig. 5.13b Mutual impedance versus separation for resonant-length filamentay dipoles in endfire configuration with 8, = 10.0 (Reproduced from Reference 10, @ 1986 IEEE)

294

Microstrip dipoles

Microstrip dipoles

295

5.5 EMC Dipoles

5.5.1 Methods of analysis Fig. 5.14 shows several ways in which one or more dipoles may be electromagnetically coupled to a transmission line. In each case the analysis involves a moment-method solution together with simple transmission-line theory [23]. The transmission line is assumed close to the ground plane, so that a TEM-like field propagates on the line. A 6-gap source is taken near the end of the line farthest from the coupled end. The exact location is not critical. The source sets up a standing-wave current on the line which is essentially a sinusoidal current, except within a small region near the coupled end where the current is perturbed by the dipoles. Away from this coupling region, the line may be regarded as terminated by a equivalent self-impedance Z, = R, + j X, at some arbitrary value of x, where

with r(x)

Top v i e w

=

SWR - 1 e+,28(" SWR + 1

- X,,")

In eqn. 5.28 x,, is the position of a minimum and is the propagation constant on the line, which may be determined from the distance between current minima on an isolated line or by separate analysis [9,10]. In this formulation only the reaction between piecewise-sinusoidal-basis functions is required. An alternative formulation using traveling-wave-basis functions on the line may also be developed [24]. An advantage of this latter formulation is the use of fewer unknowns for the line current, although it requires different types of basis functions. For the results of this Chapter, only piecewise-sinusoidal basis functions were used.

Top v i e w Fig. 5.14

Various configurations of dipoles electromagnetically coupled to a microstrip line

5.5.2 Single dipole A single EMC dipole can be either overcoupled, matched, or undercoupled according to the amount of coupling to the feed line (Fig. 5.15). Of all the possible parameters which affect the coupling, the most critical is the distance t between the line and dipole. If t is too large, then no choice of dipole length or offset will yield an input match, and the dipole is said to be undercoupled. If the line is sufficiently close to the dipole, an input match may be achieved by varying the dipole length and either the longitudinal (x-axis) or transverse (y-axis) offset, or both. The dipole is then said to be overcoupled. In this case the locus of points for the centre of the matched dipole is somewhat elliptical in shape, roughly centered about the end of the line [25]. For a given substrate, this implies a maximum distance t,,, for which an input match may be achieved,

296

Microstrip dipoles

Microstrip dipoles

297

where the locus collapses to a single point [25]. In this case the dipole may be said to be critically coupled. Figs. 5.16 and 5.17 show how an input match may be achieved for the overcoupled case by varying either the longitudinal or transverse offset, respectively, for E, = e,, = E,, = 2.35. ~

-

-

-

matched

undercoupled overcoupled

Fig. 5.1 5

Current amplitude on the strip dipole ( I , ) andmicrostrip line (I,) (Reproducedfrom Reference 2 3 @ 1984 IEEE) 1; is the incident current amplitude. The three cases correspond to h = 0.079& (overcoupled) (matched), h = 0.084A0(undercoupled), and h = 0,070d,,

Fig. 5.17 Z,/Z, as a function of dipole length L, and transverse offset (Reproduced from Reference 23, @ 1984 IEEE The longitudinal offset is 50% of the dipole length. The impedance reference plane is at the position of a current maximum on the line Fig. 5.16

Z,/Z, as a function of dipole length L, and longitudinal offset (Reproduced from Reference 2 3 @ 1984 IEEE) Offset is measured by percent overlap as KO, = (AXIL,) x 100. The impedance refaranre nlana is at the nnsitinn nf a cllrrant maxirn~~rn nn the linn

298

Microstrip dipoles

Microstrip dipoles

299

The bandwidth of an EMC dipole is almost identical to that of a centre-fed dipole on the same substrate, provided the EMC dipole is matched. Hence, it is desirable to keep the dipole significantly above the ground plane to obtain a reasonable bandwidth. On the other hand, it is also desirable to keep the line as close as possible to the ground plane, to minimise line radiation. However, for a given substrate thickness h l l , corresponding to a prescribed bandwidth, the line height should be chosen so that b > h - t,, to avoid being undercoupled, which will reduce bandwidth. Hence, the height b = h - t,,, is a good trade-off between bandwidth and line radiation. An improved coupling may be achieved by using a top layer with E, > E , between the line and dipole. This improves coupling by increasing the capacitance in between [lo]. However, a more pronounced improvement is possible by using multiple dipoles.

53.3 Miiliipk d&i'~~ The bandwidthlline-radiation trade-off may be improved by using multiple dipoles. A dominant theme in these schemes is the introduction of additional capacitance between the line and the main radiating dipole. This is usually accomplished by placing one or two coupling dipoles (parasitics) either in a stacked fashion between the line and top dipole (Fig. 5.146) or coplanar to, and near the end of, the line (Fig. 5.14~)[26]. For the stacked configuration, the bandwidth for SWR < 2.0 is shown plotted against t p / t in Fig. 5.18 for two different values of h (3 mm and 4.5 mm) with corresponding dipole lengths of 8.4mm and 8.7mm, respectively, at a frequency of 10 GHz. These lengths are close to the input-match values for a single EMC dipole. The transmission-line height b is constant a t 0.72 mm. Also shown is the minimum achieved SWR as the frequency is varied for each value of t,. From this Figure it can be seen that the thinner substrate has a lower optimum bandwidth. Also, 'as the substrate thickness changes from 3 mm to 4.5 mm the range of tpfor SWR < 2.0 becomes smaller and shifts toward higher values. Therefore, like the case of a single dipole, there is a maximum value h,, such that, for h > h,,, the SWR is always larger than 2.0 for this value of b. The addition of another dipole between the top dipole and line may further reduce the SWR and increase the bandwidth in this case. When the parasitics are on the same level with'the line and of comparable length to the radiating dipole, the bandwidth may be improved as shown in Fig. 5.19. Appropriate positioning of the parasitics may improve the bandwidth even more. An advantage of this configuration is possibly fewer alignment difficulties during fabrication. However, the improvement in bandwidthlline-radiation is much more dramatic for the case of stacked dipoles.

.

300

Microstrip dipoles

Microstrip dipoles

30 1

5.6 Finite array of EMC dipoles

5.6.1 Analysis A finite array of EMC dipoles IS shown in Fig. 5.20. Away from the coupled ends, the current o n the mth line may be written as the sum of incident and backward waves, of the form J,,(x,y) =

Jh,(x,y )

=

4,?Cv)e-'P' t,vb)e+'"'

SIDE-VIEW

Fig. 5.20 Finite array of EMC dipoles

(5.29)

OF ELEMENT #n

302

Microstrip dipoles

Microstrip dipoles

with x = 0 at the line end. The current on the mth dipole may be assumed sinusoidal as J;(x, Y) = I , d ? ( ~ ) m )

(5.30)

303

To calculate B, and D m ,dipole n may be excited with a &gap source (line n may be absent), with line-dipole pair m passive. Then

Here .,

7.1.1.3 Moments-method analysis: Recently we have studied a wide-bandwidth flat dipole, fed through the gap by means of a Lecher line which is located on a thin printed circuit parallel to a reflector plane and isolated by a sheet of air (Fig. 7.10). The general scattering problem of an arbitrary shaped tri-dimensional antenna solved by the moments method and the finite-difference approach applied to integral equations has explained the antenna behaviour. The wire-grid model is suitable for expressing the boundary conditions along the various edges of the antenna, which are, in fact, the boundary conditions on the thin wire surfaces. The antenna is equivalent to an array of conducting square

Fig. 7.11 Average surface-current vector distribution

distribution, which corresponds to the average surface current vector for each mesh. The length vector is proportional to the current amplitude. In Fig. 7.12 we present the theoretical and experimental input impedance related to the

366

Wideband flat dipole and short-circuit microstrip

Wideband flat dipole and short-circuit microstrip

367

middle of the gap in terms of frequency (GHz). The impedance is normalised to IOOQ, which is the Lecher-line characteristic resistance.: Table 7.2 gives the parameters used in Fig. 7.12 (in mm)..

Fig. 7.12

Theoretical ( 1 ) and experimental (2) input impedance of the large bandwidth flat folded dipole in terms of frequency (GHz) 1 = 100R

7.1.2 Array designs. Losses and eficiencies

A number of flat arrays with several hundred or more flat dipoles have been designed and constructed. In every array each source radiates through a window cut in one of the two metallic shields of the stripline feeding network (Fig. 7.2). 7.1.2.1 Large gain: Fig. 7.13 shows an array of 1024 radiating sources operating between 11.7 and 12.4GHz with a measured isotropic linear maximum gain of 37dB [20]. This high-gain array has been designed to receive radio-broadcasting signals sent out by geostationary satellites. It is composed of 1024 (32 x 32) flat dipoles (section 7.1.1.1) fed by a stripline network (Fig. 7.14). Like the elementary source, the array is constructed using two large compressed printed-circuit sheets with no direct connection between the feed network and the radiating sources. The symmetrical feed network comprises unequal stripline power splitters joined by stripline transmission lines, the

368

Wideband flat dipole a n d short-circuit microstrip

characteristic impedance of which is 7 5 0 . The distance between two adjacent where >., is the wavelength in air a t the mean frequency sources is 0.89 i,,, ( 12. I GHz). The square array of a 0.5 m' area was manufactured using two printed-circuit sheets ( E , = 2.1 7) I .6 mm thick. Circular polarisation is produced by a polariser embedded in a radome. Fig. 7.16 shows an exanlple of the measured patterns in one diagonal plane at 12.1 GHz. Between 11.7 and 13.5GHz the experimental maximum linear isotropic gain was equal to 36.9 F 0.3 dB, and the efficiency is better than 48% between I 1.7 and 12.4 GHz.

Wideband flat dipole and short-circuit microstrip

369

0.85 x 0-40 x 0 4 5 m . The linear isotropic maximum measured gain a t 5.25 GHz is 26.5 dB. the efficiency is about 40% and the measured sidelobe level is lower ~ h a n- 29 dB for a theoretical level of - 39 dB. Fig. 7.17 shows an example of radiation patterns in E- and H-planes at 5.25GHz for an array covered with a radome. The second array [23] (Fig. 7.18) is incorporated in a

Fig. 7.13 High-gainarray (11.7- 12.4GHIj offlatfoldeddipole.

The feeding arrangement is shown in Fig. 7.14 and the feeder dielectric a n d metallic losses are equal to 2.5 dB. The cross-polarisation level o n the axis is lower than -30dB, and, together with the polariser, the measured array ellipticity ratio along the principal axis is better than I.5dB over the frequency range. Fig. 7.15 shows the radiation patterns in E- and H-planes measured a t 12.1 GHz. 7.1.2.2 Low sidelohe level: Two passive arrays with flat dipoles showed a sidelobe level lower than - 30dB. The first array [21, 221 operates between 5.25 and 5.45 GHz in a system used to detect natural resources, and is carried o n a n aircraft. It is composed of 128 symmetrical flat dipoles which are fed by lines a n d splitters realised using stripline technique by means of two printed-circuit sheets, as has been shown for the high-gain array (Fig. 7.14); the dimensions a r e

Fig. 7.14 High-gain array (7 1.7 - 12.4GHz): feeding arrangements

Table 7.3 Measured values for the array in Fig. 7.18 9.6 9.3 f, G H z 9.1

9.9

31.3 31.9 2'30' 2'40' < - 36 < -30

10.1 31.4 2'30' < -29

26.9 Max. gain, d b 30.9 2'35' 3dBbeamwidth,deg(H-plane) 2'40' First sidelobe, dB (H-plane) < - 28 < -28 The efficiency at 9.6 GHz is equal to 33.3% (or - 4.78 dB). The cross-polar~sationlevel is lower than - 35 dB.

system used o n ground-surveillance radars. It is composed of 512 flat dipoles, it uses stripline technology and features low sidelobe radiation: it operates between 9.4 and 10.1 GHz. The distance between two adjacent sources equals

370

Wideband flat dipole and short-circuit microstrip

Wideband flat dipole and short-circuit microstrip

371

Fig. 7.16 Large-gain array (see Figs. 7.13 and 7.14) (Reference 2 0 ) Pattern in a diagonal plane at 12.1 GHz

-

e (DEGREES)

Fig. 7.17 Low-side lobe-level array. Patterns in E- and H-planes at 5.25 GHz

Fig. 7.15 Patterns at 12.1 GHz. Large gain array (see Figs. 7.13 and 7.14) (From Reference

A

e (DEGREES)

372

Wideband flat dipole and short-circuit microstrip

0.9 E., in the H-plane and 0.8 E,, in the E-plane. Some measured values are given in Table 7.3. 7.1.2.3 Vuriable r/irc.ctiiities: A flat array with four fixed beams of different directivities and gains is considered [24]. This array supports 256 flat dipoles separated by a distance of 0.85 /., together with 60 electronic switches, integrated in a stripline structure (Fig. 7.19). The global efficiency is about 50%. For each and difference (A) patterns in the two of the four states we can form sum

(z)

Wideband flat dipole and short-circuit microstrip

airborne communication systems, electronic warfare systems or ECM. We show [25]cylindrically shaped radiating elements working in octave bandwidth (Fig. 7.21). In azimuth, the theoretical angular-sector coverage can be equal to 360'. In the different meridian planes or site planes, the beamwidth and sidelobe level may be of any proportion. The antnenna consists of radiating elements arranged in vertical arrays photo-etched on a printed circuit which is wrapped around a cylindrical dielectric lens of 2a diameter. Each radiating element is a flat dipole, used as a folded slot dipole symmetrically fed. When the substrate has air as the

Fig. 7.19

Fig. 7.18 Low-side lobe-level array of flat folded dipoles (9.4 - 10.1 GHz)

orthogonal principal planes of the array. which acts between 11.7 and 12.4GHz. Fig. 7.20 shows the ratio A / x for each of the four states in terms of the deviation angle 8. The various beamwidths obtained at the mean frequency are 4"3', 7'7', 12'6' and 27', and the cross-polarisation level is always lower than - 25 dB. The efficiency is given by the formula q% = 100 1'G,w/4ns, where s is the geometrical area (0.12 m2)and G,, is the maximum isotropic linear gain. With a measured value GM = 31 dB. we obtained y = 50%. For each of the four states the mean switching losses are about 1.6dB. 7.1.2.4 Very large bunrtwidrh: This section discusses broad-angular-coverage and wide-bandwidth antennas, which are increasingly used, for example in

373

Multiple-beam flat array ( 1 1.7 - 12.4GHIJ

medium and if the thickness is increased, the flat dipole acts over wide bandwidth (sction 7.1.1.3). Thus, when it is fed symmetrically with a Lecher line, the operating range covers one octave. Each array, which is aligned along a generating line of the cylindrical lens, can be considered as a separate channel. In a plane perpendicular to the axis the antenna acts as a Luneberg lens. In effect, the n constant-index-of-refraction surfaces are cylinders of radius r such that n ( r ) = [2 - ( r / ~ ) * ] "The ~ . dielectric lens was machined from a cylindrical Teflon rod. It has longitudinal grooves which are uniformly distributed around the lens axis and which are small compared with the vacuum wavelength [26]. In the meridian section of the lens, which contains one array the optical path is deduced, by means of integration, from the continuous refraction law. Applying an asymptotic development of the Kottler formula, the radiated far field is calculated from the electromagnetic field distribution along the lens outside surface, as has been done previously, but for a small bandwidth using shortcircuited flat dipoles at quarter-wave resonance [27, 281. The antenna is composed of 64 folded flat dipoles arranged in eight vertical

374

Wideband flat dipole and short-circuit microstrip

Wideband flat dipole and short-circuit microstrip

arrays, and it acts in the 8 - 16 GHz range. The diameter of the cylindrical lens is equal to 86mm. The beamwidth in the frequency range lies between 24" and 10" in the azimuth plane, and between IS0 and 7" in the site planes. Whatever the azimuth direction, the minimum isotropic linear gain which can be expected over an angular coverage of 1lo0, and in the 8 - 16 GHz frequency range, is 18 dB. The maximum isotropic linear measured gain G,(dB) is compared with the theoretical maximum directivity D,(dB) in Fig. 7.22. The impedance matching of each array is given in Fig. 7.23. Fig. 7.24 shows the measured ratio A / C between difference (A) and sum patterns expressed on a linear scale.

(I)

Fig. Fig. 7.20 Ratio A / C of sum (CI and difference (A) patterns for the four states (F, to 12.7 GHz (see Fig. 7.19)

F,)

wad-angular-coverage and wide-bandwidth antenna

at

7.2 Short-circuit microstrip patches and arrays 7.2.1 Elementary source

Self impedance and bandwidth: Fig. 7.25 shows the half short-circuited patch configuration. It looks like a half short-circuited flat dipole acting at a quarterwave resonance. The relation between radiation conductance G, and Go can be determined from [29] Fig. 7.22 Maximum measured gain GM and maximum directivity DM

376

Wideband flat dipole and short-circuit microstrip

Wideband flat dipole and short-circuit microstrip

Eqn. 7.11 expresses the development of the input impedance of a lossy shortcircuited line whose length is assumed equal to H' = H + h. The losses comprise the radiation resistance of the patch. The main problem lies in determining the line attenuation constant. In order to do this, the radiation resistance of the half short-circuited patch, parallel to the perfect reflector plane, is identified with that of a loop constituted by the half short-circuited dipole and its electrical image in relation to the reflector plane [3]. When finite conductivity a and lossy dielectric substrate are taken into account, as has been done for the opened flat dipole acting at half-wave resonance (Patch) [30], the input conductance G, is given as follows:

377

r

r -20 degrees

-10

0 10 20 degrees

F= 8 GHz 0.05fdegree

o$ ; -

degrees

(I)

patterns in terms of Fig. 7.24 Measured ratio A / x between difference ( A ) and sum frequency. Broad-angular-coverage and large bandwidth antenna

shorting pins or electric wall

Fig. 7.23 Broad-angular-coverage and wide-bandwidth antenna Impedance matching of each array

where d, (nfha)-'I2 is the skin depth, 6 is the dielectric loss angle, 1, = and Go = ( ~ ~ / p ~ ) " ~ The bandwidth B% related to VSWR is given by

-

Lastly, the radiating source efficiency at resonance is given by

_I

The quarter-wave resonance condiction is h

+ H 1. 114.

sub;trate (E,) Fig. 7.25 Half short-circuitedmicrostrip antenna configuration

378

Wideband flat dipole and short-circuit microstrip

Mutual impedance and coupling: Explicit formulas are presented for the mutual impedance and coupling between two parallel or co-linear shortcircuited flat dipoles at resonance in air medium in terms of three dimensions with respect to wavelength [31]. Experimental and theoretical results are in good agreement and show that these small microstrip antennas are particularly well uncoupled, and therefore suitable for incorporation in a phased array with a steering beam inside a large angular sector. Thus, for the following values (Fig. 7.25):

Wideband flat dipole and short-circuit microstrip

379

Feedthrough is used to excite each radiating element from the output of the associated phase shifter by means of a short coaxial line. This 3 bit digital phase shifter was recently described [34]. A total of only eight PIN diodes is required

the coupling factor in t h e E- and H-planes is lower than - 20dB between short-circuited flat dipoles separated by a distance 0.5 i,. Radiatedfields andpolarisation: The far field radiated by this source has been calculated [32j. With the w m e notation as in Fig. 7.25 we ~btaincd: The Normalised electric field in the E-plane (4 = 0)

The normalised electric field in the H-plane (0 = n/2)

7.2.2 Array designs These short-circuited patches acting at a quarter-wave resonance (section 7.2.1) have been used in several arrays. 7.2.2.1 Phased array with steering beam: Eflect of mutual coupling: This section concerns a Ku-band phased array acting in a large angular [33] at around 15 GHz. The array has 64 short-circuited patches in air medium, located on a 8 x 8 square lattice. The element spacing is lOmm (0.5 A,), such that the coupling coefficient in the E- and H-planes is lower than - 20 dB. The measured results on each radiating element at around 15 GHz are as follows: Bandwidth for a VSWR < 2: 17% Pattern in E-plane: 1dB in an angular sector of 160" Beamwidth in H-plane at 3 dB:80°

+

Fig. 7.26 3bit digitalphase shifter with eight PIN diodes in Ku band

for the whole phase shifter (Fig. 7.26) instead of ten for a conventional type. It is arranged in such a way that no series capacitance is necessary to separate the different bias [35]. So only three wires are used to apply the DC bias to the eight PIN diodes. For each of the eight states, the phase-shifter insertion losses is equal to 3 i I dB in a bandwidth of 15% at about ISGHz. The 64 phase shifters are photo-etched on four fused-quartz substrate plates each of 5.08 x 5.08 cm (Fig. 7.27). So for every deflected beam we can form sum and difference patterns. The feeding structure, which is composed of splitters,

380

Wideband flat dipole and short-c~rcuitmicrostrip

Wideband flat dipole and short-circuit microstrip

branch lines, corporate feeds and DC bias. is also photoetched according to a microstrip technique. Four plugs are connected by pliant and thin conductors to the etched wires for DC bias feeding. The square feeding R F network is divided into four parts. The adjacents parts are deduced from each other by rotation symmetry (RS) so that the four outputs 1 , 2 , 3 . 4 are located on the four array sides (Figs. 7.29 and 7.27). This rotation symmetry is only related to the four parts of the square feed R F network, and does not concern the short-

Fig. 7.28

Phased array with steering beam i n Ku band; 6 4 radiating sources

Fig. 7.27 Phased array with steering beam i n Ku band: 6 4 3 b i t digital phase shifters and feeding arrangements

circuited radiating dipoles which are linearly polarised (Fig. 7.28). The parasitic signals at the input of the four quadrants, which are due to the radiating-dipole aerial alternately coupling in the E o r H planes, are out of phase. This concept

Fig. 7.29 Square feeding network (From Reference 3 6 ) S: output towards source ?:source electrical moment

381

382

Wideband flat dipole and short- circuit microstrip

Wideband flat dipole and short-circuit microstrip

[36] has advantages as compared with an axial-symmetry network (AS). For instance, in Fig. 7.30 we show the theoretical sum patterns in the H-plane deflected by 45' and related to (RS) and (AS). Furthermore, because of the compensation of aerial mutual coupling, the risk of scan blindness is reduced when the (RS) concept is used. Fig. 7.31 shows measured sum gains in the E, H or diagonal planes and Fig. 7.32 shows the ratio A / C between the difference and sum patterns for different deflection angles a. The measured efficiency q% is

383

8 (degrees) -60

-3 0

0

30

60

8 (degrees) Fig. 7.30

Deflected sum patterns in H-plane at f = 15GHz (From reference 36)

-(RS) - - - (AS)

deduced from the following expressions:

Fig. 7.31

Measured sum gains G ( d 8 ) for different deflection angles or (degrees)

G , is the measured maximum isotropic linear gain (dB) and A is the antenna geometrical area. In conclusion, major advances have been made in lowering side-lobe level [36], in the reduction of phase-shifter complexity [35] as well as in the manufacturing procedures developed for building the array. 7.2.2.2 Omnidirectional radiation array for a mobile telecommunication station: This section discusses a very flat antenna with circular or elliptical polarised directional radiation over a large conical angular sector, and linear omnidirectional radiation in the reflector plane [37,38]. It can be advantageously used for communication between mobile stations. The antenna comprises four short-circuited half dipoles (section 7.2.1) acting at quarter-wavelength resonance and fed in phase quadrature (Fig. 7.33 a and b). The ends of the four short-circuited half dipoles (1, 2, 3, 4) are screwed (7) on the edges of a cavity

AIC between

Fig. 7.32 measured ratio deflection angles a 1 : E-plane 7. U-nlann

difference (A) and sum

(u

patterns for different

384

Wideband flat dipole and short- circuit rnicrostrip

Wideband flat dipole and short-circuit rnicrostrip b

,

tw

Fig. 7.33 Omnidirectional radiation array configuration

Fig. 7.34 Linear directivity in E-plane (f = 1.2GHz) 11 ): , GTD ( 2 ) : GO ( 3 ) : Measurements ( m m ) 2h = 115/W = 5 0 / H = 7,5/e = 1.6 \

-I

1 I

386

Wideband flat dipole and short-circuit microstrip

in air medium (6). A printed circuit (8) of thickness e supports, on one face, the four half dipoles and, on the other face, the feed microstrip lines (lo), with quarter-wave transformers (9) which are connected to coaxial lines (1 I). The four quarter-wave-transformer ends are joined and short-circuited to the bottom of the cavity by 12. Another feed concept is possible (Fig. 7.33 c) by which the feed-point location is chosen to match the radiation resistance of the coaxial line. With the following dimensions (in mm): 2h = 115, W = 50, H = 7.5, e = 1.6,2 d = 300 (2 d is the dimension of the square reflector); the bandwidth is equal to 4.35% for mismatch losses lower than 0.5 dB, while the theoretical bandwidth given by eqn. 7.13, is equal to 4.3% for a VSWR < 2 and E, = 1. The mean frequency is equal to 1.2 GHz. Fig., 7.34 shows the linear directivity in the E-plane. The E-plane is the symmetrical plane related to the two opposite short-circuited half dipoles (Fig. 7.33 b ar cf which Ire !inear!y po!arised. Curve (!) gives the directivity when GTD on the reflector edges is taken into account. Fig. 7.35 shows the linear isotropic gain measured for different site angles 0, with horizontally or vertically polarised waves. We can see that the antenna is circularly polarised along its axis (0, = 0°), which is perpendicular to its plane, and quasi-linearly polarised in all directions (8, = 90") of the reflector plane. Another configuration is shown in Fig. 7.36. The antenna, which is vertically polarised with omnidirectional radiation, is composed of four short-circuited half-dipoles acting at quarter-wavelength resonance in air medium and fed in phase [39]. To match the radiation resistance of each half-dipole, a correct feed-point location along the symmetrical axis is found [40] and soldered to the central conductor of a coaxial line. The four coaxial lines are fed in parallel by means of a standard divider. A model was calculated and tested with the following parameters (in mm): 6, = 1, I = 40.5, W = 52, H = 2.6, h = 34.5, 2 d = 400. The measured resonance frequency was found to be 1.90GHz while the theoretical one (f, given by eqn. 7.17) is equal to 1.93 GHz.

f;' =

4ph'2~A'2 [h

Wideband flat dipole and short-circuit microstrip

387

7.2.2.3 Log-periodic array: This antennas is a microstrip travelling-wave antenna of large bandwidth [19,41,42,43]. The log-periodic array is composed of flat short-circuited half dipoles acting at quarter-wave resonance and fed in series by means of a high-characteristic-resistance microstrip line, R, (Fig. 7.38).

half short-circuited

cut AB Fig. 7.36

Vertically polarised antenna with omnidirectional radiation

+ H + 0.72H(W/H + 0.26)(W/H + 0.81)-'1

(7.17) The measured bandwidth for a VSWR of less than 2 is equal to 4.7% while the theoretical bandwidth, given by eqn. 7.13, is 4.62%. Fig. 7.37 shows the measured E-plane, co-polar and cross-polar gain patterns, and the theoretical one when diffraction corrections, obtained with GTD applied to the square reflector edges, are taken into account. Maximum isotropic linear directivity of 6.46dB occurs for 0 = 37", while the measured maximum gain of the antenna with its divider is equal to 54dB. For a constant angle 0 around the antenna, the measured radiated far field is practically constant, with variations of f l dB when 0 < 0 < 90'. The bandwidth can be improved when the height H is increased, and the maximum site directivity angle may be altered by when adjusted the I parameter. This model is particularly thin since H/1, is equal to 0.017.

8 (degrees) Fig. 7.37

Measured E-plane directivity pattern (copolar and cross-polar) 4 = n / 2 . O: variable E, = 1 , I = 40.5mm, W = 5 2 mm, H = 2.6 mmlh = 34.5mrn, 2d = 400 mm

Each half dipole has a large E-plane pattern and weak coupling, especially in the parallel position (H-plane), and so the log-periodic array can be used for a progressive wave, when a squinted beam in the H-plane and large pattern

388

Wideband flat dipole and short-circuit microstrip

-

coverage in the E-plane are suitable. Fig. 7.39 shows the geometrical parameters W,,,H,,.and /I,, for the half-dipole (D,,)of the nth order. acting at a quarter-wave (4hv%)-', where f;, is the reresonance in air medium with /I,, + H,, sonance frequency. The various radiating parts are located on one metallic face

Wideband flat dipole and short-circuit rnicrostrip

389

of a printed circuit (I). They are fed in series across a gap (G,,) by means of a stripline (M) etched on a second printed-circuit sheet (J). The classical logperiodic parameters are:

,

I,, being the distance along the stripline between the gaps (G,,) and (G, + ,) of (D,,) and (D,,, ,) separated by a distance 4+,. To limit the variation of the VSWR in the frequency band, it is necessary to increase the expansion parameter T. The distance I,, must be lower than As/2 to compensate for the various reflections appearing at each gap. The following parameters have been adopted: r = 0.95, a = 0.4, 4,/A, = 0.2, H,,/A, = 0.1, I,,/i, = 0.32, W,/1, = 0.166, R,,= 180R. With these parameters, a 50" 3 dB beamwidth and 45" deflected beam are calculated. With 50 radiating sources the antenna dimensions are 1.1 x 0.1 x 0.07m, which corresponds to a theoretical frequency band of 0.9 - 6GHz bounded by a VSWR < 2 and an efficiency of 95%. +

LA

cut AB

Fig. 7.39 Geometrical parameters of the log-periodic structure

Fig. 7.38 Log-periodic array of short-circuited patches ( 1 ) : Printed circuits and complete array (2): Cross-sect~on

The antenna performs well between 0.75 and 4.5 GHz. Fig. 7.40 shows the measured H-plane radiation patterns at three frequencies. The average values are 42" for the deflection angle and 50" for the 3dB beamwidth over all the experimental bandwidth.

390

Wideband flat dipole and short-circuit rnicrostrip

Wideband flat dipole and short-circuit microstrip

391

7.3 References I

2

3 4 5 6 7

g

9 0 . degrees

10

(A) 11 12 13 14 15 16 17 18 19 20 21 8 . degrees

22 23

Fig. 7.40 A Measured H-plane directivity patterns a t 4.5 GHz

B

Measured H-plane directivity patterns

-.-.-

Copolar at 0 4 GHz

-Copolar at 2.9GHz

---- Cross-polar at 2.9 GHz

24 25

DUBOST, G., and ZISLER, S.: 'Antennes a large bande. Theories et applications' (Masson. Paris, 1976) DUBOST, G., and VINATIER, C.: 'Doublet replie symetrique en plaques fonctionnant a t*s hautes frequences et a large bande'. Brevet Europeen 0044779 BI, 13 Nov. 1985; USA, 284702, 20 July 1981; Japan, 114526, 23 July 1981 DUBOST, G.: 'Flat radiating dipoles and applications to arrays' (John Wiley, 1981) DUBOST, G. BEAUQUET, G., and VINATIER, C.: 'Theoretical radiation admittance of a , pp. 252-253 large bandwidth flat symmetrical folded dipole', Elec~ron.L e ~ t 1984.20, DUBOST, G., and RABBAA, A.: 'Analysis of a slot microstrip antenna', IEEE Trans., 1986, AP-34, pp. 155- I63 DUBOST, G.. and VINATIER, C.: 'RCseau dedoublets replies symetriques en plaques, a large bande autour de 12GHz'. L'Onde Electrique, 1981, 61, pp. 34-41 DUBOST. G., and GUEHO, S.: 'Impedance mutuelle et couplage entre deux doublets repli6s plans paralleles en fonction de leur ecartement', CR Acad. Sci. Paris, 1985, 301, ser. 11, pp. 79-82 DUBOST, G.: 'Mutual ooupling between flat folded dipoles in terms of frequency'. Int. Symposium Antennas and EM Theory, Beijing, China, Aug. 1985, pp. 706-711 DUBOST, G., and FRIN, R.: 'Antenne plaque a double polarisation croisee'. (Brevet 36 05 990, 23 April 1986 DUBOST. G.: 'Large bandwidth dual polarized multilayer microstrip antenna'. AP-S Intern. Symp., Philadelphia. USA, June 1986, pp. 455-458 PALANISAMY, V., and GARG, R.: 'Analysis of circularly polarized square ring and crossedstrip microstrip antennas', I E E E Trans., 1986, AP-34, pp. 1340-1345 DUBOST, G.: 'Broadband circularly polarized flat antenna'. Int. Symp. Ant. &Prop., Japan, 1978, pp. 89-92 CHIBA T., et ai.: 'Suppression of higher modes and cross polarized component for microstrip antennas'. IEEE AP-S, 1982, p. 285 HUANG, J.: 'CP microstrip array with wide axial ratio bandwidth and single feed LP elements*. IEEE AP-S, 1985, pp. 705-708 DUBOST, G., FRIN, R.: 'Antenne a double polarisation associee des directeurs'. Brevet Europe, USA and Japan, April 1987 DUBOST, G., and RABBAA, A,: 'Synthbe de I'antenne plaque a double fente', L'Onde Electrique, 1987, 67, pp. 72-79 DUBOST, G., and RABBAA, A.: 'Substrate influence on flat folded dipole bandwidth', Electron. Lett., 1985, 21, pp. 426-427 JAMES, J. R., HALL, P. S., and WOOD, C.: 'Microstrip Antenna' (Peter Peregrinus 1981) IEE Electromaghehe Waves Series 12. DUBOST, G.: 'Comparison between flat radiating source bandwidth'. IEE Coloquim on Antenna bandwidth extension techniques, London, 28 Oct. 1985. DUBOST, G., and VINATIER, C.: 'Large bandwidth and high grain array of flat folded dipoles acting at 12GHz' 3rd Int. Conf. on Ant. and Ptopag. ICAP, Norwich, April 1983 DUBOST, G.: 'Improvements in printed-circuit radiating sources and arrays'. IEE Colloquim on receiving antennas for satellite broadcasting', London, April 1984 DUBOST, G., BEGUIN, D., CHAPUIS, E., AURIOL, A.: 'Reseau plat a grand gain et a faibles lobes secondaires a 5 GHz'. Conference Internationale sur le Radar, Paris, May 1984 MARCHAND, M.: 'Antenne plane a reseau en bande X', Rev. Tech. Thornson-CSF (France), 1985, 17, pp. 83-109 DUBOST, G., POTIER, P.: 'Rkseau plat a commutation tlectronique de faisceaux dans la bande des IZGHz', L'Onde elecwique, 1985, 65, pp. 56-61 DUBOST, G.. and NICOLAS M.: 'A braod angular coverage and large bandwidth antenna'. 17th European Microwaves Conf., Rome, Sept. 1987

392

Wideband flat dipole and short-circuit microstrip

26 DUBOST G.. NICOLAS, M., VALLEE, P.: 'Antenne a pas de balayage reduit dans un large secteur angula~re'.Brevet 85 07 348, 15 May 1985 27 DUBOST, G.: 'Antenne symetrie de revoloution associant une lentille dielectrique a une source plaque'. IEEE Symposium AP-S, Vancouver, Canada, June 1985, pp. 587-590 28 DUBOST, G.: 'Flat linear radiating array applied on a cylindrical lens'. Melecon'85 Mediterranean Electrotechn~calConference, Madrld, Oct. 1985, pp. 215-218 29 DUBOST, G.: 'Short-or open-circuited dipole parallel to perfect reflector plane and embedded in substrate and acting at resonance', Electron. Lett., 1981, 17, pp. 914-916 30 DUBOST. G.: 'Transmission-line model analysis of a lossy rectangular microstrip patch' Electron. Lett. 1982, 18, pp. 282-282 31 DUBOST. G.. and RABBAA, A.: 'Mutual impedance between two short-circuited flat resonant dipoles'. IEEE Trans., 1981. AP-29, pp. 668-671 32 DUBOST. G.: 'Far field radiated by short-circuited microstrip antenna acting at a quarter wavelength resonance' Electron. Lett. 1983, 19, pp. 737-739 33 DUBOST, G., GUEHO, S., and BEGUIN, D.: 'Ku band phased array in a large angular sector', 5th Int. Conf. on Antennas and Propag., ICAP 87, 1987, University of York 34 DUBOST, G., and GUEHO, S.: 'A 3 bits digital phase shifter in Ku band for microstrip ,.**.d 'r,:"v ~ --.., A..7m y..,,,, ,".,,..'.-., Q , h ,-,,I,.",.:buAuquu~a vu x r ~ r u n c a vr ~ r ~ r ~ :... u r u c d r r unug. u, ~ 7< 8".. uuddpe~i, ~ . Hu~rya~y 35 DUBOST, G., GUEHO, S., BEGUIN, D.: 'Dephaseur Clementaire en ligne microruban et dephaseur a commande numerique en faisant application', Brevet 86 11 923. 21 Aug. 1986 36 DUBOST, G . , GUEHO, S., and BEGUIN, D.: 'Antenne reseau carrk, monopulse a balayage C.lectronique'. Brevet 8720774, 13 Jun. 1987 37 DUBOST, G., ALEXIS, R.: 'Antenne formee a partir d'une cavitt resonnante comportant une face rayonnate'. Brevet 8408.392, 19 May 1984 38 DUBOST, G.: 'Antennes plaques pour les te1&communications entre stations mobiles' L'Onde Electrique, 1985), 65, pp. 41-49 39 DUBOST, G.: 'Vertically polarized flat antenna with omnidirectional radiation". Int. Symposium on Antennas and Propagation, ISAP, Aug. 1985, Kyoto, Japan, pp. 109-112 40 DUBOST, G.: 'Influence of feed-point location on radiation resistance of a short-circuited flat dipole', Electron. Lett., 1984, 20, pp. 980-981 41 DUBOST, G., BIZOUARD, A,: 'Antenne periodique plane'. Brevet 83.19.924 13 Dec. 1983 42 DUBOST, G., GUEHO, S., and BIZOUARD, A,: 'Log-periodic short-circuited dipole array with a squinted beam', Electron. Lett., 20, pp. 41 1-413 43 DUBOST, G., and GUEHO, S.: 'Theory of a large bandwidth microstrip plane array with a deflected beam'. IEEE Int. Symposium on Ant. Prop., June 1984, Boston, Mass., USA

--

A:-..

Chapter 8

Numerical analysis of microstrip patch antennas J.R. Mosig, R.C. Hall and F.E. Gardiol

8.1 Introduction 8.1.1 General description Microstrip patch antennas are thin and lightweight radiating elements, formed by a substrate, including one or several dielectric layers, backed by a metallic sheet (the ground plane). Thin metallic patches (the radiating elements) are located on the air-substrate interface and, possibly, between the dielectric layers. Microstrip antennas are manufactured by the photolithographic process developed for printed circuits. Their low profile, low weight and mechanical ruggedness make them an ideal choice for aerospace applications. They can be mass-produced, and could thus provide inexpensive receiver antennas for direct reception of microwave signals from satellites (television, mobile communications). Finally, they are ideally suited to be combined in large arrays, the individual patches sharing the same substrate. Thus directive antennas can be obtained in spite of the inherent low directivity of a single patch. The remarkable practical advantages offered by microstrip antennas are offset, to some extent, by their inhomogeneous nature, and a rigorous analysis was long considered to be a hopeless task. An accurate model should take into account the three inhomogeneities of a microstrip structure (Fig. 8.1): ( a ) The presence of at least two dielectrics (often air and substrate) ( 6 ) The boundary conditions on the interfaces between different layers are inhomogeneous since thin metallic plates making up the radiating elements and feeding the structure can partially fill the interfaces (c) Any microstrip structure is finite in dimensions; i.e. its ground plane and its dielectric substrate are bounded in the transverse directions. The edges may, however, be located at a very large distance, in which case this third inhomogeneity may be neglected (the structure is then assumed, mathematically, to extend to infinity).

394

Numerical analysis of microstrip patch antennas

Models used to study microstrip patch antennas range from very simplified ones, such as the transmission-line model, through cavity models, planar circuit analysis, segmentation techniques, and up to quite sophisticated approaches based on an integral-equation formulation. In the framework of the integralequation model, many different approaches exist, depending on the use of spectral or space quantities and on the geometries to be included.

Fig. 8.1

The three inhomogeneities of a microstrip structure. a Dielectric media of unequal permittivity, b Infinitely thin conductors introducing surface current between the dielectric media c Finite transverse dimensions of substrate and ground plane

Detailed surveys of these models are available (e.g. Reference I), and several of them are treated elsewhere in this book.

8.1.2 The integral equation model The purpose of this Chapter is to provide a rigorous treatment of microstrip antennas, free from over-simplifying assumptions. Among its principal features, the proposed model is able to handle patches of arbitrary shapes where no educated guess of the surface-current distribution is possible. Also there is no limitation in frequency and substrate thickness. The model automatically takes into account mutual coupling between elements and can predict the performance of a patch embedded in an array environment. Surface waves are included as well as dielectric and ohmic losses. Thus the model allows accurate prediction of quasistatic behaviour, dominant and higher modes of resonance, and input impedances, coupling coefficients, radiation patterns, gain and efficiency at any frequency. The model relies upon the identification of a microstrip antenna as a particular case of a stratified medium. The pioneer work on electromagnetic-wave propagation in stratified media must be ascribed to A. Sommerfeld, who investigated the radio-wave propagation above a lossy ground as early as 1909. The microstrip antenna is modelled by an integral equation where the main unknown is the electric surface current density on the patches. The Green's functions forming the kernel of this equation include the effects of the layers, and are obtained in the form of inverse Hankel transforms by the systematic use

Numerical analysis of microstrip patch antennas

395

of stratified media theory. The first Sections of this Chapter are devoted to the construction of the integral equation and of the pertinent Green's functions. Considerable attention is paid to the development of efficient numerical techniques for evaluating the Green's functions. The integral equation is directly formulated in the space domain using a vector and a scalar potential. The resulting mixed potential integral equation (MPIE), similar to that obtained for wire antennas, is better suited for numerical analysis than the customary electric-field integral formulation. The MPIE is solved by a method of moments. In the general case, rooftop subsectional-basis functions are used. For particular geometries, it can be more efficient to use entire domain-basis functions corresponding to the eigenvalues of the equivalent cavity. Finally, standard circuit analysis is used to deal with multiport antennas, loaded antennas and arrays. The final Sections of the Chapter present numerical results for the input impedance, coupling coefficients and radiation patterns of several microstrip antennas and arrays of practical interest. 8.2 Model based on the electric surface current 8.2.1 Geometry of the model and boundary conditions In order to present the theory in the clearest possible manner, the electric surface-current model will be developed for the simple microstrip structure of Fig. 8.2 with a single dielectric layer and a metallic patch. The generalisation to multilayer antennas and to multiple patches (arrays) will be considered later. The substrate is assumed to extend to infinity in the transverse directions and is made of a nonmagnetic, isotropic, homogeneous material which can be lossy. The ground plane also has infinite dimensions, and the upper conductor (the metallic patch) has zero thickness. Both the ground plane and patch are allowed to have ohmic losses. The direction perpendicular to the ground plane is selected as the z-axis (Fig. 8.2). The patch extends over part of the z = 0 plane, denoted by the surface So. The remainder of the z = 0 plane, i.e. the surface separating the two dielectric media, is denoted S and called hereinafter the interface. Indexes 1 and 2 are associated, respectively, with the infinite dielectric extending above the substrate, usually the air, and with the substrate itself. Thus, we have El

=

Eo,

E~

=

E~E,

Z

=

> 0

~ ~ ~ i ( I - j t a n 6 )- h < z < O

where h is the substrate thickness and everywhere.

(8.1)

396

Numerical analysis of microstrip patch antennas

The excitation is provided by a time-harmonic electromagnetic field. Complex phasor notation is used throughout this Chapter. Any complex scalar quantity C represents an instantaneous quantity C(t) given by: c(t)= J2 Re [Cexp (jwt)]

Numerical analysis of microstrip patch antennas

397

The induced currents in turn create diffracted or scattered electromagnetic fields. These fields, denoted E" Hd, add to the excitation fields to yield the total fields E, H existing in the entire space. On the air-dielectric interface (the plane z = 0, excluding the surface of the patch So)the boundary conditions are: ez x (El - E l )

= 0

(8.4)

e r x (HI-Hz)

= 0

(8.5)

On the metallic surfaces the boundary conditions will be inhomogeneous owing to the presence of the currents. Assuming that the patch and the ground plane are perfect conductors (this restriction will be removed later) we have on the upper side of the patch S,(z = 0+): e Z x El = 0;

e, x H, =

4,

(8.6)

and, similarly on the lower side z = Ow: e, x El = 0; e, x Hz = - J,2 Combining the above pairs of equations, we obtain e, x (El - E,)

(8.8)

= 0

e, x (HI - Hz) = J,,

+ J,

= J,

(8.9)

which apply to the fields on both sides of the patch. Eqns. 8.4-8.9 are written in terms of the total fields. However, since the excitation fields are assumed to be continuous, the boundary conditions (eqns. 8.4-8.5) and (eqns. 8.8-8.9) also hold for the diffracted fields. Hence the diffracted tangential electric field is continuous across the patch, while the jump in the diffracted tangential magnetic field equals the total surface current on the patch. Finally, the boundary conditions on the ground plane z = - h are Fig. 8.2

General view of a microstrip antenna and vertical cut in the y = 0 plane Superscripts e and d refer to the incident fields (excitation) and to the scattered (diffracted) fields. For a infinitely thin patch the currents J, and J,, can no longer be distinguished and the meaningful quantity is the total current J, = J,,+ J,, flowing on the patch.

The excitation fields are denoted by Ee and He. They can be the fields of a plane wave coming from infinity (receiving antenna) or the local fields created by a finite source located within the microstrip structure (transmitting antenna). In either case, the excitation fields induce surface currents on the upper side of the ground plane and on both sides of the metallic patch. However, since the patch is assumed to have zero thickness, the model cannot differentiate between the currents flowing on its upper and lower side. Indeed, the patch is modelled as a sheet of current 4 whose value at any point is the algebraic sum of the upper and lower surface currents 4, and 4, existing at z = 0+ and z = 0- (Fig. 8.2).

ez x El = 0 e, x Hz =

4

(8.10) (8.1 1)

It must be pointed out that the microstrip antenna problem can be completely solved without actually knowing the exact distribution of surfacepxrent on the ground plane. In fact, image theory can be used to remove the ground plane and the boundary conditions (eqns. 8.10-8.11) will then be included automatically in the Green's functions. 8.2.2 Potentials for the diffracted field Since no volume sources are considered in this model, the diffracted fields satisfy the homogeneous Maxwell's curl equations:

V V

x E L-jwp,,Hd

(8.12)

x Hd = j w ~E d

(8.13)

398

Numerical analysis of microstrip patch antennas

The resolution of antenna problems can in many cases be simplified by introducing the scalar and the vector potentials for the diffracted fields:

subject to Lorentz's gauge:

Numerical analysis of microstrip patch antennas

399

effects of the dielectric substrate and of the ground plane. Therefore, the Green's functions must satisfy the boundary conditions (eqns. 8.4-8.5) and (eqns. 8.108.11). Moreover, the boundary condition for the magnetic field (eqn. 8.9) is automatically built into the formulation of the Green's functions. These functions are dyadics, and unfortunately do not have a closed analytical expression. However, once they are formulated and numerically evaluated, the only unknown which remains is the true electric surface-current distribution on the conducting patch.

Introducing the above expressions into Maxwell's equations 8.12 and 8.13 and combining, we obtain two homogeneous Helmholtz's equations for the potentials:

where k, = ~ ( j i ~ is~the , ) wavenumber "~ in medium i. It must be recalled here that the choice of the couple A , V is not unique [2]. Indeed, any vector A* = A gradY can be used as a new vector potential provided that the scalar potential is replaced by V * = V - joy. Moreover, if Y is a solution of the homogeneous Helmholtz's equation, the new potential will still satisfy Lorentz's gauge (eqn. 8.16). We shall discuss later some convenient choices for the potentials.

+

8.2.3 Green's functions Let us consider an arbitrarily oriented Hertz dipole of moment I dl located at the point r' (Fig. 8.3). In general, the vector potential a t the point Y due to this dipole is given by the linear relationship

w h ~ E, e is a three-dimensional dyadic Green's function. The physical meaning of G, is evident: the scalar component Git gives the s-component of the vector potential existing at the point r created by a t-directed Hertz dipole located at the point r'. If the source and the observer are surrounded by an infinite homogeneous medium, the dyadic G, is diagonal and can be exp~essedas the product of a scalar Green's function GA times the unit dyadic In this case, the vector potential is always colinear with the source dipole. For a microstrip antenna it is possible to use a scalar free-space Green's function of the vector potential. However, if we do, we then need to use fictive electric and magnetic surface currents on the air-dielectric interface in order to satisfy the boundary conditions. These currents are also unknowns in the integral-equation formulation of the problem and add to the complexity of the numerical solution. The preferred solution is to include in the Green's functions

Fig. 8.3 Horizontal electric dipole ( H E D ) o n a microstrip substrate T h e fields and potentials of such an elementary source give the Green's functions associated with a microstrip antenna.

Keeping in mind the linearity of Maxwell's equations, the vector potential of a given current distribution can be written as a superposition integral involving the corresponding dyadic Green's function

The scalar potential V is obtained by introducing the above expression in the Lorentz gauge with the result:

a.

The Green's function G, associated with the scalar potential must be carefully defined. In fact, the uniqueness of G, is guaranteed only if the divergence of GA is an irrotational vector. Thus we can write [3]

where V' acts on the primed co-ordinates. Expression 8.21 is now easily transfor-

400

Numerical analysis of microstrip patch antennas

med into

where dS, is the perimeter of the patch and n is the outwards-pointing normal unit vector (Fig. 8.2). The edge condition guarantees that the normal component of the surface current vanishes on the perimeter of the patch. Hence, the line integral in eqn. 8.23 can be eliminated. We can now introduce the associated surface-charge density q, via the continuity equation:

Finally, we can express the scalar potential as:

It is worth mentioning that the edge condition can be applied even if So is a portion of a larger patch. Such a situation may arise when solving the problem with a method of moments using subsectional-basis functions. In this case the line integral in eqn. 8.23 can still be eliminated, but since 4 does not necessarily vanish on the boundary of So, the continuity equation must be interpreted according to the theory of distributions, and delta functions corresponding to line charges in the boundary of So, will appear in the expression for q,. The Green's function G,can be viewed as the scalar potential created by a point charge, even if isolated time-varying point charges do not exist in the real world. Thus, owing to the lack of a sound physical interpretation, it is better to consider G, only as a useful mathematical device. Only when the frequency goes to zero, does this function become the familiar electrostatic potential of a point charge. 8.2.4 Mixed potential integral equation ( M P I E ) The diffracted fields derived from the potentials of eqns. 8.20 and 8.25 satisfy Maxwell's equations and the boundary conditions of the problem (eqns. 8.48.5) and (eqns. 8.8-8.9). The last step is now to relate these fields to the excitation fields via conditions (eqns. 8.6-8.7). If the total tangential electric field is forced to vanish on the patch surface, we get the standard electric field integral equation. This equation can be slightly modified to account for the ohmic losses on the patch. The total tangential electric field is now proportional to the total surface current, and we can write

or, introducing the potentials

where the proportionality constant Z, is a surface impedance (measured in

I

Numerical analysis of microstrip patch antennas

407

ohms) which accounts for the finite conductivity of the patch. An accurate value for Z, can only be obtained by measurement since Z, must include technological data such as the thickness and roughness of the metallic patch. However, in most cases the patch is thick compared with the skin depth 6, and the classical expression (8.27) Z, = (1 + j)/a*6 represents a good approximation. In the above expression a* is an effective conductivity that includes roughness effects and can be several times lower than the values of conductivity found in standard tables. Finally, introducing the integral form of the potentials (eqns. 8.20-8.21) in eqn. 8.26 we get the final expression for the mixed potential integral equation (MPIE):

The validity of this equation depends on the possibility of defining the Green's function G, by eqn. 8.22. Eqn. 8.28 is a Fredholm integral equation of the second kind. However, the term Z, J, is usually small and the iterative techniques commonly used for Fredholm integral equations of the second kind that arise, for example, when using the magnetic field integral equation [4], do not apply here. The unknowns in the integral equation 8.28 are the surface current J, and the surface charge q,. However, they are not independent, and are related through the continuity equation. 8.2.5 Sketch of the proposed technique The successive steps in solving the microstrip antenna problem are now clear. We start with the theoretical determination of the required Green's functions GA and G,. In general, the Green's functions are available as definite integrals over semi-infinite intervals and they must be numerically evaluated for distances ranging from zero to the maximum linear dimension of the patch. The construction of accurate numerical integration algorithms to evaluate the Green's functions is a crucial step of the overall problem. Once the Green's functions are computed, the unknown surface current is expanded over a set of basis functions and the integral equation is tested against a set of test functions using the so-called method of moments (MOM). Here, the correct choice of these sets of functions is essential for the quality of the final results. In this way, the integral equation is discretised and transformed into a set of linear equations. The complex eigenvalues of the matrix equation provide the unperturbed resonant frequencies of the patch and its unloaded quality factor. The next step is the construction of the excitation fields. These fields depend strongly on the physical nature of the excitation. In many cases (coaxial pin, microstrip line) the computation of the excitation fields calls for the same or

.

402

Numerical analysis of microstrip patch antennas

Numerical analysis of microstrip patch antennas

related Green's functions that were calculated for the MOM matrix. Testing the excitation fields yields the independent vector of the matrix equation. The solution of the matrix equation gives a numerical estimation of the unknown surface current. Computing the voltages at the excitation points allows the determination of the impedance and scattering matrices of the antenna. Standard circuit analysis may be used to account for any load or for multiple excitations. Resonant frequencies and loaded quality factors are easily derived from the input impedance. Table 8.1 Essential steps (-) and main results (*) of the proposed numerical technique

from the boundary conditions -construct the pertinent

I

J

-find the pole and the residue associated to the GFs when expressed in the spectral domain

I

1 I

A DIPOLE

)

I

I

-evaluate numerically the GFs for the potentials in the near field region

I

GFs for the fieldsin the far field region

1 AND UNLOADED a

to the intearol eountion

complex determinant

+SURFACE CURRENT DISTRIBUTIONsINPUT IMPEDANCE AND LOADED Q

4-

4

solve the matrix equation] I -

*RADIATION PATTEF POLARIZATION. DIRECTIVITY. GAIN AND EFFICIENCY

To calculate the radiation pattern we need to go back to the Green's functions and obtain their asymptotic forms in the far field. This can be done analytically and the radiation pattern of the antenna, including polarisation and phase information, is obtained by using a superposition integral over the patch.

403

Finally, integration of the far fields over the upper half-space will give the directivity of the antenna and an estimation of its efficiency and gain. These steps are summarised in Table 8.1. 8.3 Horizontal electric dipole (HED) in microstrip The construction of the Green's functions requires the determination of the fields created by a horizontal electric dipole (Hertzian dipole) located on the air-dielectric interface of a microstrip structure (Fig. 8.3). The first investigations of a HED embedded within a stratified medium are due to Sommerfeld, who published in 1909 the exact solution for a dipole over an imperfect ground. The Hankel integral transforms which appear within such a problem are often known as Sommerfeld integrals. The vertical dipole over a conducting plane covered with a dielectric layer was studied by Lo and Brick in two articles which appeared almost simultaneo~sly 15, 61. The problem is quite similar to the one arising in microstrip antenn, s, except for the dipole orientation. However, even though the first microstrip lines were introduced around the time these articles were pubIished, no connection between the two fields was made - microstrip antennas were to be developed some 20 years later. This may explain the different approaches to the two problems, in particular the absence of a detailed study of the near field, which is essential when the source and the observer are both located on the surface of the substrate. The general theory of dipoles - either electric or magnetic, horizontal or vertical, located within an arbitrary stratified medium - was developed later, mainly by Brekhovskikh [7], Wait [8], Felsen and Marcuvitz [9], and Kong [lo]. However, as was done in previous publications, the emphasis was put on the study of radiated fields, for which approximate asymptotic analysis is sufficient. For the accurate study of microstrip radiation, however, precise knowledge of the surface currents on the patch, and hence of the near fields on the dielectric interface, are required. For this reason, the fields created by a HED located on the air - dielectric interface will be determined. 8.3.1 The vector potential Let us consider a HED of moment Idx equal to unity placed at the point r' = 0 as indicated in Fig. 8.4. In order to ease the mathematical development required for solving the Helmholtz equation 8.17 satisfied by the vector potential, we will replace the space variables x , y by their spectral counterparts k,, ky according to the double Fourier transform:

404

Numerical analysis of microstrip patch antennas

Numerical analysis of microstrip patch antennas

405

If the dipole is embedded in an infinite homogeneous medium of permittivity E,, the vector potential is parallel to the dipole and exhibits a spherical symmetry: 1 -jfmmf(kX, 2n k,)exp(jk,x +jk,y)dk,dk, (8.30) In the spectral domain the homogeneous Helmholtz equation becomes: =

where

On the other hand, it is well known [I I] that two cartesian components of A are needed to satisfy the boundary conditions in an inhomogeneous structure such as a microstrip antenna. Here, we shall adopt Sommerfeld's choice and postulate an additional vertical component for the vector potential. Hence A = e,A, ezA,. Choosing now for A, and A, general expressions of the form of eqn. 8.32, we obtain after satisfying the boundary conditions the expressions:

+

2

Fig. 8.4 Co-ordinate system for the study of an x-directed horizontal electric dipole (HED) on a microstrip substrate The air-dielectric interface is at z = 0 and the ground plane is at z = -h. The continuity equation implies that there are two point charges of value * I dxljw at both extremities of the dipole

According to eqn. 8.1 we shall adopt from now on the shorthand notation u: = U: = ki - % a n d ui = u2 = ki - E,%. The general solution of eqn. 8.31 for a cartesian component of A is (s = x, Y, 2): where the unknown factors a, b may be functions of the spectral variables. The fields are obtained by usingeqns. 8.14-8.15 and the Lorentz gauge, which also holds in the spectral domain. Since no external excitation fields are considered here, the fields of eqns. 8.14-8.15 are total fields. These fields must satisfy the boundary conditions eqns. 8.4-8.5 on the interface and eqn. 8.10 on the ground plane. In particular, the HED is equivalent to a surface current density in the plane z = 0 given by:

=

PC (,

2n

- 1) J

i

+

cosh u(z h) (DmD, cosh uh)

+

u tanh uh, and the upper and lower where D, = u, + ucoth uh, D, = E,U, expression inside the symbol { ) correspond, respectively, to the upper semiinfinite medium (z > 0) and to the substrate (- h < z i0). It can be easily shown that if er = 1 and h 4 co, the vertical component A, vanishes and A, becomes the free-space vector potential given by eqn. 8.34.

8.3.2 Scalar potential and the fields The continuity equation applied to an electric dipole implies the existence of two point charges q = Ijjw at both ends of the dipole. Since the product Idx has been assumed to be equal to unity, the moment of this pair of charges is qdx = l/jw. The scalar potential associated with the dipole is given directly by the Lorentz gauge. Introducing eqns. 8.35 and 8.36 in eqn. 8.16 we get:

+

p

j ~~xP(-w)/(DTEDTM) = -2 ~~JW Nsinh I u(z h)/(DrEDTM sinh uh)

+

(8.37)

with N = u, + u tanh uh. In the space domain, the scalar potential V of an electrostatic dipole of moment lljw is related to the scalar potential V, of a single unit point charge by the well known expression:

v

I av, jw ax

= ---

406

Numerical analysis of microstrip patch antennas

Numerical analysis of microstrip patch antennas

407

or, in the spectral domain by

Comparing eqn. 8.39 with eqn. 8.37, we can deduce by analogy that the potential of a unit point charge on the air-dielectric interface of a microstrip antenna is given by Nsinh u(z + h) DTEDTM sinh uh

i

Now, the construction of the fields is straightforward, for we have in the spectral domain:

Hence, the surface waves appear as poles of the integrands in the complex plane k, = 1 + j v . It can be shown [I31 that D , has no zeros if kOh(c;- 1)1'2< 4 2 and D , has only one corresponding to the dominant zero-cutoff TM surface wave. This condition is equivalent to the restriction:

For the sake of simplicity we shall assume from now on that this inequality holds. Higher frequencies would add new poles, but the analysis made for the single-pole case remains qualitatively valid. For substrates with moderate losses the pole 1, + jv, lies slightly below the real axis (v, < 0) and its real part is bounded by 1 < Ap/k0 < ~ f " (Fig. 8.5).

It can be easily demonstrated that the vertical component E, shows the expected jump discontinuity when crossing the air-dielectric interface. 8.3.3 Surface waves and the spectral plane k, It can be shown [I21 that the equations DTE = 0, D , = 0 are the characteristic equations for the TE and TM surface-wave modes propagating on a dielectriccoated conducting plane. Hence the zeros of D , and DTM give the phase constant of the surface waves existing on a rnicrostrip structure. The terms D, and DTMdepend on k, and k, only through the radial spectral variable $ = k2, $. For functions exhibiting such a kind of dependence, the inverse Fourier transform 8.30 can be written as

+

g-'[.&)l

=

jom~

d ~ ~ ddkQ~ ~ 3 ( ~ ~ )

(8.42~)

Pole (lossless)

Fig. 8.5

Topology of the complex plane k, with the original integration path from zero to infinity The Figure also shows the geometrical locus of the pole as a function of dielectric losses.

and More precisely, a good approximation for electrically thin substrates [I41 is where Q, 4 are polar co-ordinates and Jois the Bessel function of zeroth order and first kind. The replacement of the double Fourier transform by Hankel transforms is of great utility when performing the numerical evaluation of the fields and potentials. For instance, if the observation point is also on the interface ( z = 0) we have: The integration path of the Sommerfeld integral eqn. 8.43-8.44 is, in general, the real positive axis 1. But, if we consider the theoretical case of a lossless substrate, then v, = 0 and the pole is on the real axis. Since, by continuity, the integration path must remain above the pole, the integral from zero to infinity in the lossless

408

Numerical analysis of microstrip patch antennas

Numerical analysis of microstrip patch antennas

case is interpreted as:

409

On the other hand, it can be shown [9] that this replacement will give correct results even for the broadside direction Q = 0". The final expression of the integral in the w-plane is

where the symbolfstands for Cauchy's principal value and R is the residue of the integral at the pole k, = Finally, it should be mentioned that the function u; = ki - ki introduces a branch point at k, = ko (Fig. 8.5). However, the integral remains bounded here and no deformation of the integration path is needed.

4.

8.3.4 Far-Jield approximations Far-field approximations are essential for the evaluation of the radiation pattern of a microstrip antenna. They can be obtained by using standard asymptotic techniques, such as the steepest-descent method [9]. We shall outline briefly the application of these techniques to Sommerfeld integrals. We begin by replacing the Bessel functions in these integrals by Hankel functions. This is done recalling the identity F i g . 8.6 The integration path C closing at infinity in the k, plane and the new branch cut introduced by the Hankel function A portion (dotted line) of the path C is in the lower Riemann sheet

which holds if.f'is an even function of k, [ll]. In this way, the integration path C in the complex plane k, closes at infinity (Fig. 8.6) while the topology of the plane remains unchanged except for an additional branch point introduced by the Hankel function (Fig. 8.6). For the sake of clarity, the pole k, = is located on the real axis (lossless substrate, see Fig. 8.5). Let us consider now a typical integral in the air:

5

where C is the path shown in Fig. 8.6. To obtain an asymptotic expansion for I, the plane k, is transformed into a new complex plane w defined by the relation

The transformed path C* in the plane w is shown in Fig. 8.7. The pole is now located at w, = 4 2 jarcosh (lp/ko)and the branch cuts associated with the points k, = $. ko disappear owing to the new choice of variables. Introducing spherical co-ordinates r, 8 (z = r cos 8, Q = r sin 8) the argument of the Hankel function becomes

+

Since we want an expression useful in the far field (k,r p l), we can replace the Hankel function by its first-order asymptotic expression. The integration path can be deformed far from the origin w = 0 in order that sin w never vanishes.

= k,sin w ) showing the transformed path C*,the steepest descent path , C and the new location of the pole Also the correspondence with the four quadrants of the plane k, is given, either in the upper (U)or in the lower (L) Riemann sheet.

Fig. 8.7 The new complex plane w (k,

F(W) = j"

(

nR sin" 0 sin w )'I2 k, cos w/(ko sin w)

with R = kor and q(w) = -jcos(w - 8).

410

Numerical analysis of microstrip patch antennas

Numerical analysis of microstrip patch antennas

The saddle point w, of function q is given by w, = 0. The steepest-descent path CsD through w, is defined by Im(q) = - 1. Its particularities are easily derived (Fig. 8.7): (i) Cm is at a 45" angle with the real axis. (ii) Cs, intersects the line Re(w) = n/2 at the level Im(w) = cosh-'(l/sin 0). (iii) As a result, the pole w, is located between CsDand the positive real axis only when 0 > 0, = sin-'(k,/&). n/2. (iv) CsD possesses two vertical asymptotes at Re(w) = 0

+

Contributions from the integrals joining the two paths C* and CsD at infinity can be eliminated since the term exp (Rq) vanishes in these regions. The path C* can then be deformed into the path CsD, provided the contribution of the pole is added for angles greater than the critical angle 0,. This is written symbolically as

where U is the Heaviside unit step function and Cp is a patch surrounding the pole wp (Fig. 8.7). The first-order approximation for the integral along CsD can now be obtained by standard techniques [9]. The integral around the pole is evaluated using the residue theorem and is expressed in the original k, plane. Finally, the asymptotic expression of the integral I(eqn. 8.49), valid in the far field region, is

I

=

2j"+l cotan 0f (k, sin 0) exp(-'kor)

[I

+ ~ ( r - I ) ]- U(B - B,)

where the residue R is given by

-

R = lim (k, kg

4)f(k,)

(8.55)

AP

and the Landau notation O(f) indicates the behavior at infinity of the first term neglected in the asymptotic expansion. It must be noted here that the asymptotic approximation eqn. 8.54 is only valid if the pole rZ, is located far enough from the saddle point 1 = k,, sin 0, i.e. (k, sin O - AP)r % I. Otherwise, the contributions of the saddle point and of the pole cannot be separated and a modified saddle-point method must be used [9]. From the asymptotic point of view, the fields and potentials are the sum of two terms. The first term, due to the saddle point, represents a spatial wave with a complex factor depending on angle 0 and corresponds to the geometrical optical fields. The second term, due to the pole at Ap, represents a cylindrical wave decreasing exponentially away from the substrate that corresponds to the surface wave.

41 1

The surface wave is only relevant for angles 0 > OP, i.e. near the interface. However, its field dependence on e-'I2 can make it the dominant term of eqn. 8.54 when fields on the substrate surface at z = 0 are evaluated. Radiated electricjeld: An immediate application of the asymptotic relationship eqn. 8.54 is the computation of the radiated field. It is assumed here that 0 < OP,so that the surface wave can be neglected. In a real situation, a substrate always has finite dimensions and the surface wave can be observed directly only close to the substrate. For angles near 0 = n/2 (grazing angles) but far from the substrate, diffraction effects of the surface wave on the edges become significant. The radiation field is obtained by transforming, for z > 0, the rectangular components of E (eqn. 8.41) into spherical components and then applying eqn. 8.54 to the resulting integrals. The final expressions are

where 2, is the free-space impedance, I , the free-space wavelength, not to be confused with the spectral variable 1 = Re[k,], and go(@

=

g,(0)

= cos 0/(cos0 - jTcotank,hT)

Tcos 0/(T - j&,cosOcotan k,hT)

These asymptotic expansions have also been derived, with a different approach, by several other authors [15, 161. The result for E, shows that this component decreases faster with distance than Ilr, and is thus not a radiated component. Figs. 8.8 and 8.9 give the polar radiation patterns, respectively, in the E-plane and H-plane. In each Figure, four substrate thickness k,h = 0.05,0.1, 0.2 and 0.5 have been considered, and, for each thicknesses, curves corresponding to four dielectric constants E, = 1, 2, 5 and 10 have been plotted. The presence of a dielectric layer increases, in general, the half-power beamwidth in the E-plane, especially for thin substrates. On the other hand, the H-plane pattern is almost independent of the substrate parameters, except for very thick substrates just on the threshold for the generation of a second surface wave. Potentials at the interface: The Green's functions appearing in the integral equation 8.28 can be obtained from the potentials A, and V,. Solving the integral equation requires the knowledge of these potentials only at the interface. If we apply eqns. 8.54 to eqns. 8.43 and 8.44, transformed according to eqn. 8.48, we obtain with z = 0 and O = x/2:

472

Numerical analysis of microstrip patch antennas

4m0 %

-

-2zjRHi2)(&~)

Numerical analysis of microstrip patch antennas

(8.58)

where the residue R is given by eqn. 8.55 with f = k,N/DTEDTM.It is here apparent that the Q - ' contribution of the saddle point vanishes in both expressions. If higher-order terms in Q-' are desired for A,, which has no surfacewave component, the whole C,, integration path in the complex plane k, must be considered. E plane: kh=0.05

in all situations, but the calculations are rather complex, requiring error functions of complex arguments [9],and they will not be carried out here. Asymptotic expressions 8.58 and 8.59 will be used in the following development to check the results obtained using numerical integration of the potentials. H plane: kh=0.05

H plane: kh=O.l

E plane: kh=O.l

H plane: kh-0.2 E olane: kh=0.2

413

H plane: kh=0.5

E plane: kh=0.5

Fig. 8.8 Polarplot of the E-plane radiation pattern (in dB) of a HED on a microstrip substrate for four normalised substrate thicknesses ( a ) k,h = 0.05 ( b ) koh = 0.10 ( d ) koh = 0.50 ( c ) koh = 0.20 A:E,= 1 B:E,= 2 C:c,= 5 D : t , = 10

It can be shown that the asymptotic behaviour of the integral is mainly determined by the discontinuity of the derivative of the integral at the point k, = k,,. The dominant term in the asymptotic expansion is

with the parameter A defined as A = k , h ( ~ ,- 1)'''. It is possible to replace eqn. 8.58 by a uniform asymptotic development valid

Fig. 8.9 Polarplot of the H-plane radiation pattern (in dB) of a HED on a microstrip substrate for four normalised substrate thicknesses (6)koh = 0.10 ( a ) koh = 0.05 ( c ) koh = 0.20 ( d ) koh = 0.50 A: 8, = 1 B:E, = 2 C: &, = 5 D: E,= 10

8.3.5 Radiation resistance and antenna efficiency

If the cylindrical components of the fields are expressed in terms of the potentials by transforming eqns. 8.41, it can be shown that the term DTMappears only in the denominator of components E,E, and H 4 . Therefore, these are the components that include a surface-wave term, and thus the Poynting vector S associated with the surface wave has a radial and a vertical component, respectively, S, = - E,H4 and Sz = E,H4. Consideration of the general expression 8.54 shows that the vertical component decreases exponentially with z , and consequently does not contribute to the radiated power. On the other hand, the

414

Numerical analysis of microstrip patch antennas

radial component can be written according to expression 8.54 as

Numerical analysis of microstrip patch antennas

415

and we get

S, = (Zo/2nko)(~, - 1) ~ o s ~ ~ ~ ~ ( l d l ) ~ L ~ F ( z ) / @ (8.60)

with F(z)

=

exp (- uO~)/~TE cosh u(z

+ h)/D,cosh

uh

where the asymptotic expansion of the Hankel function has been used, and R is the residue of l/D, at the pole. It can be shown that the integral of this component over a cylindrical surface of radius Q extending from z = - h to infinity has a non-zero value independent of Q Hence, there is a net amount of power carried away by the surface wave. The surface integral must, in general, be numerically evaluated, essentially because there is no analytical formula for computing the pole Ap. However, for thin substrates we can use the approximation given in eqn 8 46 and estimate the residue appearing in eqn. 8.60 as:

Here again, the above formula becomes for E, = 1 the well known radiation resistance of a horizontal dipole above a ground plane [40]. It is worthwhile to compute numerically the integral 8.64 and plot the values of the radiation resistance R,, normalised to n ~ ~ ( d l / l , as ) ~a, function of the parameter A = koh which is proportional to the substrate thickness and to the frequency. This has been done and the results are given in Fig. 8.10 for three values of the dielectric constant. Initially, the radiation resistance increases with the square of the thickness, as predicted by eqn. 8.66. But as the normalised thickness increases, the values of the resistance oscillate and show a discontinuous derivative at the points where A is an odd multiple of 4 2 . These values correspond to the generation of higher-order surface waves [17].

m,

Then we define a radiation resistance R,,,, associated with the surface wave as

In a similar fashion, we can introduce the radiation resistance R, associated with the space wave. Starting with the asymptotic expansions 8.56 for the fields and using the fact that in the far-field zone we have Z o H = e, x E we can demonstrate that the Poynting vector is radial, its modulus being given by

Integrating this expression over the upper (z > 0) half-sphere of radius r and equating the resulting power to 1 2 R , we obtain the expression of the radiation resistance of the space wave:

0

0.2

0.4 0.6 0.8 normalized thickness

Fig. 8.10 Normalised radiation resistance O = R,l[nZo(dl/io)Z] of a HED on a rnicrostrip substrate as a function of the parameter A = kohJ(E,- 1). Z, % 120n is the free-space wave impedance.

As before, this surface integral cannot be analytically evaluated except for the case E, = 1 and h = co,where we recover the classical result for the radiation resistance of a Hertzian dipole radiating into free space. However, for thin substrates we can again estimate the surface integral 8.64 by using the approximations: jk0h(a, - sin20) g, = ; g, = jk,h cos 0, (8.65) E,

A: E, = 2 8:E, = 3 C: E, = 4

We can now evaluate the ratio between the power carried away by the surface wave and the power radiated by the space wave as: Power (surface wave) = n2 (a, - 1)'h/& (8.67) = Power (spatial wave) 2 4 -E;(E, - 1) -E, 3 15

+

476

Numerical analysis of microstrip patch antennas

Numerical analysis of microstrip patch antennas

which is proportional to the normalised thickness and shows a rather complicated dependence on the permittivity of the substrate. Finally, the radiation efficiency of a HED on a thin lossless microstrip substrate is given by

a

=

l/(l

+ 4)

(8.68)

Numerical tests have shown eqn. 8.67 to be accurate for h C 0.05 Lo. Fig. 8.1 1 gives the theoretical values of the efficiency for several dielectric constants.

Fig. 8.11

Radiation efficiency (space- wave radiated-powerltotalradiated-power) of a HED on a lossless microstrip substrate as a function of the normalised substrate thickness

A: E, = 2 8: E, = 5 = 10

C:E ,

Finite sizepatches: The above considerations refer to an elementary Hertzian dipole, but can be easily extended to finite-size microstrip patches by using superposition. The patch is excited by a unit current, and the input impedance Z,, of the antenna is obtained with techniques to be described in the following Sections. Once the radiated fields are known, a radiation resistance R, is calculated using the techniques outlined in this Section. The overall antenna If the antenna has been analysed efficiency is given by the ratio R,,/Re (Z,,,,). assuming a lossless substrate and a perfect conductor, the conservation of power R,,, = Re (Z,,,,). This is a useful check on the accuracy of the implies that R, R,, and the numerical calculations. Otherwise Re (Z,N) is greater than R, difference gives the power dissipated in the antenna in the foim of ohmic and dielectric losses.

+

+

47 7

The gain of the patch can now be defined in a customary way, as the product of the efficiency times the directivity.

8.4 Numerical techniques for Sommerfeld Integrals

When a microstrip antenna is analysed by an integral-equation technique, it is necessary to evaluate the interaction between points separated by distances ranging from zero to several wavelengths. For most of these distances the accuracy of near- and far-field approximations is not sufficient and the potentials must be numerically evaluated. For a single-layer microstrip antenna the source and the observation point are both on the interface. Hence z = 0 in the integral expressions for the fields and the potentials, and the exponential function which ensures convergence of the integrands disappears. This is the most difficult case numerically, and we will concentrate on it in this Section. Even though many deformations of the original path C of Fig. 8.6 have been tried [14, 181, we feel that the integration along C (the real positive axis A of the complex plane k,) provides the most efficient algorithm for evaluating the Sommerfeld integrals appearing in microstrip problems. 8.4.1 Numerical integration on the real axis The functions to be integrated oscillate on the real axis due to the Bessel functions. The square root uo = (A2 - k;)'l2 introduces a discontinuity of the derivative at 1 = k, that corresponds to a branch point in the complex plane. If the integrand contains D, in the denominator there is a pole just below the real axis (or on the axis itself for a lossless substrate) that produces very strong variations of the integrands. Finally, many of the oscillating integrands have an envelope which converges very slowly (A,, V,) or even diverges at infinity (A,, V). When the envelope diverges, the integral diverges in the Riemann sense since the area under the curve representing the integrand fails to converge to a finite value as the upper bound goes to infinity. However, the integral can be interpreted in the Abel sense as

lomF(1) d l

= lim Z-o

lomF(1) exp ( - u, z) d1

and the exponential guarantees convergence. This means, physically, that the potentials at the interface can be considered as the limiting case of the potentials in the air when the height of the observation point above the interface goes to zero. All these facts are clearly depicted in Fig. 8.12, which shows the integrand of the scalar potential V, for E,, = 2.55, tan6 = 0, k,h = 0.3 x, and k,e = 3. In this Figure, the substrate has been chosen quite thick for the sake of pictorial clarity. Electrically thinner, more common substrates will exhibit a pole very close to the branch point.

478

Numerical analysis of rnicrostrip patch antennas

The integration interval is decomposed into three subintervals [O, k,], [ko, koJE,] and [k,J&,, co]. In the region [0, k,] the infinite derivative in ko is eliminated with a change of variables 1 = k,cos t. The resulting smoother function is integrated numerically. In the interval [k,, k,,/~,], the singularity is first extracted if the integrand has D , in the denominator. By writing the function under the integral sign in the form F(1) = J.(~Q)f(L), we have

Fig. 8.12 Normalised values of the integrand associated with the scalar potential V of a HED on rnicrostrip ~ , = 2 , 5 5koh=0.3x k o e = 3 A: Discontinuities in the derivative 8 : Sharp peaks due to the pole C: Oscillatory and divergent behaviour at infinity -Real part ---- Imaginary part

where Here 4 + jvp is the complex pole (v, < 0) and R the residue of F at the pole. The function F,,, is integrated analytically as

Numerical analysis of microstrip patch antennas

419

It is worth mentioning that, in the lossless case (v, = O), the above integral becomes

and therefore the principal-value formulation (eqn. 8.47) of the lossless case is included' as a limiting case in this numerical technique.

Fig. 8.13 Realpart of the integrand of Fig. 8.12 for the lossy case in the interval[k,, k, J(E,)] A: Before the extraction of the singularity 8 : After the extraction of the singularity C: After the change of variables: 1 = k,cosht

Fig. 8.13 depicts the real part of the original function F(l) (solid line, A) and the difference F(1) - Eing(l)(dotted line, B) after the singularity has been extracted. There is still an infinite derivative in the curve B at I = k,; however, with a change of variables 1 = k,cosh(t) one finally obtains a very smooth integrand (the dashed line C in Fig. 8.13), which is integrated by a Gaussian quadrature. The same procedure is applied to the imaginary part of F(1) to eliminate in a similar way the sharp peak and the infinite derivative. Finally, in the region [~,JE,, co] we first extract the static term defined by F(d, ko = 0). Fig. 8.14 depicts the integrand F(1, k,) (curve A) and the difference F(1, k,) - F(d, 0) (curve B). It can be shown that the static term has the form and hence it can be integrated analytically.

420

Numerical analysis of microstrip patch antennas

Numerical analysis of microstrip patch antennas

The remaining part is a slowly convergent oscillating function over a semiinfinite interval that is integrated with specially tailored techniques.

8.4.2 Integrating oscillating functions over unbounded intervals Sommerfeld integrals, as given by eqn. 8.42, can be grouped in a more general class of integrals defined by: I(@) =

Jom

g @ d f( 4 d l

42 7

required - two features which are difficult to incorporate in an automatic computation routine. (b) Another approach applies if g(lp) is a strictly periodic function. The following decomposition is then used:

(8.74)

where (a) g(i@)is a complex function whose real and imaginary parts oscillate with a strictly periodic behaviour (sin, cos), or behave asymptotically as the product of a periodic function and a monotonic function. A typical example of this class of functions, which will be termed from now on as quasi-periodic, are the Bessel functions of the first kind. (b) f (A) is a smooth, non-oscillating function which behaves asymptotically as 2 exp (- lz). Therefore, for points on the interface (z = O), the function f ( i ) decreases very slowly or even diverges at infinity if a > 0. Here, we shall discuss the most interesting case, z = 0, which is also the most difficult from a numerical point of view. For the sake of simplicity, f(A) is assumed to be real. Complex functions can be handled by working alternately with their real and imaginary parts. (c) The lower integration bound a has been chosen conveniently to ensure that the interval [a, co) is far enough from any possible singularities of f(L). For instance in our problem, we shall take a = JE,. It is worth mentioning that the general expression 8.74 includes many integral transforms such as Fourier and Hankel transforms. Hence, the following techniques can be applied to many other problems in numerical analysis. The classical problem involving Sommerfeld integrals is the problem of radio-wave propagation above a lossy ground, where the comprehensive monograph of Lytle and Lager is the classical reference [19]. These authors have found an iterative Romberg integration satisfactory, since here the integrand displays an exponential convergence and its poles have been removed from the real axis. In microstrip problems, Romberg integration has also been used, but its effectiveness decreases considerably in the absence of a well-behaved integrand. In recent years, there has been a considerable amount of work published on the numerical evaluation of Fourier transforms, which are included in eqn. 8.74 as a particular case. The involved techniques can be classified in three groups. (a) The decomposition [a, co] = [a, A] + [A, co]. Here, Filon's algorithm is applied to the finite interval [a, A], while an asymptotic expression of the integrand is used to estimate the integral's value over [A, co] [20]. The most serious drawbacks of this approach are the choice of A and the analytical work

where P is the period of the function g. The infinite sum under the integration sign can be evaluated using standard techniques such as Euler's transformation. Recently, a more involved technique using theoretical Fourier-transform concepts has been described in connection with a problem on quantum-mechanics impact cross-sections [21]. These methods work very well for large values of Q and an exponentially decreasing integrand. Unfortunately, their extension to quasi-periodic diverging integrands seems problematic. (c) The third group of techniques, introduced by Hurwitz and Zweifel[22], are defined by the decomposition

The integration over each half-cycle is performed prior to the series' summation. As before, an accelerating device, such as the nonlinear transformations of Shanks [23] and Sidi [24] can be used to sum the infinite series. We feel that the decomposition 8.76 is particularly well suited for the Sommerfeld integrals encountered in microstrip problems and we have used it extensively throughout this work. However, instead of the sophisticated nonlinear techniques mentioned above, we have devised a new simple technique based on the concept of a weighted average between the half-cycle integrals [14]. This accelerating device has proved to be faster and more accurate for these kind of integrals.

8.5 Construction of the Green's functions Once the potentials of a HED are known, the potentials created by an arbitrary surface current J, existing on the plane z = 0 can be determined by using the superposition integrals 8.20 and 8.25. The Green's functions arising in these expressions are closely related to the potentials of a HED and can be easily obtained if the symmetry properties of microstrip structures are taken into account. We shall restrict ourselves here to the case where the source and observer are both on the air-dielectric interface (z = z' = 0). Then, according to the translational invariance of the microstrip structure in any plane perpendicular

422

Numerical analysis of microstrip patch antennas

Numerical analysis of microstrip patch antennas

to the z-axis (eqn. 8.43), we have

423

dipole. However, since only horizontal surface currents are considered we do not need to compute these expressions. It is now a matter of straightforward algebra to show that the transverse divergence of the dyadic

is given by where the angle a is given by a = tan-'{0, - yf)/(x - x')). In short, we can say that the components G F and GF are given by the Sommerfeld integrals 8.43 with the polar co-ordinates Q, cp replaced by R = lr-r'l and a. 0.4

and, correspondingly, is derived from a scalar potential according to eqn. 8.22. Therefore, provided that no vertical currents are considered, it is possible to define a Green's function associated with the scalar potential as

A

G,(rlrf) I

=

eqn. 8.44 with

Q

replaced by Ir - r'l

=

R.

(8.81)

This concludes the derivation of the Green's functions needed to solve the integral equation 8.28. A method-of-moments solution, described briefly in the next section, is used to numerically solve the equation and calculate the microstrip antenna parameters of interest. 8.6 Method of moments

Fig. 8.1 4 Real part of the integrand of Fig. 8.12 for the lossy case in the interval [k,J(&,), m] A: Before the extraction of the static term B: After the extraction of the static term

In a similar way, since a microstrip substrate shows a symmetry of revolution around the z-axis, we can write

I GP (rlr')

=

G7(rlr1)

To evaluate G;', G r , Gy we would need the potentials of a vertical electric

The integral equation 8.28 will be numerically tackled with a method of moments (MOM). This technique [25] transforms the integral equation into a matrix algebraic equation which can be easily solved on a computer. The method of moments is among the most widespread numerical techniques in electromagnetics and a detailed account of the underlying principles will not be given here. For the problem of the microstrip antenna two particular versions of the MOM deserve attention: the subsectional-basis functions approach and Galerkin's method with entire domain-basis functions. 8.6.1 Rooftop (subsectional)-basis functions If no a priori assumptions about the shape of the patches are made, a successful technique must decompose the patch into small elementary cells and define simple approximations for the surface current on each cell. The most commonly used shapes for the elementary cells are the triangle [26] and the rectangle. Even though the triangular shape is more flexible, rectangular cells involve simpler calculations and suffice for many microstrip antenna problems. Concerning the basis functions to be defined on these rectangular cells, a comparison of available possibilities [13] led to the selection of rooftop functions for the surface current J,, that have been successfully used in similar problems [27]. To implement these functions, the patch's boundary is replaced by a Manhattan-type

424

Numerical analysis of microstrip patch antennas

polygonal line (Fig. 8.15). As most commonly used antennas exhibit this kind of geometry anyway, this requirement is easily satisfied. The patch's surface is then divided into rectangular cells, called charge cells, which, for the sake of clarity, will be assumed to be of identical size. This is not an essential requirement for the theory of the algorithm, but the use of different cell sizes considerably increases the computation time.

Numerical analysis of microstrip patch antennas

4

=

Decomposition of the upper conductor in elementary cells showing the discretisation of the current and the test segments. After [38].

Two adjacent charge cells, sharing a common border perpendicular to the x-direction (y-direction) will form an x-directed ( y-directed) current cell (Fig. 8.16). An automatic overlapping of current cells is obtained in this manner so that a particular charge cell may belong to up to four different current cells. The number of charge cells is thus related to the number of current cells, though the relationship is not a simple one, since it depends on the shape of the patch. However, for rectangular patches with m x n charge cells, the number of x-directed current cells is M = (m - l)n, and there are N = m(n - 1) y-directed current cells. Every current cell supports one rooftop basis function and there is one associated test segment joining the centres of the two charge cells making up the current cell. The centre of the segment C,r, associated with the j t h x-directed current will be denoted by the vector r,,, and its ends by r,; and r; (Fig. 8.16). These three vectors are related through A similar relationship is written for y-directed segments C,(j = 1, 2,. . . N ) .

Basis functions: The Cartesian components of the surface current are expanded over a set of basis functions T,, T,:

f Z I,,T,(r - r,]) /=I

where the basis funct~onsare rooftop-type funct~onsshown In Flg 8 16:

T,( 4

F i g . 8.15

425

Fig. 8.16

-

Ixl/a

=

1x1 r a, I yl < b/2 elsewhere

Subsectional basis functions defined over pairs of adjacent cells (a), associated constant charge distribution on each cell (6). and razor testing functions (c)

A similar expression is obtained for T, by interchanging a tt b and x ++ y in the above equation. The introduction of factors I/a and llb in eqn. 8.83 yields unknown coefficients I, and I,,having the dimensions of a current. Moreover, every coefficient gives the total current flowing across the common boundary of two charge cells. The associated surface charge density is obtained from eqn. 8.83 by using the continuity equation, yielding

N

+ 2I I t J [ n ( r- r;)

- n(r - r i

)I

(8.85)

J=

where H(r) is a two-dimensional unit pulse function defined over a rectangle of dimensions a x b , centered at r = 0. The charge density within every elementary cell remains constant, justifying the name charge cell. For the charge cell of Fig. 8.15, with four test segments ending at its centre, the surface charge density is simply given by

426

Numerical analysis of microstrip patch antennas

The charge density is discontinuous on the borders between charge cells. However, the scalar potential remains bounded, while the electric field becomes singular, since q, does not satisfy a Holder condition [13]. This means that the test functions must be selected carefully, avoiding the locations where the electric field is singular. Discrete Green's functions: The notation and the computational task can be simplified by introducing 'discrete Green's functions', that have as a source a complete basis function, rather than the traditional elementary point source. The vector potential T, is created by a rooftop distribution of surface current, whereas rvis the scalar potential resulting from a rectangular distribution of unit surface charge. In practice it is convenient to deal with dimensionless quantities and in a normalised space where physical lengths are replaced by electrical lengths. The following dimensionless expressions are therefore introduced that define the discrete Green's functions:

A similar expression may be written for T:?. In these formulas rq(ro,) denotes the centre of a test segment and S,(Soj) the surface of a current (charge) cell. The discrete Green's functions exhibit the same properties of translational invariance and symmetry as the conventional Green's functions. In general, the surface integrals in eqns. 8.87 and 8.88 must be evaluated numerically. When the observation point r belongs to the source cell, some difficulties arise in the integration process. It is then recommended that the singular part of the Green's function which corresponds to the dominant term of their static value be extracted, i.e. G = G, + (G - G,) where the static value G, is given by:

Numerical analysis of microstrip patch antennas

427

When the observer is located many cells away from the sources, the sources can be concentrated at the centre of the cell. The following approximations may then be used:

Test functions: The last step of the solution with the moment method is the selection of a suitable test function. Previous work [I31 has shown that the best choice, compatible with the basis functions selected, is the use of unidimensional rectangular pulses. The use of these test functions, also called razor test functions (see Fig. 8.16), is equivalent to integrating the boundary condition (eqn. 8.26) along the segments linking the centres of adjacent cells (test segments), and therefore the testing procedure yields equations of the type:

where C,v,is the x-directed test segment extending from r,; to :r and VE1 is the excitation (impressed) voltage along the segment. A similar relationship is obtained for y-directed test segments. It is worth mentioning that this choice eliminates the need for computing field values near the edges where field singularities can adversely affect the performance of the moment method. Eqn. 8.93 is well suited for numerical treatment since all derivatives have been removed. The integration of J,, can be done easily using the expansion given by eqn. 8.83 with the result

for the vector potential and The last approximation is valid for a reasonably smooth current distribution. for the scalar potential. The singular part G, can be analytically integrated over the cell's surface. For instance, the singular part of eqn. 8.88 is 2n(e,

+ l)Tv(OIO)

with tan cr = bla.

-

2k0a In tan

(; + 3

- - 2k0b In tan ( 4 2 ) (8.91)

The matrix equation: Introducing the expansions 8.83 and 8.85 in eqn. 8.93 and using the discrete Green's functions defined above, the following matrix equation is obtained:

428

Numerical analysis of microstrip patch antennas

The elements in the submatrices are given by

where 6, is the Kronecker delta. The expression for C$yis obtained by interchanging the couples ( x , y), (a, b) and (M, N ) within eqn. 8.96. Finally, it is easily shown that C? = CT. For distances Ir,, - r,l much greater than the dimensions of a cell, the integrals in eqn. (8.96) can be replaced by

In principle, this approximation is not valid for short distances between cells. For these situations, however, the contribution of the vector potential is overshadowed by that of the scalar potential, so that the approximation of eqn. 8.98 still suffices. As a matter of fact, eqn. 8.98 may be used everywhere but on the diagonal terms. This approximation has been confirmed by extensive numerical tests. A last point worth mentioning concerns the number of discrete Green's functions that must be calculated. For a rectangular patch with rn x n charge N)2, with M = ( m - 1)n and cells, the number of matrix elements is (M N = (n - I)m. When all the cells have identical sizes, only rn x n values of T,, M values of Py and N values of Ti;Y are needed in order to completely fill the matrix. This is the great advantage of using cells of equal size, and it is generally more convenient to use a larger number of identical cells rather than fewer cells of different sizes.

+

Interpolation among Green's functions: The evaluation of the matrix in eqn. 8.95 requires a large amount of computation. For a rectangular patch divided into 10 x 10 cells, the order of the matrix is 180; hence the number of elements in the matrix is 1802 = 32400. Even when a simple 4 x 4 Gaussian quadrature is used to evaluate the discrete Green's functions, the number of Sommerfeld integrals that need to be evaluated would exceed half a million.

Numerical analysis of microstrip patch antennas

429

Fortunately, for a given structure these integrals depend only upon the distance from source to observer. It is thus possible to tabulate the integrals for a small number of distances, and then to interpolate between the tabulated values. The distances to be considered range from zero to the maximum linear dimension of the patch. Several interpolation schemes have been tried [13]. The best solution was obtained by separating the Green's functions according to eqn. 8.89, and then using a simple parabolic Lagrange interpolation for the regular part. For a square patch with 10 x 10 cells, at frequencies for which the patch's length is less than a free-space wavelength, the error obtained when interpolating from 25 tabulated values is hardly noticeable: less than 0.5%, even though the computation time was reduced by a factor of loo! 8.6.2 Entire domain basis functions If the microstrip patch has a simple regular shape (circular or rectangular) we can consider the equivalent electromagnetic cavity obtained when the patch is enclosed by a lateral magnetic wall. If the eigen modes have a simple analytical expression it is reasonable to use them as a set of entire domain basis functions. For thin substrates, the surface-current distribution on a microstrip patch at resonance follows closely the behaviour of the corresponding eigenmode except for a slight disturbance due to the antenna's excitation. Therefore, meaningful results can frequently be obtained by using a very small number of entire domain basis functions. This fact enables the analysis of microstrip arrays having hundreds of elements. The size of the linear system to be solved will be equal to two or three times the number of patches. It is clear that if only one basis function is allowed per patch, we cannot use a poor testing procedure such as point matching and match the boundary condition only at the centre of the patch. The best alternative is provided by Galerkin's method where the test functions are identical to the basis functions and the inner product includes a surface integration over the patches [25]. To be clear, let us consider a single rectangular patch of dimensions L, W. The eigen modes of the corresponding cavity are [28]

1;

=

mxx e,sin-cos-

L

nny W

mnx + e,cos-sinL

. nxy W

where the co-ordinate origin is in the lower left corner of the patch. The vectors correspond to the modes TM,,, of the equivalent cavity. The choice of the modes TM,,no in the expansion of J, is rather arbitrary and depends on the problem considered. For instance, they can be ordered according to their resonant frequencies, or we can consider only the TM,, subset if variations along the co-ordinate y can be neglected. In any case, the relation between the integers m, n and the ordinal number j in eqn. 8.99 should be clearly defined. We assume now for the unknown surface current density the following

430

Numerical analysis of microstrip patch antennas

expansion:

Numerical analysis of microstrip patch antennas

437

The above techniques can easily be generalised to the analysis of an array of patches. In this case, the domains of the ith and j t h modes do not necessarily coincide. If the distance between the centres of the patches is greater than the largest linear dimension of a single patch, we can use the approximation

and consequently

Notice that here the unknown coefficients a, are interpreted as being amplitudes of the surface current distribution [A/m] while, when using subsectional basis, the unknowns were the total currents [A] flowing across contiguous cells. If we test now the boundary condition 8.26 in the Galerkin sense, we get the set of equations

where vi, rj denote the centres of the patches. More accurate approximations can be obtained by expanding the Green's functions in a Taylor series. These mathematical tools and powerful numerical integration routines enable the total computation time to be kept within reasonable limits. 8.7 Excitation and loading

The integral involving the scalar potential can be rewritten as

+

W .f; has been used. where the identity V . ( f ; V ) = f; . V V Finally, introducing expansions 8.100 and 8.101 into eqn. 8.102 we get the linear system

where

and

The last term in the expression of c, vanishes if i # j due to the orthogonality of the eigenmodes f;. It can be seen that, essentially, each matrix element requires the computation of two fourfold integrals. Fortunately, two of the four integrations can be performed analytically, by introducing the new variables u = x - x', U' = x x', v = y - y', v' = y y'. As in the subsectional basis case, the elements c,, will include a singularity when r = r' in the Green's functions. Again, a decomposition of the type of eqn. 8.89 or a change to polar co-ordinates may be used to eliminate the singularity.

+

+

In practice, microstrip antennas are excited by many different techniques. A good survey of these has been recently given by Pozar [29]. This Section will present a brief description of those most commonly found, keeping in mind that the method of moments will be used to analyse the antenna. 8.7.1 Several microstrip-antenna excitations A very common technique used for feeding a microstrip antenna consists of a microstrip line directly connected to the patch. A thorough treatment of this excitation requires the analysis of the incident and reflected quasi-TEM current waves existing on the line, which is assumed to extend from the patch to infinity. A more realistic model assumes that the microstrip line has a finite length and introduces a mathematical excitation (for instance, a filament of vertical current or a series voltage generator) at the end of the line. The vertical filament of current is a good model for the coaxial excitation and on a physical basis is preferred to the series voltage generator. The microstrip line is then cut at a point where uniform line conditions can be assumed. In this way the discontinuity created by the line-patch junction, and possibly discontinuities of the line itself, are included in the analysis. If a vertical filament of unit current is used as excitation, the input impedance is simply the voltage at the insertion point. When using other mathematical excitations, the section of line included in the analysis must be long enough to support a standing-wave pattern that can be used to estimate the input impedance of the patch. Finally, it is worth mentioning that replacing the microstrip line by a coaxial probe at the edge of the patch is a first-order approximation that gives surprisingly good results in many practical cases. Microstrip line under the patch: A more sophisticated excitation, designed to minimise the spurious radiation coming from the feed line, uses a microstrip line under the patch to couple energy to it electromagnetically [29, 301. The presence

432

Numerical analysis of microstrip patch antennas

Numerical analysis of microstrip patch antennas

of two dielectric layers adds an additional degree of freedom to the design. The comments made above for the line directly connected to the patch also apply here. The microstrip line can be cut far from the patch and terminated in a coaxial probe or excited by some other mathematical device. Slot in the ground plane: A slot in the ground plane can be used to couple energy to the patch from, presumably, a triplate transmission line [31]. The mathematical treatment replaces the slot by an equivalent distribution of surface magnetic current. The excitation field E''' results from this current. In the numerical procedure, this modifies only the independent terms b, (eqn. 8.106). 8.7.2 Coaxial excitation and input impedance A coaxial line attached to the bottom of the patch (Fig. 8.17) is also a practical way of feeding microstrip patches. From a theoretical point of view, the coaxial excitation is of great interest because simple yet accurate mathematical models are available. While the models presented here are constant current or voltage sources and not constant power sources, that are actually used in practice, the calculated values of the input impedance agrees closely with measured results.

433

between the inner and outer conductors of the coaxial line on the ground plane (Fig. 8.17). For thin substrates, however, replacing the coaxial probe by a vertical filament of current gives results accurate enough for engineering purposes. If the Galerkin technique is used, we can model the probe as a filament of zero diameter ending in a point charge at the junction with the patch. The calculation of the excitation fields would normally require a knowledge of the fields created by vertical electric dipoles embedded in the substrate; however, the reciprocity theorem allows the evaluation of the terms bi (eqn. 8.106) using only formulas related to horizontal electric dipoles. Thus, we have

where E, is the field created by the surface current density J, = f, of eqn. 8.99 and E' is the field produced by the excitation current density Je [A/m2]entering the feed point (x,, y,). The total excitation current is normalised to IA, i.e.

Je

=

e,6(x - x,)6(y - y,)

-h < z < 0

(8.109)

and its domain V, reduces to a segment of length h in the case of zero-diameter filament. Consequently:

Finally, in terms of the Green's functions we have

an expression which can be cast in an easier form as

with the modified scalar Green's function being given by G*, = u,tanhuh/u DTM. Now, once the vector of excitation terms b = (b,) is known, the amplitudes of the basis functions are obtained by solving the linear system of equations (eqn. 8.104). The input impedance is finally given by Fig. 8.1 7 Microstrip patch antenna excited by a coaxial probe The most rigorous model of this configuration considers the probe as belonging to the patch and the whole structure excited by a frill of magnetic current. Simpler models reduce the coaxial line to a filamentary current entering the patch.

The most accurate treatment of a coaxial probe [32, 331 assumes that the portion of the inner coaxial conductor embedded in the substrate belongs to the patch. The whole structure is then excited by a frill of magnetic current existing

When the subsectional basis functions are used together with razor test functions, the coaxial probe must be modelled more carefully in order to avoid mathematical singularities in the excitation terms. The total current entering the probe must be spread over a region of the patch surrounding the insertion point. A simplified attachment mode in which the current is spread over a cell with a linear dependence has been developed and successfully tested [38]. In the frame-

434

Numerical analysis of microstrip patch antennas

Numerical analysis of microstrip patch antennas

work of this model, the expression 8.108 for the excitation terms is still valid but the excitation Ee is created by the currents belonging to the probe and to the attachment mode. Also, the expression 8.1 13 for the input impedance can still be used, but the effect of the attachment mode on itself must be added in order to obtain accurate predictions for the reactance values. Finally, owing to the discretisation inherent in this approach, the excitation point (x,, y e ) can only be located at the centre of a charge cell. The reactance of theprobe: Expression 8.11 3 gives the impedance at the patch level, i.e. z = 0. To obtain the impedance at the ground plane level, z = - h, we need to add in series the self-impedance of the coaxial probe. Assuming now that the inner conductor of radius r, carries a current I evenly distributed on its surface, we have

435

of the M-port. Therefore, the complete determination of the impedance matrix requires the solution of M linear systems, but, fortunately, the matrix C of the system remains unchanged when exciting each port. The elements Z, have been termed 'input impedances' previously (eqns. 8.1 13 and 8.117); however, it must be pointed out that these are input impedances corresponding to a single-port excitation since the remaining M-1 ports are open-circuited. These impedances may be quite different from the true input impedances for which an expression will be given now. Let us consider that each port is connected to a voltage generator U,with an internal impedance Z, (Fig. 8.18). This arrangement includes the case of a passive load Z,, by allowing U, = 0.

I

For thin substrates, we can approximate the magnetic potential due to these currents by u1

array or multiport patch

and the self impedance is given by

Ui

UZ - a m

This term is mainly inductive. Thus, finally, a better estimate of the input impedance of a coaxial-fed antenna is

Z,

=

eqn. 8.113

+ Z,,,

(8.117)

8.7.3 Multipart analysis In many practical situations the microstrip antenna is excited simultaneously at M points, for instance, in the case of a microstrip array. In this case the antenna can be considered as an M-port device and standard circuit theory may be applied to completely characterize the antenna. The first step is to solve the linear system Ccc = b, obtained by application of the method of moments, M times for M different excitation vectors bi. These vectors correspond to a physical situation in which a unit current is entering the j t h port while the remaining M-1 ports are open-circuited. After solving the matrix equation, we get the vector a, = C-I b, containing the amplitudes of the N basis functions. Then, by computing the voltage at each port we get the quantities Zv,i = 1, 2 . . . M, which is the j th column of the impedance matrix

Fig. 8.18 Equivalent circuit of a microstrip antenna array considered as a multiport device The voltage generators are replaced by short circuits at the ports terminated with a passive load

We define a vector U with elements U, and a diagonal load matrix Z , with elements Z,,. The equations relating currents I, and voltages v a t each port (Fig. 8.18) are (8.1 18) u = Z,I + v = ( Z , Z ) I

+

where Z is the matrix of impedances previously calculated. The vector of port currents is then given by (8.1 19) I = (Z, + z)-'U

436

Numerical analysis of microstrip patch antennas

and the vector of port voltages is V

=

Z(ZL

+ z)-I

U . The new vector

N

a* =

1 I'ai ,=I

Numerical analysis of microstrip patch antennas

,

437

input-impedance loci on the Smith chart, the surface current distribution at several resonances and the far-field radiation pattern.

(8.120)

contains the amplitudes of the basis functions for the real working conditions of the antenna, i.e., with all the loads and excitations simultaneously present. This is the vector to be used in the computations of the radiation pattern and when studying the surface current distribution. Finally, the input impedance at each port is

It is clear that, for a single-port antenna, this input impedance equals the parameter Z , , which is directly given by eqns. 8.1 13 or 8.1 17.

8.8.1 Entire-domain versus subdomain basis functions Section 8.6 presented several choices of basis functions that could be used in a MOM procedure. Among the choices were wide-triangle or rooftop subdomain basis functions used with razor testing and entire-domain cosine basis functions used in a Galerkin procedure, i.e. tested with cosine testing functions. Computer programs have been written using these two choices of basis and testing functions, and a comparison of the results obtained will be presented in this Section. The calculation of the far-field radiation pattern will be considered first. If subdomain basis functions are used the patch is reduced to an array of horizontal electric dipoles (HED). In this sense, each rooftop basis function is equivalent to a HED whose moment is given by the product of the total current flowing across the common border of two cells times the distance between the centres of the cells. Now, the far field for a horizontal dipole, which can be thought of as the element pattern in this procedure, is multiplied by the array factor resulting from the segmentation of the patch to give the total far field pattern. Mathematically, the far field is thus given by M

Em

=

GF(rI0)

aIx,exp(jk0e;g~) i=I N

+ GY(40) C bI, exp Woe,. Q;)

(8.122)

j= 1

Fig. 8.1 9 Geometry of a single rectangular patch 6, = 2.55 tan 8 = 0.002 h = 1.28 mm 2, = 0.9e-7

8.8 Single rectangular patch antenna In previous Sections the mathematical theory and numerical procedures have been developed for the analysis of general microstrip structures. This Section will concentrate on a single, rectangular, coaxial-fed patch to illustrate how the theory is applied, present computed results for a simple common structure and answer some of the questions that remain. Remaining questions include the convergence of the method-of-moments procedure and the advantages and disadvantages of the various choices of basis functions presented in Section 8.6. Results will be presented for a single patch as shown in Fig. 8.19 showing the

where a = 0, cp, Li and I, ark the MOM current coefficients and G, represents the far fields due to a HED. The pattern can then be integrated to calculate the directivity, gain and efficiency. When properly chosen entire domain basis functions are used, the far field for each basis function can be calculated analytically, and the total far field is a simple sum of the fields generated by each basis function. For other choices of basis functions costly numerical integration techniques may be required. Fig. 8.20 shows the far-field pattern for a single rectangular patch. The subdomain rooftop and entire-domain cosine basis functions yield identical co-polar patterns at resonance while only the rooftop basis functions yield an estimate of the cross-polar pattern. The cross-polar pattern is due mostly to currents on the patch in phase with the excitation spreading out from the coaxial probe, and to the currents in the probe. In general, the cross-polarised pattern is very difficult to calculate accurately and is sensitive in practice to the size of the ground plane; an item not included in the numerical model. The model can be used, however, to study the effect of the placement of the coaxial probe on the cross-polar pattern. Figs. 8 . 2 0 ~and 8.206 show the far-field pattern of a single patch when excited by a coaxial probe located at different points.

438

Numerical analysis of microstrip patch antennas

Numerical analysis of microstrip patch antennas

439

The entire domain functions could, in theory, model accurately the patch at frequencies away from resonance and its cross-polar behaviour, however, in practice, this is costly. Near resonance only one or two entire domain functions are needed to model surface current, and are therefore very well suited to standard geometries near resonance. The cost to include additional basis functions needed away from resonance or to calculate the cross-polar pattern is, however, relatively high compared to the subdomain basis functions. Thus it may be more efficient to use subdomain basis functions when studying a single patch or small array away from resonance or when cross-polar pattern is needed.

10

,

theta (degrees)

Fig. 8.21 Input impedance for the single rectangular patch shown in Fig. 8.19. Frequency range: 1.52-1.58 GHz. Frequency increases clockwise with a 0.01 GHz step Rooftop basis functions 0 Entire-domain cosine basis functions

theta (degrees) Fig. 8.20 Radiation pattern for the single rectangular patch shown in Fig. 8.19. Frequency = 1.565GHz. A Coaxial feed at x = 16.66 mm. y = 16.66 mm B Coaxial feed at x = 16.66 mm. y = 20 mm . . . . .E-plane co-polar H-plane co-polar

---- E-plane cross-polar --- H-plane cross-polar

The input impedance for a single patch is given on the Smith chart of Fig. 8.21. The two choices of basis functions yield approximately the same results with a slight shift in frequency. The resonant frequencies obtained differ by 0.77%, which is often much less than what arises due to uncertainties in the manufacturing process and material parameters. Fig. 8.22 shows the variation of the real part of the input impedance as a function of position for three choices of widthlaspect ratios. In each case, the coaxial line was centered in the nonresonant direction on the patch and then moved inward from the edge of the patch to the centre. Note that the results were calculated at the resonant frequency for each patch.

440

Numerical analysis of microstrip patch antennas

8.8.2 Convergence using subsectional basis functions The question of convergence must always be dealt with when using a moment method. If a numerical result has not converged there is virtually no hope of its being correct. The factors affecting convergence include: the choice of basis and testing functions, frequency, antenna shape, the dielectric used and even the numerical precision of the computer. Since this list includes nearly all the parameters of the antenna and affects nearly all of the decisions made during the development of the computer program to some degree, it is difficult to give rules that guarantee that a particular result has converged. However, several rules of thumb are applicable and can be used as a base when studying convergence. This Section will briefly demonstrate how the MOM solution using subsectional basis functions converges.

Numerical analysis of microstrip patch antennas

441

direction transverse to the resonance direction, i.e. parallel to the H plane at the first resonant frequency, may be reduced without a significant penalty, resulting in large savings in computation time. Fig. 8.23 shows how the input impedance of a rectangular patch converges when the number of basis functions in the H-plane direction is varied at frequencies near the first resonance. Note the resonant frequency changes by only 0.3% when using three basis functions in the transverse direction as opposed to using 7, however, the input impedance changes by approximately 20%. Thus, a rough study of the antenna's resonant frequency and radiation pattern can be performed quickly at low cost. The final analysis can then be performed using additional basis functions.

10

Fig. 8.22 Real part of the input impedance as a function of the position on the patch. The coaxial is centered along the non-resonant direction and moved from the edge of the patch ( x l L = 0 ) to the centre of the patch ( x l L = 0.5). For case ( a ) the antenna parameters are given in Fig. 8.1 9 where L = 60mm and W = 40mm. For cases ( 6 ) and ( c ) the width W is varied. ( a ) . . . . . L I W = 1.5 f,,,,,, = 1.555 GHz (6)----LIW=l.O f,,,,,,=1.543GHz ( c ) --- L I W = 0.667 f,,,,,, = 1.535 GHz

The general rule of thumb given in the published literature is that, when using subsectional basis functions, of the order of 10 basis functions per wavelength are needed to obtain good results. This rule also holds for microstrip antennas operating near the first few resonances when calculating the input impedance. It is interesting to note, though, that the number of basis functions in the

Fig. 8.23 Input impedance for the single rectangular patch shown in Fig. 8.19 with the coaxial centered vertically (y = 20mm) and at x = 76.66mm versus the number of basis functions in the H-plane direction, i.e. along the y-axis Frequency range is from 1.52 GHz increasing clockwise to 1.60 GHz with a step of 0.01 GHz +: 9 by 7 cells 0: 9 by 5 cells ': 9 by 3 cells

8.8.3 Surface currents The subsectional basis functions can be used to model virtually any current distribution owing to their flexibility. As an example, a rectangular patch was analysed and measured at the first four resonances, TM,,, TM,,,, TM,,, and TM,,. The patch dimensions are 60 x 40mm and the dielectric is a standard low-frequency printed-circuit substrate with high losses in the microwave range (E, = 4.34 and tans z 0.02). The excitation point has been selected at

444

Numerical analysis of microstrip patch antennas

induces currents in its neighbours affecting the element's radiation pattern and input impedance. Thus, elements in an array environment have to be studied in the actual array environment to properly account for mutual coupling [34, 351. However, when the coupling between array elements is less than 20 or 30dB, it may be possible to neglect mutual coupling and still obtain acceptable results.

Numerical analysis of microstrip patch antennas

445

current distribution on the elements. The method of moments is well suited for the task because any current distribution can be calculated to the desired precision and coupling coefficients are easily calculated. However, practical limitations exist when applying the MOM to anything but small arrays. The use of subsectional basis functions, while very flexible in modelling arbitrary geometries and current distributions, comes with a high price in the number of unknowns. To accurately model an element of the array approximately 50 unknowns are needed; thus for a linear array 10 elements long, 500 unknowns are needed. It can be seen that the capacity of even the largest currently available computer is quickly surpassed. There are, however, several techniques that can be used to study larger arrays without simply using a larger computer or more computer time. These techniques include: (a) Entire domain basis functions

(b) Infinite array techniques Additionally, specialised numerical techniques may be applied with success in certain cases. The method of conjugate gradients has been proposed as a method that would allow the solution of larger systems of linear equations [36, 371. However, normally the MOM matrix is not sparse and the slow convergence of iterative routines applied to fully populated linear systems precludes their use. Of the two techniques discussed above only the use of entire-domain basis functions will be discussed since infinite array techniques are included as a full Chapter of this handbook. Using entire-domain basis function only one or two basis functions are typically needed at resonance per element; so arrays having up to several hundred elements can be studied easily with today's computers. However, the study of circularly polarised elements or the cross-polarised fields requires the use of additional higher-order basis functions. This considerably increases the computation time and reduces the size of largest array that can be studied.

Fig. 8.25 Input impedance near the two first resonances of the patch of Fig. 8.24.After [38]. 0 Theory (9 x 6 cells) Measurements.

This section will present results for several small arrays and show how the element factor and input impedance are affected when an isolated element is incorporated in an array. 8.9.1 Array modelling To accurately model an array the model should not assume any particular

8.9.2 Mutual coupling A 2 x 2 element array was build on a lossy, inexpensive substrate and the four elements of the scattering matrix were measured and compared with the results obtained using the numerical procedures presented previously in this Chapter. The scattering matrix is defined by

where Z i s the impedance matrix with elements calculated using eqn. 8.1 17 and I is the unit dyadic. The array consisted of four identical patches, each 60 mm along the E-plane and 40 mm along H-plane. The substrate thickness was 0.8 mm and the dielectric constant was 4.34 with a loss tangent of 0.02. The elements were coaxially fed with the coaxial line centered along the H-plane and located lOmm from the

446

Numerical analysis of microstrip patch antennas

Numerical analysis of microstrip patch antennas

-1 8 1.10

1.10

1.14

1.14

1.18 1.22 frequency (GHz)

1.26

1.18 1.22 frequency (GHz)

1.26

1.30

-44

1 1.10 1.14 1.18 1.22 1.26 1.: frequency (GHz)

1.30

Fig. 8.26 Scattering parameters for a 2 x 2 microstrip array: measured versus theory Patch size: 60 mm by 40mm, h = 0.8 mm E, = 4.34 tan 6 = 0.02 E-plane separation 20mm between patch edges H-plane separation 1 6 mm between patch edges (8) S I ~ ( 6 ) s12 ( c ) S13 ( d ) Sll ---- Measured . . . . .Theory

-60

447

I

1.10

,

, 1.14

,

,

,

,

1.18 1.22 frequency (GHz)

,

, 1.26

, 1.:

448

Numerical analysis of microstrip patch antennas

edge. The separation between the patches was 20mm along the E-plane and 16 mm along the H-plane, corresponding, respectively, to 0.08 and 0.064 freespace wavelengths at the isolated patch's resonance of 1.2 GHz. The reslllts are shown in Fig. 8.26. The two algorithms, which use different basis fmctions, yield nearly identical results across the frequency band. As can 'se seen, the agreement between the measured and calculated results is good.

Numerical analysis of rnicrostrip patch antennas

449

H-plane coupling decreases faster than the E-plane coupling, which is sustained by the surface wave and becomes dominant for greater separations. It must be finally pointed out that the values of the coupling (s,, parameter) are dependent on the input impedance (z,, parameter) and are usually given for a couple of patches matched to 500. The small differences with measurements in Fig. 8.27 can be due to a slight mismatch of the patches. 8.9.3 Linear array of four patches The last example in this Chapter will illustrate, from a theoretical point of view, the relevance of mutual coupling in the computation of input impedances and mutual coupling, The selected configuration is shown in Fig. 8.28 and consists of four rectangular identical patches fed by coaxial probes and working in the lowest-order mode. The substrate parameters are h = 0.787 mm, and E, = 2.23. The patches are coupled by their non-resonant sides (H-plane coupling) and they are excited uniformly. On the other hand, their spacing is non-uniform in order to obtain a lower first-sidelobe level [39].

H

3rnm

t 4 4;;1 t 10.3

rn rn

10.3 rnrn

-

h= 0.787rnrn f = 11.9GHz relative perrnitivity=2.23 Fig. 8.27

Measured (Jedlicka, Poe and Carver [35]) and calculated mutual coupling between two coaxial-fed rnicrostrip antennas versus the separation between the patch centres D measured in free-space wavelengths W = 105.7mm L = 65.5mrn h = l . 6 m m E, = 2.53 f, = 1.414GHz Measured E-plane (From Reference 35) 0 Measured H-plane (From Reference 35) . . . . . Calculated E-plane ---- Calculated H-plane --- Calculated 45' plane

Fig. 8.27 gives the E- and H-plane coupling results as a function of the distance between two patches measured by Jedlicka, Poe and Carver [35], and compares these results with those calculated using the theory presented above. Entire-domain basis functions were used. In addition, the calculated coupling results between two antennas located along a diagonal are also presented. It is readily apparent that the H-plane coupling is stronger for small separations. This is the kind of coupling found in standard microstrip coupled line filters, and it is mainly due to quasi-static terms and to the space wave. However, the

Fig. 8.28

Linear array with four identical patches and nonuniform spacing The substrate has a permittivity of E, = 2.23 and a thickness of h = 0.787mm. The nominal resonant frequency is f,, = 11.9GHz.

Fig. 8.29 shows the normalised real and imaginary parts of the input impedance presented by an inner patch. For each of the quantities, two curves are given, corresponding to theoretical calculations without mutual coupling (the patch is considered as an isolated element) and with mutual coupling (the patch is embedded in an array environment with the three other patches terminated by 50R loads). It can be seen that, for this array, mutual coupling raises the maximum resistance from 130R to 154R. This significant change (18%) shows clearly that mutual coupling should be taken into account for properly matching a microstrip array. The influence of mutual coupling on radiation patterns is even stronger. Fig. 8.30 shows the H-plane radiation patterns of an isolated patch and of an inner patch in an embedded configuration. The asymmetries in the geometrical environment of an inner patch (coupled to two patches on one side but only to one

450

Numerical analysis of microstrip patch antennas

o! 11.0

,

, 11.4

,

,

,

,

,

11.8 12.2 frequency (GHz)

, 12.6

Numerical analysis of microstrip patch antennas

I

,

13.0 Fig. 8.30

-0.75

Calculated isolated-element and embedded-inner-element far-field radiation patterns for the array of Fig. 8.28 I n the embedded case all the other elements are loaded with 50R --- Isolated element . . . . . Embedded element

i---7-TT , , , , , , 11.0

Fig. 8.29

45 7

11.4

11.8 12.2 frequency (GHz)

12.6

13

Calculated isolated-element and embedded-inner-element input impedance versus frequency for the array of Fig. 8.28. Values are normalised to 50R a Real part b Imaginary part . . . , . Isolated element --- Embedded element

theta (degrees) Fig. 8.31

Calculated H-plane far-field pattern of the array shown in Fig. 8.28 with and without mutual coupling . . . . . With mutual coupling (MOM result) First sidelobe = -1 3 S d B coupling First sidelobe = - 18.6 dB

--- Without mutual

452

Numerical analysis of microstrip patch antennas

on the other side) are clearly reflected in the asymmetrical pattern for the embedded situation. Finally, Fig. 8.31 gives the overall radiation pattern of the array in the H-plane. A first theoretical prediction neglects mutual coupling and computes the array pattern as the product of the isolated element pattern times the array factor. The first-order sidelobe is then at - 18.6dB, well below the value of - 13.2dB which can be obtained with four equally spaced, uniformly fed elements [40]. However, if the integral-equation model presented in this Chapter is used, mutual coupling is automatically taken into account. Theoretical predictions show then how mutual coupling deteriorates the radiation pattern, raising the first-sidelobe level to only - 13.8dB.

8.10 Acknowledgments

The authors would like to thank the members of the Laboratoire d'ElectromagnQisme et dlAcoustique (LEMA) for their aid and support. Specifically, Anja Skrivewik, Lionel Barlatey and Bertrand Roudot performed many of the calculations and measurements presented in this Chapter. Also special thanks are due to Mrs. Mary Hall for typing the manuscript. 8.11 References 1 BAHL, I. J., and BHARTIA, P.: 'Microstrip antennas' (Artech House, 1980). 2 STRATTON, J. A,: 'Electromagnetic theory' (McGraw-Hill, NY, 1941). 3 MICHALSKI, K. A.: 'On the scalar potential of a point charge associated with a timeharmonic dipole in a layered medium', IEEE Trans., 1988, AP-36. 4 POGGIO, A. J., and MILLER, E. K.: 'Integral equation solutions of three-dimensional scattering problems', In M1TTRA;R. (Ed.), 'Computer Techniques for Electromagnetics' (Pergamon Press, 1973). 5 LO, Y. T.: 'Electromagnetic field of a dipole source above a grounded dielectric slab', J. Appl. Phys., 1954, 25, p. 733. 6 BRICK, D. B.: 'The radiation of a Hertzian dipole over a coated conductor', Proc. IEE, 1955, 102C, pp. 103-121. 7 BREKHOVSKIKH, L. M.: 'Waves in layered media' (Academic Press, NY, 1960). 8 WAIT, J. R.: 'Electromagnetic waves in stratified media', (Pergamon Press, 1962). 9 FELSEN, L. B., and MARCUVITZ, N.: 'Radiation scattering of waves', (Prentice Hall, New Jersey, 1973). 10 KONG, J. A,: 'Theory of electromagnetic waves', (Wiley, NY, 1975). I I SOMMERFELD, A.: 'Partial differential equations in physics' (Academic Press, NY 1949). 12 HARRINGTON, R. F.: 'Time harmonic electromagnetic fields' (McGraw-Hill, NY, 1961). 13 MOSIG, J. R., and GARDIOL, F. E.: 'A dynamical radiation model for microstrip structures'. in HAWKES, P. (Ed.) 'Advances in electronics and electron physics', (Academic Press, NY, 1982) pp. 139-237. 14 MOSIG, J. R., and GARDIOL, F. E.: 'Analytic and numerical techniques in the Green's function treatment of microstrip antennas and scatterers', IEE Proc., 1983, 130H, pp. 175-182. 15 SHASTRY, S. V. K.; Ph.D. Dissertation, Indian Institute of Science, Bangalore, India, 1979.

Numerical analysis of microstrip patch antennas

453

UZUNOGLU, N. K., ALEXOPOULOS, N. G., and FIKIORIS, J. G.: 'Radiation properties of microstrip dipoles', IEEE Trans., 1979, AP-27, pp. 853-858. MOSIG, J. R., and GARDIOL, F. E.: 'Dielectric losses, ohmic losses and surface wave effects in microstrip antennas.' Int. URSI Symposium, Santiago de Compostela, Spain, 1983, pp. 425-428. MICHALSKI, K. A,: 'On the efficient evaluation of integrals arising in the Sommerfeld halfspace problem', IEE Proc., 1985, 132H, pp. 312-318. LYTLE, R. J., and LAGER, D. L.: 'Numerical evaluation of Sommerfeld integrals'. Report UCRL-52423, Lawrence Livermore Lab., Univ. of California, 1974. PANTIS, G.: 'The evaluation of integrals with oscillatory integrands', J. Comp. Phys., 1975, 17, pp. 229-233. BORIS, J. P., and ORAN, E. S.: 'Evaluation of oscillatory integrals', J. Comp. Phys., 1975, 17, pp. 425-433. HURWITZ, H., and ZWEIFEL, P. F.: 'Numerical quadrature of Fourier transform integrals', Math. Tables Aids Cornput., 1956, 10, pp. 140-149. ALAYLIOGLU, A., EVANS, G., and HYSLOP, J.: 'The evaluation of oscillatory integrals with infinite limits,' J. Comp. Physics, 1973, 13, pp. 433-438. SIDI, A,: 'The numerical evaluation of very oscillatory infinite integrals by extrapolation', Math. Comp., 1982, 38, pp. 517-529. HARRINGTON, R. F.: 'Field computation by moment methods' (MacMillan, NY, 1968). RAO, S. M., WILTON, D. R., and GLISSON, A. W.: 'Electromagnetic scattering by surfaces of arbitrary shape', IEEE Trans., 1982, AP-30, pp. 409-418. GLISSON, A. W., and WILTON, D. R.: 'Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces', IEEE Trans., 1981, AP-29, pp. 593-603. COLLIN, R. E.: 'Foundations for microwave engineering', (McGraw-Hill, NY, 1966). POZAR, D. M.: 'New architectures for millimeter wave phased array antennas', Journees Internationales de Nice sur les Antennas (JINA), Nice, 1986, pp. 168-179. KATEHI, P. B., ALEXOPOULOS, N. G.: 'On the modelling of electromagnetic coupled microstrip antennas - The printed strip dipole,' IEEE Trans. Antennas Propagat., AP-32, pp. 1179-1 186, 1984. SULLIVAN, P. L. and SCHAUBERT D. H., 'Analysis of an aperture coupled microstrip antenna,' IEEE Trans. Antennas Propagat., AP-34, pp. 977-984, 1986. POPOVIC, B. D., DRAGOVIC, M. B., and DJORDJEVIC, A. R.: 'Analysis and synthesis of wire antennas', (Wiley, NY, 1982). HALL, R. C., MOSIG, J. R., and GARDIOL, F. E.: 'Analysis of microstrip antenna arrays with thick substrates', 17th European Microwave Conf., Rome, Italy, 1987. ALEXOPOULOS, N. G., and RANA, I. E.: 'Mutual impedance computation between pr~nted dipoles', IEEE Trans., 1981 AP-29, pp. 106-1 11. JEDLICKA, R. P., POE, M. T.. and CARVER, K. R.: 'Measured mutual coupling between microstrip antennas', IEEE Trans., 1981, AP-29, pp. 147-149. JACOBS, D. A. H.: 'A generalization of the conjugate-gradient method to solve complex systems', IMAJ of Numerical Analysis, 1986, 6, pp. 447-452. PETERSON, A. F., and MITTRA, R.: 'Method of conjugate gradients for the numerical solution of large-body electromagnetic scattering problems', J. Opt. Soc. Am. A, 1985, 2, pp. 971-977. MOSIG, J. R., and GARDIOL, F. E.: 'General integral equation formulation for microstrip antennas and scatterers', IEE Proc., 1985, 132H, pp. 424-432. GRONAU, G., and WOLFF, I.: 'Spectral domain analysis of microstrip antennas', Proc. of Workshop 'Analytical and numerical techniques for microstrip circuits and antennas', Montreux, Switzerland, March 1988. BALANIS, C. A,: 'Antenna theory: analysis and design', (Harper & Row, NY, 1982). -

-

Chapter 9

Multiport network approach for modelling and analysis of microstrip patch antennas and arrays K. C. Gupta

9.1 Introduction

The multiport network approach for microstrip patch antennas is based on the use of segmentation and desegmentation methods for analysis of planar structures. Segmentation and desegmentation techniques were developed originally for analysis of two-dimensional (planar) circuit components [I-7.Since microstrip patch antennas on thin substrates can be treated as two-dimensional planar components, segmentation and desegmentation techniques have been employed for the analysis of microstrip antennas also [8, 91. This approach has been used successfully for the analysis and design of several types of microstrip patch antennas [lo-171 and arrays [18], and promises to be an appropriate methodology for computer-aided design [19,20] of microstrip patch antennas and arrays in hybrid as well as in monolithic configurations. This Chapter describes the multiport network approach, segmentationdesegmentation techniques, and their applications to design of microstrip antennas. Relevant aspects of various models for microstrip antennas are presented in Section 9.2. The multiport network model [19], which is an extension of the well known cavity model [21,22] for microstrip patches, is discussed. Evaluation of multiport impedance matrices from the Green's functions for various types of segments is described in Section 9.3. Modelling of external fields (including fringing, radiation and surface wave) by edge-admittance networks is detailed in Section 9.4. Segmentation and desegmentation methods for analysis of planar electromagnetic structures (and for multiport networks) are discussed in Section 9.5. Various examples of microstrip antenna configurations, which have been analysed and designed using multiport network approach, are reviewed in Section 9.6. These include various types of single-feed circularly-polarised microstrip patch configurations, such as a diagonally-fed nearly square patch, .a square patch with truncated comers, a square patch with a diagonal slot, a pentagonal-shaped patch, a square ring patch, and a cross-shaped patch. The second group of antennas analysed by the multiport network approach consists

456

Multiport network approach for modelling

of broadband multi-resonator microstrip antennas. Three-resonator and fiveresonator configurations (coupled to a central patch either by a capacitive-gap coupling or by short sections of microstrip lines) are included in this group. The third category of microstrip antenna configurations, discussed in Section 9.6.3, consists of two-port rectangular, two-port circular patches, and series-fed arrays making use of these two-port patches. Discussion related to the development of CAD procedures for microstrip patches and arrays is contained in Section 9.7. It is pointed out that multiport network modelling and segmentation/desegmentation methods of analysis are ideally suitable for implementation of CAD procedures for microstrip antennas.

Multiport network approach for modelling

457

ports are located along the non-radiating edges, transmission from port 1 to port 2 can be controlled by suitable choices of distances x, and x,. Again, the two models shown in Figs. 9.2a and b do not incorporate the parasitic reactances associated with the feed-line-patch junctions.

9.2 Models for microstrip antennas The transmission-line model [23, 241 and the cavity model [21, 221 are the two most widely used network models for analysis of microstrip antennas. We will discuss these models briefly before introducing the multiport network model suitable for implementing segmentation/desegmentation methods. 9.2.1 Transmission-line model In this model, a rectangular microstrip antenna patch is viewed as a resonant section of a microstrip transmission line. A detailed description of the transmission-line model is given in Chapter 10. The basic concept is shown in Fig. 9.1 which illustrates the transmission-line models for (a) and unloaded rectangular patch; (b) a rectangular patch with a feed line along the radiating edge; and (c) a rectangular patch with a feed line along the non-radiating edge. Z,, is the characteristic impedance of a microstrip line of width W,, and E , is the corresponding effective dielectric constant. Be and G, are capacitive and conductive components of the edge admittance Y,. The susceptance B, accounts for the fringing field associated with the radiating edge of the width W,, and G, is the conductance contributed by the radiation field associated with each edge. Power carried away by the surface wave(s) excited along the slab may also be represented by a lumped loss and added to G,. In Fig. 9. lb and c, Zof and are the characteristic impedance and the effective dielectric constant for the feeding microstrip line of width Wf. In both of these cases, the parasitic reactances associated with the junction between the line and the patch have not been taken into account. Transmission-line models may also be developed for two-port rectangular microstrip patches [14]. These configurations are used in the design of series-fed linear (or planar) arrays [25, 181. Models for two types of two-port rectangular microstrip patches are shown in Fig. 9.2. Fig. 9.2a illustrates the equivalent transmission-line network when the two ports are located along the radiating edges, and Fig. 9.26 shows the transmission-line model [26] when the two ports are along the non-radiating edges. It has been shown [14,26] that, when the two

a unloaded patch

b feedline along the radiating edge

rn

c feedline along the non-radiating edge

Fig. 9.1 Transmission-line models for three rectangular microstrip patch configurations

There are several limitations inherent to the concept of the transmission-line model for microstrip antennas. The basic assumptions include: (i) fields are uniform along the width W, of the patch; and (ii) there are no currents transverse

458

Multiport network approach for modelling

to the length I of the patch. Detailed analysis of rectangular patches has shown [27] that, even at a frequency close to the resonance, field distribution along the radiating edge is not always uniform. Also, the transverse currents are caused by the feeding mechanism and are invariably present. Moreover, the circularly polarised rectangular microstrip antennas (whose operation depends upon the excitation of two orthogonal modes) cannot be represented by the transmissionline model discussed above. Clearly, a more accurate method for modelling of microstrip antennas is needed.

a feedlines olong radioting edges

b feedlines olong non-radioting edges

Fig. 9.2

Transmission-line modes for two-port rectangular microstrip patch antennas

9.2.2 Cavity model A planar two-dimensional cavity model for microstrip patch antennas [21, 221 offers considerable improvement over the one-dimensional transmission-line model discussed in the previous Section. In this method of modelling, the microstrip patch is considered as a two-dimensional resonator surrounded by a

Multiport network approach for modelling

459

460

Multiport network approach for modelling

Multiport network approach for modelling

461

perfect magnetic wall around the periphery. The fields underneath the patch are expanded in terms of the resonant modes of the two-dimensional resonator. This approach is applicable to a variety of patch geometries. These geometries, the corresponding modal variations denoted by $ ., and the resonant wave numbers k,, are shown in Table 9.1 (from Reference 21). E and H fields are related to ,$, by

Ern" =

(9.1)

*d

K . = i x V,rCl,liw (9.2) where i is a unit vector normal to the plane of the patch. Resonant wave numbers k,,, are solutions of (Vf

+ en)*,=

0

(9.3)

with

on the magnetic wall (periphery of the patch). V, is the transverse part of the del operator and p is perpendicular to the magnetic wall. The fringing fields at the edges are accounted for by extending the patch boundary outwards and considering the effective dimensions to be somewhat larger than the physical dimensions of the patch. The radiation is accounted for. by considering the effective loss tangent of the dielectric to be larger than the actual value. If the radiated power is estimated to be P,,the effective loss tangent 6, may be written as

where Pd is the power dissipated in the dielectric substrate and 6, is the loss tangent for the dielectric medium. The effective loss tangent given by eqn. 9.5 can be modified further to incorporate the conductor loss. The modified loss tangent 6, is given by

The input impedance of the antenna is calculated by finding the power dissipated in the patch for a unit voltage at the feed port, and is given by where P = P, + PC + P,, + P,.WEis the time-averaged electric stored energy, and W, is the time-averaged magnetic energy. The voltage V equals Ezd averaged over the feed-strip width (d is the substrate thickness). The far-zone field, and radiated power are computed by replacing the equivalent magnetic-current

462

Multiport network approach for modelling

Multiport network approach for modelling

ribbon on the patch's perimeter by a magnetic line current of magnitude Kd on the ground plane (xy plane). The magnetic current source is given by

463

respectively. Green's function G is usually a doubly infinite summation with terms corresponding to various modes of the planar resonator (rectangular or circular or triangular) with magnetic walls.

where ii is a unit vector normal to the patch's perimeter and iE(x, y) is the component of the electric field perpendicular to the ground plane. A cavity model for microstrip patch antennas may also be formulated by considering a planar two-dimensional resonator with an impedance boundary wall all around the edges of the patch. A direct form of network analogue (DFNA) method for the analysis of such a cavity model has been discussed in Reference 28. 9.2.3 Multiport network model The multiport network model of microstrip patch antennas [19, 291 may be considered as an extension of the cavity model discussed above. Electromagnetic fields underneath the patch and outside the patch are modelled separately. The patch itself is analysed as a two-dimensional planar network [I], with a multiple number of ports located all around the edges as shown in Fig. 9.3. Each port represents a small section (of length v ) of the edge of the patch. is chosen so small that the fields over this length may be assumed to be uniform. Typically, for a rectangular patch, the number of ports along each radiating edge is taken to be 4, and along each non-radiating edge the number is taken to be eight.

Fig. 9.3

Multiport representation of a rectangular patch

Thus, a 24 x 24 matrix is typically adequate for the characterisation of the interior fields of a rectangular patch. For patches of regular shapes (rectangles, circles, rings, sectors of circles and of rings, and three types of triangles), this multiport planar network model can be analysed by using two-dimensional impedance Green's functions available for these shapes [I]. A multiport Z-matrix characterisation representing the fields underneath the patch can be derived from the Green's function as: Z, =

w1y [&JY

~ ( x lY, ~ I ~j)dsids, X~,

where x,,, y,, denote the locations of the two ports of widths

(9.9) and

y,

Fig. 9.4

(a) A cross-shaped microstrip patch. (6) Multipart-network model of the crossshaped microstrip patch

For patches of composite shapes (such as a cross shape shown in Fig. 9.4a), a multiport network model can be written by treating the composite shape as a combination of the elementary shapes for which Green's functions are available. The cross shape of Fig. 9 . 4 ~can be considered as a combination of three rectangular segments as shown in Fig. 9.46. Segmentation and desegmentation methods [I] are used for finding the 2-matrix of a composite shape from those of the elementary segments. If the patch or one of the segments of a composite patch is of an irregular shape for which Green's function is not available, a technique called the contour integral method [I] can be used to evaluate the Z-matrix. In the multiport-network modelling of radiating microstrip patches, the fields (namely, the fringing fields at the edges, the surface-wave fields outside the and the radiation field) are incorporated by adding equivalent edge admittance networks (EAN) connected to the various edges of the patch. This representation is shown in Fig. 9.5 for the case of the rectangular patch shown in Fig. 9.3. EANs are multiport networks consisting of parallel combinations of the capacitances C (representing the energy stored in the fringing field) and the conductances G (representing the power carried away by radiation and surface waves) as shown in Fig. 9.6a. Each capacitance-conductance pair is connected to a port of the planar equivalent circuit of the patch. EANs at the non-radiating edges may be simplified to consist of capacitances only, as shown in Fig. 9.6b. Values of capacitance and conductance in the edge-admittance networks may be obtained from the various analyses reported in the literature [30-321. The flexibility of the multiport network model leads to several advantages when compared with the conventional cavity model discussed in Section 9.2.2. For example, the parasitic reactances at the junction between the feed line and the patch can be incorporated in the multiport network model by considering

464

Multiport network approach for modelling

Multiport network approach for modelling

a small section of the feed line as an equivalent planar circuit connected to the patch at a finite number of (typically five) ports. Solution of this network problem (depicted in Fig. 9.7) is equivalent to the expansion of the fields (in the feed line as well as in the patch) in series of eigen - functions and matching the fields at the interface.

465

current sources at the two corresponding sections of the edges. Similar MCNs may also be included between the non-radiating edges, between a radiating edge and a non-radiating edge, or between two edges of different patches in an array.

NR-EAN

NR-EAN

NR-EAN

Fig. 9.7 lncorporation of feed-junction reactance in multipart-network model of a rectangular patch

Fig. 9.5

Edge-admittance networks (EANs) connected to the multiport representation of a rectangular patch

Fig. 9.6 Edge admittance networks for (a) radiating edges; (b) non-radiating edges

R-EAN

Also, the multiport network model discussed above can be extended to incorporate the effect of mutual coupling between the two radiating edges [33] by inserting a mutual coupling network (MCN) as shown in Fig. 9.8. The edge-admittance terms associated with various ports at the edges constitute the diagonal terms of the admittance matrix for MCN. The non-diagonal terms of this matrix are obtained from the 'reaction' between the equivalent magnetic

I

Fig. 9.8 Incorporation of mutual coupling in multipart-network model of a ~ectangularpatch

It may be noted that, in the multiport network model, the characterisation of fields underneath the patch is conceptually similar to that used in the conventional cavity model [21, 221. In both of these models, the fields under the patch

466

Multiport network approach for modelling

Multiport network approach for modelling

are considered two-dimensional with no variations of fields perpendicular to the substrate. For this reason, the limits of the applicability of the technique in terms of substrate permittivity and thickness are similar to that for the cavity model. Also, both of these methods will not be accurate when applied to narrow-width microstrip dipoles rather than to the wide microstrip patches discussed in this Chapter. y

4

Y

A

467

9.3 Z-matrix characterisation of planar segments

9.3.1 Green's functions For practical microstrip antennas, the thickness of the substrate is much smaller than the wavelength. Therefore fields underneath the patch do not vary in the z-direction (perpendicular to the substrate). Electric field has a z-component only. Since aE,/az = 0, we may define a voltage V(x,y) given by (9.10) V(x,Y ) = - Ez(x, y)d where d is the substrate thickness. When a magnetic-wall boundary condition is assumed at the edges of the patch, V(x,y) satisfies the boundary condition given by eqn. 9.4, i.e.

If we consider a z-directed electric current source Jx(xo,yo) located at (xo,) ,), the voltage V(x,y) is related to the source current through a two-dimensional impedance Green's function G(x, ylx,, yo) defined by

microstrip patch antenna

I

I

top view

&coax connector side view Fig. 9.10 Microstrip patch antenna with a probe feed perpendicular to the substrate Fig. 9.9 Various geometries of the planar segments for which Green's functions are available

Green's functions used for evaluating impedance-matrix characterisation for patches of various shapes are discussed in Section 9.3. Derivation of the Z-matrix is also included therein.

where the source current J, is distributed over a region D in x, y plane. These Green's functions are known [I] for several regular shapes shown in Fig. 9.9. Expressions for these Green's functions are listed in Appendix 9.8. When a microstrip antenna is excited by a probe feed perpendicular to the

468

Multiport network approach for modelling

Multiport network approach for modelling

substrate, as shown in Fig. 9.10, the current density may be related to the axial current through the z-directed probe. For patches excited by a microstrip line feed, the current J,,flowing into the patch can be expressed as an equivalent z-directed electric current sheet J, as follows. At the magnetic wall surrounding the patch (as shown in Fig. 9.1 I),

-

J, =

B

x H,

(9.13)

469

and involves integration of G(x, ylx,, yo) over the extent of the two-ports corresponding to the specific element of the Z-matrix. For a microstrip line feed with an effective width y, the integral is carried out over the width 4. For a probe-feed type of external port, the integration is carried out over a circular path corresponding to the cylindrical surface of the probe. Alternatively, the circular probe maybe replaced by an equivalent strip and the integration carried over this equivalent width. Z-matrix for rectangular segments: Green's functions for various geometries, discussed in Appendix 9.8, appe8r as double-infinite summations. In numerical computations of the 2-matrix elements, order of integration and summations could be interchanged. For rectangular segments, the integrals involved may be carried out analytically. When sides of the rectangle are oriented along x- and y-axes and for the two ports (say, port p and port q), the impedance-matrix element Z,, may be written in the following form [37]:

. dJm,(~q,~,)l(k2x+ Jin

feedline

H,

4' :!tj,

k: -

where, for ports oriented along the y-direction,

6,

(x, y)

=

cos (k,x) cos (kyy) sinc

patch

and for ports oriented along the x-direction dJmn(x,y) = cos ( k p ) cos (k,,y) sin Fig. 9.11 Equivalence between the port current and the z-directed fictitious current density at the junction between a microstrip-line feed and a patch

and for the planar waveguide model of the microstrip line feeding the patch

Jm

= LxH,

Thus (J,I = I Ji,J.If the effective width of the microstrip line is port), the input current at the port j may be written as

4

=

TI JzI

(Y)

(v)

\ L / The function sinc (z) is defined as sin (z)/z, and nn mn k = - k = I a ' Y b

(9.14) (for the j t h (9.15)

9.3.2 Evaluation of 2-matrix from Green's functions Green's functions discussed above may be used to find the 2-matrix characterisation of various planar segments of the shapes shown in Fig. 9.9 with respect to specified locations of external ports. These external ports may be either of the probe-feed type (Fig. 9.10) or the microstrip-feed type (Fig. 9.11) or a combination of these. Evaluation of the Z-matrix is based on relation 9.9

6 = loss tangent of the dielectric The length of rectangle is a, its width is b, and height of the substrate is d. The points (x,, y,) and (x,, y,) denote the locations of thep and q ports, respectively. It has been shown [37] that the doubly infinite series in (eqn. 9.16), along with eqns. 9.17 and 9.18, can be reduced to a singly infinite series by summing the inner sum. The choice of summation over n or m depends on the relative locations of the ports p and q, and also on the aspect ratio of the rectangular segment. We consider two different cases

470

Multiport network approach for modelling

Multiport network approach for modelling

Case I: When both the ports ( p and q) are oriented along the same direction (x or y). We may write Z,, as

477

The sign of yl is chosen so that Im (y,) is negative. w, and w, are widths of ports p and q, respectively. Also, we use Y > = max(y,, Y,)

Y < = min(yp9 Y,)

and a similar notation for x, and x, when I = n. The choice of the integer L in eqn. 9.19 becomes a trade-off between fast computation and accuracy. A compromise is to select L so that (y,F) is less than or equal to 100. Case 2: When the two ports ( p and q) are oriented in different directions (x and y), various elements of the Z-matrix may be

.

f

cos (k,u,) cos (kp,) sinc

I=L+I

Z,

(F)

-CF-

=

1

1a,cos(k,u,)cos(k,u,)cos(y,z,)

'I /=o

where

1 " -CF cos (kp,) cos (k,u,) 'I l = L + I

and

. sinc

2

(y) ( -.iyl exp

C

=

jopd/(ab)

When the two ports are oriented in the y-direction we choose I they are along x-direction I is put equal to m. Also,

=

n, and when

(v> - v < -

T)) (9.20)

dwj

Choice of Iis made by noting that, for convergence of the last summation in the above equation, we need (v, -

V,

- wj/2) > 0

(9.21)

We choose the index of the inner summation so that this condition is satisfied. This condition may be written more explicitly as I

=

m,

if {max(y,, y,) - min ( y,, y,) - wj/2) > 0

(9.22)

and I = n,

and

if {max (x,, x,)

- min (x,,

x,)

-

w,/2} > 0

(9.23)

When both of these conditions are satisfied, any choice of I will ensure convergence. If I = n, wi corresponds to the port oriented along y-direction and w, corresponds to the port along the x-direction. On the other hand if I = m, wi is for the port along the x-direction and wj for the port along the y-direction. Z-matrix for circular segments: For circular-shaped patches, the impedance Green's function is given by eqns. (A9.10) and (A9.11) in Appendix 9.8. When ports are located along the circumference of the circle (as shown in Fig. 9.12),

472

Multiport network approach for modelling

Multiport network approach for modelling

various elements of the Z-matrix [38] may be written as follows. For any port i, the Z-matrix element Z,, may be written as

473

where HA') is the zeroth-order Hankel function of the second kind and r is the straight-line distance between the point M(s) and the source point on the periphery (given by L(so)). The integral on the right-hand side of eqn. 9.26 is carried out over the entire periphery. The RF voltage at any point just inside the periphery can be derived from the above relationship. We obtain 2jv(s)

= fc

{k cos OH$ (kr)v(so)

+ jopdJ,, (so)~h2)(kr)} ds,

(9.27)

Fig. 9.12 Various parameters for ports located at the circumference of a circular segment Fig. 9.1 3

Off-diagonal terms of the impedance matrix are found to be

{COS[n(Ai - A,)]

-

cos ["(Ai

+ A,]} cos (n+d)

(9.25)

where Similar expressions for computation of the Z-matrices for planar segments of other geometries shown in Fig. 9.9 have not been reported so far. 9.3.3 Z-matrices for segments of arbitrary shape When we come across segments of arbitrary shapes, for which Green's functions do not exist, the impedance matrix can be found by a method known as contour integral method [39]. The contour integral method is based on the Green's theorem in cylindrical co-ordinates. The R F voltage at any point M(s) inside the periphery of an arbitrarily shaped planar segment shown in Fig. 9 . 1 3 ~is given by

(a) Configuration of a planar segment for analysis by contocr integralmethod; (b) Division of the periphery in N sections for the analysis

where HI2)is the first-order Hankel function of the second kind, and J, denotes line current density flowing into the segment at so.The variables s and sodenote distances along the contour C and r is the distance between the two points M and L (specified by s and so) as shown in Fig. 9.13~.The angle 0 is the angle made by the straight line joining points M and L with the normal to the periphery at L. Line current density J,, flowing into the segment at a coupling port, is given by

For the numerical calculation of the impedance matrix, we divide the periphery into N sections having arbitrary widths W, , W ,. . . W, as shown in Fig. 9.13b. The periphery is divided in such a manner that each coupling port contains an integral number of such sections. For greater accuracy, wider coupling ports may be divided into a multiple number of sections. We set N sampling points, one at the centre of each section, and assume that each section is a straight edge. It is further assumed that the widths of the sections are so small that magnetic and electric fields can be considered constant over each section. Under the assumptions outlined above, the line integral in eqn. 9.27 can be replaced by

474

Multiport network approach for modelling

Multiport network approach for modelling

summation over the N sections. The resulting expression is given by N

2jv,

= ",=I

{kv,G,

+ jwpd i,&,}

where v, is the voltage over the Ith section and i,(= J, W,) is the total current flowing into the m th section. The matrix elements G, and fi,,, are given as

to>

otherwise

475

be deleted from ZN.If each coupling port covers only one section, the matrix thus obtained (after deleting rows and columns corresponding to the open sections from Z,) is the required impedance matrix. If some coupling ports extend to more than one section, the sections in these coupling ports are like sub-ports and the procedure detailed in Reference 1 can be used to obtain the overall admittance matrix at the coupling ports (and hence impedance matrix, if desired). 9.4 Edge-admittance and mutual-coupling networks

and

In eqn. 9.31, y(= 0.5772.. .) denotes the Euler's constant. In the above discussion we assume that the current can be fed into the planar circuit from all the N sections and ,i denotes the current fed from the m th section. This yields the impedance matrix for the N-port circuit. This matrix can be used to obtain the impedance matrix for any specified number and location of ports on the planar circuit being analysed. Eqn. 9.29 is written for each section I on the periphery of the planar circuit. All these equations combined together in matrix form become where v and i are the voltage and the current vectors at each section. A and B denote N by N matrices, determined by the shape of the circuit. The elements of these matrices, obtained from eqn. 9.29, are a , = - k G , for I

f

m

a , = 2j and bh = j w d & (9.34) From eqn. 9.32, the impedance matrix for the N sections, considered as ports, is obtained as

In practice, the coupling ports are connected to onlv a few of the N sections . .. - ..- . Rows and columns corresponding to the sections which are open-circuited can -

-

As discussed in Section 9.2.3, the multiport network modelling approach assumes that the fields outside the patch may be represented by an equivalent network model. The concept of edge admittance associated with the radiating edges has been widely used in conjunction with the transmission-line model [23, 24,261. The same concept can be extended to the multiport network modelling approach. For the multiport network model, the two-terminal edge admittance (used in the transmission-line model) is replaced by the multiport network shown in Fig. 9 . 6 ~or b. If an edge of the patch is divided into n sections, the edge-admittance network (EAN) is an n-port network with the common terminal being the ground return. In this Section, we discuss various methods for evaluating parameters of edge-admittance networks. Also, the network modelling approach can be extended to incorporate the effect of mutual coupling between the radiating edges of a single patch, as well as among the edges of adjacent patches in an array environment. 9.4.1 Edge-admittance networks Edge admittance associated with a radiating microstrip patch consist of two components: (i) a susceptance representing the energy stored in the fringing field associated with the edge; and (ii) a conductance G representing the power transmitted to the radiation field as well as the power carried away by the surface waves excited along the dielectric substrate. For incorporating edgeadmittance networks in the multiport network model for microstrip patch antennas, a capacitance-conductance pair is connected to each of the ports of the equivalent planar multiport representation of the patch. The conductance G consists of two parts: a radiation conductance G,and a surface-wave conductance G,.Radiation conductance associated with an edge of a microstrip patch is defined as an ohmic conductance (distributed or lumped), which, when connected to the edge (continuously or at discrete ports), will dissipate a power equal to that radiated by the edge (or by an equivalent magnetic current source) for the same voltage distribution. If the edge has width W and the power radiated for a uniform voltage distribution is P,,, the radiation conductance per unit length of the edge is given by 2PJ W, where P,,,is calculated for a unit

478

Multiport network approach for modelling

Two other formulas, useful for design and based on Wiener-Hopf characterisation of an infinitely wide microstrip patch edge, are given by Kuester et al. [32] and Gogoi et al. [30]. The formula of Kuester et a[. (32) for electrically thin substrates (kod < 1) may be written as

Multiport network approach for modelling

479

e, < 2.65. Accuracy of formula 9.42 is 2.6% for 0.2 < kod < 0.6 and 2.45 More rigorous formulations for edge conductance of open-ended microstrips have been reported by James and Henderson [41], and more recently by Katehi and Alexopoulos [42] and by Jackson and Pozar [43]. Analysis techniques and numerical results for a limited set of parameters have been given in References 41-43. James and Henderson [41] have pointed out that their rigorous results agree with eqn. 9.37a and a previous estimation by Lewin [44] for d/Ao < 0.09 when E, = 2.32, and for d/& < 0.03 when e, = 10. Results based on full-wave analysis using the method of moments [43] agree with results in Reference 41 for substrate thicknesses up to 0.1 &.

Edge susceptance: As in the case of edge conductance, several different results are available for edge susceptance also. One of the formulas for edge susceptance B is based on the parallel-plate waveguide model of a microstrip and is given by Reference 45 as:

y = 0.57721 (Eurler's constant)

The formula given by Gogoi et al. [30] is as:

Accuracy of eqn. 9.41 is 1.1% for 0.05 < k,d < 0.6 and 2.45 < e, < 2.65. These two formulas are accurate for wide patches (large value of b in Fig. 9.11). Results based on these formulas are also plotted in Fig. 9.14. Fig. 9.14 shows a comparison of the formulas 9.37-9.41 for the following set of data: frequency f = 7.5 GHz; dielectric constant e, = 2.48; and thickness of substrate, d = 1/32 in. It is inferred from Fig. 9.14 that formulas 9.37 and 9.38 yield close results as expected. The difference between formulas 9.37 and 9.41 increases with decreasing value of the width. This is because of the fact that formulas 9.40 and 9.41 are valid only for wide patches. Formulas 9.40 and 9.41 are both based on the Wiener-Hopf formulation and therefore yield identical results for all values of the width. From this limited discussion, it seems reasonable to use formula 9.37 owing to its simplicity. Although the power coupled to surface waves is very small compared to the radiated power, the conductance corresponding to the surface waves should be added to GR.This conductance may be expressed as [30]

where Z, and e, are the characteristic impedance and effective dielectric constant of a microstrip line of width a. Expressions for Zoand e, are well known [I]. cis the velocity of waves in free space ( = 3 x 108m/s).Another formula for B, which is based on open-end capacitance of a microstrip line [46] is given by

where

Other formulas, which are based on the Wiener-Hopf formulation and which can be used for wide patches, are given in References 30 and 32. From Reference 32,

where ~ ( 0 is) as given earlier for eqn. 9.40. According to Reference 30,

where

480

Multiport network approach for modelling

Multiport network approach for modelling

The accuracy of expression 9.48 is 2% for 0.1 < kod < 0.6 and 2.45 < E, .: 2.65. Formulas 9.43-9.48 are compared in Fig. 9.15. Expressions 9.43, 9.44 and 9.47 give close results for all practical values of the resonator width (0.25 1, < w < 0.6 1,). Eqn. 9.44 predicts an end-susceptance value of one-half of that computed using other formulas. For all practical values of interest, formula 9.43 may be used, since there is no restriction on the width of the patch for this formula. When the width is large, both expressions 9.46 and 9.47 can be used.

481

with

53

=

l +

0.5274 arctan [0.084(w/d)l94"'52] &0.9236

re

T4

=

1

+ 0.0377 arctan [ 0 . 0 6 7 ( ~ / d ) " ~ ~ ~ ]

x ( 6 - 5exp(0.036(1 - 8,)))

(,

=

1 - 0.218exp(-7.5w/d)

(9.49)

Expressions in eqns. 9.49 make use of the effective dielectric constant formula of keference 50, ;.e.

where u = wld. Accuracy df results given by eqn. 9.49 is claimed to be better than 2.5% for the range of normalised widths 0.01 < wld < 100 and E, < 50. I

0.5

I

I

1.0

1.5

normalised width ( b / h o ) Fig. 9.15

Edge susceptance of a rectangular microstrip antenna versus normalised width (From Reference 27)

More rigorous characterisation of microstrip open-edge susceptance has been reported in [41, 43, 47, 481. Results of the analysis in References 47 and 48 are available [49] as a closed form expression obtained by curve fitting of numerical data. Normalised outward extension of the radiating edge (Auld in eqn. 9.44) is given by

Non-radiating edges: For rectangular patches radiating linearly polarised electromagnetic waves, radiating and non-radiating edges can be distinguished clearly. As shown in Fig. 9.66, the non-radiating edges can be modelled by EAN consisting of capacitances only. An equivalent approach is to extend the width of the patch by moving the non-radiating edges outwards so that the edge capacitance is accounted for by the increased capacitance of the wider patch. The concept of radiating and non-radiating edges has been studied [59] by studying the total and partial reflections from the end of a parallel-plate waveguide with an extended dielectric slab. It has been pointed out [60] that the radiating or non-radiating nature of the edge depends on the angle at which the wave underneath the patch is incident on the edge. For grazing incidence there is no radiation, whereas for normal incidence the edge radiates. In between there is a critical angle where the transition from non-radiation to radiation takes place. It has been recognised that the so-called non-radiating edges of a rectangular

482

--,

Multiport network approach for modelling

Multiport network approach for modelling

patch (operating at the resonance of 1,O mode) do contribute to a crosspolarised radiation field. Compared to a single radiating edge, cross-polarised radiation from a single non-radiating edge is typically 10-15 dB lower. When we combine the radiated fields (in the broadside direction) from the two non-radiating edges, the total field is much smaller. This is caused by the fact that equivalent magnetic currents corresponding to the fringing fields at the two non-radiating edges are in the opposite direction and tend to cancel each other. However, the non-radiating edge-admittance network (NR-EAN), shown in Fig. 9.6b can be used only in cases where approximate results (obtained by ignoring the cross-polarised radiation from NR edges) are considered satisfactory. In more general cases, especially when the antenna operation is not at 1, 0 mode resonance (as for the circular polarised radiator discussed in Section 9.6.1), the EANs at all edges are similar to that shown in Fig. 9 . 6 ~ . In spite of the numerous results for edge admittance that have been reviewed in this Section. the lack of an accurate characterisation for the edne admittance is one of the major shortcomings in the design information required for precise design of microstrip patches and arrays. u

483

patch

,

E 1('

i

I

I

L-,

I

X

E1

0I I I I

'tL'

10 \

iE '%-

E-f ield distribution

-4+ I I

Fig. 9.1 6 Modelling of the fringing field at the patch edges in terms of magnetic-current line sources

9.4.2 Mutual-coupling network As shown in Fig. 9.8, the mutual interaction between the fringing fields associated with any two edges can be expressed in terms of a network model. The basis idea of using an admittance element to represent mutual coupling between two radiating edges was initially presented in Reference 51 in co&n&on with the transmission-line model of microstri~antennas. The reader is referred to Chapter 10 for details of this concept. The multiport mutual-coupling network shown in Fig. 9.8 is an extension of this concept suitable for incorporating in the multiport network model of microstrip patch antennas discussed in this Chapter.

Evaluation ofmutual-coupling networks: For computation of external mutual coupling between various edges of a microstrip patch antenna on a thin substrate, the field at the edge may be modelled by equivalent line sources of magnetic current placed directly on the ground plane at the location of the edges. This is illustrated in Fig. 9.16. Magnetic currents M are given by

where d is the height of the substrate. Product ( - E d ) is the voltage V(x, y) defined in eqn. 9.10. 4 denotes a unit vector normal to the ground plane as shown. For the E-field in the direction indicated in this Figure, both magnetic current sources M a r e in y-direction, i.e. directed out of the plane of the paper. The coupling between two magnetic current line sources is evaluated by dividing each of the line sources in small sections, each of length dl. The magnetic field produced by each of these sections (on the line source 1) at the locations of the various sections on the line source 2 can be written by using fields of a magnetic current dipole in free space [52]. The configuration and

Fig. 9.17

(a) Two arbitrarily spaced magnetic current elements; and ( 6 ) the co-ordinate system used for computation of fields

484

Multiport network approach for modelling

Multiport network approach for modelling

usually larger (typically 12). However, while using MCN for antenna analysis (by segmentation), a small number of ports along radiating edges (typically 4) is sufficient. Thus the original mutual-admittance matrix (48 x 48 for 12 ports

co-ordination system is shown in Fig. 9.17. We have

. koMdl sin8

H, = J

485

4n~or

Here ko is the free-space wave number and r is the distance between the point P and the magnetic current element Mdl. When the two edges (say i and j ) are oriented arbitrarily, as shown in Fig. 9.18a, the magnetic field H at (xi, y j ) produced by a source dliM a t ( x i , y,) may be written as H = fH, + j H y with

(9.54)

.

Hy

=

Hy,cos8, - H,. sin 0,

H,

=

Hy,sin8,

e,=

H, cos 0

+ H,cos

(9.55)

0,

(9.56)

where Hy. = -H,

+ H, sin 8 sine + H,cos0

Co-ordinate systems (x, y) and (x', y') are illustrated in Fig. 9.18b. Mutual admittance between sections j and i may be written in terms of the electric current density 4 induced in the upper surface of the edge segment j. We have

4

= ri

x H = (-H,cosaj

- Hy sinaj)j

(9.59)

The current density induced on the surface of the edge section j underneath the patch is -4. The mutual admittance between sections i and j is given by the negative of the current flow into section j (underneath the patch) divided by the voltage at section i, i.e.

The second minus sign in eqn. 9.60 accounts for the fact that the direction of current for defining the admittance matrix of a multipart network is directed into the network as shown in Fig. 9.19. The two edges shown in Fig. 9 . 1 8 ~may be the edges of the same radiating patch or those of the different patches in a n array environment. When coupling between two adjacent patches in an array environment is being computed, several individual edges of the two patches contribute to the mutual coupling network (MCN). An MCN configuration taking the four radiating edges into account is shown in Fig. 9.20. Here, the MCN is connected to four ports along each radiating edge. In practice, the number of sections considered on each edge for mutual-coupling calculations is

Fig. 9.18 (a) Configuration showing sections i and j of two patch edges; and (b) two different co-ordinate systems used for mutual coupling calculations

Fig. 9.1 9 Representation of the mutual coupling by an admittance matrix

along each edge) is reduced to a smaller size (16 x 16 as shown) by paralleling the ports in subgroups of three each. Contributions of non-radiating edges can also be incorporated in MCN. This is not shown in the Figure. Detailed computations [53] point out that the mutual-coupling contribution by non-

486

Multiport network approach for modelling

Multiport network approach for modelling

radiating edges is usually much smaller and may be ignored as a first-order approximation. Mutual coupling computations based on the above formulation have been verified [53] by comparison with the available experimental results [54]. Some of EAN edge 1

1

patch 1

EAN edge 3

I

I

MCN

I

I

487

mond points) is seen. Also shown in these Figures are results of Van Lil et al. [51], based in transmission-line theory. 1t may be noted that the preceding method of evaluating mutual coupling (based on the equivalent magnetic current model shown in Fig. 9.16) is valid only for electrically thin substrates where the effect of surface waves along the substrate is negligible. This modelling approach has been recently extended to microstrip patches on thin substrates, but covered by a relatively thicker dielectric cover layer [61,62]. The equivalent magnetic current model used in this case

patch 2 a=6.698 cm b=10.56 crn x = 1.84crn f GHz

Fig. 9.20 A mutual coupling network (MCN) representing the coupling between two adjacent patches in an arrav

-15-

m

a =6.698 crn b=10.56cm

-20

-

-25

-

0 -.-30 ;; v, -

network model

Fig. 9.21 Comparison of theoretical and experimental results for E-plane mutual coupling between two rectangular microstrip patches (Reproduced from Reference 5 3 )

these results are shown in Fig. 9.21 for E-plane coupling and in Fig. 9.22 for H-plane coupling between two probe-fed rectangular patches. A very good agreement between the computation (solid line) and experimental results (dia-

Fig. 9.22

Comparison of theoretical and experimental results for H-plane mutual coupling between two rectangular microstrip patches (Reproduced from Reference 53)

is shown in Fig. 9.23. The basic approach is similar to that for the case without a cover layer discussed earlier. Eqns. 9.52 and 9.53 are replaced by H, and H, in the presence of the cover layer. These field components are now dominated by the effect of surface waves in the thicker cover layer. When the substrate thickness is increased, equivalent magnetic current models for Figs. 9.16 and 9.23 become more and more inaccurate. Conceptually, multipart-network modelling of mutual coupling between two patches is still possible if more rigorous analytical/numerical techniques [63, 641 could be extended to arrive at a network representation of mutual coupling.

488

Multiport network approach for modelling

Multiport network approach for modelling

9.5 Analysis of multiport-network model The most outstanding advantage of the multiport-network model is the fact that various analysis and optimisation techniques available for multiport networks can now be used for analysis and optimisation of microstrip antenna elements and arrays. Most widely used techniques for planar networks are segmentation [I-3, 6-81 and desegmentation [4, 5, 81 methods. These two network-analysis techniques are reviewed in this Section. Examples of various microstrip antenna configurations where these techniques have been used are reviewed in Section 9.6.

cover layer


,

H plane

O

Fig. 11.63 Coupling coefficient versus distance d between edges 6, = 2.5, t = 1.575 mm, patch radius = 3.85 cm, probe radial distance = 1.1 cm Frequency: Measurement = 1.44 GHz Theory = 1.4127

Q

O measured microstrip disk coupling

------

calculated circular waveguide fed aperture coupling (Bailey and Parks) our theory

Fig. 11.64 Coupling coefficient versus orientation ( f = 5.5GHz)

4,

normalised to the E-plane coupling

(a) Input impedance Z, The input impedance Z, of the elements can be readily calculated by applying the impedance matrix equations of network theory. Fig. 11.66 illustrates Z, variations of the previous two-element array against the edge distance d. It can be observed that, for d > 0.3& ( R > 0.68&), the coupling effect on Z , is negligible. In studying 2, as a function of 4 and frequency, we have chosen a very short distance ( d = 0.1&) in order to observe the coupling influence. Fig. 11.67 shows that in the E-plane ( 4 = 0°), Z, x Z,, = 61.7 /-Y ohms, where Z , , is the proper impedance of the disc antenna. However, in the H-plane ( 4 = 90') where the coupling is stronger, Z, is very different. (b) Circular sub-array of three identical elements (Fig.11.68) [68] In Fig. 11.69 one observes that the coupling effect on the input impedances Z,, , Z,, and Z,, becomes negligible for d > 0.31,. The dependence of the input impedance on feed angular position 0 is presented in Fig. 11.70. Although two of the three impedances can be equal for certain values of 0, nowhere they are identical simultaneously. 82

I

Fig. 11.65 E- and H-plane coupling coefficients for m = I , n = I , versus angle OZ(B, = 0)

642

Design and technology of low-cost printed antennas

Design and technology of low-cost printed antennas

643

( c ) ConcIusion The cavity method and reaction theorem represent very suitable ways to calculate and predict free-space mutual coupling between array elements of simple shape. According to these results, it seems that the H-plane coupling is stronger for the disc than for the patch (see Figs. 11.54 and 11.63) and identical in the E-plane ( d < 0.31,).Mutual coupling effects become important when the edgespacing distance d is lower than 0.31, for an array of few elements.

I I

1 z,, 1

=61.7/

F i g . 11.67 2, of a two-identical-element array against @ ford

Fig. 11.66 Input impedance 2, of each array element as a function of d E Plane ---- H Plane f = 1.391 8 G H z

-

=

O . I I , and f = 1.3918GHz

11.3.3 Linear series array of corner-fed square patches [69] The feed network of microstrip antenna arrays exhibits loses which lead to a limit on the expected gain, and consequently a limited number of elements. The Schelkunoff unit circle, Dolph-Chebyshev and Villeneuve methods are well suited for the design of fairly small arrays; Taylor's method, sampling line source and Fourier's series expansion are better for large arrays. However, the previous synthesis methods consider only the array factor, while the overall diagram obviously needs the element patterns to be taken into account; for e.g. the cos 0 variation in the H-plane of most printed antennas has a strong effect for arrays with few elements; the - 40dB Chebyshev design example previously

644

Design and technology of low-cost printed antennas

mentioned shows a high sidelobe level (- 23 dB) in Fig. 11.50. The sidelobe disappears completely in the H-plane element pattern (Fig. 11.71), and the initial specification is obtained. Two synthesis methods, taking the elementary radiation pattern into account, are developed in Section 11.4.

Fig. 11.68 Geometry of a planar circular array of three microstrip disc antennas

Only one simple structure using square-shaped microstrip antennas is considered here. The corner-fed square patches are easily excited with a single microstrip line (Fig. 11.72); a tapered distribution is readily obtained using quarter-wavelength transformers along the line. In order to get a broadside pattern, one wavelength spacing is necessary; half-wavelength spacing is also possible, with alternate elements to keep the equi-phase condition. The corner-fed square patches have been chosen because they provide a high input impedance well suited for series array. It is also very easy to feed each element on the corner. Two new aspects are considered here: reduction of cross-polarisation using altenate location of the elements on the feeding line, and reduction of sidelobe level using simple tapering for a linear series array.

Design and technology of low-cost printed antennas

645

646

Design and technology of low-cost printed antennas

Design and technology of low-cost printed antennas

647

11.3.3.1 Radiation of corner-fed square patches

(a) Theory: When the patch is excited at one corner (Fig. 11.73a), the cavity model [4, 251 shows that the main part of the internal field is the sum of two degenerate modes with equal amplitudes, i.e. modes (0, 1) and (1, 0). If the higher modes are ignored, the Ex and E, fields along the edges exhibit the

I

input I

A,

1

Fig. 11.72 Corner-fed square-patches array Fig

geometry of the patch

a

Fig. (O.l)and (1.0) modes contributions

Fig.

(1.1) mode contribution

point

-2

In1

fK,(x)

---- z,"2 . . . . . z,

M

T

(

x

)

~

o

Fig. 11.70 Input impedance versus frequency: d = O.7& MO(Y) geometry and magnetic currents of the corner fed patch

Fig. 11.73 Geometry and magnetic currents of the corner-fedpatch

variations shown in Fig. 11.736. The far field is linearly polarised either in the E-plane (I(/ = 0") or in the H-plane ($ = 45"). For instance in the H-plane,

EQ,

=

sin 2C

-jM, -

(2C)' - n2

where M, is proportional to the amplitude of the magnetic current ( x = 0, Y = 0) J 2 sin 8 2C = k,a 2 deg

Fig. 11.71 Chebpshev pattern of a six-microstrip antenna linear array (H-plane, spacing = 0.752,)

a

=

side length

648

Design and technology of low-cost printed antennas

Design and technology of low-cost printed antennas

AS long as the cross-polarised field is needed, higher modes must be considered. The next mode (1, l ) adds a contribution with a magnetic line distribution as shown in Fig. 11.73~.The E,, far-field component is given by E,, = - 2M, cos2C

2C

(1 1.38)

(2C)2 - n'

an anti-phase relationship which cancels the different contributions. The diagram is shown in Fig. 11.77. It shows a large reduction of the cross-polar level, which is close to -28dB instead of - 17dB as previously. Obviously, as the length of this array is half that of the first one, the 3 dB beamwidth is larger. To attain the same directivity, 20 elements spaced 112 would be necessary.

where MI is proportional to the amplitude of the magnetic current ( x = 0, y = 0). It will be noticed that M I is much smaller than M,. The previous formula shows that the cross-polarised component is null for B = 0 and increases with 0.

UNIFORM LlNE ARRAY A1

1-1 I

****it****

FIG.

Uniform linear array A1(FO-

21.3GHz)

fig. H plane pattern of the untform array A1 (FO=Z1.3GHz) copolar cross-polar

-

r10 ELEMENTS *SPACING

-

1 GUIDED WAVELENGTH

*SUBSTRATE PTFE

El-

tgs THICKNESS

-

2.17 0.001

!----

0.38

+FEEDING LlNE lOOn +COAXIAL OUTPUT (AND TWO QUARTER WAVELENGTH TRANSFORMERS) Fig. 11-74 Uniform line array A, (F, = 21.3GHz)

( b ) Examples o f linear arravs When the' spacing along the feeding line equals one guided wavelength, the different elements are uniformly excited (Fig. 11.74). Here the ten-element array is printed on the usual PTFE substrate (dielectric constant 2.17 and thickness 0.38 mm). The quarter-wavelength transformer enables good matching to the 50 i2 coaxial output. As expected, the H-plane diagram exhibits the well-known - 13 dB first sidelobe; the cross-polarisation component is very low at @ = 0 and then quickly increases with 0 to - 17dB (Fig. 11.75). This cross-polarisation component can be reduced in a simple and efficient way. Let us consider each patch located alternatively on each side of the feeding line (Fig. 11.76). Considering half-wavelength spacing, the different co-polar fields (Emfor Hplane) add in phase, while the different cross-polar components ( E B Imaintain )

649

Fig. 11.75 H-plane pattern of the uniform array A , --- co-polar ---- cross-polar

(F, = 21.3GHz)

650

Design and technology of low-cost printed antennas

Design and technology of low-cost printed antennas

657

1I .3.3.2 Tapered linear series array (a) Theory: The previous arrays were uniformly excited; high sidelobes are the consequences of this illumination. The idea was to produce a non-uniform amplitude distribution while keeping the simplicity of the previous series feeding. Let us consider a linear array with wavelength spacing (guided wavelength);

UNIFORM LINEAR ARRAY WITH ALTERNATE ELEMENTS A2 I FIG.

.

I

Uniform array A2 alternate alaments

Fig. 11.76 Uniform linear array with alternate elements A,

as the radiating elements are identical, impedance transformers are necessary to obtain the given amplitude current. To do this, a two-step quarter-wave transformer can be used in each cell (Fig. 11.78). The transformed admittance & in the IT: plane is given by

+

l), and Y,, and Y,, are the characwhere Y,,, is the admittance of node (i teristic admittances of each quarter-wavelength transformer. If necessary, four quarter-wave transformers can be inserted when the spacing equals one wavelength. When the input voltage leads to a unit current in the first element, the current distribution is readily obtained with the following relations:

-

----

Fig. H plane pattern of uniform array A2 (FO=21.3GHz)

copolar cross polar

I

Fig. 11.77 H-plane pattern of the uniform array A, co-polar ---- cross-polar

-

(F, = 21.3GHz)

However, the various ratio nican be deduced step by step from the known values of I,, I,,&, etc. The input impedance at element 1 is z,, =

Z"

1

+ n: + nini + n:n:n: + . . . . .

(1 1.41)

652

Design and technology of low-cost printed antennas

Design and technology of low-cost printed antennas

653

( b ) Results A ten-element array has been constructed (Fig. 11.79). The requirement was to get a sidelobe level lower than - 20 dB. Only eight transformers were used (four

TAPERED LINEAR SERIE'S A R R A Y ***a******

lA~ INPUT

---7aI

- 1, 10 YAV

i,

-

I,

1

n,Y,+V = n l n,n,,

...n,

Fig. 11.78 Tapered linear series array: current distribution

TAPERED LINEAR SERIE'S A R R A Y A3

~~~ **********

fig.

I

FIG.

H plane pattern of tapered array A , (Fo = 21.3 G H z )

I

Tapered array A3

* 10 ELEMENTS *SPACING = ONE GUIDED WAVELENGTH Fig. 11.80 H-plane pattern of tapered amy A, (F, = 21.3GHz)

* 4 TRANSFORMERS (ON EACH SIDE)

* FEEDING LINE lOOn * COAXIAL OUTPUT I

Fig. 11.79 Tapered linear series array A,

I

on each side), because Y,, was chosen equal to the characteristic admittance of the half-wavelength following line. Taking the characteristic impedance of the main line as about loon, the various transformers exhibit impedances between 75 and 95 0 , which are easily realised with microstrip lines. The experimental H-plane diagram is plotted in Fig. 11.80. It shows that the sidelobe level is lower

654

Design and technology of low-cost printed antennas

than - 20 dB while the gain and input-impedance matching remain very similar to those of the uniform array. A combination of alternate elements and tapered distribution yields a pattern with low sidelobe level and low cross-polarisation over the whole space. Fig. 11.81 shows a ten-element array with quarter-wave transformers. The diagrams

deg

Design and technology of low-cost printed antennas

655

are plotted in Fig. 11.8 1, which clearly shows that no degradation occurs to the cross-polarisation level within the frequency band. 11.3.4 Two-dimensional cross-fed arrays [TI, 721 The combination of identical linear sub-arrays leads to a planar array. The feeding network of such structures is developed in Section 11.4. Another simple two-dimensional arrav named the cross-fed structure can be considered as a combination of non-identical linear sub-arrays. Cross-fed printed aerials have already been described by Williams [70]. The basic radiating elements were 45' dipoles inclined along the feeding lines. No analysis was proposed; however, the structure appears very attractive owing to its simple feed geometry which avoids having any transformer. Corner-fed patches were chosen because they are easily fed along a straight microstrip line. Moreover, the discontinuities introduced near the corner of each element are symmetrical and identical for all of them. Thus co-polar and cross-polar :omponents remain symmetrical around the broadside direction. Figure 11.82 shows a typical cross-fed array. Matching networks can be added for a coaxial feed. Inter-element spacing equals one guided wavelength. Design equations for a uniform array are given below.

Fig. 11.81 H-plane pattern of tapered array with alternate elements

11.3.4.1 Uniform illumination and impedance matching: The overall array is constructed from parallel sub-arrays. The number of elements is reduced from N, to N, - 2, considering ith and (i I) th sub-array, respectively. When N is the number along the diagonal, we find:

+

N,

=

(N - 2)N/4 elements for the upper or lower group of subarrays

N, = N2/2 elements for the whole array The input impedances are different for the half main-line section (R,) and the upper or lower group of sub-arrays (R,) (Fig. 1133). The impedance matching needs one or two quarter-wave-section transformers to get suitable characteristic impedances (Z;, Z,, Z',, 2,).The uniform illumination condition yields a second relation (same voltage V for all the elements). Then the transformer impedance ratios are equal on each side as follows:

where R, = resistance of a corner-fed antenna; R, = desired input impedance; N = number of elements on the main line.

Fig. 11.82

11.3.4.2 Radiationpatterns: The total array factor results from the combination of sub-array factors. The expression is P sin(N - 2i)(py/2 (1 1.43) 2 cosicp, sin qy/2

+ 1

Typical cross-fed array of square patches (without matching network)

I

656

Design and technology of low-cost printed antennas

Design and technology of low-cost printed antennas

657

where 4, = kd, cos 4 sin 0; q, = kd, sin 4 sin 0; d, and d, are the inter-element spacing along Ox and Oy; P = number of sub-arrays (above or below the central line); N = number of elements along the central line and S,, = N 2 / 2 .

Fig. 11.83 Input matching transformers of the cross-fed array

It is interesting to consider this expression for d, = dy = d i n the two main planes. In the H-plane, ST is the sum of the usual uniform array factors Si= sin (Micp,/2)/sin(cp,/2). However, the nulls of each Si function have different locations because the sub-arrays have a different number of elements. Then all S, components are added in phase in the broadside direction while a compensation occurs from the oscillating functions outside 9 = 0. The following results are given for usual substrates (6, x 2.2), and the spacing equals one guided wavelength (A8 2, 00.5&). Fig. 11.84 shows the three components So, S , , S, for the case N = 6 and P = 2 (six diagonal elements and four sub-arrays). Summation then leads to a diagram with a large reduction in the previous oscillations of each of the subarrays. In the E-plane, cp, = 0 and ST is the array factor of an equivalent array exhibiting a linear tapered excitation. Fig. 11.85a, b and c show the computed patterns in the three main planes,

Fig. 11.84 Sub-array contributionsSfof the globalarray factor S, (six diagonal elements and four subarrays)

658

Design and technology of low-cost printed antennas

Design and technology of low-cost printed antennas pattern of crass-fed array PHI =go element NB:6 (diagonal) equiampl~tude equ~phase

659

which clearly show that the sidelobe level (SLL) is greatly reduced. However, the = 45' plane yields the - 13 dB sidelobe of the uniformly illuminated square structure. On the other hand, the half-power beamwidth &dB remains very similar in the three planes ( 4 = 0°, 45', 90'). &dB and SLL,, versus the number N of elements on the diagonal feed line is given in Table 11.10.

4

Table 11.10 Half-power beamwidth and sidelobe level of cross-fed array

20

40

60

80

pattern of cross - fed array

elernent NB=6 equiamplitude

-60

-40 -20

0

20

40

60

80

pattern o f cross -fed array PHI - 0 element NB = 6 (diagonal) equ~amplitude equiphase

Fig. 11.85 Computedpatterns of the cross-fed array (six diagonal elements, uniform distribution) ( a ) H-plane 6 = 90" (6)45"-plane 4 = 45" ( c ) E-plane = 0'

N

= number of elements along the

diagonal feed line

It will be noticed that only using the impedance matching condition does not provide a uniform illumination; for instance, if different quarter-wave transformers are used on each arm of the previous structure (N = 6 elements on the diagonal arm), the voltages on each element of the upper and lower sub-arrays differ from the voltages of the central line. The computed patterns are plotted in Fig. 113 6 when the voltage equals 1 on the main line and 0.8 on all the other elements. It appears that the E-plane is quite transformed, sidelobes reaching - I6 dB and 0, dB = 17.8'. 11.3.4.3 Results: Various arrays have been built either with coaxial or waveguide output. Each of them was printed on a PTFE substrate ( E , = 2.17, tg6 = lo-), thickness = 0.38 mm) or on polypropylene, as described in Chapter 5. An 18-element cross-fed array designed for 23.5 GHz is considered first. The same quarter-wave transformer was used on each arm to obtain a SWR better than 1.5 at the coaxial output (Fig. 1137). The measured gain equals 20dB, while a uniform aperture of the same area yields a 21 dB gain. E- and H-plane diagrams are given in Fig. 11.88; the sidelobes reach - 18dB in the E-plane and are lower than -20dB in the H-plane, and beam widths are 15" (H-plane) and 18" (E-plane), as expected. Another 50-element array, printed on polypropylene of the same thickness, has been realised for a frequency near 20 GHz. The number of elements in the upper and lower groups of sub arrays is 40, and the impedance to be matched equals 8 a. The transformer then needs three quarter-wave sections as shown in Fig. 11.89 to get equal voltage on each patch and good impedance matching. The radiation patterns are given in Fig. 11.90. No sidelobes larger than - 25 dB appear in the H-plane while the E-plane exhibits - 18dB sidelobes. In both cases the cross-polarisation level remains acceptable. The measured gain is

660

Design and technology of low-cost printed antennas

Design and technology of low-cost printed antennas

667

Pattern of cross-fed array

0-

PH 1.90 element NB=6 (diagonal) variable ampl equiphase

-10-

-20-

-30-

-"PO

-fi4!-i0 i

i l \ o ~ idoo

a

F(GHz)

Fig. 11.87 VSWR of a 78-element cross-fed array (six diagonal elements, F, = 23.5GHz) pattern of cross-fed array element NB-6

Pattern of cross-fed array

-10

/

\

PH 1.0 element NB=6 (diagonal) variable am01 equiphase '

Fig. 11.86 Computed patterns of the crass-fed array (six-diagonal elements; non-uniform distribution)

b Fig. 11.88 E-plane and H-plane measured pattern of the 78-element cross-fed array

662

Design and technology of low-cost printed antennas

23.2 dB; the uniform aperture of the same area would yield 25.48 dB. Losses reach approximately 2.3dB; the VSWR is lower than 1.8 between 193 and 20.4 GHz. 11.4 Synthesis methods for linear arrays 173, 74, 751

663

Design and technology of low-cost printed antennas

Let F(8) be the directivity pattern of a linear array; then where f (8) = array factor; g(8) = directivity pattern of the source. As usual printed antennas have different diagrams in the two main planes (E-plane and H-plane), so it is better to synthesize F(8).

The usual analytical synthesis methods (Fourier, Chebyshev, Woodward-Lawson) are not always suitable when the directivity pattern is specified by a given outline. Thus, the mean-squared error criterion is a global criterion that does not permit the separation of the main-beam and the sidelobes contribution. Prescribing equi-level sidelobes does not always fit the Chebyshev requirement.

plan

I

E

FzI9.55GHz

CROSS-FED ARRAY A4 **********

+4 4 + ++4 +4+

+ 4 4 + 4 4 4 + + 4 4 4 4 4 + 4 4 + +4++?44++

SO E U M N T S W L L Y EXCITED SILPLE CORPORATE FEED SIMPLE OUTPUT MACHINC (A THIEE SECTION TRANSFORMER ON THE VERTICAL B W H WAS MCESSARY) LOW SIDE LOBES I N E-PLANE H-PLANE s F E W Y BM9 19.5-20.4 CHz VSWR < 1.8 GAIN 23 dB

.

FIG. Cross fed array with coaxial output A4

Fig. 11.89 50-element cross-fed array printed on polypropylene

1

-80

1

~

60

'

~

40

~

20

~

~

0

~

20

~

~

40

~

~

60

~

80

~

'

'

deg b

Lastly, the Woodward-Lawson sampling method needs a great number of sources, and the choice of sample is sometimes critical. Numerical methods can take into account the envelope specification, the directivity pattern of the source and the inter-element spacing. Two numerical methods have been studied:

Fig. 11.90 E-plane and H-plane patterns of a 50-element cross-fed array printed on polypropylene

The relaxation method which enables real excitation coefficients The simplex method which uses the Dantzig algorithm and yields symmetrical or non-symmetrical pattern synthesis (real or complex coefficient).

11.4.1.I Method: Let us consider a symmetrical linear array of 2N elements; FJ8) is the desired directivity pattern and a = (a,):-, is the unknown excitation vector:

11.4.1 Relaxation methods

'

~

664

Design and technology of low-cost printed antennas

Design and technology of low-cost printed antennas

N

Fd(0)

=

1 a, cos j- l

d, = symmetrical-axis relative position of source + j ; A, = free-space wavelength. The following linear system is obtained using discrete values of 0:

C = [c,,],.~, cv

=

)

cos 2a 2 sinei , a T = (a,, a,. . .a,);

(:

The functionals to optimise are those like

We denote a' and a E RNsuch as J(af) = Min J(a) in the sense of the chosen criterion. To realise this, a series of vectors d is built, such as J ( d + 1) < J ( h ) . The search directions are the co-ordinate axes, each of them being taken such as at the periodically. For each component aj, we realise = (k 1) th iteration:

Fig. 11.91

Outline of desired directivity pattern (example of sector of pattern)

4+'

+

For a given quality criterion and choice of convenient functionals to optimise, the relaxation method provides fast convergence. Some portions of the outline pattern can eventually be preferred. Two examples illustrate the method: sector pattern and directive broadside pattern. 11.4.1.2 Sector-pattern case: Let us define the desired directivity pattern from an outline symmetrical on 0 (Fig. 11.91). RIimis the maximum ripple value for 0 E [0, 0, - a] and R = 1 - D(8),. S L L , is the maximum sidelobe level for 0, a < 0 < a/2 and SLL = D(B),,. The pattern in the transition region is related to u values. An initial value can be chosen, such as la:1 = 1 j3(i - l)/(N-1) 0 6 j3 < 1, or it can be equal to the excitation obtained from classical methods. The functional J(a) is replaced by two functionals R(a) and SLL(a), and min J(a) can be expressed by the following improvement criteria

+

Fig. 11.92 (a) Sector pattern of a 10-element array (H-plane). Relaxation synthesis: a C, criterion b C, criterion c

C3criterion

665

666

Design and technology of low-cost printed antennas

c,, c,, c,: let a + be the actual vector of the iteration, c,: [R(a+) < R(a) and SLL(a+) 5 SLL(a)] or [R(af) 6 R(a) and SLL(af) < SLL(a)] c2: [R(a+) < R(a) and

SLL(af) 5 SLL,]

c,: [SLL(a+) < SLL(a) and R(a+) 5 R,;,] The c, criterion application improves the ripple and the sidelobe level. c, gives the best ripple for a given sidelobe level SLL,, and c3the best sidelobe level for a given ripple R,. The c,, c,, c, criteria can be applied successively, depending on the ripple and the sidelobe level requirements.

Fig. 11.93 Directional broadside pattern of a six-element array (H-plane) -Relaxation synthesis ---- Experimental results

11.4.1.3 Directive broadside pattern case: For a broadside array of N equispaced elements with equal excitations, the beamwidth between first nulls is equal to 21,lNd radians. Applying c3 with R , , = 1 and 0, > Ao/Nd provides a main beam with the lowest sidelobe level, taking d/lo and g(0) into account. If d < 0.52, and g(0) = constant, we obtain the Chebyshev excitation. When d > 0.5A0, the Chebyshev method does not always maintain equal sidelobe levels. The relaxation method avoids such limitations, and printed antenna arrays with guided-wavelength spaced sources can be considered. 11.4.1.4 Results: Let us consider a linear printed antenna array on a substrate, having a relative dielectric constant E, = 2.17 (PTFE). For microstrip transmission lines a, = z 0.75&.

(a) Sector pattern We want to design a 10-source array with a 90' sector pattern and a transition width, 2a = 20'. If the sources are equally spaced, the array amplitude factor will be zero with any excitation vector for sin 0 = &/2d. To avoid a null in the sector region, the first distance to the symmetry axis can be taken as 0.252,. With aoT= (1; - 0.75; 0.5; - 0.25; O), g(0) = cos (0) and application of the

667

Design and technology of low-cost printed antennas

c, criterion, we obtain R = - 0.8 dB and SLL = - 29 dB for a solution vector S (Fig. 1 1.92~). With a0 = S, SLL,, = -25dB and application of c,. we obtain R = - 0.3 dB and SLL = - 26 dB (Fig. 11.92b). With a0 = S, R,,,, = - 1.5dB and application of c,, we obtain R = - 1.5 dB and SLL = - 36 dB (Fig. 11.92~). (6) Directive broadside pattern On the same substrate, let us design a linear array of six sources with interelement spacings ,$. For equal excitations, the beamwidth between the first nulls is 25.5" and the first sidelobe is at - 13dB. For 20, z 35", 2u = 10' (outline corresponding to a - 40 dB sidelobe level, Chebyshev excitation), R,, = 1, a: = 1, and a," = 0 V j # I, g(0) = cos(O), the c3 application provides a - 40 dB sidelobe level (Fig. 11.93). The experimental pattern obtained with a linear array of square patches is plotted in Fig. 11.93. The theoretical and experimental outlines agree well if the low-level measurement difficulties are taken into account. 11.4.2 Simplex method Dantzig's algorithm [76] has been developed for linear programming with a real variable. Under symmetrical amplitude and antisymmetrical phase conditions, it is possible to compute real or complex excitations. The desired diagram is also defined with an envelope specification. 11.4.2.1 Symmetrical pattern: If the pattern is considered at M angular values (without correlation with N), the following inequalities are obtained: F ( 0 J 5 F,

F(&) L

F 2

(1 1.45)

F(0M) 5 FM The problem is to find the ensemble V:

c, has been previously defined, and a functional J(a) = ElrJaj has to be optimised (minimum or maximum) in order to promote some part of the diagram for instance. 11.4.2.2 Asymmetrical pattern: Choosing a, = a-j and q5] array factor can be written in the following form: N

f (0) =

1 a, cos (k4 sin 0 + 4,)

j= l

= -q5-j,

the

668

Design and technology of low-cost printed antennas

Design and technology of low-cost printed antennas

669

The expansion of the cosine term leads to: N

F(0)

=

f (0)g(0) =

element

(A, cos (ko4sin0) - B,sin (k04sin0)) g(0)

I

j= l

2 3

1.000 0667 0267

A, and B, are the real unknowns to be determined from the new 2N-dimensions linear problem. The algorithm can be used again, and at the end:

The introduction of M difference variables leads to a new linear system of M equations (instead of inequalities) with N M unknowns associated with the functional J(a) (or 2N M unknowns for an asymmetrical patterns). The Dantzig algorithm shows that only one solution exists (if there is a solution), which is found in a finite number of steps [73, 761.

+

+

element

./-I +I-2 +I-3 4-4 +I-5

m

1.000 -0.236 0.097 -0.073 0.054

D

m 'I)

deg

Fig. 11.94 Sector pattern of a 10-element array (H-plane). Simplex synthesis

deg g(O)=g (0)

11.4.2.3 Examples: The second pattern previously mentioned has been computed using the simplex method (Fig. 11.94). It appears that the amplitudes, sidelobe level and ripple are very similar to the relaxation solution. Directional

Fig. 11.95 Directional patterns of a six-element array for various source patterns. Simplex synthesis a Isotropic source b E-plane pattern c H-plane pattern

670

Design and technology of low-cost printed antennas

patterns are plotted in Fig. 11.95 for an array of six elements spaced 0.75 &; three-element patterns have been considered (isotropic, E-plane and H-plane). The directional patterns of a linear 32-equi-spaced-element array (spacing = 0491,) in the H-plane are plotted in Fig. 11.96. The sidelobe levels were

Design and technology of low-cost printed antennas

671

constrained by the CCIR-TVRO conditions with an extra limitation of - 20dB for the highest one. A cosecant-squared pattern (with a 30' window) was achieved for a 30-element array with half-wavelength spacing. The E-plane-

degrees

Fig. 11 3 7 Computed cosecant squared pattern of 30-element linear array (E-plane and d l l = 0.5). Simplex synthesis

degrees

Fig. 11.98 Fig. 11.96 Computed directional broadside pattern of a 32-linear-element array (H-plane and d l l = 0.87). Simplex synthesis a Equi-amplitude b CCIR-TVRO constraints and -20dB first sidelobe

Computed 30' steered-beam pattern of 20-element linear array (H-plane and d / L = 0.5). Simplex synthesis

element pattern is considered in Fig. 11.97. A 30" steered beam of a 20-element array (with half-wavelength spacing) in the H-plane, with a sidelobe level lower than - 25 dB, is shown in Fig. 11.98.

672

Design and technology of low-cost printed antennas

Design and technology of low-cost printed antennas

673

11.4.3 Experimental results [73]

Both methods have been used to design sector and directional patterns in the X-bands and K-bands, using corner-fed square patches. 11.4.3.1 Sector pattern: The specification is as follows:

ripple SLL


3.2 mm) substrates, and at higher frequencies than recommended by the manufacturer. The characterisation of connectors is sensitive and accurate while using the interferometric methods. The reactance of the connector may even by used for broadband matching of antennas. Printed lines and structures can be tested accurately by the resonant method given in this Chapter. Of special interest is the TDR technique, which can identify local defects with accuracy of several millimetres. Near-field probing is a qualitative tool which can help in understanding the behaviour of printed antennas and finding local defects. The main limitation is the interpretation of these mappings. The radiometric technique is useful, especially for large printed arrays with high losses. One can expect to find the dissipation losses of medium- and high-gain arrays with accuracies better than 1 dB. Future developments in the instrumentation for printed antennas will probably include the following: better substrates with accurate data sheets; novel calibration sets for accurate measurement of connectors and printed structures; new feed lines and new feed techniques for the radiators. Another promising area is the combination of radiators with active devices and MMIC chips. Such combinations will also lead to better measurement techniques and instrumentation. In the future there will be also combinations of printed antennas with electro-optical devices and optical fibres. Such combinations will, of course, require special measurement techniques. Finally, one may expect in the future to find some miniature probes, fed by optical means, for near-field probing. 16.8 References 1 HOLLIS, J. S., LYON, T. J., and CLAYTON, L. (Eds.): 'Microwave antenna measurements' (Scientific Atlanta, 1970) 2 APPEL-HANSEN, J., DYSON, J. D., GILLESPIE, E. S. and HICKMAN, T. G.: 'Antenna measurements' (in RUDGE, A. W., MILNE, K., OLVER, A. D., and KNIGHT, P. (Eds): 'The Handbook of antenna design' (Peter Peregrinus, 1982) Chap 8 3 BALANIS, C. A,: 'Antenna theory - analysis and design' (Harper and Row, NY, 1982) Chap. 15. 4 BLAKE, L. V.: 'Antennas' (Artech House, Mass., 1984) chap 8. chap 9-9 5 GUPTA, K. C., GARG, R., and BAHL, I. J.: 'Microstrip lines and slotlines' (Artech House, Mass., 1979) pp. 28-38, 184-193, 331-336 6 EDWARDS, T. C.: 'Foundations for microstrip circuit design' (John Wiley, 1981) pp. 172-207 7 LAVERGHETTA, T. S.: 'Microwave materials and fabrication techniques' (Artech House, Mass., 1984) p. 56 8 NAPOLI, L. S. and HUGHES J. J.: 'A simple technique for the accurate determination of the microwave dielectric constant for microwave integrated circuit substrates', IEEE Trans., 1971, MTT-19,pp. 664-665

996

Special measurement techniques for printed antennas

9 HOWELL, J. Q.: 'Quick accurate method to measure the dielectric constant of microwave integrated circuit substrates', IEEE Trans., 1973, MTT-21, pp. 142-143 10 LADBROOKE, P. H., POTOK, M. H. N., and ENGLAND, E. H.: 'Coupling errors in cavity resonance measurements on MIC dielectrics', IEEE Trans., 1973, MTT-21, pp. 560-562 11 OWENS, R. P., AITKEN, J. E. and EDWARDS, T. C.: 'Quasi static characteristics of microstrip on an anisotropic sapphire substrate', IEEE Trans., 1976, MTT-24, pp. 499-505 I2 RICHARDS, W. F., LO, Y. T. and BREWER, J.: 'A simple experimental method for separatmg loss parameters of a microstrip antenna', IEEE Trans., 1981, AP-29, pp. 150-151 13 ITOH, T.: 'A new method for measuring properties of dielectric materials using a microstrip cavity', IEEE Trans., 1974, MTT-22 pp. 572-576 14 GERHARD, A. R.: 'Measuring dielectric constant of substrates for microstrip applications', lEEE Trans., 1976, MTT-24, pp. .. 485437 IS BUSSEY, H. E.: 'Measurement of RF properties of materials - survey', proc. IEEE, 1967, 55, pp. 1046-1053 16 LYNCH, A. C.: 'Precise measurements on dielectric and magnetic materials', IEEE Trans., 1974, IM-23, pp. 425-431 17 KOBAYASHI, Y. and KATOH, M.: 'Microwave measurement of dielectric properties of low loss materials by the dielectric rod resonator method', IEEE Trans., 1985, MTT-33, pp. 586-592 18 AFSAR, M. N.: 'Dielectric measurements of millimeter wave materials', IEEE Trans., 1984, MTT-32, pp. 1598-1 609 19 PUES, H. F. and VAN D E CAPELLE, A. R.: 'Wideband impedance matched microstrip resonator antenna'. Proc. 2nd ICAP, 1981, pp. 402-405 20 GRIFFIN, J. M. and FORREST, J. R.: 'Broadband circular disc microstrip antenna', Electron. Lett., 1982, 18, pp. 266-269 21 FONG, K. S., PUES, H. F., and WITHERS, M. J.: 'Wideband multilayer coaxial fed microstrip antenna element', Electron. Lett., 1985, 21, pp. 497-499 22 CHEW, W. C. and KONG, J. A.: 'Analysis of a circular disk antenna with a thick substrate', IEEE Trans., 1981, AP-29, pp. 68-76 23 YANO, S. and ISHIMARU, A,: 'A theoretical study of the input impedance of a circular microstrip disk', IEEE Trans., 1981, AP-29, pp. 77-83 24 HENDERSON, A. and JAMES, J. R.: 'Design of microstrip antenna feeds. Part I: Estimation of radiation loss and design implications', IEE Proc., 1981, 128H. pp. 19-25 25 HENDERSON, A. and JAMES, 1. R.: 'Estimation of radiation from microstrip antenna feed transition', Radio Sci., 1981, 16, pp. 1119-1 123 26 PINHAS, S., and SHTRIKMAN, s.: 'Vertical currents in microstrip antennas', IEEE Trans., 1987, AP-35, pp. 1285-1289 27 WIGHT, 1. S., JAIN, 0. P., CHUDABIAK. W. J., and MAKIAS, V.: 'Equivalent circuits of microstrip impedance discontinuities and launchers*, IEEE Trans., 1974, MTT-22, pp. 48-52 28 AJOSE, S. 0 . and MATHEWS, N. A,: 'Equivalent circuit of coaxial to microstrip connector over the 8-12 GHz range, Electron. Lett., 1977, 13, pp. 465-466 29. HALL, P. S. and JAMES, J. R. 'Design of microstrip antenna feeds. Part 2: Design and performance limitations of triplate feeds' IEE Proc., 1981, 128H, pp. 26-34 30 MAJEWSKI, M. L., ROSE, R. W. and S C O T , J. S.: 'Modeling and characterization of microstrip to coaxial transitions', IEEE Trans., 1981, MTT-29, pp. 799-805 31 PUES, H. F. and VAN DE CAPELLE, A. R.: 'Computer aided experimental charaterization of microstrip to coaxial transitions'. Proc. 14th European Microwave Conference, 1984, pp. 137-141 32 EMC Technology: Microwave components catalog 882-15, 1982, p. 38 33 MIA-COM Omni Spectra Inc: Microwave coaxial connectors catalog, 1983, p. I I 34 ENGLAND, E. H.: 'A coaxial to microstrip transition', lEEE Trans., 1976, MTT-24, pp. 4748 35 AJOSE, S. O., MATHEWS, N. A. and AITCHISON, C. S.:'Characterisation of coaxial to

Special measurement techniques for printed antennas

1

i

i

I

1 i

I

997

microstrip connector suitable for evaluation of microstrip Zports', Electron. Lett., 1976, 12, pp. 430-43 1 36 GOURLEY, S. E. and CHAPMAN, A. G.: 'Broadband characterization ofcoaxial to microstrip transitions'. Proc. 12th European Microwave Conference, 1982, pp. 622-627 37 RICKARD, D. C.: 'Thick film mic components in the range 10-20 GHz. Proc. 6th European Microwave Conference, 1976, pp. 687-691 38 FINLAY, H. J., HOPKINS, L. G. T. and OZAMIZ, J. M.: 'Design and applications of precision microstrip multioctave attenuators and loads'. Proc. 6th European Microwave Conference, 1976, pp. 692696 39 KDI-Pyrofilm: RF resistive components catalog, PSA 1/80, 1980 40 EMI-Varian: Microstrip circuits data sheets, mc2m/10/70 41 EISENHART, R. L.: 'A better microstrip connector'. IEEE Int. Symp. Digest MTT-S, 1978, pp. 318-320 42 LEVINE, E., and TREVES, D.: 'Test technique improves coax to microstrip transitions', Microwaves and RF, July 1986, pp. 99-102 43 GUPTA, C. D., and TOMAR, R. S.: 'Resonance method of measurement of input impedance of any broadwall launched discontinuity in microstrip transmission lines', IEEE Trans., 1986, IM-35, pp. 126-129 44 SEALECTRO Co.: SMA catalog, SMA-9, 1980, pp. 25-26 45 WILTRON Co.: K Connector and semirigid cable, data sheet, 35K, Oct. 1984; K l I0 Series sliding contacts data sheet, DS 110-1, April 1985 46 HEUVEN, VAN 1. H. C.: 'A new integrated waveguide microstrip transition', IEEE Trans., 1976, MlT-24, pp. 144-147 47 SCHIEK, B. and KOHLER, J.: 'An improved microstrip to microslot transition', IEEE Trans., 1976, MTT-24, pp. 231-233 48 SHEPHERD, P. R. and POLLARD, R. D.: 'Direct calibration and measurement of microstrip structures on Gallium Arsenide'. IEEE Int. Symp. Digest MTT-S, 1986, pp. 629-632 49 CARLTON, D. E., GLEASON, K. R. and STRID, E. W.: 'Microwave wafer probing', Microwave J . Jan. 1985, pp. 121-129 50 HEWLETT PACKARD COMPANY: 'On wafer measurements using the HP 8510 network analyzer and Cascade Microtech wafer probes'. Product note 8510-6, May 1986 51 TROUGHTON. P.: 'Measurement techniques in microstrip', Electron. Lett., 1969, 5, pp. 25-26 52 WOLFF, I. and KNOPPIK, N.: 'Microstrip ring resonator and dispersion measurement on microstrip lines', Electron. Lett., 1971, 7 , pp.779-781 53 OWENS, R. P.: 'Curvature effect in microstrip ring resonators', Electron. Lett., 1976, 12, pp. 356-357 54 DEUTCH, J. and JUNG, H. J.: 'Measurement of the effective dielectricconstant of microstrip lines in the frequency range from 2 GHz to 12 GHz', Nachrichtenlech Z., 1970,12, pp. 620-624 55 EDWARDS, T. C. and OWENS, R. P.: '2-18 GHz dispersion measurements on 10-100 ohm microstrip lines on sapphire', IEEE Trans., 1976, MTT-a, pp. 506-513 56 ROMANOFSKY, R. R., BHASIN, K. B., PONCHAK, G. E., DOWNEY, A. N. and CONNOLLY, D. J.: 'An experimental investigation of microstrip properties on soft substrates from 2 to 40 GHz' IEEE Int. Symp. digest MTT-S, 1985, pp. 675-678 57 RICHINGS, J. G.: 'An accurate experimental method for determ~ningthe important parameters of microstrip transmission lines', Marconi Rev. 1974, pp. 209-216 58 BELOHOUBEK, E. and DENLINGER, E.: 'Loss considerations for microstrip resonators', IEEE Trans., 1975, MTT-23, pp. 522-526 59 PUCEL, R. A,, MASSE, D. J. and HARTWIG, C. P.: 'Losses in microstrip', IEEE Trans., 1968, MTT-16, pp. 342-350, 1064 60 DENLINGER, E. J.: 'Losses in microstrip lines', IEEE Trans., 1980, MTT-28, pp. 513-522 61 JAMES. J. R. and HENDERSON, A,: 'Planar millimeter wave antenna arrays in Infrared and millimeter waves'; Vol. 14 (Academic Press, 1985) pp. 189-247

,

998

Special measurement techniques for printed antennas

62 TROUGHTON, P.: 'High Q factor resonators in microstrip', Electron. Lett., 1968, 4, pp. 520-522 63 AITKEN, J. E.: 'Swept frequency microwave Q factor measurement', Proc. IEE, 1976, 123, pp.855-862 64 KAJFEZ, D. and HWAN, E.: 'Q factor measurement with network analyzer', IEEE Trans., 1984, MTT-32, pp. 666-669 65 LADBROOKE, P. H.: 'Some effects of field perturbation upon cavity resonance and dispersion measurements on MIC dielectrics', IEEE Trans., 1977, MTT-25, pp. 892-903 66 GETSINGER, W. J., 'Measurement and modeling of the apparent characteristic impedance of microstrip', IEEE Trans., 1983, M'IT-31, pp. 624-632 67 SHEPHERD, P. R., and DALY, P.: 'Modeling and measurement of microstrip transmissionline structures', IEEE Trans., 1985, MTT-33, pp. 1501-1506 68 STEPHENSON, I. M. and EASTER, B.: 'Resonant techniques for establishing the equivalent circuits of small discontinuities in microstrip', Electron. Lett., 1971, 7, pp. 582-584 69 EASTER, B.: 'The equivalent circuit of some microstrip discontinuities'. IEEE Trans., 1975, MTT-23, pp. 655-660 70 MENZEL, W. and WOLFF, I.: 'A method for calculating the frequency dependent properties of microstrip discontinuities', IEEE Trans., 1977, MIT-25, pp. 107-1 12 71 EASTER, B., GOPINATH, A. and STEPHENSON, I. M.: 'Theoretical and experimental methods for evaluating discontinuities in microstrip', Radio & Electron. Eng., 1978, 48, pp. 73-84 72 RIZZOLI, V.: 'A general approach to the resonance measurement of asymmetric microstrip discontinuities'. IEEE Int. Symp. Digest MTT-S, 1980, pp.422424 73 GARG, R. and BAHL, I. J.: 'Microstrip discontinuities', Int. J. Electron., 1978,45, pp. 81-87 74 ENGEN, G. F.: 'The six-port reflectometer: an alternative network analyzer', IEEE Trans., 1977. M'IT-25. DD. 1075-1080 75 CRONSON, H. M. and SUSMAN, L. A.: 'Six-port automatic netowrk analyzer' IEEE Trans., 1977, MTT-25, -DD. - 1086-1091 76 CULLEN, A. L.: 'The six-port and the microprocessor in microwave measurements'. Proc. 9th European Microwave Conference, 1979, pp. 74-82 77 SOMLO, P. I. and HUNTER, J. D.: 'A six-port reflectometer and its complete characterization by convenient calibration procedure' IEEE Trans., 1982, MTT-30, pp. 186-192 78 EL-DEEB, N. A,: 'The calibration and performance of a microstrip six-port reflectometer', ZEEE Trans., 1983, MlT-31, pp. 509-514 79 ELLIOT, B. J.: 'High sensitivity picosecond time domain reflectometry', IEEE Trans., 1976, IM-25, pp. 376-379 80 PILLER, U.: 'Time domain immittance measurements'. Proc. 4th European Microwave Conference, 1974, pp. 61-65 81 CASPERS, F.: 'Precision time domain measurement system', Electron. Lett., 1980, 16, pp. 29-30 82 'Microprocessor based fault finder pinpoints transmission line faults within inches', Microwave J., Nov. 1981. *DD. - 49-57 83 'Real time measurements in a wideband network analyzer', Microwave J., Jan. 1984, pp. 138-145 84 HEWLETT PACKARD COMPANY: H P 8510 network analyzer, operating and service manual, 1984, pp. 127-149 85 DYSON, J. D.: '~easurement of near fields of antennas and scatterers', IEEE Trans., 1973, AP-21, pp. 445-460 86 JOHNSON, R. C., ECKER, H. A. and HOLLIS, J. S.: 'Determination of far-field antenna patterns from near-field measurements', Proc. IEEE, 1973, 61, pp. 1668-1694 87 PARIS, D. T., LEACH, W. M. and JOY, E. B.: 'Basic theory ofprobe-compensated near field measurements', IEEE Trans., 1978, AP-26, pp. 373-379 88 JORY, V. V., JOY, E. B. and LEACH, W. M.: 'Current antenna near field measurement

..

Special measurement techniques for printed antennas

999

research at the Georgia Institute of Technology'. Proc. 13th European Microwave Conference, 1983, pp. 823-828 89 YAGHJIAN, A. D.: 'An overview of near field antenna measurements', IEEE Trans., 1986, AP-34, pp. 30-45 90 BASSEN, H. I. and SMITH, G. S.: 'Electric field probes - a review', IEEE Trans., 1983, AP-31, pp. 710-718 91 SMITH, G. S.: 'Analysis of miniature electric field probes with resistive transmission lines', IEEE Trans., 1981, MTT-29, pp. 1213-1224 92 BATCHMAN, T. E. and GIMPELSON, G.: 'An implantable electric field probe of submillimeter dimensions', IEEE Trans., 1983, MTT-31, pp. 745-751 93 KANDA, M. and RIES, F. X.: 'Dipole based EM probe grabs complex fields', Microwaves & RF, Jan. 1981, pp. 63-66 94 SOLBACH, K.: 'Electric probe measurements on dielectric image lines in the frequency range of 26-90 GHz', IEEE Trans., 1978, MTT-26, pp. 755-758 95 DAHELE, J. S. and CULLEN, A. L.: 'Electric probe measurements on microstrip', IEEE Trans., 1980, MTT-28, pp. 752-755 96 WEEKS, W. L.: 'Antenna engineering' (McGraw Hill, 1968) pp. 179-180 97 CHUNG, I., ANDREWS, C. L. and LIBELO, L. F.: 'Near field diffraction on the axes of disks'. J. Opt. Soc. Am., 1977, 67, pp. 1561-1566 98 LEVINE, E., SHTRIKMAN, S. and TREVES, D.: 'Near field mapping of microstrip antennas'. Proc. 12th European Microwave Conference, 1982, pp. 337-342 99 -KERNWEIS. N. P. and McILVENNA, J. F.: 'Liquid crystal diagnostic techniques -An --- .. antenna design aid', Microwave J., Oct. 1977, pp. 41-44 100 GIANNINI, F., MALTESE, P. and SORRENTINO, R.: 'Liquid crystal technique for field detection - - .- ..... in microwave integrated circuitry' AIta Frequenza, 1977, XLVI pp. 170-178 101 GIANNINI, F., MALTESE; P. and SORRENTINO, R.: 'Liquid crystals improved technique for thermal field measurements', Applied Optics, 1979, 17, pp. 3048-3052 102 NEWHAM, P.: 'Monolithic patch array antenna for small missile applications'. Military Microwaves Conf. MM-86, 1986, pp. 335-340 103 HASEGAWA, H., FURUKAWA, M. and YANAI, H.: 'Measurements on high frequency transmission characteristics of metallization patterns in monolithic ICs', Electron & Commun. in Japan, 1971.54-B, pp. 52-60 104 LADBROOKE, P. H.: 'A novel standing-wave indicator in microstrip', Radio & Electron. Eng., 1974,44, pp. 273-280 105 HUBBELL. S. and ANGELAKOS, D. J.: 'A technique for measuring the effective dielectric constant of microstrip line', IEEE Trans., 1983, MlT-31, pp. 687-688 106 GAJDA, G., STUCHLY, M. A. and STUCHLY, S. S.: 'Mapping of the near field pattern in simulated biological tissues', Electron. Lett., 1979, 15, pp. 120-121 107 DAVIES, D. E. N. and VAKIL, S. M.: 'Field probe for measuring both amplitude and phase of antenna radiation patterns', Electron. Lett., 1980, 16, pp. 873-875 108 HELIER, M. and BOLOMEY, J. C.: 'Test of monolithic microwave integrated circuits with radiating probes', Proc. 13th European Microwave Conference, 1983, pp. 621-645 109 NEWMAN, E. H., BOHLEY, P. and WALTER, C. H.: 'Two methods for the measurement of antenna efficiency', IEEE Trans., 1975, AP-23, pp. 457461 110 KUMMER, W. H. and GILLESPIE, E. S.: 'Antenna measurements-l978', Proc. IEEE, 1978, 66, pp. 483-507 111 ASHKENAZY, J., LEVINE, E. and TREVES, D.: 'Radiometric measurement of antenna efficiency', Electron. Lett., 1985, 21, pp. 111-112 112 LEVINE, E., MALAMUD, G. and TREVES, D.: 'High gain modular microstrip antennas', Proc. 16th European Microwave Conference, 1986, pp. 655-660 >

>

-- -

.

-

Chapter 17

Computer-aided design of microstrip and triplate circuits J-F. Zurcher and F.E. Gardiol

17.1 Introduction, definition of the structure 17.1.1 Outline The basic purpose of this Chapter is to provide general background information about circuits in microstrip and balanced stripline (triplate) technologies, that are currently used to interconnect elements and realise antenna feed networks. It will describe the general appearance of the circuits, the techniques utilised to fabricate them and interconnect them, the materials most currently used and, finally, the very powerful computer programs presently available to analyse, design and actually draw the pattern and cut the masks required for the manufacturing process. The Chapter will be completed with worked examples and an extended Bibliography. 17.1.2 Microwaves The field of microwaves extends over the frequency range 300 MHz -300 GHz or, in terms of wavelengths, from 1 mm up to 1 m. The sizes of instruments required to generate them and to measure them are thus of the same order of magnitude as a wavelength. One cannot assume that circuits are much smaller than a wavelength, as one generally does in circuit theory. One cannot either assume that they are much larger, as is the case in optics. This means, in fact, that the finite velocity of light must be taken into account. The traditional applications of microwave antennas, in radar and communications, cover the frequency bands below 12-15 GHz, while heating and medical applications are restricted to a narrow band around 2450 MHz and, in certain countries, 915 MHz [14]. Recently, frequency bands in the millimetrewave range (up to 100 GHz) are also being considered. 17.1.3 Transmission lines for microwaves Metallic waveguides, i.e. hollow metallic tubes of rectangular, circular or ellipti-

7002

Computer-aided design of microstrip and triplate circuits

'cal cross-sections, have generally been used in the past to carry microwave signals, in particular in antenna feed systems. They are most often rigid and bulky, difficult to interconnect with discrete components (diodes, transistors), for which special fixtures must be designed and machined. They are presently used only when specifically required, for high power levels or at very high frequencies. In all other situations, they are replaced by a variety of planar lines (Fig. 17.1).

Strlpllne

Mlcrostrlp

Slotllne

Suspended

Coplanar

stripline

lnuerted

llne

Computer-aided design of microstrip and triplate circuits

7003

critical). A mask of the circuit is made, and the conductor outline $then imprinted on a suitable photoresistive layer deposited on the printed-circuit material. Metal is then either etched away from the exposed region, or deposited onto it (Section 17.4). The main difference between low-frequency printed circuits and microwave planar structures is that, at microwaves, all dimensions are significant. Microstrip antennas are also planar structures, similarly realised by the photolithographic process, but adapted for their larger size (in particular for arrays). When the antenna patches are fed by microstrip lines or striplines, one obtains a fully integrated system, in which both the radiators and the circuit elements are realised using the same technology. Solid-state components like transistors can be inserted to realise active antennas, while whole monolithic antenna structures are deposited on a semiconductor substrate. In contrast, waveguide or fin-line feeds (at millimetre wavelengths) are better suited for use with horn radiators. 17.1.4 Balanced stripline or triplate A thin centre conductor, of width w, is located between two flat metal plates, or ground planes (Fig. 17.2). The material between the two plates is a low-loss

stripllne

Dielectric Flnllne

Metal

Fig. 17.1 Planar transmission lines

Planar lines make use of the photolithographic technique developed to realise electronic circuits, permitting miniaturisation and series production. A sheet of insulating material (ceramic or plastic), the substrate, provides mechanical rigidity and permits the accurate positioning of components, while metal strips desposited on the substrate provide the necessary connections (at low frequencies, only a low-resistance path is required; i.e. strip dimensions are not

Fig. 17.2 Ideal homogeneous balanced stripline

dielectric, which may be air (in which case some provision is needed for mechanical support). The structure is homogeneous; i.e. the electromagnetic fields extend over one single propagation medium of uniform dielectric properties - at least in theory. In practice, however, the centre conductor is deposited on a dielectric substrate, and a dielectric plate of the same thickness is then placed on top. Since the metal layer cannot be infinitely thin, an air-filled gap remains between the two dielectric layers (Fig. 17.3). When very high performance is required, this gap may in turn be filled with a special dielectric glue, of the same permittivity as that of the two plates.

7004

Computer-aided design of microstrip and triplate circuits

Basically, the balanced stripline is a homogeneous transmission line, whose dominant mode is purely transverse electromagnetic (both the electric and the magnetic field are perpendicular to the longitudinal direction of the transmission line). While it is an open structure, since the ground planes do not

Fig. 17.3 Balanced stripline with air gap between the two dielectric layers

extend to infinity, the fields decay quite rapidly in the transverse direction and there is practically no radiation. 17.1.5 Microstrip A microstrip line may be considered to be one-half of a balanced stripline (Fig. 17.4), in which one of the ground planes and half of the dielectric have been

Fig. 17.4 Microstrip line

removed. This means that the line is inherently open and inhomogeneous, with fields extending all the way to infinity over both the dielectric substrate and the air. Radiation and surface waves (see Chapter 8) can to somt: extent be avoided, by using thin substrates of high-permittivity material. The fields are then mostly concentrated within the dielectric, up to a certain frequency limit. The velocity

Computer-aided design of microstrip and triplate circuits

7005

of propagation for a plane wave is different in the two media, so that the dominant mode of the structure cannot be tranverse electromagnetic: longitudinal field components are required to satisfy the boundary conditions on the air-dielectric interface. The longitudinal components, however, remain much smaller than the transverse ones and can be safely neglected in most pratical situations. The dominant mode of the transmission line is then called quasiTEM. 17.1.6 Adjustments 'Classical' microwave designs, based on waveguide technology, always permit final adjustments: one may always reduce a mismatch by placing an inductive post or a dielectric plate in a waveguide. Frequency-sensitive waveguide components such as filters generally require a 'final tuning' step to meet their specifications. Printed structures, on the other hand, have little or no capability for adjustments, because they result from a lengthy fabrication procedure. One must first prepare a layout, analyse its theoretical response, optimise it to meet the desired performance, draw the circuit's outline, cut the mask, reduce it photographically, expose it, etch it, dry it, and then mount the finished circuit and measure its actual performance (Section 17.8). If the circuit does not meet expectations, the entire procedure must be carried out again. The design of printed circuits should therefore be right the first time. Accurate descriptions of the components must be available, resulting from a thorough theoretical analysis. The performance predicted should coincide with the measured data (since Maxwell, electromagnetics is an exact science). The realisation of feeds for microstrip antennas, however, is not as critical as that of filters: microstrip or striplines provide fairly broadband operation, whereas the frequency band of microstrip patches is notoriously narrow. As a result, feeds may be easier to realise than the antenna itself. A waveguide design is assembled by bolting components together. In microwave printed-circuit technology, on the other hand, connectors introduce mismatches that can badly damage the performance of the system. These are difficult to avoid or to compensate for. Wherever feasible, one should realise and assemble all the components on the same substrate. In the case of microstrip antennas, the feed system can be deposited on the same substrate, or a multiplelayer system can be used. 17.1.7 Multiple inhomogeneity In terms of the electromagnetic field distribution, printed structures (circuits or antennas) are quite complex, since most of them possess three different types of inhomogeneity: (a) With the exception of the balanced stripline (Fig. 17.2), the fields on printed microwave structures extend over an inhomogeneous region, formed partly of dielectric (one or several layers) and partly of air. Waves propagating along the structure cannot be transverse electromagnetic, and therefore exhibit dispersion (fortunately, this effect is small for microstrip) [14].

1006

Computer-aided design of microstrip and triplate circuits

(b) A metal layer extends only partially across the structure (center or upper conductor): the boundary conditions for the fields are not the same at all points on a plane, e.g. the air-dielectric interface of inhomogeneous structures. (c) The whole structure has finite transverse dimensions. Circuits are enclosed in a box, while antennas are open. Radiated waves and surface waves on the air-dielectric substrate bounce back and forth, scattered by the edges, producing spurious coupling between elements.

Computer-aided design of microstrip and triplate circuits

1007

The longitudinal dependence of the fields on the line is expressed in terms of the line voltage U ( z )and of the line current I(z). Complex phasors simplify the notation when the time dependence is sinusoidal. The actual voltage and current

An accurate analysis of the electromagnetic fields on printed structures becomes almost prohibitively difficult, owing to the presence of inhomogeneities. Circuits in stripline and microstrip can, however, be designed quite satisfactorily using electrostatic and quasi-static approximations, which are quite adequate for most practical applications (radiation and surface waves can be neglected at sufficiently low frequencies). 17.1.8 Measurement problems In all technical developments, measurements are used to check the validity of theoretical derivations and the accuracy of numerical calculations. When analysing stripline or microstrip structures, the measurements are never made on the structure itself. Instruments are always connected to the coaxial line or waveguide, so that the structure is 'seeen' across transitions and connectors (like through a glass, darkly?). It is then difficult to analyse its behaviour, since transitions and connectors add reflections, attenuation and phase shifts that combine in a complex manner with the characteristics of the structure itself (Fig. 17.5). Several ways of 'de-embedding' the circuit were proposed. One may compare it with straight sections of line (assuming connections to be identical). Also, one may insert the circuit within a resonant structure, and deduct its properties from the measured changes of the resonance parameters (Fig. 17.6). The 'time gating' function of modem vector network analysers permits one to separate connector and circuit parameters. No reliable data can, however, be obtained across a transition that is very lossy or mismatched. The difficulties encountered in the measurement process mean that it may be difficult to check the validity of a model and to determine the accuracy of the computation process. This, in turn, affects the capability of CAD procedures.

17.2 Basic relationships for uniform lines 17.2.1 Uniform lines We first consider straight transmission lines, aligned with the longitudinal co-ordinate z. Sliding the whole structure along this axis does not modify it, the cross-section and the material parameters being independent of z (Fig. 17.7). The transmission line is then called uniform or translation-invariant. It is then possible to separate the transverse and longitudinal dependences of the fields along the line [16].

Fig. 17.5 Connections from microstrip to coaxial line a Soldered strip b Pressed beam c Direct soldering d Sliding sleeve

are given by the real part of the corresponding complex quantities multiplied by J2 e x p m t ) (17.1) U(z, t) = Re [$ U ( z ) exp (jot)] IV] I(z, t) = Re [$ I(z) exp (jot)] [A]

(17.2)

In complex phasor notation, all time derivatives are replaced by the factor jw.

1008

Computer-aided design of microstrip and triplate circuits

Computer-aided design of microstrip and triplate circuits

The time dependence is thus altogether suppressed. Solving the line equations (derived from Maxwell's equations) yields the longitudinal dependences of the voltage and the current along the line: U(z) I(z)

= =

U+ exp ( - yz)

+ U - exp (+ yz)

Y, [U+ exp ( - yz)

-

[vl =

of them (inhomogeneous conditions). In a homogeneous transmission line, the transverse-wave equation becomes Laplace's equation in the two-dimensional transverse plane [16]. Since the boundary conditions are inhomogeneous, La-

(17.3)

U- exp (+ yz)] [A]

where y is the propagation constant (metre-') and Y,

1009

(17.4)

I/Z, is the character-

Fig. 17.7 Uniform infinite straight transmission lines

Fig. 17.6 Resonant ring with slot [used to determine the equivalent circuit of the slot (Section 17.3.8)]

istic admittance of the line [Siemens]. Both quantities depend on the transverse distribution of the fields across the line. The quantities U+ and U- are, respectively, the amplitudes of the forward wave (travelling towards increasing values of z) and the reverse wave (travelling towards decreasing values of z) (Fig. 17.8). These two terms are determined from boundary conditions at the ends of the line (generator and load).

17.2.2 Conformal mapping In stripline and microstrip lines, the conductor boundaries within the transverse plane are located along rectangular co-ordinate lines, but cover only over part

place's equations cannot be solved directly in the rectangular system of coordinates. Particular cylindrical co-ordinate systems can, however, be defined by conformal mapping, a technique based on transformation properties within the complex plane [45]. One may then obtain exact solutions within the transformed system. A complex number z is assigned to every point in the transverse plane of the transmission line, referenced by its rectangular co-ordinates .u and y (the complex number z should not be confused with the direction of propagation z)

In another complex plane, there exists another complex number w: that is connected to z by a complex function, which defines the conformal mapping (Fig. 17.9)

701 1

Computer-aided design of microstrip and triplate circuits

Computer-aided design of microstrip and triplate circuits

The function f(z) must be analytical, meaning that its derivative is continuous and single-valued. The basic idea is to map the transverse plane of the transmission line (z-plane) onto the complex plane of the transformed function w in

17.2.3 Schwartz-Christoflel transforms When boundaries are located along straight lines, the Schwartz-Christoffel transform provides the conformal mapping for the problem. It allows one to 'straighten up' the angles. A polygon is thus transformed into a straight line, which is most often taken as the real axis. This provides an integral equation, and the function w = f(z) is then obtained by integration. A similar transform is applied to a section of parallel-plate capacitor. The desired conformal mapping is the combination of the two transforms. The integration is the most crucial part of the whole process. When this integral cannot be evaluated analytically, z cannot be expressed as an explicit function of w. In the case of striplines and microstrip, the integration can be performed analytically, but yields rather exotic functions.

1010

* forward

17.2.4 Zero-thickness balanced stripline Outside the centre conductor strip, the two transverse co-ordinate axes (Fig. 17.2) form electric-field lines, or perfect magnetic conductors. Assuming that the two ground planes extend sideways to infinity, and that the centre conductor is infinitely thin (b = O), the Schwartz-Christoffel transform maps one quarter of the stripline's cross-section to a section of parallel-plate capacitor [ I 31. Carrying out the calculations eventually yields the characteristic impedance of the balanced stripline [9, 211

wave

z, =

-

k = [cosh (rrwl4h)l-' [l]

Fig. 17.8 Forward and reverse travelling waves

2

[a]

(17.8)

where K(k) is the complete elliptic integral of first kind [l] and reverse wave

Y

( w & ) R(k)/K(k)

plane

(17.9)

The symbol [I] indicates that a quantity is dimensionless. v

qy plane

17.2.5 Finite-thickness balanced stripline 0, An exact analysis by means of conformal mapping is also feasible when b i.e. when the thickness of the centre strip is taken into account [59]. However, the resulting developments become quite involved, yielding an implicit expression for the characteristic impedance. Calculated values have been published in Tables [21]. A simplified approximate formula for the impedance, derived from the exact values, is

+

where Fig. 17.9 Principle o f conformal mapping

F(x)

x such a way that the transforms of the conductor boundaries become straight lines. The mapping process replaces the complex geometry of the transmission line by a simple two-plane geometry.

=

=

(x

+ I)'"

+

"/(x - 1)'" - ') [I]

l/(l - b/2h) [l]

(17.11) (17.12)

The characteristic impedance of a balanced stripline is displayed in Fig. 17.10 as a function of geometrical dimensions.

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Computer-aided design of microstrip and triplate circuits

Computer-aided design of microstrip and triplate circuits

7073

17.2.6 Equivalent homogeneous microstrip line The inhomogeneous microstrip line is replaced by an 'equivalent' homogeneous line (Fig. 17.1 I) with conductors having exactly the same geometry (w, h, b), but

The relative error included in these approximations is smaller than 0.2% for 0.01 ,< w/h < 100 and 1 < E, < 128. The phase velocity v4 and the line wavelength ig are related to the effective permittivity by v4

= GI/&

[m/d

(17.16)

Ag = &I& [ml (17.17) Both the velocity and the wavelength are functions of the transverse geometry of the transmission line.

h Oo

1

3

2

4

5

wlh

17.2.7 Characteristic impedance of microstrip T h e homogeneous microstrip (Fig. 17.1 1) structure was analysed by means of the Schwartz-Christoffel transform by Schneider [55]. The mapping is carried out by means of the logarithmic derivative of the theta function 0, (t, k):

Fig. 17.10 Characteristic impedance of balanced stripline

z ( t ) = - (2hK/7c) 8,In [8,(t, K)] [I]

(17.18)

where K

=

K'(m)/K(m) [I]

(17.19)

with K(m) the complete elliptic integral of the first kind with modulus m. The characteristic impedance 2, of the microstrip having width w, substrate height h and thickness b = 0 is obtained by solving the set of simultaneous equations

all the other parameters remain unchanged

Fig. 17.11 Definition of the equivalent homogeneous microstrip

surrounded by a single homogeneous dielectric of effective permittivity E,. This permittivity is determined by calculating the DC capacitance of the inhomogeneous structure [23] E,

E (E,

+ 1)/2 + [(E, - 1)/2][1 + IO~/W]-'~[I]

(17.13)

where E(m) is the complete elliptic integral of the second kind, and dn is the Jacobian elliptic function. The characteristic impedance cannot be expressed explicitly from these equations, so that approximate design formulas have been derived by Hammerstad and Jensen [23], which provide an accuracy better than 0.01% for w/h < 1 and 0.03% for w/h ,< 1000 with respect to the SchwartzChristoffel transform

with where F,

=

6

+ (2a - 6) exp [ -

(30.666 h / ~ ) ~ "[l]~ ~ ~ ]

(17.24)

1014

Computer-aided design of microstrip and triplate circuits

and where Zo 2. 12077 = 376.6 ohms The characteristic impedance of microstrip is displayed in Fig. 17.12. 17.2.8 Finite-thickness homogeneous microstrip The thickness b of the upper conductor can be approximately taken into account

Computer-aided design of microstrip and triplate circuits

1075

17.2.9 Microstrip line synthesis for b = 0 The equations given in the previous Sections yield the line's electrical characteristics E,, Z, and IZ, in terms of the geometrical and material parameters (analysis of a specified structure). Most often, in practice, one wishes to determine the wlh ratio that yields a specified impedance 2,. This reverse operation of synthesis is carried out by means of approximate expressions (within 1% accuracy) derived by Wheeler [60]. For wlh < 2:

wlh r 4[(1/2) exp (A) - exp (- A)]-' [I]

(1 7.26)

with

while for wlh 2 2:

with Fig. 17.12

Characteristic impedance of microstrip

17.2.10 Dispersion in microstrip For high frequencies, the fields tend to concentrate within the dielectric substrate, so that the effective permittivity E, increases. This may be taken into account by means of the following approximation [17]:

all the other parameters remain unchanged

Fig. 17.13 Microstrip with conductor of finite thickness

where E, is the low-frequency permittivity defined in eqn. 17.13,f is the frequency of the signal and the remaining parameters are given by

by defining an effective width we to be used instead of the actual width in the calculations [2 11 (Fig. 17.13):

with x = h if w > h/2n and x = ~ X W if h/2n > w > 26.

17.2.11 Effect of an enclosure The relations presented above were all obtained for structures assumed to be 'uncovered', in which the air-filled half space above the microstrip extends to

10 7 6

Computer-aided design of microstrip and triplate circuits

infinity, the structure also being infinite in the tranverse directions. In practice, a circuit is always placed within a box, the walls and covers of which are relatively close to the circuit. The characteristic impedance and the effective permittivity may then be affected, in ways difficult to determine accurately [27]. Rules of thumb determine roughly when the uncovered line expressions are valid. For aluminia (E, = 9.8), this is the case when the height to cover is more than eight times the substrate thickness and the distance to the walls is more than five times the conductor thickness.

Computer-aided design of microstrip and triplate circuits

1017

The characteristics of lossy microstrip can be evaluated using a program developed by Kajfez and Tew [37]. 17.2.13 Higher-order modes and radiation Just like any other transmission line, striplines and microstrips cannot be utilised above a certain frequency limit, since other modes of propagation,

17.2.12 Attenuation Three kinds of losses are encountered: Ohmic losses within the conductors, owing to the finite conductivity of the metal. The losses may be increased by the presence of an adhesion layer between the substrate (in the case of ceramics) and the conductor. Also, the surface roughness increases the attenuation. For striplines, the ohmic-loss contribution to the attenuation is given by 1301

x

wz

{

x

+

+ "'(I

b'h'

In

*}

x - 1

for w/2h 2 0.35 (17.33)

where x is defined in eqn. 17.12. In microstrip lines, an approximate value is given by Janssen [36] Fig. 17.14 Circuit with bends and junctions

with the metal-wall resistance

Dielectric losses are produced by the energy dissipated in the substrate, proportional to its dielectric loss factor tan 6. In stripline, the resulting attenuation is given by [30]

-

called higher-order modes, would then start to propagate. In the homogeneous stripline, these modes are either transverse electric (TE) or transverse magnetic (TM) modes, similar to the ones encountered in hollow metallic waveguides. In the inhomogeneous microstrip, higher-order modes are hybrid modes (like modes on optical fibres). Since both structures are open, i.e. not completely enclosed within a metal envelope, they may also start radiating when the frequency increases, then behaving like antennas. For a microstrip line, radiation becomes significant for frequencies larger than [22]:

while for microstrip lines, they become [22]: ci,

27.3

E, -E,

1 E, tan 6

- 1 E,

- [dB/ml A8

Radiation losses: An infinite straight transmission line propagating in the dominant mode does not radiate. However, at every discontinuity, higher-order modes are excited, some of which radiate part of the signal (Section 17.2.13).

17.3 Discontinuities: bends, junctions 17.3.1 Dejnition In actual circuits, transmission lines are neither straight nor infinite; they start, and then stop, at some definite points, bend, change width, branch out, etc (Fig.

1018

Computer-aided design of microstrip and triplate circuits

17.14). The discontinuities most often encountered in microstrip are sketched in Fig. 17.15, while the main mathematical techniques used for their study are listed in Table 17.1. Discontinuities produce reflections of the propagating mode Open line

Computer-aided design of microstrip and triplate circuits

1019

nuity; these modes store electric and magnetic energy locally. An increase in charge density on a conductor can be represented by an additional capacitance, while changes in current distribution produce inductances. Discontinuities can therefore be represented by LC equivalent circuits, in which the components are frequency-independent at low frequencies (static/ quasi-static models), becoming generally frequency-dependent as frequency increases (dispersive models). Reactive elements can further be combined to form sections of transmission lines with particular characteristics. An alternative description provides the scattering parameters of the discontinuity (more generally used for high-frequency studies). The relationships between different representations of a discontinuity were considered by Mehran 1471.

Double step Discontinuity infinite

Fig. 17.15

with

impedance

- I 7-

Common discontinuities Discontinuity

(TEM or quasi-TEM), with accumulation of reactive energy in evanescent higher-order modes, and also radiation. The latter effect only becomes significant for very large signal frequencies; i.e. when the structure cannot be used for signal transmission anyway (Section 17.2.13). Microstrip discontinuities are difficult to analyse, due to their inhomogeneous nature (Section 17.1.7) and the presence of radiation together with propagation phenomena. 17.3.2 Models The boundary conditions for the fields in the presence of discontinuities can only be matched by the complete set of modes in the structure. Higher-order modes are excited, but if the dimensions of the lines are selected properly, they cannot propagate along the transmission line and remain evanescent (Section 17.2.12: the same situation is encountered in metallic waveguides [14]). The fields of the higher-order modes decay as one moves away from the disconti-

with

zero impedance

Fig. 17.16

-r 7-

Zero- and infinite-impedance discontinuities

While one might expect results from dispersive models to be more accurate, this is not always true. The DC extrapolation of results provided by a dispersive model was found to yield incorrect values in many situations [lo]. Discontinuities can generally be separated into two main families (Fig. 17.16): With zero DC resistance, with a continuous upper conductor extending completely across the discontinuity. The equivalent circuit then contains both capacitances and inductances. With injnite DC resistance, when the upper conductor is interrupted between

1020

Computer-aided design of microstrip and triplate circuits

the ends of the discontinuity. No direct current can flow across the structure, which is represented by a purely capacitive equivalent circuit. 17.3.3 TEM-line models The shunt capacitance of an open microstrip line is given by a perturbation of the uniform line (Section 17.2), that takes into account the fringing fields at the open edge [33, 321. Fairly approximate results were obtained, and the approach could not really be extended to consider other discontinuities. 17.3.4 Variational techniques A variational (stationary) mathematical expression for the shunt capacitance of an open circuit was established by Maeda [42]. The unknown potentials within a closed structure are expanded over the infinite set of solutions for Laplace's equation. The approach is rather involved and would be difficult to generalise in order to analyse more complex discontinuities. 17.3.5 Fourier transform The approach used for an uniform transmission line [62] was extended to cover also three-dimensional structures [31]. The Green's function is solved in the spectral domain by a Galerkin technique [34]. The calculated capacitance of an open microstrip line agrees quite well with measured data. This approach was used by Koster and Jansen [39] to analyse step discontinuities. 17.3.6 Dielectric Green'sfunction This flexible approach to determine capacitance remains accurate even in the DC limit. It was applied to most geometries (Table 17.1) by Farrar and Adams [ l l , 121, and by Silvester and Benedek [6, 56, 5 7 . A three-dimensional Green's function is defined by generalising the one introduced for the uniform microstrip line. The integral equation is solved with the moment's method, either with functions defined over the whole discontinuity [56], or with step functions that are constant over a rectangular sub-domain and vanish everywhere else [I I]. A similar approach was developed to solve the much more complex problem of radiation from microstrip antennas (Chapter 8). 17.3.7 Integral equations for induttances The inductance of a bend was determined from the magnetic energy, replacing the surface current by a wire net [18]. Since inductance becomes infinite for infinitely thin wires, some approximations were introduced, but they proved to be rather inaccurate. These drawbacks were avoided by the use of an integral equation based on the skin effect. Results were obtained for the microstrip bend [58] and for the impedance jump in Xand Yjunctions [19]. Since this technique considers actual surface currents, the magnetic energy can be determined without mathematical difficulties. However, the computation process becomes quite involved, and one

Computer-aided design of microstrip and triplate circuits

1021

7022

Computer-aided design of rnicrostrip and triplate circuits

Computer-aided design of rnicrostrip and triplate circuits

1023

must first compute a scalar-potential solution of Laplace's equation at the discontinuity, which becomes the kernel of the integral equation. 17.3.8 Green's function and integral equation The two techniques presented in previous Sections were improved upon, simplified and combined to determine the complete equivalent circuit of a slot [52], of a double step and a mitred bend [5]. 17.3.9 Green's function and electrostatic-inductance computation Another combined technique determines the capacitance by means of a dielectric Green's function. Inductances are then assumed to be proportional to the square of the difference of the electrostatic potentials with and without the discontinuity, producing a virtual lengthening of the microstrip line. The impedance step [28] and the bend [29] were analyzed by this approach. Calculated results did not compare well with measured data. 17.3.10 TLM (transmission-line-matrix) method A technique developed for uniform transmission lines was extended to study discontinuities like impedance steps [3] in completely enclosed structures. The technique provides resonant frequencies for discontinuities of variable length, but the equivalent circuit is not uniquely defined by these resonances. 17.3.11 Waveguide model The first development of the waveguide model for stripline discontinuities is due to Altschuler and Oliner [4]. Babinet's principle allows one to replace the original problem by an equivalent rectangular waveguide, for which solutions are known [44]. This approach was applied directly to microstrip T-junctions 1411. The width and the internal permittivity of the waveguide are 'effective' values obtained from the static analysis of the uniform line (Section 17.2). The frequency-dependent scattering parameters were determined for the impedance step [61, 381, the simple bend [46], the mitred bend [48], the T-junction [61,46], the Y-junction [49] and the X-junction [50]. The LC equivalent circuit of a slot was determined using a simplified version of this model [24, 251. 17.4 Technological realization: materials and manufacturing process

17.4.1 Introduction Physically, any microstrip structure - circuit or antenna - is made of two parts: the substrate, a dielectric material with losses as small as possible, and a metallisation (partial or total) on the substrate's faces. Various processes can provide the desired metallisation pattern.

7024

Computer-aided design of microstrip and triplate circuits

17.4.2 Dielec?ric substrate The substrate fulfils two different functions: it is the mechanical support for the structure, and it is also an integral part of the transmission lines, determining the electrical characteristics of the circuit or antenna (Section 17.2, Chap. 8). Mechanically, the following properties of the substrate must be considered: 0 Mechanical strength (e.g. breaking point), which determines the impact and vibration resistance Shape stability, in particular for encasing 0 Dilatation factor, which should be small, as close as possible to that of the metal used for the conductors and the enclosure Long-term behaviour in the presence of difficult environmental conditions (moisture, temperature cycling).

The electrical parameters that must be considered are: 0 Relative permittivity E , , which determines the miniaturisation factor. When all other parameters are kept equal, the size of a circuit is proportional to ~ / J E , . By choosing a large permittivity one may reduce the circuit dimensions 0 Uniformity of the permittivity 8, over the whole circuit 0 Low dispersion of the permittivity E, and the thickness among different batches of a given material (circuit reproducibility) 0 Small dielectric losses (one should have tan 6 < 0.001) in order to have high-performance circuits and acceptable quality factors for resonant circuits, filters and radiating elements 0 No absorption of water (water exhibits a high permittivity and high losses). The following physico-chemical parameters are significant: 0 Mechanical stability up to high temperatures (soldering, deposition of components in the thick-film technique) Resistance to chemicals, in particular during the different stages of the photolithography process 0 Surface flatness (bending tends to render the encasing procedure difficult) Smooth surface, to reduce losses and ensure good adhesion of conductors, 0 Easy machining, for the cutting and drilling of holes. Production requirements are: 0 Low cost 0 Guaranteed availability of the material Availability of adequate sizes 0 Non-hazardous machining. 17.4.3 Comment Considering all the above requirements, some being conflicting, it is fairly obvious that no actual substrate would simultaneously meet them all. For every application, one must carefully consider the different requirements and select the material providing the best compromise. There are, in fact, many kinds of

Computer-aided design of microstrip and triplate circuits

1025

substrates, and they can be grouped in four main categories: inorganic, plastic, semiconductor and ferrite. Table 17.2 provides the relevant data on some common substrate materials. 17.4.4 Inorganic substrates This category contains mainly ceramics. Alumina (AI,03) is one of the most commonly used substrate materials. It is characterised by good surface quality, very low losses and very little dispersion between batches. However, it is slightly anisotropic. Common thicknesses are 0.254, 0.635 and 1.27 mm, while dimensions are generally stated in inches (1 x 1 in to 4 x 4 in). Alumina is a very hard and brittle material; hence it is quite difficult to machine and its permittivity depends on its porosity. Since adhesion of copper and gold to alumina is poor, an intermediate layer of chromium (or of some other lossy conductor) is required. Sapphire is the monocrystalline form of alumina. It is used in particular applications at very high frequencies, when a very smooth surface is required. Sapphire exhibits crystalline anisotropy. Beryllia (BeO), with a lower permittivity than alumina, presents a very large thermal conductivity, which makes its use particularly appropriate for highpower applications (removal of heat produced by semiconductors). However, Be0 powder is highly toxic, so that particular precautions must be taken while machining. Rutile (TiO,) has a very high permittivity, and is unfortunately temperaturesensitive. 17.4.5 Plastic substrates Pure synthetic materials may be used, such as PTFE (Teflon) or polyolefin. Their permittivity is generally low (E, = 2-3) and the mechanical properties are rather poor (mechanical distortion, poor temperature behaviour). By adding ceramic powders or glass fibre, the mechanical stability can be improved and the permittivity increased, but losses also become larger. PTFE has a low permittivity and very low losses. It is quite poor mechanically. (e.g. dilatation). Glass-Jibre reinforced plastics (such as RT-Duroid 5870) are much better substrates mechanically, but their permittivity is slightly higher, as well as their losses, and they present some anisotropy (in particular, for woven fibres). Ceramic-loaded plastics (such as RT-Duroid 6006 and 6010.5) can have a permittivity approaching that of alumina, with very good mechanical properties. Machining and drilling is easy, and they can adequately replace alumina during prototype development, even though their losses are somewhat higher. Synthetic substrates are available in large sizes, which is very convenient in practice. A slight anisotropy can be tolerated in most usual applications.

1028

Computer-aided design of microstrip and triplate circuits

17.4.9 Circuit realisation A particular metallisation pattern has to be realised on the substrate: centre conductor in stripline, upper conductor in microstrip. In all cases, this is done by means of a mask, first designed and cut to a larger scale (on a co-ordinatograph or plotter, Section 17.6), then photographically reduced to the proper size. A photosensitive lacquer is deposited on the structure; several processes may be used to do this: Dipping: The entire structure is dipped into the lacquer, and then pulled out at constant speed. The thickness of the layer depends on the withdrawal speed and the viscosity of the photoresist. This process generally yields rather thick layers, with a bulge on the lower edge. Spraying: The photoresist is sprayed on the structure through a nozzle. It is difficult to obtain a constant thickness in this manner. Centrifuge: The structure rotates rapidly, and the photoresist is deposited at the centre of rotation, being swept towards the outside by the centrifugal force. Thin and uniform layers are obtained in this manner, but the technique can only be used for small substrate sizes.

Computer-aided design of microstrip and triplate circuits

17.4.12 Removal of photoresist Once the previous steps have been completely carried out, the remaining photoresist is removed with a solvant or a concentrated alkaline solution. The metallic layer is sometimes thickened by electrolytic deposition of metal, or a protective layer (e.g. gold) is deposited to prevent oxidation. metal dielectric

17.4.11 Metal deposition This is the opposite process, in which one deposits metal on the substrate throught the holes in the photoresist (Fig. 17.18).~everalprocesses may be used: vacuum evaporation, sputtering, electroless plating. The layers obtained are generally thin (2-1 5 pm).

printed circuit material

-metal

After deposition, the photoresist must be cured at a high temperature, becoming tougher and more adhesive. The photographic mask is then vacuum-pressed on the structure, with the emulsion side next to the photoresist layer. The photoresist is exposed to ultraviolet rays through the mask. The UV radiation must be parallel and the photoresist layer thin, to ensure accurate reproduction of the pattern. By developing in a suitable chemical, either the UV-exposed part of the photoresist layer (positive photoresist) or the non-exposed one (negative photoresist) is removed. The circuit is then ready for the next step, which is either the deposition or the removal of metal. 17.4.10 Etching When starting with an entirely metallised substrate, part of the metal must be removed by etching (Fig. 17.17). The structure is exposed to an acid that dissolves the metal but does not affect the remaining photoresist. The process can become complex when several metallic layers are involved, since specific etching solutions are required to remove each metal layer. Careful rinsing is necessary between the different baths.

1029

development

etching

proter tiue lacquer

photo1 esirt remoudl

Fig. 17.17 Realisation af a circuit by the etching process

All the steps in the procedure must be carefully separated by rinsing and cleaning operations, sometimes followed by drying in an oven. Drying is particularly critical for some plastic substrates, which tend to absorb water.

7030

Computer-aided design of microstrip and triplate circuits

1

I

Computer-aided design of microsfrip and triplate circuits

1031

I

17.4.13 Under-etching

Of course, one wishes to realise a circuit having a pattern as similar as possible to the one of the photographic mask. However, in both the etching and the metal-deposition processes, the most annoying phenomenon of under-etching takes place. Considering the cross-section of a transmission line (Fig. 17.19), one

,

so long as the electrical conduction requirements are satisfied. Under-etching is a predictable process, which can be taken into account when designing the circuit and cutting the mask (Section 17.6).

cerarnlc substrate

chromium gold

mask

enporure t o

/

uu

electrolytic gold

deuelopment

Fig. 17.19 Effect of under-etching m e t a l deposition

17.4.14 Thin and thick film The techniques described so far realise 'thin-film' circuits, used, in practice, for most microwave circuits. The 'thick-film' approach deposits a paste through a silk screen. It is not usually accurate enough for microwave circuits, but is used to realise components like resistors or capacitors (Section 17.7.5).

pholorerisl removal

17.5 Analysis and synthesis programs Fig. 17.18 Realisation of a circuit by metal deposition

17.5.1 Introduction

notices that the conductors do not have rectangular, but trapezoidal crosssections. The acid does not remove the metal uniformly, while metal-deposition processes do not yield constant growth. Under-etching is more important when the metal layer is thick: for this reason, thin conductor strips are preferred,

While CAD packages for the design of low-frequency electronics systems have been available for some time, the choice of microwave programs used to be limited and expensive. As a result, traditional 'cut and try' methods still remain a commonly used way to realise circuits, despite their many drawbacks and inadequacies.

.

7032

Computer-aided design o f microstrip and triplate circuits

The situation has changed radically since the arrival of personal computers: considerable computing power has suddenly become available, while increasingly sophisticated microwave CAD packages have appeared on the market. The designer, faced with a wide variety of choice, must now determine which software is best suited to his particular requirement. Software comes in many kinds, and it is therefore difficult to make comparisons. Most packages are based on models and equivalent circuits, while some make use of electromagnetic-field analysis. Programs can be classified into two main categories: those devoted to analysis, in which the user describes a structure and wishes to know its electrical response; and those devoted to synthesis, where the program defines a physical structure meeting a specified electrical behaviour. The latter can be done either by circuit-synthesis techniques, or by an analysis software inserted into an optimisation loop (many packages then require an approximate solution as starting point). The models used must be rigorous enough to provide an accurate analysis, but not too complex, as computations would become too lengthy [26]. Some software packages were developed specifically to design particular devices (couplers, filters, amplifiers), while others have more general scope. The next Sections describe some of the present programs for microstrip design (the list is not exhaustive), on the basis of available literature and opinions received from users. Surveys of available CAD software appear occasionally in the technical literature [51, 151. 17.5.2 EEsof: Touchstone (IBM-PC, HP 9000, Apollo) Touchstone is a very fast general-purpose RF and microwave circuit-design, analysis and optimisation program, specifically developed for personal computers. More than 80 elements, including microstrip, stripline, waveguide and co-planar lines and discontinuities, lumped elements and electronic-device models are contained in its catalogue. In addition, the user can define his own elements, specifying their scattering matrix. It offers possibilities of adjustment, and two optimisation algorithms (random perturbation and gradient method) for up to 15 variables. The companion program Monte Carlo determines the sensitivity of the circuit. Touchstone is the CAD software most often used nowadays in microstrip circuit design. EEsof also provides several device-synthesis programs compatible with Touchstone: waveguide, microstrip and stripline bandpass, low-pass and bandstop filters, and coaxial low-pass and band-stop filters. The program E-Syn synthesises matching circuits. Microwave SPICE provides nonlinear circuit analysis and synthesis. The program Anacat is geared towards measurements, particularly with vector network analysers, and provides embedding and deembedding functions (Section 17.1.8). A graphics program MICAD, running on the same software, draws the artwork and can generate masks on co-ordinatographs and photo-plotters [43] and on some regular plotters as well, using a diamond stylus (Section 17.6.3).

Computer-aided design o f microstrip and triplate circuits

703.3

17.5.3 CCC: The Supercompact Family (VAX, IBM, IBM-PC, Apollo, PC, HP 9000) Supercompact is a general analysis and optimisation design tool for microwaves and RF. Four-port circuit analysis and optimisation can be achieved, as well as transistor impedance modelling (its library includes specifications of commercially available transistors) and matching network synthesis. Single, coupled and inter-digitated microstrip designs can be created. Microstrip and other planar lines can be specified, both in terms of their electrical and physical dimensions; approximate expressions are included, with accuracies of I % or better. The effects of dispersion, radiation, discontinuities, multi-layers, metallisation, surface roughness, and dielectric and conductor losses are taken into account. An FFT time-domain option is available. Circuits are optimised by the random perturbation and gradient techniques, their parameter sensitivity is determined with a Monte Carlo algorithm. The companion program Autoart, that uses the same hardware, was the first microwave CAD layout package offered commercially (Section 17.6.2). Super-compact and Autoart were f rst developed on main-frame computers; they are also available now for perso1.al computers. Microcompact is a simpler program, that runs on HP computers of the 200 series. 17.5.4 CCC: CADECf (Computer-Aided Design of Electronic Circuits, on HP 200/500, Tektronix and IBM-PC XTIAT) CADEC, a circuit analysis and optimisation package, is one of the oldest programs (1973), and became commercially available in 1980. Covering the range VLF-40 GHz, it performs frequency- and time-domain analysis, utilising matrix representation and nodal analysis for two-ports, including lumped elements, stripline, coplanar lines and discontinuities, and couplers [53]. Dispersion is taken into account, and the domain of validity determined. Amplifier analysis also evaluates the noise parameters. The optimisation is based on a search technique followed by a gradient approach, and the sensitivity is determined. Design kits run on the same hardware: Microwave Design Kit, (amplifiers), Filter Design Kit, (filters) and Sonata (oscillators). 17.5.5 Acline (VAX, Apollo and HP 9000) A c h e is a high-level program, somewhat similar to Supercompact, developed by Professor C. Vidallon of the Universite Paul Sabatier in Toulouse, France. It provides impressive optimisation facilities to its users, and a number of microstrip elements are available in an interactive way. A new version, called AC-LINE, offers considerably increased performances. Unfortunately, little information about Acline has appeared so far in the technical literature. 17.5.6 Thom'6: Esope (Vax, IBM, Apollo) Esope is an interactive software for the analysis and optimisation of linear microwave circuits. Most components (lumped RLC, transmission lines,

1034

Computer-aided design of microstrip and triplate circuits

waveguides, coupled lines, microstrip) are implemented. Active circuits are described by their scattering parameters. Optimisation can be carried out with one or several objectives: three algorithms are available (min-max, least squares, fixed tolerance), the sensitivity and worst case are determined, and results are represented graphically. The program is in Fortran 77. Drafting of the circuit's outline is carried out by software Hyper'6-D.

Computer-aided design of microstrip and triplate circuits

1035

direction algorithm, in terms of reflections, gain, insertion losses, ripple, noise and stability, as defined by 60 or more parameters. The sensitivity with respecr to those parameters is analyzed. Very high accuracy, wide validity range and a high computation speed drastically expand the range of applications. It is highly portable, since 98% of its code is written in Fortran 77.

/

metal strip

17.5.7 RCA: Midas (UNIX and SUN on most 32 bit processors) This program analyses and optimises circuits with up to 20 nodes and five ports, utilising algebraic expressions to define the parameters required to analyse the circuit. It is compatible with the PIana software for two-port measurements on the HP 8409 network analyser. All the usual components (lumped RLC, transmission lines, coupled lines, discontinuities, gyrators, ideal transformers and controlled sources) are implemented. Particular emphasis is placed on striplines an? nicrostrip. Inter-element coupling is determined for an arbitrary net of h e s , in order to analyse comb and inter-digitated structures. The companion program N-Fet is specifically devoted to the design of FET amplifiers. 17.5.8 LINMIC (HP 9000 series 500 and 300, Microvax 11) The CAD package LINMIC introduces a significant new approach to the layout-oriented design of single or multi-layered planar and monolithic structures: it combines, apparently for the first time, a rigorous field analysis - based on an enhanced spectral-domain technique [34] - with the more usual models and equivalent circuits (for simple and coupled lines, discontinuities, T-junctions, capacitances, resistors, transistors and other lumped elements) [35]. The LINMIC package can actually describe complex structures for which no analytical models are available: interdigitated capacitors (Fig. 17.20), multi-turn

j i e l e c t r i c bridge

substrate

dielectric br

1

Fig. 17.21 Multi-turn square inductor

MCAD comes from the same source as LINMIC, for considering various simple and coupled planar lines (up to 20 coupled lines) on multi-layer substrates (up to 4 substrates). It is used to analyse discontinuities, junctions, couplers and filters, as well as lumped elements. Three optimisation algorithms are provided.

Fig. 17.20 Interdigitaced capacitor

17.5.9 High Tech. Tournesol: Micpatch ( V A X , PC) The package Micpatch was developed by Dr. Mosig at LEMA. Lausanne, Switzerland, primarily to analyse microstrip patch antennas. It can just as well be applied to the study of microstrip circuits of arbitrary shape. The scattering matrix of multiple-port components is determined, taking into account radiation and surface waves, metal and dielectric losses. It is written in Fortran 77, and a more detailed description of the procedure used is given in Chapter 8.

square inductors (Fig. 17.21) and coupled meander lines. Up to four dielectric layers can be considered, including passivation and metallisation layers, ohmic and dielectric losses, coupling and higher-order-mode effects. Up to 40 connecting points to the outside can be considered, and the structure can be divided into 20 sub-lattices. An interactive optimisation procedure is provided, based on a conjugate

17.5.10 Spefco Software: CiAO (IBM PC-XT or AT) CiAO is a general analysis and optimisation program for circuits composed of RLC lumped elements, controlled sources, gyrators, lossy or lossless transmission lines, and one- and two-ports described by their scattering matrix. The companion program Design synthesizes wideband matching circuits for linear-gain amplifiers.

7036

Computer-aided design of microstrip and triplate circuits

17.5.11 Made-it-associates: Mama (Measurement And Microwave Analysis, HP 9836 or HP 9000 series 300) This program analyses and designs: quarter-wave transformers, Lange couplers, directional couplers, microstrip lines and discontinuities, hybrid circles, power dividers [in fact, most of these elements can be realised by Micros (Section 17.6.4), which additionally draws them and cuts the masks]. It synthesizes filters and rectangular printed antennas. It can be used for de-embedding components (Section 17.1.8) and interfaces with Microcompact (Section 17.5.3). 17.5.12 Ampsa: Multimatch ( I B M PC) Multimatch is a matching package for microwave loads and amplifiers developed by Abrie [2]. The potential performance of a transistor is determined from its scattering matrix, and matching circuits are directly synthesized for stable operation, either with lumped components or with transmission-line sections. Discontinuities are taken into account and corrected for. The approach provides the user with several possible designs to choose from, together with their electrical performances. If needed, the circuits developed can be used as starting points for an optimisation program. In many practical applications, the solutions proposed by Multimatch were found to be close enough to optimal not to require further refinements. 17.5.13 Radar systems technology: Analop (IB-PC and CP/M-80) The program analyses and optimises, on 15 variables at 15 frequencies, twoports having up to 200 elements: lumped RLC components, series and parallel resonators, transmission lines, transformers, impedance inverters, microstriplines and discontinuities, rectangular waveguides (dominant mode), controlled sources, filters and couplers. 17.5.14 MicrokoplSuspend (IBM PCJXT) An iteration algorithm allows both analysis and synthesis of coupled lines for microstrip and suspended substrates [8]. 17.5.15 Microwave software applications (MS-DOS or PC-DOS) A series of small programs specifically dealing with couplers is proposed: single-section, symmetrical or asymmetrical multiple-section, Lange in various technologies: balanced stripline, microstrip, rectangular and ridged waveguides. 17.5.16 Planim The planar circuit approach to the characterisation of microstrip circuits is combined with the image-parameter method to give a new powerful technique for integrated-circuit design of microstrip filters [54]. The inclusion of twodimensional effects in the synthesis procedure makes the Planim approach particularly suited for monolithic microwave circuits.

Computer-aided design of microstrip and triplate circuits

1037

17.5.1 7 DGS Associates: SIFilsyn (PC, HP 9000, V A X ) A broad series of programs for the synthesis of filters, active and passive, analog and digital, lumped component design or microstrip, that were developed in 1967 by Dr. Georges Szentirmai. 17.5.18 Webb Laboratories: Transcad (IBM PC-XTIAT) This specialized program is devoted to the study of transitions between transmission lines (coaxial, bifilar, planar structures) and waveguides.

17.6 Layout of circuits and cutting of masks 17.6.1 Description When a design has been analysed with the most accurate decription available, and then optimised by sophisticated CAD techniques (Section 17.5), a most critical part of the procedure still remains to be carried out: its physical realisation. Before moving on to the photolithographic process (Section 17.4.9), the pattern of the upper conductor must be drawn, and then the scaled mask must be cut. Co-ordinatographs or photoplotters can generate very accurate masks, but these machines are quite expensive, and well beyond the reach of many small research laboratories or academic institutions. The layout and cutting of masks can now be done accurately enough, but at a much lower cost, directly on a standard plotter connected to a desktop computer. 17.6.2 CCC: Autoart The Autoart program converts to artwork microwave circuit models described by their physical dimensions (single and coupled transmission lines, circular radial stubs, tapered lines, Lange couplers, circuit discontinuities). It is presently restricted to planar geometries with a single path from input to output (this restriction may, however, be overcome by declaring other ports to be open or short-circuited). Circuit data provided by the Supercompact package (Section 17.5.3) can thus be used to prepare the conductor pattern, and the geometrical data is then transferred to a co-ordinatograph or a photoplotter. Autoart interfaces directly with Wild Heerbrugg precision flat-bed plotting tables, with Aristo Graphics automatic co-ordinatographs, with Gerber Scientific photoplotters and, through an Initial Graphics Exchange Specification, with pattern generators and mechanical drafting equipment (these instruments can all be used to generate masks) [40]. 17.6.3 EESOF: Micad In a similar manner, the data provided by the general-purpose program Touchstone can be transferred through the Micad software to generate a mask on a co-ordinatograph or a photoplotter [43]. Using a specially configured diamond stylus (MICknife), masks can also be cut on standard plotters.

1038

Computer-aided design o f microstrip and triplate circuits

17.6.4 High Tech. Tournesol: Micros (HP 9000 series 200 and 300) In contrast with the two previous packages, which are additions to general analysis/synthesis software packages, Micros is a complete design tool, that generates the drawings of selected components, interconnects them and cuts the mask on a standard plotter [63]. The program is 'user-friendly' and completely

Computer-aided design o f microstrip and triplate circuits

1039

nect them at will, with compensated bends and sections of line, right on his computer screen, in order to prepare his layout. He may also define his own elements, e.g. patch antennas. The mask is then cut on a Rubylith sheet with a specifically designed sharp cutting tool, all in a matter of minutes to computer accuracy. Circuits realised with Micros were measured on a vector network analyser, and showed very good agreement between specifications and measured data, even for highly frequency-sensitive elements. The design of frequency-sensitive components such as filters requires a precise knowledge of the substrate characteristics (permittivity and thickness). Some manufacturer's specifications were found to be much too loose for design purposes, particularly for composite high-permittivity substrates. A companion program, Epsilon, was developed to measure the substrate's permittivity under actual operating conditions. A circular resonant ring is designed to resonate close to the operating frequency, and a mask is generated. When the resonant frequency has been measured, the program determines the permittivity [64]. 17.6.5 British Telecom: Temcad ( H P 9000 series 200 and 300) A general program for the layout of planar circuits was recently developed by British Telecom, combining theoretical models with experimental data, and including a wide range of flexible facilities to improve designer productivity [20].

17.7 Insertion of components 17.7.1 Definitions Lumped elements, such as capacitors, resistors and inductors, can either be manufactured by metal or dielectric deposition, right on the microstrip or in the balanced stripline, or alternatively discrete manufactured miniature components can be connected on the microstrip, or within the stripline (the last procedure is somewhat more complex, since a cavity must be carved within the dielectric materials). A number of semiconductor devices, diodes and transistors, as well as nonreciprocal ferrite devices (isolators and circulators), can also be inserted into planar circuits to realise active antenna feeds and interconnecting networks. These two categories are distinguished in the forthcoming Sections, and labelled, respectively, 'deposited' and 'discrete'. Fig. 17.22 Microstrip components realised by the program Micros

self-contained (it does not require extensive reading of manuals before use). The operator specifies circuit dimensions, operating frequency, substrate permittivity and width, and characteristic line impedance. A number of elements then become available to design the circuit: couplers, hybrids, dividers, step transformers, bandpass and low-pass filters (Fig. 17.22). He can position and intercon-

17.7.2 Discrete components Discrete components are in general commercially available, and ready to be inserted into a circuit. Most of the common electronic components - active and passive - are presently available at microwave frequencies in a package suitable for insertion within a microstrip circuit. Their main characteristic is their small size: a lumped element is small with respect to the wavelength. In addition, parasitic effects must be kept as small as possible, so that wire connections are extremely short or altogether absent, being replaced by metallised

1040

Computer-aided design of microstrip and triplate circuits

connecting surfaces. Special device cases were developed, to reduce the discontinuities as much as possible. Resistors: are small 'blocks' with sides from a few tenths of a millimetre up to a few millimetres (Fig. 17.23). They are generally made of a ceramic block, on which a resistive layer is deposited, between two metallised regions for connection purposes. The geometry of the resistive layer is adjusted with a laser during the fabrication process. It is possible in this way to meet tight tolerances. resistive

laser trimming

Computer-aided design of microstrip and triplate circuits

104 1

can be either series or shunt connected (in which case a hole must be drilled through the substrate). These capacitors are a few millimetres in size, so that their use is limited up to a few gigahertz, while resonances appear at higher frequencies. These adjustable components are most useful for fine tuning, or to compensate for component non-uniformity. Miniature inductors for microstrip are fairly recent additions. They consist of helically deposited metal strips on very thin multi-layer ceramic substrates, connecting from a layer to the next at each turn. A multi-turn 'coil' of very small dimensions is obtained in this manner. Large inductance values with small loss can be realised in a small volume. In practice, however, inductances are directly deposited on the microstrip (Section 17.7.5). Junction isolators and circulators can be mounted on microstrip. They are small ferrite discs, a few tens of millimetres in diameter, with small ribbons for connection within the circuit (Fig. 17.25). Holes must be drilled into the substrate to permit insertion. These components are relatively heavy and large, owing to the presence of permanent magnets.

for connections Fig. 17.23 Miniature resisto~

Sometimes, two connecting ribbons are attached, to facilitate the insertion procedure. Resistive loads and attenuators (Fig. 17.24) are manufactured by the same technique. connecting strips Fig. 17.25 Circulator for insertion in microstrip circuit

connecting strips Fig. 17.24 Miniature attenuator

Seen from the outside, capacitors look very much like resistors, they consist of a sandwich of ceramic and metal layers. Available capacitance values range from fractions of a picofarad up to several nanofarads. Adjustable capacitors are available for insertion into microstrip circuits, and

Most kinds of diodes suitable for mounting on microstrip are presently available: Schottky, PIN, varactors, Gunn, Impatt, Trapatt, etc. The diodes can be either inserted in chip form, or encased in various packages: LID ( Leadless inverted device, Fig. 17.26a), beam lead (connection with thin strips, Fig. 17.266) or cylindrical cases, with or without a mounting screw (Fig. 17.26~).The last package is mounted through the substrate, with the lower part in close contact with the ground plane to ensure heat removal. The increasing significance of microstrip circuits is closely related to the availability of transistors, both bipolar and MESFET, that have steadily improving characteristics. Cases that degrade as little as possible the performances of the chip have been designed. The usual cases (Fig. 17.27) permit easy insertion, with minimal discontinuities. A hole must be drilled through the substrate for power devices. However, the best performances are achieved when using chip-mounted transistors.

,

7042

Computer-aided design of rnicrostrip and triplate circuits ceramic support

I

/

Computer-aided design of microstrip and triplate circuits

1043

Precautions are required to avoid overheating of delicate components during the mounting procedure Connections may deteriorate owing to aging (oxidation, etc). Since components are generally quite small, their mechanical stability is most often ensured by the electrical connections themselves.

\

metallization

metal bond ceramic case(Be0)

a. Leadless I n v e r t e d Oeuice ILIOI

connecting strips b. "beam-lead"

Fig. 17.27 Transistor for microstrip circuit

c. t h r e e cyllndrlcal ceramic cares Fig. 17.26

Various diode packages a Leadless inverted device (LID)

b Beam lead c Three cylindrical cases

17.7.3 Mounting procedure Particular care must be taken when mounting lumped elements on microstrip substrates:

The electrical connections must be made very carefully Discontinuities between component and circuit must be as small as possible The mounting must be mechanically rigid

The classical soldering, currently used in electronics, can be used for mounting components on a microstrip substrate, but particular care and equipment are required. The soldering iron must have a very narrow tip, and a number of solders based on indium, tin and lead can be used, with melting points in the range 143OC to 280°C [40]. Thermocompression bonding, applying heat and pressure at the same time, produces an inter-atomic diffusion, and thus a high-quality weld. This process usually utilises gold as the welding material. Several bonding methods are shown in Fig. 17.28~-c.The duration of the bonding operation (typically in the 1-3 s range) is a critical parameter in the bonding process. Ultrasonic welding uses the same physical principle as bonding: heat and pressure. In this case, the heat is produced by mechanical rubbing by a point vibrating at ultrasonic frequencies (Fig. 17.29). This technique is particularly well suited to very sensitive components. Welding can also be realised by Joule heating, by circulating a current between two electrodes (Fig. 17.30). The interest of this process lies in the fact that heat can be applied very locally. On the other hand, semiconductor devices may become damaged.

1044

Computer-aided design of microstrip and triplate circuits

Computer-aided design of microstrip and triplate circuits

7045

Finally, devices can also be glued using conductive epoxy, loaded with fine metal particles, generally gold or silver. This process is extremely useful for mounting very delicate components, and also for encasing microstrip circuits

ultrasonic transducer

I

heating plate

Fig. 17.29 Ultrasonic welding gold thread

\

Tungsten Jube

lifting

pressure

!I!!

current source

electrode

drop

I

torch

electrode pressure \

solQer

conductor

b heat and pressure

gold thread

sudstrate

Fig. 17.30 Electric-current welding

17.7.4 Drilling holes in the dielectric substrate Several components require a hole to be drilled through the substrarte. either to provide a ground connection or a good thermal contact to remove the heat ,dissipated in the device. With plastic substrates, the process is straightforward, and perfect holes can be drilled, so long as the drill and the speed are selected correctly. The matter is far more complex with ceramic substrates, which are hard and brittle. Two techniques can be used: cutting of thread C

Fig. 17.28

Themocornpression bonding a Edge bonding b Drop bonding c Lateral-point bonding

Drilling with an abrasive powder (carborundum) and a rotating tube (Fig. 17.3 1) or an ultrasonically driven point. This approach is rather time-consuming A laser can realise perfect holes, even non-round ones, in a fraction of a second. However, a special drilling set-up is required. In all situations one tries to drill as few holes as possible in ceramic substrates.

7046

Computer-aided design of microstrip and triplate circuits

17.7.5 Deposited components These components are not introduced from the outside, but are built right on the substrate, and thus are an integral part of the circuit. Resistors, capacitors and inductors can be realised by this process. They are, in general, better suited to very high-frequency operation, since they do not present the discontinuities that always appear when a component is inserted. They are also generally smaller. Resistors are realised with either of two techniques (Fig. 17.32). A resistive rotation

Computer-aided design of microstrip and triplate circuits

7047

can be used to realise resistors in an easy way: one just has to remove the superior high-conductivity layers. Capacitors can be realised by the successive deposition of dielectric and metal layers, either by silk screening (thick-film process) or by evaporation (thin-film process). Additionally, a single-layer capacitor can also be made by the photolithographic process, using an interdigitated geometry (Fig. 17.20). Inductances are also realised by the photolithographic process, in the form of a loop or a spiral. In the latter case, the inner connection must be 'pulled out', either by bonding a thin gold wire, or by building a dielectric bridge with a metal strip deposited on top (Fig. 17.21).

17.8 Examples nickel tube

pressure

abrasiue Substrate

-

Fig. 17.31 Drifting of microstrip substrate with a rotating tube resistive paste lPd/PdOt

flu Cr ri substrate a. r e s l s t l v e p a s t e deposlted by silk screening

b.

use o f t h e adheslue Cr or TI l a y e r

Fig. 17.32 Resistors deposited on circuit

paste (palladium-oxide mixture) may be deposited by silk screening (thick-film technique), and then cured. This process can only be applied to substrates that can withstand high temperatures. Alternately, the low-conductivity nickel or chromium layers required for adhesion on ceramic substrates (Section 17.4.8)

17.8.I Design of a broadband amplifier One of the most current applications of microstrip CAD is the design of amplifiers to have a constant gain over a specified frequency band. As an example, an amplifier with a gain as flat as possible over the range 3-5 GHz was designed around a GaAs MESFET of the type DXL-2501 (Dexcel). The first step in the procedure is the actual measurement of the transistor parameters, carried out on a specialised transistor test fixture connected to an automatic vector network analyser. The complete test set-up is first calibrated to compensate for recurrent errors. The transistor is then mounted on the test fixture, and measurements are carried out at 101 frequency points over the range 2-8 GHz. The scattering parameters of the transistor are then obtained by computerised 'de-embedding' of the measured data, making use of the equivalent circuit of the transistor test fixture. The values obtained agreed quite well with the manufacturer's indications. The transistor was found to be practically unilateral (very small values of s,,). It was noted that the values of r provided by a commercially available program were erroneous, apparently due to inconsistent definitions. The CAD program used, Touchstone, is an analysis and optimisation program, but not a synthesis program. This means that a first approximation must be provided as starting point. This step is carried out by using the Smith chart, and conjugate match is provided at 5 GHz at the input and output. The first design proved unacceptable, as a transmission-line section was too short. A suitable matching structure was obtained on the second try and it is sketched in Fig. 17.33. The corresponding structure and values are then introduced into the CAD program Touchstone (Section 17.5.2), and optimisation was carried out, requiring a flat gain within the range 9.5 dB < G < 10.5 dB over the range 3-5 GHz. The microstrip losses are taken into account, as well as the effects of discontinuities at T-junctions and at steps. The predicted gain of the amplifier, prior to

1048

Computer-aided design of microstrip and triplate circuits

optimisation, is given in the curve a of Fig. 17.34, whereas the optimised value appears in curve b. The two circuits then realised, the layout was drawn with the help of the program Micros (Section 17.6.4), and the mask was cut on a plotter. The

Computer-aided design of microstrip and triplate circuits

7049

mask is cut on a Rubylith sheet. The mask is reduced and the circuit realised by means of the photolithographic process (Section 17.4.9). After mounting and connecting, the filter is measured on a vector network analyser; the transmission factor is shown in Fig. 17.36. The passband falls right in the specified range, and the 25 dB off-band requirement is also met.

Transistor

-

Fig. 1 7 . 3 3 Transistor amplifier with matching circuit

complete photolithographic process was carried out (Fig. 17.17), and the transistor was soldered on the microstrip circuit, under a microscope. Measurements were then carried out on an automatic network analyser, that had been previously calibrated, and the measured results are presented in Fig. 17.34, curve c, showing the unoptimised amplifier, and curve d the optimised one. It will be noted that the measured amphfication curve (d),while showing the same general behaviour as the predicted one, lies a few dB lower and is shifted somewhat towards lower frequencies. 17.8.2 Bandpass filter design We wish to realise a bandpass filter for the range 3.8-4.2 GHz, that has to meet the following requirements:

Passband ripple: Stopband attenuation: Substrate permittivity: Substrate thickness:

0.3 dB 25.0 dB at 4.6 GHz 2.33 (relative) 0.51 mm

These requirements are introduced into the CAD program Micros [63], which determines the response for a Chebjrshev design, formed of anti-resonant series cells and resonant shunt cells. The program determines the order of the filter that is required to meet the specification, and the operator can check the theoretical response before proceeding further with the filter design. The microstrip structure is then realised with broadside-coupled resonant strips. The program carries out the complete synthesis process, taking into account the effect of open ends (Section 17.3). The dimensions of the strips and the spacings are determined, and the layout is drawn (Fig. 17.35). The filter structure is in turn connected to the sides of the circuit, and a scale

I

\\\

\c

' "'

IC

------ measurements mpned

values

frequency (GHz)

Fig. 17.34 Amplifier gain a Predicted unoptimised gain b Predicted optimised gain c Measured unoptimised gain d Measured optimised gain

17.8.3 Design of a miniature Doppler radar It is possible to combine circuit and antenna functions on the same microstrip substrate, and this was used to develop a small proximity detector, sensitive to

1050

Computer-aided design of microstrip and triplate circuits

the presence of moving objects. A rectangular patch antenna resonates at 2.45 GHz and is also used as the frequency-sensitive element (filter) in the feedback loop. A MESFET amplifier is connected across the resonatorantenna. The low-frequency Doppler signal is detected directly at the MESFET connections, taking advantage of its nonlinearity to provide signal mixing. The mask of the circuit is shown in Fig. 17.37. While this circuit is quite simple, its

Computer-aided design of microstrip and triplate circuits

1051

performance is limited: the dielectric permittivity and thickness that are adequate for the design of a circuit are far from optimal as far as antenna radiation is involved, and vice versa. A better approach would be to separate the two functions by making use of a multi-layer structure (Section 8.12).

3.6-6.2 GHZ Fig. 17.35 Bandpass-filter design 52 1 l o g MAG REF 0 . 0 dB

A

s.ade/

Fig. 17.37 Mask for miniatwised Doppler radar

17.9 Conclusion

START STCP

3.000000000 M x 5.000000000 GHz

Fig. 17.36 Measured bandpass filter response

Computer-aided design requires suitable mathematical descriptions of the elements, which should be accurate enough, but not too complex mathematically [26]. The particularities of microwave printed circuits, outlined in Sections i7.1.6-1-711.8, make the design particularly demanding in terms of accuracy. It is seldom possible to define equivalent circuits that are at the same time general, simple and easy to use, and whenever electromagnetic-field calculations are required within an optimisation loop, the resulting computation time may well prove prohibitive. Highly accurate approximate expressions are now available for straight transmission lines and for many discontinuities, sometimes with errors smaller than fractions of a percent (Sections 17.2 and 17.3). However, these approximations are only valid over specified ranges of parameters, because they neglect radiated and surface waves: this is quite acceptable for microstrip lines, but obviously not

I

!

7052

Computer-aided design of microstrip and triplate circuits

for radiating patches. Furthermore, the number of structures analysed until now is limited, and proximity effects cannot be evaluated as accurately. The interactions of a line with a nearby wall, with the edge of a microstrip substrate, with a discontinuity or with a patch have not as yet been determined to a similar degree of accuracy, and much remains to be done in this respect. In fact, the possible combinations of components are almost infinite in number. The problem becomes particularly stringent for microwave- and millimetre-wave monolithic integrated circuits, where different lines, circuits and components are located very close to one another. It must also be kept in mind that the physical dimensions are generally not accurately known: substrate thickness is specified within 5% or even 10% by some manufacturers. This means that one should measure it before actually drawing the circuit pattern and cutting the mask. A given design is valid only with the substrate material for which it was prepared - or an almost identical one. Dimensional effects like under-etching also introduce errors that are much larger than the ones encountered in the theory. Fortunately, systematic errors can be compensated for. Section 17.5 shows that there is no shortage of CAD software packages for microstrip design. Some are rather broadband general-purpose analysis/ synthesis packages, while others have been specifically elaborated to design a single kind of component. The task of the designer, who is supposed to select one particular software is clearly not obvious, since many of the programs apparently fulfil similar tasks. To compare different software packages, one should actually use several of them to develop the same circuit, and compare them in terms of the results actually measured, their ease of operation, the computer time and memory requirements, compatibility and portability, service, bugs etc. Many different computer systems are presently available and in constant evolution, so that the task is by no means simple. Cost, availability and service are non-technical parameters that become most significant in actual operation. The accuracy provided by a program is a most significant parameter for selection; in particular, when optimisation processes are involved. Besser [7] noted that the use of low-accuracy models in the initial microwave CAD packages considerably slowed down their actual implementation within the industrial market, but this problem has been corrected to a large extent in more recent designs. It was also noted that many optimisation algorithms did not perform as well as was claimed, and they did not always converge towards the best possible solution. In conclusion, one must remember that the CAD is a most valuable tool, useful to a designer who understands its operation and is aware of its limitations, but useless and wasteful when put in the wrong hands. It can significantly increase the capabilities of a skilled operator, both in terms of time and quality. On the other hand, the GA+A principle applies (garbage in, garbage out): for instance, if the substrate properties are not accurately introduced, the

Computer-aided design of microstrip and triplate circuits

I

7053

results cannot be expected to be accurate (even though miracles sometimes happen - but generally at random!). An expert microwave designer will immediately detect possible trouble areas, where lines are too close to one another, or too close to an edge etc., but it would be practically impossible to program a computer to detect and take care of all such possible combinations. In microstrip and stripline circuit design, like in many other technological areas, the computer does not replace the skilled designer.

1

17.10 Acknowledgments

The authors wish to thank Miss Anja Skrivervik, Mr. Lionel Barlatey and Dr. Juan Mosig, who contributed to the realisation of circuits and to the elaboration of parts of the text. The continuous support of the Swiss National Research Foundation is gratefully acknowledged. Thanks are also extended to the firm High Tech Tournesol, that granted permission to reproduce Figures originally prepared for the intensive short course 'Initiation to Microstrip'. I

17.11 References I

2 3 4 5

6 7 R-

9 10 II

12 13 14

ABRAMOWITZ, M., and STEGUN, I. A. (1972): 'Handbook of mathematical functions' (New York, Dover) ABRIE, P. L. (1986): 'The design of impedance-matching networks for radio-frequency and microwave amplifiers' (Norwood, MA, Artech House) AKHTARZAD, S., and JOHNS, P. B. (1975): 'Dispersion characteristics of a microstrip line with a step discontinuity', Electron. Letts., 11, pp. 31&311 ALTSCHULER, H. M., and OLINER, A. A. (1960): 'Discontinuities in the center conductor of symetric strip transmission line' IEEE Trans. MTT-8, pp. 328-338 ANDERS, P., and ARNDT, F. (1980): 'Microstrip discontinuity capacitances and inductances for double steps, mitered bends with arbitrary angle, and asymetric right-angle bends' IEEE Trans. MTT-28, pp. 1213-1217 BENEDEK, P., and SILVESTER, P. (1972): 'Equivalent capacitances for microstrip gaps and steps' IEEE Trans. MTT-20, pp. 729-733 BESSER, L. (1985): 'What is the direction of commercial microwave technology?, Microwave Syst. News, 15, pp. 65-67 ROCHTLER. U.. and ENDRESS, F. (1986): 'CAD program designs stripline couplers', -. Microwaves and RF, 25, pp. 91-95 COHN, S. B. (1955): 'Problems in strip transmission lines', IEEE Trans. MTT-3, pp. 119-126 EASTER, B. (1975): 'The equivalent circuit of some microstrip discontinuities', IEEE Trans., MTT-23, pp. 655-660 FARRAR, A,, and ADAMS, A. T. (1971): 'Computation of lumped microstrip capacities by matrix-methods: rectangular sections and end effect', IEEE Trans, MTT-19, pp. 495-497 FARRAR, A,, and ADAMS, A. T. (1972): 'Matrix method for microstrip three-dimensional problems', IEEE Trans.. MTT-20. pp. 497-504 FRANKEL, S. (1977): 'Multiconductor transmission line analysis' (Artech House, Dedham, MA) GARDIOL, F. E. (1984): 'Introduction to microwaves' (Artech House, Dedham, MA) - - - - -

7054

Computer-aided design of microstrip and triplate circuits

15 GARDIOL, F. E. (1986): 'Microstrip computer-aided design in Europe', IEEE Trans. M m 34, pp. 1271-1275 16 GARDIOL, F. E. (1987): 'Lossy transmission lines' (Artech House, Norwood, MA) 17 GETSINGER, W. J. (1973): 'Microstrip dispersion model', IEEE Trans., MTT-21, pp. 34-39 18 GOPINATH, A., and EASTER, B. (1974): 'Moment method of calculating discontinuity inductance of microstrip right-angle bends', IEEE Trans. MTT-22, pp. 880-883 19 GOPINATH, A., THOMSON, A. F., and STEPHENSON, I. M. (1976): 'Equivalent circuit parameter of microstrip step change in width and cross junctions', IEEE Trans, MlT-24, pp. 142- 144 20 GOSLING, I. G. (1985): 'A new microwave CAD layout program'. IEE/EI2 Colloquium on Computer Aided Design of Microwave Circuits, London, Nov. 1985 21 GUNSTON, M. A. R. (1972): 'Microwave transmission line impedance data' (Van Nostrand Reinhold, NY) 22 HAMMERSTAD, E. O., and BEKKADAL, F. (1975): 'Microstrip handbook'. Norwegian Institute of Technology, Trondheim, report ELAB STF44 A74169. 23 HAMMERSTAD, E. O., and JENSEN, 0. (1980): 'Accuratemodels for microstrip computeraided design', IEEE MTT-S International Microwave Symposium Digest, pp. 407-409 24 HOEFER, W. J. R. (1977): 'Theoretical and experimental characterization of narrow transverse slits in microstrip', Nachrichrentechni. Zfr, 30, pp. 582-585 25 HOEFER, W. J. R. (1977): 'Equivalent series inductivity of a narrow transverse slit in microstrip', IEEE Trans., MlT-25, pp. 822-824 26 HOFFMAN, G. R. (1984): 'Introduction to computer aided design of microwave circuits'. Proceedings of the 14th European Microwave Conference, Likge, Belgium, pp. 731-737 27 HOFFMANN, R. K. (1983): 'Integrierte Mikrowellenschaltungen' (Springer, Berlin) 28 HORTON, R. (1973): 'The electrical characterization of a right-angle bend in microstrip line' IEEE Trans., MTT-21, pp. 427-429 29 HORTON, R. (1973): 'Equivalent representation of an abrupt impedance step in microstrip line', IEEE Trans., MlT-21, pp. 562-564 30 HOWE, H. (1974): 'Stripline circuit design' (Artech House Dedham, MA) ITOH, T., MITTRA, R., and WARD, R. D. (1972): 'A new method for solving discontinuity problems in microstrip lines'. IEEE-GMTT International Symposium Digest, pp. 68-70 JAIN, 0. P., MAKIOS, V., and CHUDOBIAK, W. J. (1971): 'Coupled-mode model of 405-406 dispersion in microstrio'. - . Electron Letts. 7. DO. rr -JAMES, D. S. and TSE, H. S. (1972): 'Microstrip end effects', Electron. Letts., 8, pp. 46-47 JANSEN, R. H. (1985): 'The spectral domain approach for microwave integrated circuits', IEEE Trans., Mm-33, pp. 1043-1056 JANSEN, R. H. (1986): 'LINMIC, a CAD package for the layout-oriented design of singleand multi-layer MICs/MMICs up to mm. wave frequencies', Microwave J., 29, (2) JANSSEN, W. (1977): 'Hohlleiter und Streifenleiter' (Hiithig, Heidelberg) KAJFEZ, D., and TEW, M. D. (1980): 'Pocket calculator program for analysis of lossy microstrip:, Microwave J., 23, pp. 39-48 KOMPA, G. (1976): 'S-matrix computations of microstrip discontinuities with a planar waveguide model', Archiv Elekr. Uber~ragun~stech., 30, pp. 58-64 KOSTER, N. H. L., and JANSEN, R. H. (1986): 'The microstrip step discontinuity, a revised description', IEEE Trans., MTT-34, pp. 213-223 LAVERGHETTA, T. S. (1984): 'Microwave materials and fabrication techniques', (Artech House, Dedham, MA) LEIGHTON, W. H., and MILNES, A. G. (1971): 'Junction reactance and dimensional tolerance effects on X-band 3-dB directional couplers', IEEE Trans., MlT-19, pp. 814-824 MAEDA, M. (1972): 'An analysis of gap in microstrip transmission line', IEEE Trans., MTT-20, pp. 390-396 MARCH, S. L. (1984): 'Microwave circuit layout: a dynamic plot emerges', Microwaves and RF, 23, pp. 59-161

-. .

Computer-aided design of microstrip and triplate circuits

7055

44 MARCUVITZ, N. (1951): 'Waveguide handbook'. MIT Rad. Lab. Series, 10, (McGraw-Hill, New York) 45 MARSDEN, J. E. (1973): 'Basic complex analysis' (W. H. Freeman, San Francisco) 46 MEHRAN, R. (1975): 'The frequency-dependent scattering matrix of microstrip right-angle bends, T-junctions and crossings', Arch. Elek. Uberrragungstech., 29, pp. 454-460 47 MEHRAN, R. (1976): 'Frequency dependent equivalent circuits for microstrip right-angle bends, T-junctions and crossings', Arch. Elek. Ubcrrragungstech., 30, pp. 80-82 48 MENZEL, W. (1976): 'Frequency-dependent transmission properties of truncated microstrip right-angle bends', Elecrron. Lett, 12, pp. 641 49 MENZEL, W. (1978): 'Frequency-dependent transmission properties of microstrip Yjunctions and 120' bends', IEE J . Microwaves. Optics and Acoustics, 2, pp. 55-59 50 MENZEL, W., and WOLFF, 1. (1977): 'A method for calculating the frequency dependent properties of microstrip discontinuities', IEEE Trans., MTT-25, pp. 107-1 12 51 Microwaves and RF (1984): 'The software selector', 23, pp. 70-95 52 MOSIG, J. R., and GARDIOL, F. E. (1977): 'Equivalent inductance and capacitance of a microstrip slot'. Proceedings 7th European Microwave Conference, Copenhagen, pp. 455-459 53 ROHDE. U. L. (1985): 'Models and nonlinearities: major factors in microwave CAD software', Microwave Syst. News, 15, pp. 123-143 54 SALERNO, M., and SORRENTINO, R. (1986): 'Planim: a new concept in the design of MIC filters'. Electron. Letts, 22, pp. 1054-1056 55 SCHNEIDER, M. V. (1969): 'Microstrip lines for microwave integrated circuits', BeN Syst. Techn J.. 48. pp. 1421-1444 56 SILVESTER, P., and BENEDEK, P. (1972): 'Equivalent capacitances of microstrip opencircuits' IEEE Trans., MTl-20, pp. 51 1-516 57 SILVESTER, P., and BENEDEK, P. (1973): 'Microstrip discontinuity capacitances for rightangle bends, T-junctions and crossings', IEEE Trans., MlT-21, pp. 341-346 58 THOMSON, A. F., and GOPINATH, A. (1975): 'Calculation of microstrip discontinuity inductances', IEEE Trans., MTT-23, pp. 648-655 59 WALDRON, R. A. (1970): 'Theory of guided electromagnetic waves' (Van Nostrand Reinhold, London) 60 WHEELER, H. A. (1965): 'Transmission line properties of parallel strips separated by a . dielectric sheet', IEEE Trans., MTT-13, pp. 172-185 61 WOLFF, I., KOMPA, G., and MEHRAN, R. (1972): 'Calculation method for microstrip discontinuities and T-junctions', Electron. Letts., 8, pp. 177-179 62 YAMASHITA, E., and MITTRA, R. (1968): 'Variational method for the analysis of microstrip lines', IEEE Trans., MTT-16, pp. 251-256 63 ZURCHER, J. F. (1985): 'MICROS3 - A CAD/CAM program for fast realisation of microstrip masks'. Proceedings IEEE MTT-S International Microwave Symposium, Saint Louis, Missouri 64 ZtiRCHER, J. F., BARLATEY, L., and GARDIOL, F. E. (1986): 'Computer-aided method to measure the permittivity of microstrip substrates'. Proceedings MIOP Symposium, Wiesbaden, Germany

Resonant microstrip antenna elements and arrays for aerospace applications A.G. Derneryd

18.1 Introduction Several advantages associated with microstrip antennas, namely light weight, low profile and structural conformity, make them ideally suited to aerospace applications. A number of single microstrip-patch antenna elements and microstrip arrays for communication and radar systems are described in this Chapter. The objective is to demonstrate practical designs and results, together with the engineering tools used. Antennas for dual frequency bands, dual beams and dual polarisations are considered. The frequency range covered is from L-band to c-band. Patches that are resonant in the dominant mode are usually employed. However, in Section 18.2 different mode structures actually excited on a circular disc are displayed using a liquid-crystal detector. This is an effective tool for visualising the RF field excited on a microstrip antenna. In Section 18.3 a dual-band circularly polarised patch antenna element is presented. The antenna is a low-gain antenna used for data communication. It was successfully flown on the Giotto space probe that encountered the comet Halley at its recent appearance. A monopulse array antenna for secondary surveillance radar applications is discussed in Section 18.4. The array aperture consists of two rows of microstrip antenna elements. A corporate feed network in stripline is mounted as an integrated part behind the antenna aperture. A low-density foam is used as a dielectric to achieve a lightweight design. An array-antenna concept suitable for a space-borne imaging radar system is described in Section 18.5. It is an integral feed-array structure with two separate feeding networks to enable horizontal and vertical polarisations to be obtained using a single antenna aperture. This antenna was designed and tested by Dr Lars Pettersson of the National Defence Research Institute, Sweden.

7058

Resonant microstrip antenna elements

18.2 Circular antenna element

Various design techniques for resonant microstrip antenna elements of simple geometries are available. The simplest method, useful for predicting radiation characteristics, is the cavity model. This model has been used to predict the resonant frequencies of a circular disc. An antenna element was manufactured and the different mode structures were visualised using a liquid-crystal detector. The basic circular antenna element comprises a conducting circular patch on a thin dielectric substrate backed by a ground plane, as shown in Fig. 18.1. The antenna can be viewed as a cylindrical cavity bounded at its top by the patch and at its bottom by the ground plane.

Resonant microstrip antenna elements

Thus, for each mode configuration, a resonant frequency is evaluated from [I]:

where Xis a zero of the derivative of the Bessel function of order n, and c is the velocity of light in free space. In practice, only the first few zeros are of interest. These are listed in Table 18.1 in ascending magnitude of X for convenience, since no closed-form expression exists for the roots X of J;(X). For any given radius, the mode corresponding to n = 1 has the lowest resonant frequency, and is known as the dominant mode. Table 18.1 Roots of J i ( X )

Fig. 18.1

Circular microstrip antenna element and liquid-crystal detector in wooden mount (Courtesy: N. P. Kernweis and J. F. Mcllvenna. RADC)

The resonant frequencies are functions of the radius a of the patch, the thickness h of the dielectric and the dielectric constant E,. However, an effective radius a,, slightly larger than the physical one, is introduced to account for the fringe field along the edge of the resonator cavity. The relation between the effective and physical radii is given by [I]:

This expression is derived assuming a quasi-static field distribution. However, it can be used to estimate the higher-order resonant frequencies as well.

7059

=

0

An antenna element was manufactured from a 1/16 in (1.58 mm) doubly-clad Teflon glass-fibre board with a dielectric constant of 2.55. The actual radius of the disc is 18.3mm but the effective radius is 5% larger, as calculated using eqn. 18.1. The 5 0 n feeding point is located at a radius 0.3 times the total radius of the patch. There is a shorting pin at the centre of the patch in order to reject the static mode (n = 0). The calculated resonant frequency for the dominant mode is 2.8 GHz using eqns. 18.1 and 18.2. The next two higher-order resonant frequencies are 4.7 GHz and 6.5 GHz, similarly calculated. The theoretical E-field structures for these three modes are shown in Fig. 18.2 [2]. It is possible to monitor mode changes as antenna patch dimensions or frequency are varied, by using a liquid-crystal detector. This consists of an encapsulated liquid-crystal solution that changes colour with applied heat. When a resistive coating is sprayed onto the back of the crystal, RF field components produce localised heating. Thus, a colour display results that varies with the intensity of the field. The liquid-crystal detector shown in Fig. 18.1 was placed on top of the circular patch [3].Visual colour displays of the E-field, corresponding to the first three modes, were observed using a liquid crystal with a resistive backing of 1100 Rlsquare. Black-and-white reproductions of the different mode structures actually excited on the circular patch are shown in Fig. 18.3. To effectively excite the second higher-order mode, the feed had to be repositioned closer to the

7060

Resonant microstrip antenna elements

Resonant microstrip antenna elements

7067

centre of the patch. The new feed position produces changes both in the dominant mode and in the first higher-order mode behaviour, which can be observed with the liquid-crystal detector.

Fig. 18.2 Calculated E-field structures on a circular microstrip antenna element at resonance a Dominant mode, TM, b First higher order mode, TM, c Second higher order mode, TM,

The photographs were taken with about 1 W of power applied to the antenna input. The liquid-crystal detector was directly on top of the patch. The loading effect on the antenna is thus at its maximum, but the displays are always bright and well defined. There is about 1% decrease in resonant frequency with the detector at this maximum loading position. However, the liquid-crystal detector is an effective aid in experimentally determining the relation between the feed position and the mode structure actually excited on a patch antenna. 18.3 Dual-band circularly polarised antenna element On 13 March 1986 the European Space Agency (ESA) spacecraft named Giotto encountered the comet Halley at a distance less than 500 km from the nucleus.

762

Resonant microstrip antenna elements

Resonant microstrip antenna elements

7063

Among the antennas on board was an S-band microstrip antenna for data communication between Earth and the Giofto space probe [4]. The antenna is a low-gain antenna providing an omnidirectional radiation-pattern coverage, together with a second low-gain antenna of the helix type.

The principal requirement of these two antennas was to provide real-time receiveltransmit of telemetry and telecommand signals during the geostationary transfer orbit. The antennas operate on a right-hand circular-polarisation mode in both frequency bands. The microstrip antenna is located on the outer surface of the dust-protection shield of the spacecraft. The gain requirement, including a 1 dB allowance for cable loss, is given in Table 18.2. This provides the necessary radiation-pattern overlap in the overall coverage pattern. Table 18.2

Gain requirement including cable loss

Angular interval, deg

Fig. 18.3 Observed mode structures on a circular microstrip antenna element (Courtesy: N. P. Kernweis and J. F Mcllvenna, RADC) a Dominant mode (2.8 GHz) b First higher-order mode (4.7 GHz) c Second higher-order mode (6.5 GHz)

Minimum gain, dBi

The microstrip antenna is a square radiating element resonant in its dominant mode. The element is etched on one side of a doubly clad PTFE board. The thickness of the laminate is 1/16in (1.58 mm) and the dielectric constant is 2.32.

1064

Resonant microstrip antenna elements

Resonant microstrip antenna elements

The element is fed at two adjacent sides via a 90" hybrid to generate right-hand circular polarisation. Each feeding line between the patch and the hybrid contains a two-section impedance transformer for double tuning [5]. The geometry of the transformer and the radiating patch is shown in Fig. 18.4. The input impedance, as seen from the 50R line, can be expressed in terms of the transformer parameters and the input impedance ZAof the radiator alone as

1065

The impedance matching transformers and the hybrid are etched on a thin doubly clad board which is contained in a stripline network bonded to the rear side of the radiating element board. A layout of the different boards is shown in Fig. 18.5. The transmission lines on the top board and in the stripline board are connected via copper strips surrounded by mode-suppressing pins. The fourth arm of the hybrid is terminated in a matched load placed inside the stripline board.

The explicit expression is Zin

=

Z* 2, Z2

+ jZz tan (k21z) + jZL tan (k21z)

where

z, Z, + jZ,

tan (k, I,) Z , jZA tan (k, I, ) and k, and k, are the propagation constants of the two transformer sections, respectively.

z,

=

+

Fig. 18.5 Layout of the complete microstrip antenna boards

rodlalor

2-section transformer

5011

Fig. 18.4 Dual-frequency microstrip antenna using an impedance-matching transformer

The characteristic impedances Z, and Z, of the transformer and the corresponding lengths I, and I2 are the parameters to be chosen to fulfil the matching conditions

The single and double prime signs refer to the two frequencies to be matched. In this case the input impedance is set to 50R, i.e. the characteristic impedance of the feed line. The input impedance of the patch alone is found from measurements at the two frequencies to be matched.

The overall dimensions of the complete antenna, including a mounting frame, are 139mm x 139 mm and the weight is 0.2 kg. The front surface is covered with a thin layer of black thermal paint with low electrical conductivity to prevent electrostatic charging in space. A picture of a prototype antenna is shown in Fig. 18.6. The measured return loss of the antenna including the cable, is presented in Fig. 18.7. The voltage standing-wave ratio is better than 1.2:1 at both the telecommand frequency (2116.7MHz) and at the telemetry frequency (2298.7 MHz). Recorded antenna patterns at three different cuts through the broadside direction are plotted in Fig. 18.8. The antenna is mounted on a ground plane to simulate the dust-protection shield. The specified gain as a function of the angle is shown as a broken line. The dual-band circularly polarised microstrip antenna was successfully flown on the Giotto spacecraft, and it was proved to fulfil all the specified data.

1066

Resonant microstrip antenna elements

Resonant microstrip antenna elements

1067

Fig. 18.6 A prototype microstrip antenna for the Giotto space probe

-50

-25 0 25 angle from broadside, degrees

50

75

Fig. 18.8 Recorded antenna patterns at 2298.7 MHz for three different cuts (0". 4 5 , 90")

frequency, MHz

Fig. 18.7

Measured return loss of the antenna including the cable

Fig. 18.9 Monopulse microstrip-array antenna

7068

Resonant microstrip antenna elements

Resonant microstrip antenna elements

18.4 Monopulse-array antenna In this Section an L-band planar-array antenna of the monopulse type intended for a secondary surveillance radar is described. Besides the usual sum radiation pattern, the antenna also generates a difference radiation pattern in one plane. In the current application the latter is used to separate signals received in the main beam from those received in the sum sidelobe region. This requires that the difference sidelobe level exceeds the sum sidelobe level at all angles. The antenna array consists of an aperture with 2 x 6 rectangular patches, as shown in Fig. 18.9. A stripline feed network is placed on the rear side of the aperture. The size of the antenna is 650 mm x 1300mm and the weight is 10 kg. Mechanically, the antenna is of sandwich design with foam as a spacer to achieve low weight and low losses. A cross-section of the aperture and the stripline feed network is shown in Fig. 18.10. The radiating patches, the transmission lines and the ground planes are supported by glass-fibre-reinforced plastic (GFRP) skins. Standard techniques are used to etch the radiating elements and the feed lines. The final assembly is done by bonding the different layers together in a step-by-step procedure.

radiating elements

-.

GFRP skin foam

feed network

-

ground plane ---,

A stripline corporate feed network is connected to the microstrip elements from underneath. Unequal power dividers of the Wilkinson type are used to get a 25 dB Chebyschev amplitude taper in the H-plane. A layout of the corporate feed network is given in Fig. 18.11. The first power divider, however, is a rat-race hybrid with equal power split to feed the two antenna halves. The sum signal of the two identical antenna halves is formed at one port of the hybrid, while the difference signal is formed at an opposite port. The far fields are calculated assuming a two-slot model for each patch [6]. However, this model does not take into account the effect of the finite ground plane. The edge eiYects are included by adding the field components diffracted from the edges to those radiated directly from the slots [7]. This effect is particularly noticeable at angles close to endfire and in the backward direction.

GFRP skin foam

ground Plane

1069

GFRP skin foam GFRP sktn

Fig. 18.1 0 Cross-section of the monopulse-array antenna

The basic radiating element used in the array is the rectangular patch with dimensions 90mm x 121 mm, resonant in the dominant mode. Two such elements, spaced 258 mm and fed in series from a single feed point, are employed to form the E-plane radiation pattern. The element pair is fed at the lOOQ input-impedance point of one of the patches. The second patch is connected to the first one by a half-wavelength microstrip line. The resulting input impedance of the pair is thus 50Q since the elements act in parallel when transformed to the common input port. The H-plane pattern is generated using six such pair of elements. The centre-to-centre spacing is 175mm.

Fig. 18.11 Layout of the corporate feednetwork (Courtesy:J. P.Starski, Chalmers University of Technology)

The radiation mechanism in the E-plane of a single slot in a finite ground plane is illustrated graphically in Fig. 18.12. The pattern is calculated by summing three rays; i.e. the direct geometrical-optics field, the singly edgediffracted field and the doubly edge-diffracted field. The direct field is obtained by assuming the ground plane to be infinite in extent. Using the co-ordinate system of Fig. 18.12, the normalised direct field in the E-plane from each slot can be written as sin (nh& sin 8) e-jk" Eoo = e ~ h &sin 8 s where k is the propagation constant in free space, h is the slot width normalised to the free-space wavelength, E, is the relative dielectric constant of the substrate and s is the distance from the slot centre to the observation point. The slot width is usually assumed to be equal to the substrate thickness. The singly diffracted field from each edge, generated from the same slot, is given as the incident field at the edge times a hard-boundary diffraction coefficient neglecting the dielectric effect [a]:

1070

Resonant microstrip antenna elements

Resonant microstrip antenna elements

The far field diffracted from the edges is thus expressed as ( + sign refers to edge 1 and - sign to edge 2) E: =

(xh&) e-jkdt + e sinah& -Dr(e Jz

= d,,

Pi,

n = 2)

1077

where n + P C + ( p , n) = cot 2n a - P C - ( p , n) = cot 2n

+ cos (/I - 2 n n N + ) + cos ( p - 2 n n N - )

g+ (P) = 1 g-(P) = 1

Fig. 18.12 Co-ordinate system and geometry in the E-plane of a slot in a finite groundplane

with

.

-90

.

.

.

.

.

-60

-30

b

.

o

0

.

l

l

l

l

l

30

.

60

a

I

90

angle from broads~de~degrees

and D' is the reflected diffraction coefficient given in eqn. 11.716 of Reference 8 and reproduced here:

Fig. 18.13 Recorded and calculated E-plane radiation patterns of an element pair at 1060 MHz

in which N + and N - are the integers that most closely satisfy the equations 2nnNf 2nnN-

-P -P

=

n

=

- n.

(18.15)

1072

Resonant microstrip antenna elements

Resonant microstrip antenna elements

Since the edge is relatively close to the slot, cylindrical-wave propagation is assumed. The doubly diffracted field is expressed as in eqn. 18.9. However, the incident field in this case is the singly diffracted field from the other edge assuming cylindrical-wave propagation. A calculated radiation pattern along the E-plane of an element pair is plotted in Fig. 18.13. The far field is computed using eqns. 18.8 and 18.10 referred to the same phase centre and assuming four radiating slots. The double edgediffracted fields are also included; e.g. fields diffracted from a first edge and incident on a seond edge. Diffracted rays on both sides of the aperture are considered. The corresponding measured pattern at 1060 MHz is included in Fig. 18.13 as well. The half-power beamwidth is 27'.

18.5 Dual-polarised-array antenna

Part of the active microwave instrumentation on board the European Remote Sensing Satellite 1 (ERS-I) developed for the European Space Agency is a scatterometer. It is an incoherent radar system at 5.3 GHz which measures the back scattering of the ocean. The values are used to calculate wind speed and wind direction.

Fig. 18.1 5

-90

-60

-30

0

30

60

7073

Series-parallel fed array of square microstrip patches

90

angle from broads~de.degrees

Fig. 18.14 Recorded and calculated sum-and-difference radiation patterns along the Hplane at 7060MHz

Recorded H-plane sum and difference patterns of the antenna are presented in Fig. 18.14. Calculated patterns using the method outlined in Reference 7 are also included as broken lines. The sum sidelobe level is below - 22 dB and the half-power beamwidth is 16'. The gain measured at the sum input port is 17 dBi and the losses are estimated to 1.3 dB. The difference sidelobe level exceeds the sum sidelobe level as required.

The scatterometer antenna is a narrow-band (2 MHz) planar array generating a fan beam. As an alternative to the current slotted-waveguide antenna solution a microstrip array is presented. The advantage of such a design is that the same aperture can be utilised for two orthogonal polarisations simultaneously [9]. A section of the microstrip array is shown in Fig. 18.15. It consists of 6 x 6 square microstrip patches arranged in 12 identical linear sub-arrays with three elements each. Every element is excited in two orthogonal modes from two separate feed networks. The feed point of the network for vertical polarisation is marked with an A on the central feeding line in Fig. 18.15. The feed network for horizontal polarisation is split into two symmetrical parts. These are fed 180° out of phase

7074

Resonant microstrip antenna elements

Resonant microstrip antenna elements

at points B and C on the outer feeding lines in order to generate a broadside beam. Each square element is fed at the mid-point of the edge of the element. This is the low-impedance point of the orthogonal mode in each case, thus maximising the isolation between the two polarisations. This cross-coupling is further surpressed by the symmetric feeding of the array. The three elements in each sub-array are fed by resonant feed networks. In the vertical-polarisation case the elements are fed from a common microstrip line of constant-impedance level at positions spaced one wavelength apart. The total input admittance of a sub-array is thus the sum of all patch admittances first transformed through a quarter-wave section. This is matched to the rest of the feeding structure by two quarter-wave transformers. In the horizontal-polarisation case the elements are fed in series separated by half-wave transmission lines. The input admittance of the three series patches is the sum of the patch admittances transformed through a quarter-wave section. The networks to feed the 12 identical sub-arrays are non-resonant to make them less sensitive to internal reflections and to enable future beam shaping by feeding the sub-arrays with different amplitudes and phases. The feed networks for the two polarisations are basically identical since the input impedance of a three-element sub-array for vertical polarisation is chosen to be twice the input impedance of the sub-array for horizontal polarisation.

1075

(TEM) method [lo]. The radiation resistance at each end of the patches is assumed to be 360R, a value found from measurements on test circuits. A microstrip substrate of the type shown in Fig. 18.16 is used. The base plate is a carbon-fibre-reinforced plastic (CFRP) skin to provide high mechanical stiffness and low thermal expansion. The metallic coating forming the ground plane is realised by an aluminium foil of 0.1 mm thickness. The top dielectric skin, carrying the patches and the feed network, is made from three layers of Kevlar-epoxy prepreg. A prefabricated 0.005 mm copper foil on an aluminium carrier is cured to the skin in a vacuum press. The aluminium carrier is then removed by means of an alkaline etching solution and the etching of the pattern is carried out by the standard photo-etching technique. Spacers in CFRP are used to support the dielectric skin, and they are positionedat locations with low electric field. c~rcutt

spacer dielectrtc layer

l g r o u n d plane

Fig. 18.16

Cross-section of the microstrip substrate

Table 18.3 Impedance levels and dimensions of the microstrip lines in the feed network

Line

Impedance,

Length, mm

Width, mm

The characteristic impedances of the feed lines are given in Table 18.3, together with the corresponding lengths and widths. The effective dielectric constants and the line widths have been determined using a low-frequency

The dimensions of the radiating patches and of the microstrip transmission lines are functions of the substrate thickness and the dielectric constant. The thickness has been determined from a minimum-loss point of view. The variation of the different types of losses as a function of the substrate thickness at a fixed impedance level can be derived, for example, from References 11-13. The proportional factors are determined by calculating the various losses for different thicknesses. The total losses in this particular design and for the substrate used, given a fixed impedance level, depend on the height h (in mm) approximately as Conductor loss

0.2/h dB

Dielectric loss

0.3 dB

Radiation and surface wave losses

0.05h2dB

The minimum-loss substrate thickness calculated from the above is 1.3 mm. The calculations were made on the assumption of a uniform dielectric. However, a suspended Kevlar skin is used, and instead the dielectric loss decreases slightly with increasing thickness. The actual optimum is therefore slightly larger than found above. A thickness of 1.6 mm is used, i.e. 0.4 mm for the Kevlar skin and 1.2 mm for air with sparsely scattered spacers. A photograph of a section of the antenna is shown in Fig. 18.17. The size of

7076

Resonant rnicrostrip antenna elements

Resonant rnicrostrip antenna elements

7077

the radiating patches is 23.5 mm x 23.5 mm and the element separation is 23.7mm. Two recorded radiation patterns of the array are presented. A cut along the H-plane for the vertical-polarisation case is plotted in Fig. 18.18. The sidelobe level is about -13dB, as expected from a uniform amplitude distribution. The corresponding pattern cut for the horizontal-polarisation case along the E-plane is shown in Fig. 18.19. The measured sidelobe levels are somewhat unsymmetrical, mainly owing to an amplitude unbalance at the input ports. The half-power beamwidth is 10" for the measured patterns. The isolation between the two polarisation ports is 31 dB, and this will improve with a better amplitude balance.

Fig. 18.17 Dual polarised rnicrostrip array antenna

a n g l e from b r o a d s ~ d e ,degrees '

Fig. 18.19 Recorded radiation pattern along the E-plane at 5.3GHz. Horizontal polarisation

18.6 Concluding remarks

- 401

-180

I, 620

\

-60 0 60 a n g l e from broadside, degrees

8

120

I

180

Fig. 18.18 Recorded radiation pattern along the H-plane at 5.3G M Vertical polarisation

The procedures employed for designing the microstrip antenna elements and arrays make use of transmission-line and cavity models coupled with experimental iterations of the initial designs. This is adequate for antennas with moderate requirements in terms of bandwidth and sidelobe levels. The effect of a finite ground plane on the radiation-pattern predictions is included by adding fields diffracted off the edges to the direct radiated fields. By doing this, the

1078

Resonant microstrip antenna elements

radiation patterns are more accurately estimated in the backlobe and wide-angle regions. Chapter 19

18.7 References 1 SHEN, L. C., LONG, S. A,, ALLERDING, M. R., and WALTON, M. D.: 'Resonant frequency of a circular disc, printed-circuit antenna', IEEE Trans., 1977, AP-25, pp. 595-596 2 WATKINS, J.: 'Circular resonant structures in microstrip', Electron. Lett., 1969, 5, pp. 524-525 3 KERNWEIS, N. P., and McILVENNA, J. F.: 'Liquid crystal diagnostic techniques, an antenna design aid', Microwave J., Oct 1977, 20, pp. 47-51, 58 4 BENGTSSON, P., HALM, R., and CRONE, G. A,: 'The Giotto spacecraft antenna subsystem design', IEEE Int. AP-S Symp. digest, 1986, pp. 711-714 5 DERNERYD, A. G.: 'Microstrip disc antenna covers multiple frequencies', Microwave J., May 1978, 21, pp. 77-79 6 DERNERYD, A. G.: 'Linearly polarized microstrip antennas', IEEE Trans., 1976, AP-24, pp. 846-851 7 HUANG, J.: 'The finite ground plane effect on the microstrip antenna radiation patterns', lEEE Trans., 1983, AP-31, pp. 649-653 8 BALANIS, C. A,: 'Antenna theory: Analysis and design', (Harper & Row, 1982), pp. 502-514 9 DERNERYD, A. G.: 'Microstrip array antenna', Proc. 6th European Microwave Conf., 1976, pp. 339-343 10 SMITH, J. I.: 'The even- and odd-mode capacitance parameters for coupled lines in suspended substrate', IEEE Trans., 1971, MTT-19, pp. 424-431 11 DENLINGER, E. J.: 'Losses of microstrip lines', IEEE Trans., 1980, MlT-28, pp. 513-522 12 JAMES, J. R., HALL, P. S., WOOD C., and HENDERSON, A.: 'Some recent developments in microstrip antenna design', IEEE Trans., 1981, AP-29, pp. 124-128 13 LEWIN, L.: 'Spurious radiation from microstrip', Proc. IEE, 1978, 125, pp. 633-642

Applications in mobile and satellite systems K. Fujimoto, T. Hori, S. Nishimura and K. Hirasawa

19.1 Introduction

Mobile communications often require antennas having small size, light weight, low profile and low cost. Microstrip antennas (MSA) are a type of antenna which can meet these requirements, and various MSAs have so far been developed and used for mobile communication systems. The practical applications for mobile systems are in portable or pocket-size equipment and in vehicles. UHF pagers, manpack radars, and car telephones are typical of those. Base stations for mobile communications need antennas with sector radiation patterns. Small, simple antennas are also favoured, since the antenna tower built for the base station can then be smaller and need less support for the weight. Ships and aircraft also demand small, lightweight antennas, and sometimes conformal structures are desirable to allow antennas to be mounted flush on the body of the moving vehicle. MSAs are considered to be suitable for such conditions and many antennas have been developed and installed on ships and aircraft. Examples are a marine radar antenna and a surveillance radar antenna. In satellite communications, circularly polarised radiation pattefns are required and MSAs of either square or circular patches with one or two feeding points can be used for generating the circular polarisation. Beam shapes such as a sector beam and a multi-beam can be produced by an array of MSA elements, which can be easily fabricated to form a flat structure, even though thousands of elements are used, by means of a photo-etch technique applied to the copper-clad dielectric substrate. A flat structure can be a feature of an MSA array used for receiving satellite broadcasting. Parabolic antennas are very popular for receiving broadcasts from satellites, but replacing them by small, flat antennas is preferable, especially for the home use. A large parabolic antenna, with the primary feed placed in front of the reflector, needs a wide area for installation, while a small, flat antenna can possibly be mounted flush on the wall of the house or even placed inside the window at home, depending on the field strength at the receiving environment. Several types of flat antennas have

1080

Applications in mobile and satellite systems

Applications in mobile and satellite systems

been developed: antenna elements used are the crank type, four-element square patch of either single- or two-point feed, etc.. In this Chapter, various types of MSAs which have been developed and applied in mobile and satellite systems are described. 19.2 Mobile systems

19.2.1 Design considerations MSAs used for land, maritime and aeronautical mobile systems are described in this Section. Antennas for land-mobile base-stations are also included. In these applications, the features of MSAs, such as flat structure, lightweight and compactness, which are generally required for mobile systems, are fully taken into account in the design. Antennas used for cellular mobile base-stations are described in the first part of this Section. In the cellular mobile phone system a service zone covered by a base-station antenna is divided into small sectors to increase the use of radio-frequency channels. The antennas are then designed to have a sector or a multi-beam pattern to form three to six zones in a 360' coverage. These patterns can be synthesised by an antenna array and MSAs are employed as being the most suitable array elements. Using antennas such as a dipole and a paraboloidal or corner reflector, beam shaping cannot easily be realised. In addition, the utilisation of MSA elements for the base-station antenna is advantageous, because the array can be made in flat structures and of light weight; and the antenna tower construction is easier and less costly from installing the MSA array on the tower than by using conventional heavy metallic antennas. A base station of small power, applied, for example, to home security, may represent an interesting problem. To overcome severe multipath fading in signal reception during indoor operation, the system is designed to receive both electric (E) and magnetic (H) field components at the same time, thereby obtaining smooth signal output. For this purpose, a system with a combined slot and rectangular patch antenna has been developed to receive both E- and H-field components simultaneously. Those antenna elements are placed flush on the panel of the equipment box, which can be hung on the wall of a room when used operationally. The second part of this Section describes the applications of MSAs to the automobile. Two types of antennas have been introduced: one is an antenna which can be used in the interior of an automobile and the other is an antenna which is installed on the roof of a vehicle. Both should be a thin and compact antennas, and MSAs can satisfy such requirements. Two antennas are located in the interior: one on the dashboard and the other on the back of the rear seat, for the purpose of the diversity performance. Successful operation of the diversity system has been reported after an experiment was undertaken in the Tokyo metropolitan area.

1087

When an antenna is placed on the roof of a car, the radiation pattern usually tends to be directed upwards; however low-angle radiation is preferred for urban mobile operations. An annular slot is used to obtain a relatively low-angle pattern when installed on the roof of a car. Also its flat structure is preferable, because a thick or bulky antenna cannot be mounted on the roof. The next Subsection introduces antennas for pedestrians. This application requires special consideration, especially when the equipment is used in an operator's pocket or near a human body. The effect of adjacent materials on antenna performance can scarcely be avoided; however, by using an antenna excited by a magnetic current, instead of electric current, the degradation of antenna performance due to adjacent materials can be reduced. The ground plane of an MSA acts as a type of shield against adjacent materials such as circuit components and other metallic materials, and yet the image of the magnetic current, with respect to the ground plane, will provide enhanced radiation in front of the MSA element, which results in reducing the degradation of the radiation. Four types of modified quarter-wavelength MSAs used for the pocket-size equipment are introduced. The remainder of the Section deals with radar antennas. The first is a marine radar antenna. Antennas used on ships are mainly either reflector antennas or slot arrays. An MSA array, formed as a flat structure and placed on a rotating pedestal similar to the usual radar antennas, is introduced. The MSA application reduces the weight, and makes the antenna rotation simple, smooth and tolerable over a long period of time. This is very important for use in small boats, because a heavy and large antenna with bulky counterweight cannot be mounted on the top of a mast. 19.2.2 Base stations

(a) Sector-beam array: The microstrip-antenna concept is applied to basestation antennas for land-mobile communications to create small, simple and low-cost antennas. The configuration of base-station antennas which have sector beams is shown in Fig. 19.1 [I]. Fig. 19.l a shows a 60"-120" sector-beam array [2], and Fig. 19.lb shows a 180' one [3]. The former is composed of two or four sub-arrays, and the sub-array is composed of 2 x 4 microstrip patch elements. The patch element is a broadband microstrip antenna with a parasitic element. This antenna radiates vertical and horizontal polarisation in the 900 MHz band. It has 60"-120" sector-beam patterns in the horizontal plane. For realising these patterns in the horizontal plane, a two-element excitation method is used, in which two elements are excited with different amplitudes and out of phase. The feeder section is composed of two hybrids and a phase shifter. The amplitude ratio of the two elements can be changed by controlling a phase shifter. The measured radiation patterns are shown in Fig. 19.2. The gain deviation is less than 4 dB within the

7082

Applications in mobile and satellite systems

60"-120" beam. The measured VSWR is less than 1.5 over a frequency bandwidth of 9%. The other array (shown in Fig. 19.lb) is composed of 8 or 16 printed dipole elements with a corner reflector. This antenna radiates vertical polarisation in the 900 MHz band. It has 180" sector-beam patterns in the horizontal plane.

Applications in mobile and satellite systems

7083

(b) Multi-beam array: The configuration of the multi-beam base-station antenna for land-mobile communications is shown in Fig. 19.4 [4]. This antenna is composed of 8 x 8 microstrip patch elements. The patch element is a broadband microstrip antenna with a parasitic element. The antenna operates in

Parasitic, Element

-30 1 -180

-90

0 Angle

90

180

(')

Fig. 19.3 Measured azimuthal radiation patterns of the 180' sector-beam array (@ 1988 IEICE)

--- 860 MHz -900 MHz

- - - 940 MHz

. . . . Cal (900 MHz)

Fig. 19.1

Configuration of the sector-beam base-station antenna (Courtesy: NTT, Japan) ( a ) 60-120' sector-beam array (V/H polariation) ( b ) 180' sector-beam array (V polarisation)

Input/Output

Butler matrix

Fig. 19.4 Configuration of the multi-beam base-station antenna (@ 1988 IEICE)

Fig. 19.2 Measured azimuthal radiation patterns of the 60- 12LT sector-beam array (@ 1988 IEICE) ( a ) amplitude ratio, 1 :0.27 (6)amplitude ratio, 1 : -0.33. V polarisation, - - - H polarisation.

-

The corner angle of the reflector is optimised to realise these patterns in the H-plane. The measured radiation patterns are shown in Fig. 19.3. Here, the corner angle is 26O0, and the reflector size is 0.62 wavelength width. The measured VSWR is less than 1.2 over a frequency bandwidth of 9%.

vertical/horizontal polarisation, and has eight beams within 120" area. The eight beams are switched by a Butler matrix circuit. For simplicity and low cost, the microstrip antenna elements and the feed circuits are arranged and etched on the same surface. The measured radiation patterns are shown in Fig. 19.5. The measured gain is more than 22 dBi at 900 MHz, and the circuit loss is less than 2 dB. (c) E-H antenna: Conventional or shortened dipole antennas have been used as base-station antennas for small indoor communication systems. One of the biggest problems is that indoor communication is sometimes interrupted

7084

Applications in mobile and satellite systems

when a receiving antenna happens to be located near the minimum points of a standing-wave distribution of electric fields, as shown in Fig. 19.6. Several techniques, such as space diversity or frequency diversity, have been introduced to the communication system to solve the problem. However, the system may be rather bulky and expensive for most small base stations.

Applications in mobile and satellite systems

7085

by a standard dipole antenna, but the solid line shows little fluctuation in the combined signals received by the E-H antenna. In addition, the present antenna can receive both vertically and horizontally polarised waves using a proper signal combiner. This will be quite useful for Indoor communication. wide strip microstrip

Angle

(')

out

Fig. 19.5 Measured azimuthal radiation patterns of the multi-beam base-station antenna (@ 1 9 8 8 IEICE) measured --- calculated

-

Fig. 19.7 Configuration of the E-H antenna (@ 1988 IEEE)

antenna standing waves

I

....................

present ................................................. antenna

.....-.... ...

,,.........*.

metal 1 ic -1

...

1

i standard dipole

I

... ,,,,' .\! .

! , :

'*

.. t i

y

floor

measured

Fig. 19.6 Idealised standing- wave distribution (@ 1 9 8 8 IEEE)

Ito et al. [5] have proposed a simple printed antenna, as shown in Fig. 19.7, composed of a half-wavelength slot, a wide strip and a signal combiner. The antenna can receive transmitted signals through both magnetic and electric fields, so that there will be almost no interruption from standing waves. The antenna is referred to as an E-H antenna. The slot and the strip are constructed on both sides of a printed circuit board. Received signals from the slot and the strip are combined directly and sent to a receiver. A reflector is placed under the ground plane of the substrate to form a unidirectional pattern. Fig. 19.8 shows an example of received-signal fluctuations for varying antenna location. Each maximum value was normalised to unity. D denotes the distance of the antenna from a metallic wall in wavelengths (the frequency was 320 MHz). The dotted line shows the standing wave of the electric field received

Fig. 19.8 Example of received-signalfluctuations (@ 1 988 IEEE) Each maximum value was norrnalised to unity -E-H antenna - - - standard dipole antenna

19.2.3 Wheeled vehicles ( a ) Cabin antenna: The circular microstrip antenna is used for cabin-antenna applications [6].It is necessary for a cabin antenna to have 1 dB more gain than a haif-wavelength dipole, based on the assumption that the degradation in the average received power caused by installing an antenna inside the vehicle is 3 dB, and the improvement caused by receiving both dominant and cross-

7086

Applications in mobile and satellite systems

polarisation is 2 dB. The cabin antenna is a broadband microstrip antenna with a parasitic element, as shown in Fig. 19.9. The measured radiation patterns are shown in Fig. 19.10. The relative gain compared with a half-wavelength dipole is about 1.5 -- 2 dBd for a microstrip antenna with a parasitic element.

Applications in mobile and satellite systems

7087

switching the capacitance loaded on the slot by the bias supply. This type of pattern can be considered for a vehicular antenna system to reduce the multipath fading in urban mobile communications. 1

Fig. 19.9 Outer view of cabin antenna (Courtesy: NTT, Japan)

( b ) Rooftop (annular slot): The annular slot [7, 81 is a candidate for use in vehicular antennas for mobile communications, since it can radiate power at low elevation angles. In urban mobile communications, incident waves to mobile stations come mostly from directions having low elevation angles, - about 30" up from the horizontal plane. The antenna structure is shown in Fig. 19.1 I . The radiation pattern depends on the radius of the slot, and its variation is shown in Figs.19.12 - 19.14, where the antenna radius is taken as a parameter. Fig. 19.15 illustrates a way of mounting an annular-slot antenna on the roof of a vehicle. An example of an annular-slot antenna with k, = 0.5 (k = 2n/l, where I is the wavelength) is shown in Fig. 19.16. The radiation pattern can be controlled by loading a capacitor on a slot as shown in Fig. 19.17 and by varying its capacitance electronically. One method is to make the radiation pattern asymmetric. An almost one-sided radiation pattern is obtainable, and a typical example is shown in Fig. 19.18, where the antenna parameter k, = 1.5, the loaded reactance is - 80 ohms, and the operating frequency is 1.5 GHz. The radiation pattern can be rotated electronically by

Fig. 19.10 Measuredradiation patterns of cabin antenna (Courtesy: NTT. Japan) (a) Vertical plane (E- lane) (b) Vertical plane ( ~ i p l a n e ) (c) Horizontal plane

19.2.4 Railways A train antenna is required to have wide beamwidth, with a low profile and small structure. TOsatisfy these requirements, a short-circuit rectangular micro-

1088

Applications in mobile and satellite systems

Applications in mobile and satellite systems

1089

z

X

/

' f e e d point "

10 ABAIV.

C

10 WOIV.

ielectrlc material 0 0' 10 dB/DIV.

Fig. 19.13 Radiationpatterns

Fig. 19.11 Annular-slot antenna structure and the co-ordinate system ( a ) Antenna structure and co-ordinate system ( b ) Feed point

b Fig. 19.12 Radiation patterns

10 dWOIV.

d

10 WON.

Fig. 19.14

Radiation patterns

d

10 W l V .

7090

Applications in mobile and satellite systems

Applications in mobile and satellite systems

1091

strip antenna is used [9]. A train antenna is shown in Fig. 19.19; it is 2300 mm in width, 350 mm in height and 90 mm in depth. The antenna is composed of the transmitting antenna and the receiving antenna. Each antenna is a fourpatch array, and it operates at 413 MHz and 452 MHz. The measured radiation

Fig. 19.15 Concept of mounting an annular-slot antenna on the roof of a vehicle

Fig. 19.18 Measured radiation patterns Fig. 19.16

Example of annular-slot antenna element

rodlotor feeder

&N#M~B&Y~

i $5 t'i $5 j J1 ! mn i,

,

!

Dower d i v i d e r

Fig. 19.19 Configuration of train antenna (@ 1988 IEICE) reactance component

Fig. 19.17 Dimensions of antenna

'feed

point

patterns are shown in Fig. 19.20. The half-power beamwidth is more than 34' in the horizontal plane, and more than 153" in the vertical plane. The measured gain is 5.8 dBd at 452 MHz, and the VSWR is less than 1.4.

7092

Applications in mobile a n d satellite systems

Applications in mobile a n d satellite systems

I 1

7093

units in the VHF/UHF bands. A practical example of one of these antennas mounted in a pocket-size pager at the 900 MHz band is shown in Fig. 19.21 [IO]. The gain required for this type of pager antenna is about -4 dB compared to a

Fig. 19.20 Measured radiation patterns of train antenna (@ 1988 IEICE) -measured - - - calculated

19.2.5 Pedestrian Antennas for VHF/UHF hand-held portable equipment, such as pagers, portable telephones and transceivers, must naturally be small in size, light in weight, and compact in structure. Some of this equipment, especially that used most of the time in an operator's pocket, demands either flush-mounted or built-in antennas. It is well known that the smaller the antenna size, the lower the antenna efficiency. There is a growing tendency for portable equipment to be made smaller and smaller as the demand for personal communication rapidly increases, and the development of hand-held or hand-portable units has become urgent. Requirements on antenna performance for such small equipment are becoming increasingly severe, since the antenna performance should not be significantly degraded as the size becomes smaller. The microstip antenna is one of the most preferable for small equipment, especially when a flush-mounted or built-in antenna is required. Since the microstrip antenna can be made with a very thin and compact structure, it can easily match various types of portable units. One possible problem to be considered when using a microstrip antenna is its narrow bandwidth, which is usually only a few percent, depending on the thickness of the antenna and the manner of feeding. Efforts have been made to increase the bandwidth, but a wide bandwidth of, say, 10% would be hard to obtain in the present state of the art. Fortunately, some systems such as pagers do not need a wide bandwidth in their operation, and so the microstrip antenna can be applied to small VHF/UHF equipment used in such systems. Four types of microstrip antennas (MSA) are introduced in this Section QMSA, PMSA, WMSA and FVMSA: Q stands for quarter-wavelength, P for post-loading, W for window-attached, and FV for frequency-variable. Antennas other than QMSA are modified from QMSA. They have basically similar radiation patterns. The difference is that PMSA has two radiation apertures in order to increase the gain, WMSA has a reactance slit on the patch to make the QMSA length shorter, and FVMSA is a QMSA with its resonance frequency electronically variable. Any of these antennas can be applied to small portable

Dimensions Weight Display Sensitivity Battery life Spurious -

Freauencv . -

1 (

1

1

I /

8 5 x85 x 1 9 mm 140g 12 digits numerals 5pVh

3 months -40dB 9OOMHz band with frequency stobility 2.5 part in 1 0 ~ ( - 1 0 + 5 0 ~ )

Fig. 19.21 Example of pocket-sized pager having an MSA element (Courtesy: Matsushita Communication Ind. Co. Ltd., Japan)

half-wave dipole. The four types of MSA variations for 900 MHz pagers are as follows: ( a ) Quarter-~avelengtlmicrostrip antenna ( Q M S A ) : QMSA is a quarterwavelength rectangular patch antenna with one end of the patch shorted electrically. (Fig. 19.22) There are slight differences from an ordinary quarter-

7094

Applications in mobile and satellite systems

wavelength patch antenna; the sides of the patch are cut so that the ground plane has the same width as the radiation patch, and a part of the ground plane is extended from the radiation aperture by a length of G, as shown in Fig. 19.22.

Applications in mobile and satellite systems

1095

(6, = 2.4), Teflon ( E , = 2.5), and glass-fibre-reinforced epoxy resin ( E , = 3.7); E, is the relative permittivity of the substrate. 0 dB in the Figure is the gain of

the standard half-wave-dipole antenna. This is also used in later Figures in this Section. 0-

; i

-cB -0

d

[?$,/

. 5

-

.

patch radiator\ -10

.feed

; 1

0

Fig. 19.22 Quarter wavelength microstrip antenna (OMSA) structure

v

polyethylene teflon

X

epoxy-fibreglass

50

L

Fig. 19.24 Gain versus patch length L (QMSA)

f

teflon x

epoxy-f lbreglasr

Fig. 19.23 Gain versus length G,

Fig. 19.25 Gain versus patch width W (QMSA)

The length G, plays an important role in increasing radiation. The variation of gain of a QMSA with respect to the length G, is shown in Fig. 19.23: Three types of substrate material are treated as typical: polyethylene

The gain versus the total length L is illustrated in Fig. 19.24. The patch width W also affects the gain, as shown in Fig. 19.25. An example of measured radiation patterns of the QMSA is shown in Fig. 19.26, where patterns in the

7096

Applications in mobile and satellite systems

three planes XY, Y Z and ZX are illustrated. Consideration of the radiation patterns in these three planes is important, since their evaluation becomes meaningful when the antenna is used in an urban environment for mobile communications, where multipath fading problems exist. The antenna performance should be evaluated three-dimensionally: not only in the horizontal plane, but also in the two other planes. For example, the antenna-pattern maximum may exist in a plane other than the horizontal, and incoming waves may often come from directions not in the horizontal plane. For these reasons, gain defined only in the XY plane is not sufficient for evaluation of the actual antenna performance. The antenna parameters used are as follows: L = 76.7 mm, G, = 27.9 mm, W = 30 mm, t = 1.2 mm and 8, = 2.5 (Teflon).

Applications in mobile and satellite systems

i I

7097

form another radiation aperture at its end. The ground plane is further extended from the end of the radiation aperture by a length G, as shown in Fig. 19.27. The dimensions of the antenna and the co-ordinate system are also shown in the Figure. radiator /patch

post

L Fig. 19.27 PMSA antenna structure

m

-

.c

-5-

9

%

-

- 10 o

polyethylene

0

teflon

a epoxy-fibreglass

I

Fig. 19.26 Radiation pattern (G, = 27.9 mm) (QMSA)

0

'0

,

, , ,

.

, 20

, , (mr

Gz

(b) Post-loaded microstrip antenna (PMSA): PMSA [I 1 , 121 is an antenna modified from an ordinary QMSA and designed to have two radiation apertures driven by a single feed, as shown in Fig. 19.27. Several reactance posts are used to replace the shorted termination of the QMSA, and the patch is extended to

Fig. 19.28 Gain versus length G, (PMSA)

The gain of the PMSA with three posts versus the length G, ( = G, = G,) is shown in Fig. 19.28. The operating frequency is 930 MHz. Three kinds of substrate materials (8, = 2.4,2.5 and 3.7) are again taken into account, and the

1098

Applications in mobile and satellite systems

Applications in mobile and satellite systems

Table 19.1 Dimensions of PMSA used in the experiments (see Fig. G m = G, = Gz) Substrate er t W a G, b (mm) (mm) (mm) (mm) (mm) (mm) Poly1.2 30 48.9 4.5 24.5 ethylene 47.9 7.0 24.2

Teflon

1.2

30

apoxyglassfibre

1.2

30

- -

O

-

19.27,

L

(mm) 82.1 85.1

47.4 46.1

20.0 3.8

24.0 23.9

111.4 77.9

39.6 38.8

4.0 7.5

20.2 22.0

66.9 75.3

7099

antenna parameters t = 1.2 mm, W = 30 mm, and lengths a and b in Table 19.1 are used. The gain versus total length L is shown in Fig. 19.29. The length b is about a quarter wavelength, while the length a is about 24 mm, which is slightly altered by the change in G,. Fig. 19.30 shows the variation of gain with length a, where the parameters used are the number of posts. Two examples of measured radiaton patterns are shown in Figs.19.31 and 19.32. They resemble those of QMSA, although there is a difference in two apertures driven in this instance.

e polyethylene 0

teflon epoxy-fibreglass

Fig. 19.30 Gain versus length a (PMSA)

m

9

-10

0

50 L

Fig. 19.29 Gain versus patch length L (PMSA)

100

(mn)

( c ) Window-reactance-loaded microstrip antenna (WMSA): WMSA [I31 is designed to have a shorter length than QMSA by putting a reactance window (slit) with a length W, on the patch, as shown in Fig. 19.33. The window acts as a reactance component and its value is altered by the length W, of the window. The resonance frequency versus the length W, of the window is given in Fig. 19.34, which also gives the dimensions of the antenna. The gain is affected by the length W,, and is shown in Fig. 19.35.The gain differs depending upon the location of the window, and the distance S-W of the window from the end of the patch (see Fig. 19.35). For larger S-W, the gain is higher. Two slits placed on the patch, as shown in Fig. 19.36a, can also form a reactance component in the antenna structure, and the length of the radiation patch can be shortened. If the length Wsis altered, the resonant frequency alters as shown in Fig. 19.36b. It increases with W,.

7 700

Applications in mobile and satellite systems

Applications in mobile and satellite systems

7 707

( d ) Frequency-variable microstrip antenna (FVMSA): The resonance frequency of a QMSA can be altered electronically by varying the value of a reactance loaded on the antenna structure. For this pirpose, the shorted termination of the QMSA is replaced by a reactance component and the reactance is varied by its bias supply. This type of antenna is called FVMSA (Frequencyvariable MSA) [14]. A diode can be used as a reactance element, and its

substrate

-

Fig. 19.31 Radiation pattern

(G, = 7.0 mm)

(PMSA)

Fig. 19.33 Window reactance loaded microstrip (WMSA no. 1 )

(unit rnm)

Fig. 19.34 WMSA no. 1 ( a ) Dimensions ( b ) Resonant frequency versus slot width W,.,

Fig. 19.32 Radiation pattern

(G, = 20.2 mm)

(PMSA)

resonance frequency, depending on the bias voltage to the diode, is shown in Fig. 19.37, which also shows the gaintfrequency as the bias voltage is altered from 6 to 10 V. The diode used is an MA325 (Fig. 19.38) and its characteristics,

7 702

Applications in mobile and satellite systems

Applications in mobile and satellite systems

0

1103

- 8

0 0

o

bias voltage

- 7

0

0

5

10

0

20 (mm)

15

0

Ww

I

~

8 50

Fig. 19.35 Gain versus slot width W, (WMSA no. I )

~

~

~

900 950 FREQ (MHz)

Fig. 19.37 Gain versus frequency and bias voltage (FVMSA)

Unit :mm

"

Jl.

I"

Ws (mm) a

b

__H___

Fig. 19.38 WMSA no.2 ( a ) Dimensions ( b ) Resonant frequency versus slot width W,

1' Cathode 2 Anode Fig. 19.38 Dimensions of M A 325

~

~

1704

Applications in mobile and satellite systems

Applications in mobile and satellite systems

7 105

and capacitance variation with bias voltage, are shown in Fig. 19.39. The antenna structure and its dimensions are given in Fig. 19.40 and Table 19.2, respectively.

40

30

-a 20

LL

0 U

10

0 0.1

0.3050.71

v,

35710 (v)

3050X)lOO

Fig. 19.39 Bias voltage V, versus capacitance C, ( M A 325)

Fig. 19.41 Microstripline planar antenna for manpack radar

19.2.6 Radar

Fig. 19.40 FVMSA antenna structure

Table 19.2 Dimensions of FVMSA (see Figs. 19.22 and 19.40) er

t

(mm)

W (mm)

F~ (mm)

b (mm)

Gz

(mm)

Diode type

( a ) Manpack radar: Portable manpack radars operating by the pulse Doppler method can serve as detectors of moving targets such as people, vehicles etc. They are small, light devices which utilise microstripline antennas, as shown in Fig. 19.41. such-an antenna is constructed of 16 centre-fed Franklin-type microstripline antennas [15]. It is centrally fed through the front side hybrid networks. Each network is fed through the parallel-feeding network on the rear side. Each microstripline . . antenna works as a standing-wave antenna terminated by an open clrcult. The characteristics of this antenna are as follows: frequency, X-band; antenna

1106

Applications in mobile and satellite systems

aperture, 34cm x 45cm; half-power beamwidth, about 4.5"; gain, 30dBi; weight, about 2 kg. ( 6 ) Marine radar: Microstrip arrays have been used in marine radars [16]. Fig. 19.42 shows an inside view of a radar system installed on ocean vessels. This type of radar system has been in service since 1981. The antenna array consists of 48 (3 x 16) circular patch microstrip elements and is mounted on a rotating pedestal. The specification of the system is given in Table 19.3. Fig. 19.43 shows

Applications in mobile and satellite systems

1107

( c ) Radar rejector: A bidirectional communication system is shown in Fig. 19.45 [17, 181. The radar reflector can transmit information from the reflector site to a radar station as well as receiving signals from a radar station. The reflector consists of a Luneburg lens with a reflector plate on it. Fig. 19.46 shows

I

I

0.97

I

I

I

I

I

I

0.98

0.99

1.00

1.01

1.02

1.03

flfo

Fig. 19.43 Sidelobe level and gain versus frequency

Fig. 19.42 Marrne radar antenna (Courtesy: Japan Rad~oCo. Ltd.)

Table 19.3 S~ecificationsof marine radar Frequency Gain Beamwidth Dimension

X band over 22 dB 6.0" in azimuth 25" in elevation 367 x 88.0mm

the gain and first-sidelobe characteristics against frequency in the azimuth direction. Typical radiation patterns are shown in Fig. 19.44. By replacing the metallic waveguide-fed antennas with microstrip elements, the antenna system can be made smaller and lighter, so that smoother rotation of the antenna and increased reliability is achieved. In addition, the production cost can be reduced and mass production becomes easier.

Fig. 19.44 Radiation pattern

details of the reflector plate. The two quarter-wavelength sections A and B are an impedance transformer and RF blocks, respectively. When the diode is off, signals are received. When the diode is switched on/off by coded pulses to be

1708

Applications in mobile and satellite systems Reflecting

Demodulator Encoder

Transmitter

Recorder Fig. 19.45 Block diagram of bidirectional communication systems (@ 1988 IEICE) Switching circuit

( MSA

n

To Recewer

Applications in mobile and satellite systems

7 109

transmitted from the reflector to a radar station, the radar cross-section is modulated by them and is detected at the radar station. Thus no transmitter is needed to transmit information from a reflector site to a radar station. A Luneberg lens focuses on incoming R F waves at any angle incident on the antipodes of the lens sphere. Then a reflecting plate placed on the antipodes reflects the waves back exactly in the incident direction. The same lens sphere can be used to establish communication channels with other radar stations in different directions by placing reflecting plates at the corresponding antipodes. The gain is 26.5 dB and the beamwidth is 7" at 9.375 GHz when the relecting plate is used as a receiving antenna. At the same frequency the radar crosssection is 33 m2 and the beamwidth is 3" when the reflecting plate is used as a reflector. Fig. 19.47 shows the VSWR when the diode is off, and the return loss when the diode is on, as a function of frequency. At the centre frequency, a VSWR of less than 1.1 and a return loss of 0.5 dB are obtained. Fig. 19.48 shows the radar cross-section of the reflector normalised to that of a metal plate of the same area. A modulation ratio of 13 dB is obtained when the diode is switched on and off. Field experiments using a marine radar and the reflector have been carried out successfully.

Rodidor top view

-2 1 Bias ON

Bias side view C

Fig. 19.48 Configuration of reflector plate (@ 1988 IEICE) a Equivalent circuit b Top view c Side view

Fig. 19.47 VSWR and return loss of reflector without lens (@ 1988 IEICE)

Fig. 19.48 Radar cross-section of reflector with lens (@ 1988 IEICE)

( d ) Secondary surveillance radar: In order to cope with the rapidly increasing air traffic, replacement of the existing secondary surveillance radar (SSR) with the next generation of SSR (mode S) is being studied at an international level. For the purposes of improving data rate, the cylindrical electronic scanning antenna, which can be turned instantaneously in any direction and aimed at any target, is believed to be more promising than the existing SSR with a constant rotation. Fig. 19.49 shows an experimental antenna. This is a cylindrical array of one-third arc, and it has a 90" active sector. Its radiating elements are vertically polarised circular patch antennas, and it operates in the frequency range 10301090 MHz. A paper honeycomb substrate is used. Ten radiating elements are arranged in elevation, forming a cosecant-squared pattern. The azimuth is

111 0

Applications in mobile and satellite systems

Applications in mobile and satellite systems

1 1 11

composed of 32 active sector lines and a pencil beam is formed on the azimuth plane, which can be scanned horizontally by gradually changing the transfer switch.

( e ) Three-faced array: The vertically polarised antenna, which has an omnidirectional pattern in the horizontal plane and a desired pattern in the vertical plane, is mainly utilised for broadcasting, telecommunications and as a transponder. In addition, this antenna can be used in an aircraft system. When used together with the MLS (Microwave Landing System) it works as a DME (Distance Measurement Equipment) antenna.

Fig. 19.49 Cylindrical-array antenna for SSR mode S

reflector

microstrip line slot feed point 3 way power

Fig. 19.51 Three-faced microstrip slot array antenna (Courtesy: Japan Radio Co., Japan) Fig. 19.50 Three-faced array antenna a antenna configuration b Feeding network (After Hara, and Goto [I91,@ 1988 IEEE)

The shape of the antenna is shown in Fig. 19.50. The antenna gives an omnidirectional pattern when a suitable flared reflection board is set on each of the three faces. Each face produces a cosecant-squared pattern through pattern synthesis.

1 1 12

Applications in mobile and satellite systems

Applications in mobile and satellite systems

1 1 13

Fig. 19.51 shows a trial antenna. The characteristics of this antenna are: frequency, 3 GHz; height, about 80 cm; peak gain, 9.5 dBi; antenna efficiency, 85% [19].

antenna is not considered wise, owing to its large size and the complexity of manufacture. Again, an array structure is preferred to a large-aperture antenna, and MSA elements in the S- and L-bands have been employed in such array systems.

19.3 Satellite system

19.3.2 Direct-broadcasting reception Several planar antennas for satellite TV reception using circularly polarised printed arrays have been proposed. In Japan, with the start of satellite broadcasting in December 1986 utilising the satellite Yuri 26 (BS-2b), efforts have been made with the R & D of the planar antenna. When the characteristics of a planar antenna are set at 11.7-12.0 GHz and the gain is 33-34 dBi, the antenna will receive signals in the high-field-strength area (except during heavy rains), as shown in Fig. 19.52.

19.3.1 Design considerations This Section describes MSA applied to three areas of satellite systems: direct broadcasting systems (DBS), the earth stations and the satellite-borne systems. ( i ) DBS antennas: In the design of the DBS antennas, there are the problems of reducing the size and weight, and yet it must~havea gain high enough to be competitive with the popular parabolic reflector antennas. A number of flat antennas using MSA elements have been developed so far with the features of light weight and ease of installation on the walls of a house or a building, or location inside a room. Another advantage of using a flat structure is that its performance is less affected by the snow or wind than by using parabolic reflector antennas. (ii) Earth stations: The general requirements for an earth-station antenna are: simple structure, low cost, tracking capability and fading-suppression performance. Two types of satellite tracking are considered: the first is to use the radiation patterns of either a wide beam or a conical beam, thereby ensuring that the antenna beam always tracks a satellite, and the second is to use either a spherical array or a phased array. Antenna-beam shaping in the vertical plane is designed to achieve fading suppression. By making best use of the MSA feature, wide-beam or the conical-beam antennas of simple structure and low cost have been developed and are presently in practical use. MSA elements are also considered to be suitable as L-, S- and C-band antennas, and applicable to spherical (switching) arrays, phased arrays and sector-beam arrays. A unique transportable equipment for satellite communications has been developed and tested by using a link with the Japanese communication satellite ETS-V. The equipment hardware is put in an small attachk case which the operator carries. Two antennas, one for the transmitter and the other for the receiver, are used instead of only one antenna operating as both a transmitter and a receiver. By this means the heavy diplexer can be eliminated. As the antennas must be located on the back of the attachk-case lid, the MSA element is chosen as the best fit antenna. (iii) Satellite-borne antennas: Light weight, compactness, vibration-tolerable characteristics etc. are the major requirements for satellite-borne antennas. Although high gain in the L-, S- and C-band is desirable, the use of an aperture

Fig. 19.52 Operational area (Japan)

We shall describe a few types of planar antennas for satellite-TV reception, and a parabolic-cylinder reflector. These antennas have the following characteristics; Frequency range Polarisation Gain Axial ratio VSWR

: 11.7 - 12.0 GHz : right-hand circular polarisation : more than 33 dBi : less than 1 dB : less than 1.5

( a ) Circular-patch array: Fig. 19.53 shows a sub-array of singly fed circularly polarised patch elements [20]. In order to provide wide-bandwidth axial ratio and impedance characteristics, the paired elements, described in Chapter 4, form the fundamental element of the antenna.

1 1 74

Applications in mobile and satellite systems

Fig. 19.54 shows a circular-patch array. The antenna exhibits a 30' inclination of the beam direction (towards the front side of the board), it has 1024 elements (size of the antenna is 48 cm x 64 cm) and has about 33 dBi gain. In order to decrease the feeder loss, the main feeding line for four 256-element panels tY

I

I

Applications in mobile and satellite systems

1 1 15

( 6 ) Square-parch array: Fig. 1 9 . 5 6 ~shows the structure of the elements. In order to increase the bandwidth and to decrease the feeder loss of the patch element, the thickness of the substrate, which supports the patch and the feeder, was altered. In this case the substrate has a complex two-layered structure which results in increased bandwidth and efficiency of the antenna [21].

I

di=0.6h0, dzr0.8ho Fig. 19.53 Sub-array of singly fed patch elements

Fig. 19.55 Flat antenna (Courtesy: Yagi Antenna. Japan)

Fig. 19.54 Planar array of circular patch elements (Courtesy: Yagi Antenna, Japan)

utilises the rear-mounted rectangular waveguide. As shown in Fig. 19.55 the beam-tilt type can be set almost vertically. Thus, it has advantages such as being easily installed on a wall, and snow does not affect it.

Fig. 19.57 shows a square-patch planar array which has 512 patch elements (see Fig. 19.566). The main feeding line for the eight 64-element panels has a rear-mounted rectangular waveguide. The size of the antenna is 32 cm x 64 cm and its gain is 34 dBi. ( c ) Crank-rype tnicrostrip-line array: Fig. 19.58 shows the configuration of a crank-type microstrip-line antenna. This antenna, described in Chapter 13, is formed by crank-type undulation of two strip conductors of a microstrip line.

11 1 6

Applications in mobile and satellite systems

Applications in mobile and satellite systems fundamental element

11 77

dielectric substrate

feed

*x g r o u n d plate

s t r i p conductor

Fig. 19.58 Configuration of crank-type microstripline antenna

gap (height 1 m m )

Er

Fig. 19.56

= 2.17

-

A1 -4 circularly polarised microstrip patches

Circularly polarised patch element and sub-array a Patch element with two-layered structure b Sub-array (After Murata and Ohrnaru [Zl],@ 198 IEICE)

Fig. 19.57 Planar array of square patch elements (Courtesy: NHK, Japan)

Fig. 19.59 Planar array of microstripline antennas terminated in patch element (Courtesy: DX Antenna, Japan)

7 118

Applications in mobile and satellite systems

The two strip conductors are shifted by half their periods with respect to one another. In the Figure, the section surrounded by a dotted line shows the fundamental element of a travelling-wave array [22]. Fig. 19.59 shows a crank-type microstrip-line planar array, and Fig. 19.60 shows the same antenna array set in its actual position. This antenna, with 332 elements, has a gain of 33-34.2 dBi at a frequency of 11.7 - 12.0 GHz. The size of the antenna is 40cm x 60 cm, its thickness is 2.1 cm and its weight is 4.7 kg [23]. As shown in Fig. 19.59, an open end of each microstrip-line antenna terminates in a square-patch element. The power at the patch element is totally radiated in order to improve the efficiency of the antenna [24].

I

,

I

Applications in mobile a n d satellite systems

7 719

( e ) Circular-patch-slot array: Fig. 19.64 shows the structure of a circularpatch-slot array. This antenna consists of a ground plate, a patch and feedingline plate, a slot plate and a radome. The circularly polarised patch elements, with a single feeding point 1201and the feeding line, are printed on a plastic-film radome -radiation plate (slot and patch) feeding line plate ground plate

/ Fig. 19.61 Structure of rectangular-slot array

feeder

slot

patch

Fig. 19.60 Actual position of planar antenna (Courtesy: DX Antenna, Japan)

(d) Rectangular-slot array: Fig. 19.61 shows the structure of a rectangularslot array. This antenna consists of a ground plate, a feeding-line plate, a radiation plate and a radome. Each plate is supported by a honeycomb-foam spacer in order to reduce the feeder loss. The radiating element consists of a rectangular slot with a patch, and it operates by electromagnetical coupling to the feeding line. The feeding line and radiating elements are printed on a film substrate as shown in Fig. 19.62. The fundamental element of this antenna seems to be complementary to the square-patch element with the slot open on its surface. Fig. 19.63 shows a rectangular-slot planar array. This antenna with 512 elements has a gain of 35 dBi. The size of the antenna is 36 cm x 72 cm, its thickness 1.7 cm and its weight is 6 kg.

Fig. 19.62 Mask of sub-array a Feeding-line plate b Rad~ationplate

substrate. The substrate is covered with two sheets of shield board. Both the upper and lower board are at a distance of 1 mm from the substrate, with air between. The feeding line has the form of a suspended line system having low loss. The circular-patch element radiates through a circular slot open on the upper board.

1720

.

Applications in mobile and satellite systems

Applications in mobile and satellite systems

Fig. 19.65 shows a scaled-down mask of the patch elements and the slots. Fig. 19.66 shows a circular-patch-slot planar array. The main beam direction of this antenna is inclined at 10' to the front board. With 476 elements it has a gain of 34.1 dBi. The size of the antenna is 42 cm x 50.4 cm, its thickness 2.2 cm and its weight is 4.2 kg.

~atch

feeder

slot

(b) Fig. 19.65

Mask of sub-array a Feeding line with patches plate b Slot plate

Fig. 19.63 Planar array of rectangular-slot elements (Courtesy: Matsushita Electric Works, Japan)

n

radome slot plate

p a t c h and f e e d i n g line plate ground p l a t e

/ Fig. 19.64 Structure of circular-patch-slot array

(f) Parabolic-cylinder rejector: Fig. 19.67 shows a parabolic-cylinder reflector antenna. It is an example of the microstrip-line antenna application. The antenna utilises a side-looking circularly polarised microstrip-line antenna [25] on the line-source feed of the parabolic-cylinder reflector. The reflector can be

&,'

7 -

Fig. 19.66 Planar array of orcular-patch-slot elements (Courtesy Sony, Japan)

1121

1122

Applications in mobile and satellite systems parabolic-cylinder reflector

Applications in mobile and satellite systems

1123

installed in the vertical position because the direction of line-source feed is inclined. Consequently, it has advantages such as ease of installation on a wall and ;now does not affect it.

line-source feed (side-looking microstrip line antenna) Fig. 19.67

Configuration of parabolic-cylinder reflector-antenna

Fig. 9.69

Fig. 19.68 Parabolic-cylinder reflector with side-looking line-source feed (Courtesy: DX Antenna, Japan)

GPS microstrip antenna (Courtesy: Toyo Communication Equipment Co. Ltd., Japan)

Fig. 19.68 shows an experimental antenna. It has a reflector of :size 60 cm x 70 cm, the size of line-source feed is 4 x 42 cm, and the gain at 12 GHz is 34 dBi. The axial ratio is 0.8 dB and the VSWR is less than 1.5.

1124

Applications in mobile and satellite systems

iI

Applications in mobile and satellite systems

I

19.3.3. E a r t h stations I

( a ) Wide-heam antennas

1125

Fig. 19.72 shows the vertical radiation pattern. Although the gain near the horizontal direct~onis less than -5 dBi, the low-noise amplifier provides enough gain to receive signals in this direction.

(i) G l o b a l positioning system: Microstrip antennas are being developed for automobile navigation using the NAVSTAR satellite global positioning system (GPS). They are designed to be installed on the roof of an automobile. The antenna of a GPS receiver presents characteristics little different from those of most satellite systems. Hemispherical beamwidth and right-hand circular polarisation are required to receive signals from NAVSTAR satellites anywhere in the sky. Fig. 19.69 shows a microstrip antenna fed by two feeds from the bottom, where the two feed voltages are of equal magnitude and 90" out of phase. In the frequency range 1574-1577 MHz, the axial ratio is less than 2 dB in the boresight direction and the gain is greater than -3 dBi in the direction between 6.5' and 90" above the horizontal plane. The vertical radiation pattern is shown in Fig. 19.70.

Fig. 19.70 Vertical radiation pattern (Courtesy: Toyo Communication Equipment Co. Ltd., Japan)

Fig. 19.71 shows another GPS microstrip antenna viewed from the top and the bottom. The antenna is fed at the two points from the bottom, with feeds of equal amplitude and 90' out of phase. The thickness of the antenna is 1.6 mm. In the frequency range 1573 - 1577 MHz, the axial ratio is less than 1 dB and the gain is 5.5 dBi, both in the boresight direction.

Fig. 19.71

GPS microstr~pantenna (Courtesy: Toyota Central Research Laboratory, Japan)

( i i ) Transportable earth station: A hand-held message-communication terminal (HMCT), shown in Fig. 19.73 for a very small earth station, can transmit and receive messages of 20 - 30 characters via geostationary Engineering Test

1726

Applications in mobile and satellite systems

Applications in mobile and satellite systems

7 127

Satellite - Five (ETS-V) at 150' east 1261. The HMCT is contained in an attach6 case. On the lid are stuck very thin and light circular-patch antennas as shown in Fig. 19.74, and they are left-hand circularly polarised. The lid is opened and placed to face the satellite at a suitable angle to communicate with a fixed earth station. Each antenna is used, respectively, for transmitting (1645 MHz) and receiving (1543 MHz). The advantages of this configuration are that each antenna can be designed independently to maximise its efficiency, and a diplexer, which is usually heavy, is unnecessary. The gain and axial ratio of each antenna in the boresight direction are about 7 dBi and 2.5 dBi, respectively.

Fig. 19.72 Vertical radiation pattern (Courtesy: Toyota Central Research Laboratory, Japan)

Fig. 19.74 Circular microstrip antennas for the HMCT (@ 1988 IEEE)

( b ) Conical-beam antennas: T o create a low G/T and low-cost antenna for land-mobile and maritime satellite communications services, conical-beam antennas are required because there is no need for tracking. For this requirement, three types of circularly polarised microstrip antennas with a conical baam have been developed: (i) six-element circular array, (ii) higher-mode microstrip antenna and (iii) circular array of strips and slots.

a '' Fig. 19.73 Schematic view of the HMCT (@ 1988 IEEE)

( i ) Six-element circular array: A conical-beam microstrip array which is fabricated in the S-band and radiates circularly polarised waves is shown in Fig. 19.75 [27]. The antenna is a six-element circular array, and each pair, located symmetrically with respect to the array centre, is fed out of phase. Therefore the antenna has radiation null at the boresight, and hence a conical beam. The radiation pattern is calculated using the following equation:

7 728

Applications in mobile and satellite systems

I

I

Applications in mobile and satellite systems

I

1129

where g(%,4-$,) is the element pattern, k , is the propagation constant in free space, and e, and e, are the vectors of the radiation and element position, respectively, and are given as: e,

=

(sin Q cos 4 , sin % sin 4 , cos 8)

(19.2)

e,

=

(d cos $, d sin $, 0)

(19.3)

Here, the variable d represents the radius of the circular array, and angular position of nth element, given as:

I//,, is the

For simplicity of feeding, elliptical patches with a single feed which can radiate circularly polarised waves are used. 0.9 dBi at 30" from the The measured gain of the fabricated antenna is 6.6 vertical axis. The measured axial ratio is less than 2.5 dB in the same direction. The measured radiation patterns are shown in Fig. 19.76. (ii) Higher-mode microstrip antenna: A higher-mode microstrip antenna can be designed to have a conical beam. In the case of the TM,,,-mode microstrip antenna, circular polarisation can be obtained by exciting the patch with two feeds which are 90" out of phase and displaced 45" and 135" apart. For the purposes of mobile communication services, the earth-station antennas must have broadband characteristics.

Fig. 19.75 Outer view of conical-beam microstrip array (@ 19 8 8 IEICE)

tic element Excitation element Fig. 19.77 Configuration of conical-beam broadband microstrip antenna

Fig. 19.76

Measured radiation patterns of conical-beam microstrip array (circular polarisation) (@ 1 9 8 8 IEICE)

(01 9 8 8 IEICE)

A circularly polarised broadband microstrip antenna with a conical beam is shown in Fig. 19.77 [28]. This antenna is a TM,,,-mode microstrip antenna with a parasitic element which is placed in front of the excitation element. The parasitic element is used to broaden the usable frequency band. The frequency dependence of VSWR with and without a parasitic element is shown in Fig. 19.78. The parasitic element increases the bandwidth more than

7 730

Applications in mobile and satellite systems

.

,

2 5 1 p 1 a l f l l ~1 ,,

,96

I

,

1 1.04 Normal lzed frequency

Applications in mobile and satellite systems

1131

1

Fig. 19.78 Frequency dependence of measured VSWR with and without parasitic element (@ 1988 IEICE)

radiation pattern

0

Fig. 19.79 Measured radiation patterns of conical-beam broadband microstrip antenna (circular polarisation) (@ 1988 IEICE)

8=3 5-

___---- ---------------- --------------_-8=45' -2 -

-1

strip dipole

/ ref lector

\

p I ane

subst r a t e

Fig. 19.80 Configuration of the circular array (Courtesy: J.P. Daniel, University of Rennes; and Koichi lto, Chiba University) (Windows and feed network are not shown)

Fig. 19.81 Calculated co-polar radiation patterns and axial ratios (Courtesy: J.P. Daniel, University of Rennes; and Koichi Ito, Chiba University) a Vertical plane -4 = 0' plane - - - 4 = Wplane b Conical-cut plane -0 = 3 5 plane - - - 0 = 4 5 plane

1732

Applications in mobile and satellite systems

six times. The measured directive gain of the fabricated antenna is 6.5 dBi in the frequency band of 8%. The measured radiation patterns are shown in Fig. 19.79. (iii) Circular arra.v of strips and slofs: The third type of conical-beam antenna with circular polarisation can be realised by modifying a circularly polarised printed array composed of strip dipoles and slots [29]. Fig. 19.80 shows an example of a circular array consisting of four-pair strip dipoles and slots. Windows, not shown in the Figure, are placed in the ground plane to increase the gain and bandwidth of the strip dipoles [29]. The radiating elements are arranged radially and fed by an appropriate microstrip feed network. A substrate with high dielectric constant should be used to reduce the antenna diameter. Fig. 19.81 shows calculated results of co-polar radiation patterns and axial ratios for a four-pair array with a larger reflector. The frequency was 2.5 GHz and the diameter and height of the antenna were about 10 cm and 3 cm, respectively. The axial ratio was less than 2 dB over most of the hemisphere. The ripples of both the radiation pattern and the axial ratio in the conical-cut planes were less than I dB.

Applications in mobile and satellite systems

1133

as shown in Fig. 19.83~.The switching circuit is composed of two SP-3T switches and one DP-DT switch. Each radiator is electronically switched one by one through a control which compares its received power level with that of the

Array Element

A

(a) C o o r d i n a t e S y s t e m

Fig. 19.82 Outer view of six-element switched-element spherical array (@ 1988 IEE)

( c ) Spherical arrays ( i ) six-element switched-element spherical array: An outer view of six-element switched-element spherical array, which is fabricated in the L-band and radiates circularly polarised waves, is shown in Fig. 19.82 [30]. It is 40 cm in diameter and 20 cm in height. This antenna comprises the radiator section, the switching circuit and the controller. The radiator section is composed of six circularly polarised elements. Each element is a circular microstrip antenna with a parasitic element for broadening the bandwidth, and is located on the limited sphere tilted at an angle a from the vertical axis (Z-axis)

( c ) 2-dimensional

radiation patterns

Fig. 19.83 Calculated two-dimensional radiation patterns of optimised six-element spherical array (@ 1988 IEE)

adjacent radiators. It is postulated that the coverage area of the antenna is between B,, - AB, and Oo+ AO, from the vertical axis and omni-directional in the horizontal plane, as shown in Fig. 19.83~.

Applications in mobile and satellite systems

Applications in mobile and satellite systems

1134

The radiation pattern is calculated from the following equation:

1 135

4

where, ko is the propagation constant in free space, and JI, is the phase of the nth element. e, and e, are the vectors of the radiation and element position, respectively, and are given as

4, sin 0 sin 4, cos 0) a (sin ct cos p,, sin a sin fin, cos a)

e, = (sin 0 cos

(19.6)

ep =

(19.7)

Here, the variable a represents the radius of the spherical array. g(l, p) is the radiation pattern of the array elements. Assuming the use of a broadband microstrip antenna, g(l, p) can be approximated by the following equation: The relation between 0, cos l =

4 and 1 is therefore given as follows:

(er .ep) -

lerllepl The calculated 2-dimensional radiation patterns of an optimised six-element array antenna are shown in Fig. 19.83. The angle 0 from the antenna vertical axis is indicated by the distance from the origin, and the angle 4 rotated about the vertical axis is indicated by the angle from the horizontal axis. The six radiators are located at a position a = 44" as shown in Fig. 19.83. The solid and dotted curves in Fig. 19.83 indicate the contour lines in which the directive gain for each beam is 7 and 8 dBi, respectively. It can be seen in Fig. 19.83 that the minimum coverage gain is 7 dBi when the coverage area is between 40' - 20' 20". and 40" The measured directive gain of the fabricated array is more than 7 dBi for a coverage area of within 20"-60" from the vertical axis and a frequency band of 8%. The peak gain is 8.5 0.3 dBi given the same frequency band. The measured axial ratio is less than 3 dB and the measured VSWR is less than 1.4. The total insertion loss for the switching circuit is less than 1.6 dB. Therefore, actual coverage gain can be more than 5.4 dBi.

Fig. 19.84 Configuration of 86-element spherical array (Courtesy: KDD, Japan)

Antenna

-

+

+

(ii) 86-element spherical array: The configuration of an 86-element spherical array is shown in Fig. 19.84 [31]. This array is composed of 86 microstrip radiators, and the sub-array, which is composed of six or seven radiators, is switched one by one. The coverage gain of this antenna is more than 12 dBi within 115' from the vertical axis. The configuration of feeder section is shown in Fig. 19.85. The active elements are used in order to provide higher G/T. The calculated radiation patterns of an 86-element spherical array are shown in Fig. 19.86.

8x6 Switch Matrix

611

Combiner

/

Group #8

Fig. 19.85 Configuration of feeder section of 86-element spherical array (Courtesy: KDD, Japan)

1136

Applications in mobile and satellite systems

Applications in mobile and satellite systems

( d ) Sector-beam array: The sector-beam array is used for shipborne antennas [32]. The outer view of the sector-beam array, which is fabricated in the L-band and radiates circularly polarised waves, is shown in Fig. 19.87. The size of the array is 1000 mm x 1200 mm. The array is composed of 48 circular microstrip discs. This antenna has a 40" sector beam in the elevation plane. The measured radiation pattern of the fabricated antenna is shown in Fig. 19.88. The half-power beamwidth is less than 39" in the vertical-plane and less than 20" in the horizontal-plane. The sidelobe level is lower than -25 dB, the axial ratio is less than 1.5 dB and the measured gain of the antenna is more than 16 dBi.

Fig. 19.87 Outer view of sector-beam array (@ 1988 I EICE)

Fig. 19.86 Calculated radiation patterns of 86-element spherical array (Courtesy: KDD, Japan)

( e ) Phased arrays (i) Slot antenna: The airborne antenna shown in Fig.19.89 is a 16-element cross-slot antenna (XSA) developed for satellite communications at L-band [33, 341. The element spacing is 97 mm and its volume is about 560 x 560 x 20 mm. Fig.19.90 shows the configuration of the XSA element. It is called a cavitybacked cross-slot antenna and is fed with equal amplitude and phase at the two points shown in Fig.19.90 in order to get wider-band impedance matching characteristics compared with a centre-fed slot. The two perpendicular slots are fed with a 90' phase difference through hybrid circuits to obtain right-hand circular polarisation. The length and width of the slots are about 112 mm and 5 mm, respectively, and the volume of the cavity is about 80 x 20 x 20 mm.

Azimuth Angle

(')

Elevation Angle

Fig. 19.88 Radiation patterns of sector-beam array (@ 1988 IEICE) I

(')

7 137

1738

Applications in mobile and satellite systems

Applications in mobile and satellite systems

1139

Beam scanning is performed by controlling 4-bit variable phase shifters attached to each antenna element. Fig.19.91 shows the patterns at 1.6465 and 1.545 GHt. In this Figure, there is a slight difference between the beam direction to scan and the actual beam direction. The boresight gain is 15.7 dBi.

I I

I

I

slot

feed Lircuit

I

dielectric

I

I

I

metal

Fig. 19.90 Element configuration (@ 1988 IEE)

Fig. 19.89 Cross-slot antenna (@ 1988

IEE)

(ii) Patch antenna: The airborne antennas shown in Fig.19.92 is a 3 x 3element microstrip antenna (MSA) developed for satellite communications at L-band [33, 341. The element spacing is 94 mm (about half a wavelength at 1.6113 GHz) and its antenna volume is about 300 x 300 x 10 mm. Fig.19.93 illustrates the configuration of an MSA element. This is a newly developed two-layer patch antenna. Glass-microfibre-reinforced PTFE with a dielectric constant of 2.3 (thickness = 3.2 mm) is used as a dielectric substrate because of its good temperature characteristics. The two-layer MSA is adopted in which the upper and lower parts are used for transmissin (16465 GHz) and reception (1.545 GHz), respectively. Each layer is independently fed at two points with a 90' phase difference to obtain right-hand circular polarisation. The upper antenna is a conventional circular MSA and is used for transmission, while the lower one is a circular MSA with an electric shielding ring to separate

1140

Applications in mobile and satellite systems

Applications in mobile and satellite systems

e ('1 b

Fig. 19.91 Antenna patterns (@ 1988 IEE) a Radiation b Reception

1$) X

Fig. 19.92 3

x 3-element microstrip antenna

(@ 1988 IEE)

1141

1 142

Applications in mobile and satellite systems

the lower from the upper MSA and to feed the upper MSA easily. The diameters of the upper and lower MSA and the shielding ring are about 66 mm, 84 and 27 mm, respectively. The distance from the centre to the feed points are about 10 mm and 20 mm for the upper and the lower MSA, respectively. Beam scanning is performed by controlling the 4-bit variable phase shifters attached to each antenna element. Fig.19.94 shows the antenna patterns of radiation (1.6465 GHz) and reception (1.545 GHz). In this Figure, there is a slight difference between the beam direction to scan and the actual beam direction. The boresight gain is 15.2 dBi.

Feed Point

(1.545 GHz) Feed Point

(1.6465 GHz)

Dielectric Substrate

I

Receive Port

\ Transmit Port

Fig. 19.93 Element configuration (@ 1988 I E E )

(iii) Sequential-array antenna: Japanese experimental domestic mobilesatellite communications, using Engineering Test Satellite-V (ETS-V) launched in 1987 [35], will provide high-quality links for ships and aircraft at L-band. For this purpose the antenna shown in Fig.19.95 has been developed [36]. It is mounted in the fairing of a Boeing 747 Jumbo Jet. Each of the two array panels consists of 2 x 8 microstrip circular patches, and only one of the array panels facing the satellite is used for communication. The beam can be scanned only in the horizontal plane. Thus each of eight 4-bit digital phase shifters is connected to two vertical elements, as shown in Fig.19.96. Each circular patch fed by two points is sequentially rotated and differentially phase-shifted [35]. In such a sequential array, perfect circular

Applications in mobile and satellite systems

1143

1144

Applications in mobile and satellite systems

polarisation is obtained at a boresight direction independently of the polarisation of elements, and the reflected waves returned to the input port cancel1 each other. For the rectangular sequential array shown in Fig.19.95 high cross-

995mm-4 sequential phased array (2x8)

substrate (6 = 2.8)

A

Applications in mobile and satellite systems

Table 19.4 Sequential phased-array characteristics

Frequency

1545-1548 MHz (transmitting) 1647-1 650 MHz (receiving)

Polarisation

left circular

Gain

12-14.5 dBi (beam scanning)

Bandwidth

8% (VSWR < 2)

Antenna element

circular patch antenna

Array type

2 x 8 element sequential phased array

Phase shifter

4 bits (digital)

Substrate

Teflon ( E , thickness

Volume

15 x 40 x 90cm3 18 kg

Weight

= =

2.6) 4mm

Fig. 19.95 Airborne phased array (@ 1988 IEEE)

sequential arravs

1

feed circuit

in fairing -1-

in fuselage I

~ w rDIV.: . Power divider

Fig. 19.96 Configuration of antenna systems (@ 1988 IEEE)

polarisation discrimination is obtained over a wide angle in the two principal planes, which is useful for reducing fading due to reflections from the sea surface. The characteristics of the array in Fig.19.95 are given in Table 19.4.

1 745

Fig. 19.97 Outer view of synthetic aperture radar (Courtesy: MELCO, Japan)

7 746

Applications in mobile and satellite systems

Applications in mobile and satellite systems

19.3.4 Satellite-borne antenna

( a ) Synthetic-aperture radar (SAR): A rectangular microstrip array is applied to a synthetic-aperture radar (SAR) [37]. The outer view and the configuration of this radar are shown in Figs.19.97 and 19.98, respectively. This antenna is composed of eight panels, the size of leach being 1390 mm x 2060 mm. Each panel has eight sub-arrays and each sub-array has 16 rectangular microstrip antennas, which radiate linearly polarised waves. The substrate is made of honeycomb foam, the dielectric constant being 1.14. The amplitude distribution of the array is uniform in the E-plane, and it is tapered in the H-plane so as to obtain -18 dB sidelobe level. The measured gain is more than 26 dBi in the 1.3 GHz band. The calculated two-dimensional radiation patterns are shown in Fig.19.99. The half-power beamwidth is less than 8.7' in the E-plane and less than 6.3' in the H-plane; the sidelobe level is lower than -12.7 dB in the E-plane and lower than - 17.9 dB in the H-plane.

U b . 1.3 9m

-$*k

1m

flexible

!microstrip

array coax. cab

cable

4

Iflcxlble coax. wave

joint

gu l do

Fig. 19.98 Configuration of synthetic-aperture radar (@ 1988 IEICE)

( b ) 19-element muliibeam array: The outer view of a 19-element multibeamarray antenna for a data-relay satellite is shown in Fig. 19.100 [38]. The antenna operates at 2.1 and 2.3 GHz. The receiving system employs a fixed multibeam antenna of 19 contiguous beams, while the transmitting system uses a singlebeam phased array; 12 radiating elements are shared by both transmission and reception, and the remaining seven elements are dedicated to reception. The sub-array of the 19-element array is composed of seven circular microstrip patches, as shown in Fig.19.101. To broaden the bandwidth, these patches are printed on a Nomex honeycomb substrate of 10 mm thickness. Each patch is excited at two points with 90' phase shift by the rear feeding circuit. The

1747

1148

Applications in mobile and satellite systems

Applications in mobile and satellite systems

7 749

microstrip antenna is arranged so that each patch has small notches to cancel the elliptically polarised components generated owing to the asymmetrical feed structure. The measured gain of this sub-array is more than 15.1 dBi at 2.1 GHz. The measured radiation patterns are shown in Fig.19.102.

Fig. 19.100 Outer view of 19-element multi-beam array (@ 1 988 IEICE)

Fig. 19.102 Radiation patterns of sub-array of 19-element multi-beam array (@ 1 988 1 EICE)

honey-comb-core substrate

19.4 References

2.2 h h:2.3GHz

I feeding circuit 1

Fig. 19.101 Structure of sub-array of 19-element multi-beam array (@ 1 9 8 8

IEICE)

I KURAMOTO, M., and SHINJI, M. (1986): 'Second generation mobile radio telephone system in Japan', IEEE Commun. Mag. 24, pp. 16-21 2 HORI, T., and NAKAJIMA, N. (1983): 'Sector-beam base station antenna for land mobile communication' Natl. Conv. Rec. IECE Japan 754 (in Japanese) 3 NAKAJIMA, N., NARA, T., KAMEO, S., ABE, H., and TAKAMATSU, Y. (1985):A major angle comer reflector antenna with 180" beam width'. Natl. Conv. Rec. IECE Japan 752 (in Japanese) 4 NAKAJIMA, N., and HORI, T. (1984): '900 MHz-band multibeam antenna using butler matrix', IECE Japan Technical Report, AP84-50 (in Japanese) 5 ITO, K., and SASAKI, S. (1988) 'A small printed antenna composed of slot and wide strip for indoor communication systems', IEEE Int. Antennas and Propagation Symp. pp. 716-719

1150

Applications in mobile and satellite systems

Applications in mobile and satellite systems

6 MISHIMA, H., and TAGA, T . (1982): 'Antenna and duplexer for new mobile radio unit', Rev. Elect. Commun. Labs NTT, 30, pp. 359-370 7 JASlK H, (1961): 'Antenna Engineering Handbook' (McGraw Hill, NY) 8 OHISHI, Y. (1983): 'Analysis of reactance-loaded annular slot antenna directivity performance'. Graduation Thesis, University of Tsukuba, Japan (in Japanese) 9 KONDO, M., SASAKI, S., MATSUMOTO, K., ABE, H., CHATANI, Y., FURUNO, T., and MANO, S. (1986): 'A train antenna for a leaky coaxial cable'. Natl. Conv. Rec. IECE Japan 618 (in Japanese) 10 YAMAMOTO, J. (1985): '900 MHz numeric pager' Nat. Conv. Rec. IECE Japan 2411 (in Japanese) 11 KUBOYAMA, H., el al. (1985): Post loaded microstrip antenna for pocket size equipment at UHF'. Int. Symp. on Antennas and Propagation, Japan, pp. 434-436 12 FUJIMOTO, K., er al. (1986): 'Small Antennas' (Research Studies Press, London). pp. 243-249 13 BABA, T. (1987): 'Analysis of reactance-loaded square microstrip antenna performance'. M.S.C. Thesis, University of Tsukuba, Japan, pp. 78-84 (in Japanese) 14 BABA, T. (1987): 'Analysis of reactance-loaded square microstrip antenna performance'. M.S.C. Thesis, University of Tsukuba, pp. 85-89 (in Japanese) 15 NISHIMURA, S., NAKANO, K., and MAKIMOTO, T. (1979): 'Franklin-type microstrip line antenna'. IEEE Int. Antennas and Propagation Symp. pp. 134-137 16 FUJII, K., and ISHIKAWA, H. (1984): 'Low sidelobe microstrip array antenna', Nat. Conv. Rec. 49, Optical and Electronics, IECE Japan (in Japanese) 17 HASEBE, N., and ONOE, M. (1984): 'Radar reflector with bidirectional communication capability'. IEEE Int. Antennas and Propagation Symp., pp. 788-791 18 HASEBE, N., er 01. (1985): 'Radar reflector with bidirectional communication capabaility', Trans IECE Japan, J66-B, pp. 1177-1 184 (in Japanese) 19 HARA, Y., and GOTO, N. (1984): 'An omnidirectional vertical shaped-beam three faced microstrip slot array antenna', IEEE Int. Antennas and Propagation Symp., pp. 527-530 20 HANEISHI, M. (1985): 'A circularly polarized SHF planar array composed of microstrip pairs-element', Int. Symp. on Antennas and Propagation, Japan, pp. 125-128 21 MURATA, T., and OHMARU, K. (1986): 'Characteristics of circularly polarized printed antenna with two layer structure'. IECE Japan Technical Report, AP86-101 (in Japanese) 22 NISHIMURA, S., SUGIO, Y., and MAKIMOTO, T. (1983): 'Crank-type circularly polarized microstrip line antenna'. IEEE Int. Antennas and Propagation Symp., pp. 162-165 23 WATANABE, T., FUJITA, T., and DEGUCHI, F. (1987): 'Microwave planar array antenna design'. ITE Japan Technical Report R E 8 7 4 (in Japanese) 24 NISHIMURA, S., NISHIGAKI, A., WATANABE, T., SUGIO, Y., and MAKIMOTO, T. (1987): 'Circularly polarized microstrip line antenna terminated by patch antenna'. IECE Japan Technical Report, AP86-124 (in Japanese) 25 NISHIMURA, S., SUGIO, Y., and MAKIMOTO, T. (1985): 'Side-looking circularly polarized microstrip line planar antenna', Int. Symp. on Antennas and Propagation, Japan, pp. 129-132 26 HASE, Y ., et al. (1987): 'Very low speed message communication system using hand-held earth station'. IEEE Int. Conf. on Communicatins, pp. 520-524 27 HORI, T., ITAMI, Y., and NAKAJIMA, N. (1982): 'Circularly polarized microstrip array antenna with conical beam'. Natl. Conv. Rec. IECE Japan 655 (in Japanese) 28 HORI, T., TERADA, N., and KAGOSHIMA, K. (1986): 'Circularly polarized broadband microstrip antenna radiating conical beam'. Natl. Conv. Rec. IECE Japan 637 (in Japanese) 29 ITO, K. (1987): 'Circularly polarized printed arrays composed of strip dipoles and slots', Microwave Jol, 30, pp. 143-153 30 HORI, T., TERADA, N., and KAGOSHIMA, K. (1987): 'Electronically steerable spherical array antenna for mobile earth station'. IEE Int. Antennas and Propagation Conf., pp. 55-58 31 SHIOKAWA, T., WATANABE, F., and NOMOTO, S. (1984): 'Spherical array antenna for

32

33

34 35 36 37

38

1 151

general mobi!e satellite communications', IECE Japan Technical Report, AP84-30 (in Japanese) OHMORI, S., MORIKAWA, H., MIYANO, N., SUZUKI, Y., and CHIBA, T., (1980): 'Circularly polarized sector-beam shipborne antenna', Nat. Conv. Rec. IECE Japan S1-4 (in Japanese) SHIOKAWA, T., er 01. (1986): 'Cross slot array antenna for aeronautical satellite communications', IECE Japan Technical Report, AP86-59, pp. 17-21 (in Japanese) YASUNAGA, M., el al. (1987): 'Phased array antennas for aeronautical satellite communications'. IEE lnt. Antennas and Propagation Conf., pp. 47-50 OHMORI, S. el al. (1986): 'Aircraft earth station for experimental mobile satellite system'. IEEE Int. Conf. on Communications, pp. 1392-1395 TESHIROGI, T., er al. (1986): 'Airborne phased array antenna for mobile satellite communications:. IEEE Int. Antennas and Propagation Symp., pp. 735-738 HISADA, Y., ITO, Y., AKAISHI, A,, IMURA, N., and ONO, M. (1983): 'The results of partial experimental manufacturing of syntheticaperture radar antenna', IECE Japan Technical Report, AP83-39 (in Japanese) TESHIROSI, T., CHUJO, W., AKAISHI, A,, and HIROSE, M. (1986): 'Multibeam array antenna for data relay satellite'. Trans. IECE Japan, J69-B, pp. 1441-1452 (in Japanese)

Chapter 20

Conical conformal microstrip tracking antenna P. Newham and G. Morris

20.1 Introduction This Chapter describes the design, construction and testing of a prototype monopulse tracking antenna that is realised as a thin microstrip/triplate structure conformal to the surface of a cone. The main application of such an antenna configuration is to provide gul'ded-weapon seeker antennas for high speed ( > Mach 2.5) missiles and shells where the pointed (high fineness) front ends make conventional antenna (reflector or flat plate) plus radome designs impracticable owing to severe radome aberration effects. The latter is due to the high angles of incidence with which the antenna must necessarily illuminate the radome, as well as radome-tip scattering and blockage. Other applications exist where conical, or near conical, geometries are found - there are obviously many possible aircraft sites, and the antenna configuration described should find applications here. In the context of guided weapons, tracking antennas are required for both narrow and broadband applications: narrow band for active and semi-active seekers and broadband for passive anti-radiation seekers. The design as discussed is narrow band, having a bandwidth of 10% centered at 10 GHz; techniques to extend the bandwidth to over 50% are discussed at the end of the Chapter. The antenna as described consists of microstrip radiators on the conical surface with an adjacent (underneath) triplate feed network. Emphasis is given in the chapter to the practical engineering problems that have been encountered and solved during the design and development programme.

-

20.2 Single patch element 20.2.1 Choice of array element The choice of a sutable printed array element is governed mainly by its performance in the endfire direction. The directivity of an antenna array in a particular

1 154

Conical conformal microstrip tracking antenna

direction is only as good as that of its constituent elements in that direction. Thus, for the conical array, a radiator with almost omnidirectional coverage in the plane containing the cone axis is required. The choice is essentially limited to either a half-wavelength rectangular patch element or its quarter-wavelength short-circuited version. Other alternatives, such as the slot or dipole, possess a natural null in their radiation patterns at endfire. Others, such as the V-antenna, with good directivity at endfire, are seriously degraded by the necessary presence of a ground-plane associated with the inner, but adjacent, conformal feeding circuitry. The effect here is to squint the pattern considerably from endfire. For several reasons the quarter-wavelength patch is seen to offer the best solution. In particular: (a) Its theoretical pattern is more omnidirectional than that of the halfwavelength patch. For example, in the E-plane at endfire (with a substrate of relative dielectric onstant E, = 2.45), the pattern drops to - 6 dB below peak, as against - 11 dB for the half-wavelength patch [I]. For the case of the 20' cone under consideration, the main interest is in the performance at 10' from endfire, i.e. along the cone axis. Here the values are -2 dB and -8 dB, respectively; and since the theoretical gains are 5 dBi and 7 dBi, respectively [2], the gain of the quarter-wavelength patch along the cone axis exceeds that of the halfwavelength patch by 4 dB. (b) The quarter-wavelength patch occupies approximately half the area of the half-wavelength patch. One particular drawback of the quarter-wavelength patch, however, is the difficulty in feeding it from microstripline, owing to the high input impedance present at its radiating edge - this is typically 240R. It becomes necessary to break into the patch via a notch in order to find a suitable impedance level. The design of the single patch element is now considered in detail. , 20.2.2 Choice of substrate Several factors govern the choice of substrate for the microstrip layer onto which the antenna arrays are printed. First and foremost is the requirement that the substrate must be capable of being formed into a truncated cone without physical damage, and preferably without changing its electrical properties. Secondly, the material should be low loss with a low relative dielectric constant. This is in order to maximise the available bandwidth of the patch element to allow for small performance differences between array elements owing to manufacturing tolerances. For this purpose the substrate should also be as thick as possible, but not so thick as to generate excessive surface-wave energy. The criterion adopted for the maximum thickness h is such that h < 0.071, for E, = 2.32 [3]; at 10 GHz this gives h < 2.1 mm. RTIDuroid 5880, manufactured by Rogers Corporation with E, = 2.2 and loss tangent tan 6 = 0.001, has been found to be a suitable material, using a standard thickness of 1.57 mm. Rogers provide valuable information on bending their Duroid products [4], and

1

I

i

Conical conformal microstrip tracking antenna

1 155

it is the randomness of the glass microfibres embedded in the PTFE base material that suppresses any tendency for the material to fracture under bending stresses. 20.2.3 Feeding the patch A patch antenna may be fed either from a microstrip line on the same substrate or via a probe extending through the ground plane. Probe feeding was rejected for the conical array application for two important reasons. First it would have entailed a combination of both the power division and hybrid tracking circuitry on the same triplate feed network. Owing to the limited space available on the triplate substrate, as will be evident from Section 20.4, this was not possible to achieve in practice. Secondly the additional probe inductance, associated with the thick antenna substrate, would also need to be matched within the limited space on the triplate. As mentioned in Section 20.2.1, the quarter-wavelength patch is difficult to feed via a microstrip line owing to the high input impedance at its radiating edge. In order to feed the patch at a suitable impedance level, it is necessary to break into the patch via a notch in the radiating edge. At frequencies below about 5-6 GHz, the size of a patch becomes large relative to the width of a typical microstrip feed line, which remains almost constant with frequency for a given impedance. In this case, the patch may be fed through its short-circuit plane with negligible effect on its performance [5]. However, at 10 GHz this is no longer possible unless a very narrow high-impedance feed line is used. Even at 100 R, the width of the line is comparable to that of the patch. For reasons which will become apparent later, the 100 R feed line was the most suitable means of feeding the patch, and for this reason the patch was fed through its radiating edge. Weinschel [6] has measured the impedance variation with the notch width ( s in Fig. 20.1) for a half-wavelength patch. From his graphs it is apparent that the measured impedance corresponds to that of a probe-fed patch when the notch width is nearly equal to the substrate thickness. The notch width for the patch design was thus fixed at 1.5 mm. 20.2.4 Theoretical design method The design of the quarter-wavelength patch is based on the procedure outlined in Reference 7, and considers the patch as a short-circuited length of resonant transmission line. Fig. 20.1 shows the geometry of the patch together with its equivalent circuit. Yo is the characteristic admittance of the microstrip (patch) transmission line. The feed point is located a distance x from the short-circuit plane and d from the radiating edge. The patch resonant length x + d is somewhat less than a quarter wavelength in the transmission line owing to the fringing field extension beyond the physical edge of the patch. This field extension is incorporated into the susceptive part of the aperture admittance Yo of the radiating edge, which is made up of a radiation conductance G, and the susceptance B,.

1156

Conical conformal rnicrostrip tracking antenna

Conical conformal microstrip tracking antenna

Looking into the right-hand side of the transmission line from the feed point, the admittance, assuming a lossless line, is given by Gh -

= G, (Yo - B, tan pd)

+

+

G, (B, Yo tan pd) tanpd (Yo - B, tan pd)' + Gi tan2 pd

yo

(20.1)

i

1157

The f sign in eqn. 20.3 is chosen according to whether the denominator is negative or positive. On evaluation, Podis then inserted into eqn. 20.2 to obtain B,,. Resonance occurs, of course, when the shunt susceptance to the left of the feed point cancels that to the right; i.e. when: - j Yocotp0X = - j B , , ,

Bi,, - B, Yo + (Y: - Gi - &) tan pd- B, Yo tan2 Dd (20.2) (Yo - B, tan fld)2 Gt tan2 j d YO where is the propagation constant at the frequency in question. Note that eqns.20.1 and 20.2 are in error in Reference 7.

+

short circuit plane

The patch resonant length x + d is thus obtained, together with the feed-point position relative to the short circuit plane. An expression for 2, = l/Y,, the characteristic impedance of the microstrip (patch) transmission line, has been taken to be [8]:

radiating edge

quarter wavelength patch

where murostrtp feed lfne

and

short circuit

transmission line model

I /

driving polnt

d

,$

/

where W = patch width h = substrate thickness t = conductor thickness E, = substrate relative dielectric constant The aperture conductance Gois taken to be [8]:

Fig. 20.1 Microstrip quarter-wavelengthpatch and its equivalent transmission-line model

The short circuit to the left of the feed point simply presents a shunt susceptance of value - j Yo cot px. To proceed, Gin is set equal to the desired driving-point admittance G,, at the centre frequency (P = Po), and eqn. 20.1 is then solved for d. This takes the form of a quadratic equation with solution:

where ko =

2n and Lo is the free space wavelength. 20

It should be noted that the expression for the aperture susceptance B, differs considerably between References 7 and 8. In Reference 7 the aperture fringing capacitance is given by:

1758

Conical conformal microstrip tracking antenna

where L is the patch resonant length. Then B, = jw,C', where w, is the resonant angular frequency. In Reference 8 B, is expressed in terms of the fringing field extension, AI:

Conical conformal microstrip tracking antenna

7 159

choice of 100 R input impedance is that a superior performance dual patch element - described in Section 20.3 - can be fed directly and symmetrically from a 50 Cl coaxial probe without the need for impedance transformers. Table 20.1 Single patch design at 70 GHz

where

Susceptance term

Width (mm)

Post and Stephenson [7] Bahl and Bhartia [8]

11.9 11.9

-

Length (mm)

Short-circuit to feed (mm) 50R l OOR

4.17 4.59

1.35 1.40

1.94 2.02

Both expressions have been examined experimentally and the results are discussed in Section 20.2.5. The width W of the patch is given by the following well-proven formula [8]:

Finally, it should be noted that it is, in practice, convenient to realise the short circuit at one end of the patch by using a grid of conducting pins, as shown in Fig. 20.4. However, this produces a residual inductance at the patch edge rather than the desired perfect short circuit, so that the patch will need to be shortened slightly. James et al. [9] provide an expression for the shift Alin the short-circuit plane, based on the equivalent circuit of an array of posts across a parallel-plate transmission line backed by an open circuit: Fig. 20.2 Measured return loss for alternative parch designs Aperture susceptance (from Reference 7) - - Aperture susceptance (from Reference 8)

-

where r = radius of each post, a = distance between posts, 1, = free-space wavelength; A1 is positive when the short circuit plane lies away from the patch and behind the grid. Eqns. 20.1 - 20.14 were incorporated into a patch design software package, requiring inputs of patch width, substrate thickness and dielectric constant, input impedance and resonant frequency, and producing the patch resonant length and feed position as output data.

20.2.5 Patch design Table 20.1 lists the computed patch dimensions for an input impedance of 100 R at a resonant frequency of 10 GHz. The choice of 100 R rather than the usual 50 R is twofold. First, the width of a 50 12 microstrip feed line on 1.57 mm thick RT/Duroid is 5.13 mm, which is close to 50% of the patch width, and hence an unacceptable choice of feed. On the other hand, the width of a 100 R line is 1.52 mm, and is thus suited to the patch dimensions. The second reason for the

The patch dimensions of Table 20.1 are given using both expressions for the aperture susceptance B, (eqns. 20.10 and 20.1 1) taken from References 7 and 8. Fig. 20.2 shows the measured return loss for two patches built to the two alternative designs. It is evident that the measured resonant frequency of 9.88 GHz for the patch designed using B, taken from Reference 7 is in better agreement with theory than that designed using Reference 8, which resonates at 9.08 GHz. The former patch was therefore taken as the design. However, the resonant frequency of the patch is still 120 MHz below the theoretical value. This problem was investigated further with the aid of liquid crystal diagnostic techniques. Liquid crystals of the cholesteric variety possess a molecular structure which enables them to exhibit colour changes over a narrow temperature band. As the temperature increases, the crystals reflect the spectral range of colours from red to blue over a temperature range dependent on the concentration of a dopant additive. This technique has been used to observe the electric field in the vicinity of the patch. The approach taken was to

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Conical conformal microstrip tracking antenna

Conical conformal microstrip tracking antenna

mount a commercially available sheet of liquid crystal material, sensitive to a temperature range around 35"C, onto a resistive card, and to place this card over the patch, which was radiating several watts of R F power at the resonant frequency. The resistive card is sensitive to the electric field component tangential to its surface and dissipates power as heat, which results in bands of colour in the liquid-crystal sheet dependent on the electric field strength. Fig. 20.3 shows the results of this test applied to the patch, and indicates a concentration

7 161

20.3 Dual patch element 20.3.1 Choice of design Endfire radiation may be further enhanced by constructing the basic array radiating element out of two quarter-wavelength patches phased for constructive interference in the endfire direction. Fig. 20.5 shows such an arrangement, in which the two patches are set 'face-to-face' and joined by a straight length of microstrip line. The feed point position has to be chosen to produce the required excitation phase of each patch. Using the 100 R input impedance patch design of the previous Section implies that the microstrip connecting line is of 100 R impedance, thus making for a 50 R termination at the element feed point. This dual patch element, with its 50 R feed point on a microstrip line, is eminently suitable for a through-substrate probe connection to an underside feeding network. The design of this element is now considered in detail.

Fig. 20.3 Liquid-crystal display showing coupling between patch and feed line, for patch resonant at 9.88 GHz

U loon

of the fringing field around the centre of the radiating aperture. Under normal conditions the dominant mode within the patch should yield a uniform electric field strength across the aperture. This concentration is therefore indicative of a coupling between the patch aperture and the microstrip feed line. This results in an extension of the fringing field, equivalent to an apparent lengthening of the patch resonant length and hence lowering the resonant frequency. By shortening the patch in the ratio of the measured to the desired resonant frequency, the patch was made to resonate at 10 GHz. Fig. 20.4 shows the final dimensions of the single patch element design.

microstrip Fig. 20.4

Final single patch design

Dimensions in rnm

20.3.2 Location of patch phase centre In order to produce the required beam at an angle of 10" to endfire, corresponding to the axis of the cone, it is necessary to know the location of the apparent phase centre of each patch of the dual patch element. This position is some

7 7 62

Conical conformal microstrip tracking antenna

Conical conformal microstrip tracking antenna

distance beyond the physical boundary of each patch, owing to the extent of the fringing field. It was assumed that this extension dl (eqn. 20.12) defined the postion of the phase centre, being exactly one quarter-wavelength in the dielectric from the patch short-circuit plane. This position is indicated in Fig. 20.5. Knowing the wavelength in the dielectric and the physical size of the patch from Table 20.1 it may be shown that A1 x 1.2 mm at 10 GHz.

m-

fi $-

forward d~rection

-- phasb

7163

relate to RTIDuroid 5880 substrate with E , = 2.2 and thickness 1.57 mm. VSWR measurements made on a prototype element, fed from below by a coaxial surface launcher, showed a shift in the resonance frequency to 9.6 GHz from the case of a single isolated patch. This was attributed to mutual coupling, and the original 10 GHz resonance could only be restored by empirically adjusting the notch depth of the patch closest to the feed probe. A reduction of approximately I mm was found to be optimum.

centre

0.9A element size

19. 5

elemenl feed point

-

mod~fied feed posilion

Fig. 20.5

Dual-patch element design Dimensions in mm; other patch dimensions as for Fig.20.4

20.3.3 Design and optimisation The distance between the patch phase centres was taken to be 0.9 wavelengths at 10 GHz. This value was chosen for several reasons. First it enables a more directive four-patch array to be constructed, if desired, by interleaving two dual patch elements with correct phasing, as shown in Fig. 20.6. The inter-patch spacing of 0.451 would thus be suitable for minimising the grating lobe structure in the endfire radiation pattern. If the size of a dual patch element were halved (to 0.451) then interleaving would not be possible in a four-patch array, and' more space would be required for the array. Fig. 20.6 contrasts these two alternative constructions. The four-patch array was not used in the final construction since the intention was only to investigate the performance of dual patch elements mounted on the conical surface. Secondly, mutual coupling between the two patches of the dual patch element at 0.9 wavelength spacing is less than at 0.45 wavelength, thus requiring only small changes to the original single patch design. Finally, the two nulls in the far field pattern for the dual patch element (clearly defined by the 0.9 wavelength spacing) enable an independent check to be made of the true phase centre positions. The feed-point position was chosen to phase the element at 10" to endfire with due regard being taken of the 180" phase difference inherent in the face-to-face array configuration. The dimensions are given in Fig. 20.5. These dimensions

3ci I

O.45h element size

Fig. 20.6 Comparison in overall width of four-patch array for different element size

w, < w2 Fig. 20.7 shows the measured far-field E-plane radiation pattern for the dual patch element. From the angular positions of the two nulls, an estimate was made of the actual phase centre position of each patch. This was found to be 1.4 mm from the physical boundary of each patch and is in close agreement with the 1.2 mm prediction of Section 20.3.2. The radiation pattern displays a slope beyond 60" from broadside and is attributable to the single patch element factor which tends to fall off as endfire is approached. Nevertheless, at 10" from endfire the fall off is only 3 dB below the peak level.

20.4 Hybrid feeding network 20.4.1 Overview The most efficient means of generating a tracking signal using four circum-

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Conical conformal microstrip tracking antenna

Conical conformal microstrip tracking antenna

ferentially mounted antenna elements is shown in Fig. 20.8 [lo]. Both sum and difference channels are generated by a combination of three 180" hybrid couplers, one 90" hybrid and phase-matched lines. It can be shown that each port of the 90" hybrid will provide a progressive 360" phase shift around the cone circumerence, with opposite sign for each port. This corresponds to a circularly polarised sum channel along the cone axis, with opposite hand of polarisation

antennas positioned at 90' mtervals around c~rcumference

-element

1 A channel

polor~~tion perpendicularto cone surface

I channel

0. I phase (0). A phase Fig. 20.8 Schematic of monopulse tracking feed network hybrid element

elevalion angle.deg

Fig. 20.7 Measured E-plane radiation pattern of dual-patch element

for each of the two ports, provided the other port is well matched. One port of the first 180° hybrid will generate equi-phased signals at each antenna element. In this case a difference channel is formed which is sensitive only to horizontal polarisation in the horizontal plane, and vertical polarisation in the vertical plane. The second port generates alternate 0°, 180°, 0°, 180" phasing around the cone circumference. This is a difference channel sensitive to vertical polarisation in the horizontal plane and horizontal polarisation in the vertical plane. With the addition of one further 90" hybrid in front of the first 180" hybrid, these two

1 165

antenna feed port

substrate 'periphery

A channels

Fig. 20.9 Schematic of triplate feeding network

9

channels

1 7 66

Conical conformal microstrip tracking antenna

Conical conformal microstrip tracking antenna

modes can be generated in phase quadrature, resulting in a circularly polarised difference channel. This last refinement has not been adopted in the current design. A monolithic version of the hybrid feeding network requires that the antenna elements be situated within the confines of the circuit itself in order to avoid the crossing of lines. This can be most easily achieved by placing the complete feeding network on a triplate layer beneath the antenna substrate and joining the two electrically by coaxial probes. A schematic arrangement of this circuit is shown in Fig. 20.9, where each hybrid is represented in block form. The physical implementation of this arrangement is complicated by the need to mount the assembly on the surface of a cone. The procedure undertaken was to design the circuit on an opened-out section of the cone, using tracks of variable curvature dependent on their distance from the cone apex. The triplate substrate components have been chosen again to be RT/Duroid 5880 with thickness 0.79 mm. The resulting triplate is therefore of the same thickness as the antenna substrate, and hence uses the same bending procedure. The main track impedance was chosen to be 50 0,since the corresponding track width of 1.21 mm is well suited to the limited available space, as well as being able to be fed directly from standard SMA edge connectors. A further advantage is in the fact that the antenna elements can be fed directly from 50 Q, as mentioned in Section 20.3.1. The following Sections deal with the design of each circuit component. 20.4.2 Hybrid designs The conventional narrow-band 90" hybrid coupler is essentially a four-port device comprising four arms, each of length one quarter-wavelength at midband. Two configurations are shown schematically in Fig. 20.10 for the case of 50 R output lines. The two configurations are, in effect, identical. However, the second configuration is more suited to our purposes since it comprises, essentially, two continuous 50 R tracks joined by two parallel arms of impedance 5 0 1 4 = 35.35 Q. The operation of the coupler is to split a signal entering at port 1 into two equal output signals at ports 2 and 4, but with a 90" difference in phase. Port 3 is loaded with its characteristic impedance. The device is totally symmetric in that port 3 could be used as the input port with port 1 loaded. Implementation of the 90" hybrid in triplate is complicated by the effect of the junctions on reference plane positions. Ifjunction effects were absent, each arm of the hybrid would be exactly one quarter-wavelength in length and the complete device would be square. However, each corner of the hybrid is actually a T-junction, and may be represented as shown in Fig. 20.1 1 for the general case of series arm impedance Z,, and shunt arm impedance Z,,, with corresponding track widths W, and W2.The reference plane for each track is displaced from the geometric centre by an amount dl and 4 , respectively. Consequently, the series arms of the hybrid are extended by an amount 2d, and the shunt arms by 2d2. Reference 11 provides design curves for these displacement factors in

4

-

in both cases

0

@ 1s

Fig. 20.10 Atternative 9V hybrid configurations

Fig. 20.11

T-junction in triplate

@ i @ "=soe

loaded

7 767

1 168

Conical conformal microstrip tracking antenna

Conical conformal microstrip tracking antenna

air-filled stripline, together with suggestions for the case when 8, > 1. For the triplate configuration defined, these values are calculated to be d, = 0.23 mm and d, = 0.87 mm. Fig. 20.12 shows the layout of the final theoretical 90" hybrid design operating at a mid-band frequency of 10 GHz. The 90" hybrid design may be simply converted into a 180' design by extending one of the output arms by one quarter wavelength. In this case the two output signals are either equi-phased or displaced by 180°, depending on which input port is energised.

1 769

The even and odd-mode characteristic impedances for coupled triplate lines are given by 94.15

( W/b

+ [ln2 + In (1 + tanh m/2b)]/n)

JE,{W/b

+ [In2 + In (1 + coth ns/2b)]/n)

ZOe

= Je.

2 ,

=

94.15

and 2;; = Z , Z ,

(20.16) (20.17)

Voltage coupling Cois given by

and CJb = - 20 logl0CO where s = distance between coupled lines W = width of each line b = triplate thickness

Fig. 20.12 Final SO' hybrid design Dimensions in mm

20.4.3 90" benak Several 90" bends are required in the triplate circuitry, and consequently a suitable design is required to minimise the bend VSWR. At the same time it is necessary to know the effect of each bend on the reference plane in order that the correct phasing can be applied to each antenna element. Fig. 20.13 shows a mitred bend in which the optimum mitre dimension a for minimum VSWR has been given in Reference 11 as a = 1.1 W for the triplate parameters under consideration. For a 50 R track, W = 1.21 mm; hence a = 1.33 mm. The electrical line extension associated with the bend is also given as I = 0.58 W = 0.7 mm.

Fig. 20.13 Mitredbend I= electrical length of bend between two reference planes

20.4.4 Minimum track distance The narrow confines of the triplate substrate required that tracks be brought close to each other. It is therefore necessary to know the minimum acceptable distance between neighbouring tracks in order to avoid excessive cross coupling. Howe [I21 provides formulae for the evaluation of cross-coupling, and these are surnmarised in eqns. 20.15 - 20.19.

For 50 R coupled lines in 1.57 mm triplate with E, = 2.2, it can be shown that, for s/b = 1, the coupling factor is -40 dB, and for s/b = 2 it is -66 dB. A minimum distance between tracks corresponding to s/b = 2 was chosen, corresponding to 5 mm between track centres.

Conical conformal microstrip tracking antenna

Conical conformal microstrip tracking antenna

rn~crostrlp

probe tab

50a tnplate track

feed track

7.62 rnm

cross-section

plan (in tr~plate)

Fig. 20.14 Feed-point termination

cone apex

1171

20.4.5 Feed-point terminations The triplate hybrid network is connected electrically to the antenna elements on the upper microstrip layer via four probes soldered to the track terminations. These probes possess a flat tab to enable a clean soldered joint to be made at each triplate junction. A typical track termination is shown in both plan and cross-section in Fig. 20.14. A discontinuity of this type in triplate, however, tends to generate parallel-plate waveguide modes which emanate from the probe and couple to adjacent tracks, degrading circuit performances. These modes may be suppressed by a grid of conducting pins surrounding the discontinuity. The grid design has been taken from the positions of the mode suppression screws in standard SMA surface-launch connectors. The grid is also shown in Fig. 20.14. 20.4.6 Track lengths The individual track lengths of the feeding network must be accurately calculated and realised in order to avoid any phase error at the antenna ports. The situation is complicated by the need to design these tracks on an opened-out section of a cone. For convenience and to facilitate the drawing of the circuit mask, the tracks were divided into two classes: radial and circumferential. These are shown in Fig. 20.15 together with the shape of the substrate. The angular width of the substate is given by the expression

Om,,

=

360 sin 0, degrees

(20.20)

where 0, is the semi-angle of the cone of which the substrate is a part. For the required 0, = lo0, Om, = 62.5'. The circumferential track is just an arc of a circle of radius r centered on the cone apex. Its length a, can be expressed in terms of its angular width AO: 7cr a = AO180

radial track

/ clrcurnferent~al track

Fig. 20.15 Types of triplate track on opened out conical surface

where A0 is in degrees The length of a radial track is simply its physical length along a radial line from the cone apex. This track classification is particularly useful in that all circumferential tracks are parallel and are always perpendicular to radial tracks, thus simplifying the design of 90" bends. The main design problem, however, is related to the hybrid couplers. The use of radial rather than parallel tracks results in unequal circumferential track lengths, as illustrated in Fig. 20.16, and thus introduces phase errors. The typical phase error, however, is only 1.3' at each hybrid, resulting in a maximum of 2.6' for each antenna port. These errors are negligible in comparison to that expected at the electrical connections between triplate and antenna elements, and can thus be safely ignored.

1 1 72

Conical conformal rnicrostrip tracking antenni,

Conical conformal microstrip tracking antenna

20.4.7 Overall design The hybrid network was designed for the cone (semi-angle 10' and length 300 mm) with the substrate extending to the base perimeter. The substrate width was taken to be 55 mm, which is the minimum possible to enable all circumferential tracks to be spaced apart by a minimum of 5 mm according to the criterion given in Section 20.4.4. These dimensions are indicated in Fig. 20.15. The circuit layout is shown in Fig. 20.17, where each track is represented by a line. Extra quarter-wavelength sections of track have been added to create 180' hybrids from 90" hybrids as required. All other tracks have been designed, with due regard to their radial distance from the cone apex, to ensure correct phase matching at each antenna port.

mode suppression grid circle

\

output pwt

cone apex

\substrate periphery

Fig. 20.17 Final hybrid-circuit layout

Fig. 20.16 Phase error at each hybrid

It is of interest to note the position of the first 90° hybrid in the difference channel. This position, although resulting in exceptionally long input tracks, gives the network an elegant symmetry and minimises the total number of bends in the tracks. On bending the triplate around the cone, it also results in all input ports being situated within the same region of the cone base.

antenna element

radius 47.32mm

20.5 Conical antenna array

The dual patch antenna elements are printed on a microstrip layer lying immediately above the triplate hybrid network to form the conical antenna array. As such, there is an inherent problem associated with the different radii of curvature of the two layers. It is necessary to ensure that, on assembly, each antenna-

trtplate track termmatson

Fig. 20.18

Geometry of triplatelmicrostri~interface

1 7 73

1 1 74

Conical conformal microstrip tracking antenna

Conical conformal microstrip tracking antenna

element feed point lies immediately above its associated triplate output port to enable the two to be joined electrically. Consider the situation as depicted in Fig. 20.18. It is assumed for the moment that both the microstrip and triplate layers terminate at the base of the cone and that the connecting probe is in position. From Fig. 20.17 it is known that the triplate track terminations are situated midway along the substrate, and thus 272.5 mm from the apex of the 20' cone of which the circuit is a part. The radius of the cone at this point is then 272.5 sin 10' = 47.32 mm. From the geometry it can then be shown that the antenna element feed point, which is at a height of 2.38 mm above the circuit, is situated cone aoex

7 175

20.6 Substrate fabrication 20.6.1 Overview There are several stages involved in the fabrication of the three substratelayers comprising the antenna array and feeding network. The procedure commences with the drawing of all the masks, corresponding to the two sides of each substrate layer, on a CAD computer-graphics terminal. The output, in the form of photoplots, are then reduced to the required scale via precision photographic reproduction. The resulting masks are used in the substrate etching process. The three substrates are then cut to the correct shapes. All necessary holes are then drilled and various sections are milled out. Finally the two triplate components are bonded together. At his point the substrates are ready for bending into the required shape, prior to final assembly and attachment of electrical connectors. 20.6.2 Mask drawing and preparation A standard CAD system was used to produce the masks. The main difficulty in drawing the feeding network was due to the fact that the majority of tracks are arcs of circles of large radius of curvature. This necessitated defining each curved track by a set of three points which could then be used by the CAD software to generate the curve passing through the points. By necessity, a rectangular co-ordinate system was required, and the origin was defined at the lowest point of the substrate periphery, denoted as '0' in Fig. 20.17. The rectangular co-ordinates of each point are easily calculated from its radial distance r from the cone apex and angle 0 from the central axis passing through the origin: y = 300 - r cos 0

x antenna element

Fig. 20.19

micrdstrip substrate outline

Layout of antenna array elements

on another coaxial 20" cone at a radius of 49.66 mm, corresponding to a distance of 286.0 mm from the apex. Thus the feed points of all four antenna elements on the opened-out microstrip substrate surface will lie on an arc of radius 286.0 rnm centered on the cone apex. This is depicted in Fig. 20.19, where the microstrip track of each element is oriented along the radius at that point to ensure that, in the final assembly, all elements lie along the generatrices of the cone. The base of the substrate was chosen to allow an 8 mm overlap by the triplate on final assembly to facilitate the attachment of edge connectors. The overall width of the microstrip substrate was taken to be 70 mm. This ensured a one wavelength ground plane extension beyond the forward patches in order to minimise edge diffraction effects. The antenna elements are situated at equal angular intervals on the substrate as shown in the Figure.

=

r sin 0

(20.22)

where 300 is the radial distance in millimeters from the substrate lower periphery to the cone apex. The substrate periphery was included in the mask to facilitate cutting to the correct shape. A second mask was drawn for the upper triplate ground plane comprising the outer substrate periphery and four small circular non-metallised regions opposite the antenna output ports. These regions prevent the probes from shortcircuiting to the ground plane and form a quasi-coaxial region with the probes, of approximately 50 C2 impedance. Outside the substrate periphery, each of the two masks was provided with four fiducial crosses at the corners to enable the two to be lined up accurately with each other during the etching process. A further mask was drawn, comprising only the outer substrate periphery, to define the shape of the lower triplate half. In a similar manner the two masks for the microstrip antenna substrate were drawn, one comprising the four antenna elements and the other containing the four circular non-metallised regions at the feed input positions. The antenna

1 176

Conical conformal microstrip tracking antenna

mask was drawn using four identical dual patch elements oriented at the angks shown in Fig. 20.19. All masks were drawn to a scale of 2: 1, and the resulting photoplots were then photographically reduced and printed in reverse on clear plastic film to form the final masks. 20.6.3 Etching

Etching involves the removal of copper cladding in a controlled manner in order to print the mask pattern onto the surface of a substrate. The process is standard in a well equippedlaboratory and will not be described here. It should, however, be emphasised that the alignment of the two masks defining both the triplate circuit pattern and its upper ground plane (as well as those of the antenna substrate) is crucial in order that the circular non-metallised regions in the ground plane are accurately positioned at the antenna feed ports. For this purpose holes were punched, centered on each of the four fiducial crosses on each mask. Four additional holes were drilled through the substrate, and the three layers were aligned by the use of dowel pins prior to etching. This process gives an alignment accuracy of 0.1 mm.

Conical conformal microstrip tracking antenna

1 177

of Duroid were prepared for filling the cut-outs at the track input points. The complete assembly is shown in Fig. 20.20. 20.6.5 Triplate bonding

Bonding of two substrates under high pressure and temperature, using an intermediate layer of thermoplastic dielectric film, is a well established procedure in microstrip circuit technology, and details are given in the Rogers' literature [4]. For the case of RT/Duroid. the surfaces are pre-etched to provide a key for the thermoplastic (Dupont FEP) film by immersion in a sodiumnaphthalene solution. Alignment of the two components was maintained during bonding by dowel pins passing through both the bolt holes and edge connector holes. A heated hydraulic press was used to provide the necessary pressure and temperature.

20.6.4 Substrate preparation

After etching, the substrates were cut to shape and drilled while still in their flat state. For the case of the upper microstrip layer, holes were drilled at marked positions on each patch to take the short-circuit grid of conducting pins. Additional holes, defined by the mask, were drilled through the substrate to take the bolts through which the antenna would eventually be attached to the cone. The position of the feed probe for each antenna element had been defined by a small circle of etched copper on the microstrip track, and this was accurately drilled to a diameter of 0.92 mm to take a standard OSSM probe. In a similar manner, the various holes in the upper triplate layer were drilled. These comprised: the antenna feed ports, the circular grid of mode-suppression screw holes (defined by the mask), bolt holes (aligned with those of the microstrip substrate) and two holes on either side of the track input points to take the triplate edge connectors. The two triplate halves were then brought together and the various hole positions were marked through to the lower substrate, including the positions of the track input points. The bolt and edge connector holes were then drilled as before. It is impossible to solder the antenna feed probes into position prior to bonding the triplate halves and subsequent bending. Consequently, in order to gain access to the track terminations, a circular hole centered on the output probe position and of 10 mm diameter was milled out at each of the four antenna feed points on the lower triplate half. In addition, a semicircular cut-out was milled at each track input point to enable the edge connectors to be attached. Four Duroid discs were punched out to fill the feed-probe holes, and were drilled to take mode-suppression screws. Finally small semicircular discs

Fig. 20.20 Substrate components

20.7 Forming the antenna 20.7.1 Bending the substrates

It is possible to bend RT/Duroid at room temperature. However, the large degree of springback imposes an excessive strain on the substrate when it is

1 1 78

Conical conformal microstrip tracking antenna

clamped in postion and may result in a fracture. It is necessary to first stressrelieve the substrate by passing it through a temperature cycle which exceeds the PTFE glass/rubber transition temperature of 130°C; beyond this temperature, stresses are minimised [4]. For this purpose, two conical aluminium mandrels were fabricated for bending both the triplate and microstrip layers. Each mandrel contained an inner depression for seating the substrate, and an outer depression to take a stainless-steel clamping band. In each case the substrate and band were bent slowly around the mandrel at room temperature and held in postion with studs. The assembly is shown in Fig.20.21~.The mandrel was then placed in an oven at 100°C in an inert atmosphere. The temperature cycle consisted of a warming-up period of one hour to 180°C, one hour at that temperature, and a one hour cooling-off period. Upon disassembly, no major faults were seen in either the dielectric or the copper ground plane, except for some very minor wrinkling in the copper. The smooth walls of both the mandrel and clamping band provided excellent surfaces against which the substrate could rest and thus avoid distortion. Any springback tendency for both substrates was found to be minimal.

a

Conical conformal rnicrostrip tracking antenna

into place on both the patch surfaces and the ground plane. These can be seen in Fig.20.216, which shows the microstrip layer in its final shape, prior to assembly.

b

the antenna substrate

c

the triplate (fully assembled)

the mandrel

Fig. 20.21 Bending the substrates

20.7.2 Attachment of components Once the substrates have been bent into shape, the various probes, pins and mode-suppression screws can be attached. For the upper microstrip layer, the short-circuit grids of pins were inserted into the patch elements and soldered

7 7 79

1180

Conical conformal microstrip tracking antenna

For the case of the triplate layer, the antenna feed probes were inserted through the access holes in the lower substrate and their tabs soldered into place on each track. Small relief channels were cut into the circular Duroid discs into which the soldered tabs could sit without creating an air gap, and the discs were pushed in place into the four access holes, ensuring that the mode-suppression screw holes lined up with those of the upper triplate half. The discs were held in position by the mode-suppression screws themselves. The countersunk screw heads were embedded into the upper ground plane to produce a uniformly smooth surface. Both the upper and lower ground planes around the screws were coated with a conducting silver paint to ensure good electrical continuity. In order that the probes simulate a coaxial line, it is essential that good electrical continuity exists between the upper triplate ground plane and that of the microstrip in the vicinity of the probes. It is very unlikely that this can be guaranteed when the two substrates are finally brought together because of the large surface areas in contact with each other. For this reason thin metallic shims, milled from the flanges of standard OSSM surface launchers, were inserted past the probes and bonded to the ground plane with conducting epoxy. The shims were bent slightly to conform to the shape of the triplate surface. The final triplate assembly is shown in Fig. 20.21~.

Conical conformal microstrip tracking antenna

7 18 7

feed holes in the microstriplines and the two units bolted together with nylon screws. Finally the probes were soldered into place and DC electrical continuity was checked between the exposed triplate track terminations and the patch surfaces. 20.7.3 Final assembly The cone itself was machined from aluminium. A de~ressionat the rear end allowed the triplate to seat properly while the upper microstrip layer could rest on the main body of the cone. The remaining bolt holes were used to attach the assembly to the cone using nylon screws. The free ends of the substrates were brought together and held in position with Duroid fishplates against the pressure of the residual springback. The final procedure involved the attachment of the triplate coaxial connectors. These were standard OSM in edge launchers. Curved shims were fabricated to interface between the flat connector flanges and the curved substrate surface. After soldering each centre tab to the exposed triplate track, the access cut-out was filled with the semicircular Duroid disc and the complete connector unit with shims was screwed into position. The final antenna assembly is shown in Fig. 20.22. 20.8 Antenna performance

Fig. 20.22

Final antenna assembly

On mating the triplate and microstrip substrates together, the shim surfaces were coated with a thin layer of conducting epoxy to ensure good electrical continuity between the substrates. The probes were then inserted through the

Electrical measurements have been carried out on the conical conformal antenna over a 1 GHz bandwidth centered at 10 GHz. Both sum and difference radiation patterns have been obtained from all four ports of the antenna using a linearly polarised source antenna. With reference to Fig. 20.8, the scan axis is taken to be the x-axis with the individual antenna elements oriented at 45' to this axis. In this way, both the difference-channel ports could be tested individu-' ally without needing to rotate the cone. From Section 20.4.1 it will be recalled that the two difference channels are sensitive to orthogonal linear polarisations; thus the equi-phased channel will receive horizontally (x-directed) polarised signals, whereas the alternate 0°, 180" channel will receive vertically @-directed) polarised signals. Measured radiation patterns at 9.5, 10.0 and 10.5 GHz are shown in Fig. 20.23 for the two sum channel ports and in Fig. 20.24 for the two difference ports. Fig. 20.25 shows the measured response in one sum channel to rotating linear polarisation at 10 GHz. Finally, Fig. 20.26 shows the measured antenna boresight gain matched to the linearly polarised source antenna for vertical @-directed) polarisation. The antenna-performance results of Fig. 20.23-20.26 require some detailed explanation, because, on careful consideration, many characteristics cannot, of course, be explained by recourse to conventional (planar) array behaviour. The subjects of grating lobe supression, axial ratio, gain and tracking slope are now

1 182

7 183

Conical conformal microstrip tracking antenna

Conical conformal microstrip tracking antenna

considered in more detail. This treatment is largely qualitative owing to the electromagnetic complexity of the problem and the bounds of this book. A detailed mathematical treatment of conformal array antennas may be found in References 13 and 14.

demand explanation. The most prominent feature is the lack of grating lobes in the sum channel for horizontal polarisation, whereas those for vertical polarisation are well developed. This phenomenon may be explained, most easily in the porl 1

- horizonlal polarisation

port 2 -vertical oolarisotion

port 2

port 1

m P

-301

-30

I

ri

-40

-20

9.5 GHz -20

0

-301 20

9.5 GHz

9.5 GHz

9.5 GHz

u

40 -40 -20 Azimuth anale (dea

0

20

-40

-20

0

20

40

40 -40 -20 Azimuth angle (deg. )

Or

m u

I 0

20

40 -40 -20 Azimuth angle (deg.) 0

0

20

0

20

40

0

20

40

-2 0

I -40

I -20

40

Or

-30

-40

20

0

10.0 GHz I

-20

0

20

40 0r

L

,

40 -40 -20 Azimuth angle (deg.) 0r

-10

-20

-30

B -2 0 I \ I \ I \ l

\ \ 10 5 GHz

\I -40

-20

0

20

40 -40 -20 Azimuth angle (deg.)

0

- vertical

-- horizontal

20

1

40

polarrsatlon

Fig. 20.23 Sum channel radiation patterns (measured)

20.8.1 Grating lobe suppression Although the sum and difference patterns are well defined over the frequency band in the angular region close to boresight, there are several features which

-30 -40

10.5 GHz -20

0

-3 0 20

40 -40 -20 Az~muthangle (deg.)

Fig. 20.24 Difference channel radiation patterns (measured)

transmit mode, by the difference in the fields radiated towards an observation point between a visible antenna element and one hidden by the presence of the cone. Use of GTD surface-field methods in the analysis of radiation from conical arrays is well documented [15] and only a summary need be given here. With reference to Fig. 20.27, each diametrically opposed pair of array ele-

1184

Conical conformal microstrip tracking antenna

Conical conformal microstrip tracking antenna

1 185

ments are equi-phased with respect to the observation point in the sum channel. The opposite pair, in phase quadrature, may be ignored in this explanation. Grating lobes will appear when the path difference between diametric elements at the observation point is an integral number of wavelengths. The cone diameter at the centre of the array elements is 110 mm, and therefore the horizontal distance between diametric pairs is 1 1 0 ~ = 4 78 mm. At 10 GHz the condition for grating lobes is that sin 0 = &Id = 30178 = 0.384; this corresponds to 0 = ) 22.5', and indeed corresponds exactly to the measured positions at 10 GHz for vertical polarisation. At 22.5' from boresight, one array element is in the lit region and is therefore sensitive to both vertical and horizontal polarisations. The diametrically opposed element, however, is in shadow. In this

iurface ray

- 40

-20

0

20

LO

I

A z ~ m u t hangle (degrees)

Fig. 20.25 Rotating linear sum pattern at 10 GHz (measured)

I

i1 1 I

Fig. 20.27 Rad~atlonfrom a h~ddenarray element on a conical surface

case a surface ray creeps around the cone on a geodesic with respect to the observation point, radiating tangentially as it proceeds. The ray that is eventually directed towards the observation point will radiate from the cone horizon as perceived by the observer. Now the magnetic field vector associated with the surface ray remains parallel to the cone surface over which it travels, and therefore the observer will perceive this vector as parallel to the cone horizon, which itself subtends a small angle to the horizontal at the 22.5" scan angle. This implies that the diffracted field is predominantly vertically polarised as seen at the observation point, and will thus contribute to the observed grating lobes seen in vertical polarisation, but not to horizontal polarisation. This further implies that the grating lobes in the vertical polarisation pattern are about 6 dB higher than the mean signal level at the same scan angle in the horizontal polarisation pattern. On normalising the co-polar peaks to each other in Fig. 20.23 this is seen to be indeed the case. 20.8.2 Axial ratio The second important feature requiring explanation is the difference in boresight amplitude in each sum channel between vertical and horizontal pol-

Fig. 20.26 Measured antenna boresight gain in sum channel for vertical polarisation

1 186

Conical conformal microstrip tracking antenna

Conical conformal microstrip tracking antenna

1187

arisations. The effect is reversed between the two ports, so that for one port the vertical component exceeds the horizontal by an average of 3.5 dB across the frequency band, whereas for the other port the reverse is the case. The effect is clearly visible in the response to rotating linear polarisation, as seen in Fig. 20.25. ~ , = c o s ( w t + 2~ * ~ )

E, ' C O S W ~

\

Thus the maximum amplitudes in the vertical and horizontal directions are given by:

and the ratio in decibels is

X

Fig. 20.28 Effect of phase error in the sum channel

For the opposite hand of circular polarisation the 2 factor changes sign and:

This feature may be explained if it is assumed that a constant phase error exists at the input to each antenna array element. This may be due to differing path lengths at the interface between the triplate and microstrip layers. Consider the situation depicted in Fig. 20.28 for the case of two adjacent elements in phase quadrature, each element polarised at 45' to the vertical. Let one antenna element possess a constant phase error 4 with respect to the other, both radiating at equal amplitude. The time-dependent electric field amplitudes for one hand of circular polarisation are then: Element 1 : El = coswt Element 2 : E2 = cos(wt

+ 4 + Z) X

The resultant component in the + y direction is then (ignoring constants):

Ey

= coswt

+ cos(wt + 4

X

and in the + x direction: E, = coswt - cos(wt

+ - 4 + -)2 X

(20.24)

=

- I0 log,,

r3

cot2

-

= -Rm,

This is equivalent to saying that the difference between vertical and horizontal polarisation is reversed between the two sum channels, as seen in the measured results. The average measured difference of 3.5 dB is then equivalent to an inherent phase error of 22.5'. It must be remembered, however, that this phase error is distributed around the four antenna elements in a random manner. It is therefore clear that the inherent phase error in each element is typically 5.5'.

20.8.3 Antenna gain The measured antenna boresight gain, shown in Fig. 20.26, depends to a great extent on the tilt angle of the polarisation ellipse, which in turn depends on the inherent element phase error as discussed above. As such, the measured am-

7 188

Conical conformal microstrip tracking antenna

plitude is somewhat irrelevant, and it is the shape of the response as a function of frequency which is of interest. The gain around 10 GHz exhibits a sinusoidal frequency dependence which drops off rapidly above 10.3 GHz. Two mechanisms are attributable to this shape. In the former case the element phase error is changing as a function of frequency, thus changing the tilt angle of the polarisation ellipse, resulting in a fluctuating vertical polarisation component. The latter effect is attributable to the bandwidth of the elements. With reference to Fig. 20.2, the single patch return loss increases to - 3 dB at 10.5 GHz. This implies that half the power is no longer radiated. The gain is therefore expected to drop by 3 dB from that at resonance. It can be seen in Fig. 20.26 that this is indeed the case.

Conical conformal microstrip tracking antenna

1 189

radius of the antenna substrate, resulting in a spacing of several wavelengths between adjacent elements. However, it is noted that the measured 12' coverage could be acceptable for many purposes.

20.8.4 Tracking slope Fig. 20.29 shows the tracking characteristics at band edges and centre extracted from the sum and difference patterns. The tracking parameter is defined as the ratio, in amplitude, of the difference signal to the sum signal, and is plotted as a function of scan angle for both vertical and horizontal sum channel patterns. It is important that the tracking slope remain constant over the angular region of interest in order that a single parameter at each frequency may be used to locate the angular position of a target. It is evident from the Figure that, for the conical conformal antenna, this is true over an angular width of about 12' across the frequency band; although some degradation is seen at 10.5 GHz. This angular width is totally dependent on the positions of the two main lobes in the difference channel, which are in turn dependent on the cone circumference at the antenna elements. The only means of increasing this coverage is to mount the elements closer to the cone apex. With the mechanical construction described in this Chapter this is not possible. The 12" angular coverage is thus a limitation of the present design, but may be acceptable for many purposes. 20.9 Conclusions and future developments This Chapter has described in detail the application of microstrip technology to a particularly demanding requirement - the fabrication of a conical microstrip tracking antenna. The antenna element design has centered on the need for acceptable endfire performance and a suitable solution has been described. The problem associated with the siting of the tracking circuitry has been solved by the use of an independent triplate feed network located beneath and adjacent to the printed antenna substrate. This, however, raises additional problems in the electrical interfacing of the two units when mounted in position on the surface of the cone. One possible technique has been described in detail. The antenna electrical performance has been measured and analysed, and suggestions have been given to explain some of the peculiarities and trends in the data. Angular tracking coverage is found to be somewhat limited owing to the minimum bend

X ----

(vertical)

X (horizontal)

Fig. 20.29

Tracking characteristics of conical conformal antenna (measured)

The development and fabrication of the antenna has shed light on the various engineering problems associated with the design of a cone-mounted system. In particular, the need for designing the antenna and feed circuitry on an opened-

1190

Conical conformal microstrip tracking antenna

out conical surface has emphasised the procedures necessary for non-linear track layouts. It is evident, however, that several enhancements to the design are possible in order to improve further the electrical performance and to facilitate easier manufacture; these are now briefly described. The antenna bandwidth, being a function of both the thickness and dielectric constant of the substrate, may be increased by increasing the former and decreasing the latter. However, the improvement is limited by the onset of higher order modes, which result in additional circuit inductance and degraded VSWR. The effect has been used to advantage in a novel procedure outlined by Griffin [16]. He uses the unwanted inductance, together with that of the probe feed, of a microstrip disc antenna to design an impedence-matching network in the triplate feed track. He reports impressive performance, using a thick, low dielectric constant (8, = 1.2) substrate, with a VSWR bandwidth of 20%. The technique is applicable to any probe-fed patch antenna. Increased antenna directivity at endfire is desirable to reduce the high sum channel grating lobes seen in Fig. 20.23. It can readily be shown that an eight element linear patch phased array will suppress all sidelobes in the forward hemisphere to below - 10 dB over the 20% bandwidth, provided the interelement spacing is less than 0.45 wavelengths. antenna elements printed on this layer antenna substrate (expanded foam) upper triplate (power divlsion and broad bonding) -lower tr~plate (tracking) Fig. 20.30 Cross-section through a broadband conformal antenna

A single triplate circuit containing the hybrid tracking network together with power-division and impedance-matching components is not feasible within the limited space available over the cone circumference. A more attractive solution is to share the circuitry between two triplate layers linked together electrically. By careful choice of track impedances, the two layers could be made extremely thin and bonded together as one unit before being bent into shape. The use of a thick low-permittivity foam as the antenna substrate for broadband performance means that the antenna elements cannot be printed onto such a surface. A possible solution would be to print the arrays onto a thin sheet of copper-clad Kapton or similar material, and then to bond this to the foam, which will have been pre-formed into conical segments and bonded to the triplate. The final antenna assembly would therefore comprise six substrate layers as shown in Fig. 20.30.

Conical conformal microstrip tracking antenna

1191

Acknowledgment

The authors wish to thank the directors of the Marconi Company Ltd. for permission to publish this chapter, which is an expanded version of a paper presented at the Military Microwaves 1986 Conference held at the Metropole Hotel, Brighton, England, 24th-26th June 1986.

20.10 References JOHNSON, R.C., and JASIK, H. (1961): Antenna engineering handbook, (McGraw Hill, NY, pp. 7-10) RUDGE, A.W., et al. (1986): Handbook of antenna design, (Peter Peregrinus) Section 7.4 JAMES, J.R., HALL, P.S., and WOOD C, (1981): Microstrip antenna, theory and design, (Peter Peregrinus) Deduced from Fig.3.16~ Mektron Circuit Systems Ltd. (1983): Product information-RTIDuroids; and private communication HALL, P.S., WOOD, C., and JAMES, J.R. (1981): Recent examples of conformal microstrip antenna arrays for aerospace applications. 'Antennas and Propagation'. IEE Conf. Publ. 195, Pt. 1, pp. 397-401 WEINSCHEL, H.D. (1979): Measurement of various microstrip parameters, Proc. Workshop on Printed Circuit Antenna Technology, New Mexico State University, pp. 2-1 POST, R.E., and STEPHENSON, D.T., (1981): The design of a microstrip antenna array for a UHF space telemetry link, IEEE Trans. AP-29, pp. 129-133 BAHL, LJ., and BHARTIA, P. (1980): Microstrip antennas (Artech House, London) Reference 3, Section 4.6 Reference 2, Section 12.6 MATTHAEI, G.L., YOUNG L., and JONES, E.M.T. (1964): Microwave filters, impedance matching networks and coupling structures (McGraw Hill, NY Section 5.07) HOWE, H. (1974): Stripline circuit design (Artech House, London) RIZK, M.S.A.S., MORRIS, G., and CLIPTON, P. (1985): Projected aperture synthesis method for the design of conformal array antennas. 'Antennas and Propagation' IEE Conf. Publ. 248, pp. 48-52 SHAPIRA, J., FELSEN, L.B., and HESSEL, A. (1974): Ray analysis of conformal antenna arrays, IEEE Trans, AP-22, pp. 49-63 Reference 2, Section 11.6 GRIFFIN, J.M. (1985): Broadband microstrip disc antenna for satellite communications, M.Phil./PhD Transfer Thesis, GEC Hirst Research Centre, Wembley, Middx.

Chapter 21

Microstrip field diagnostics P. G. Frayne

21.1 Introduction

In this Chapter we are concerned with the relatively undeveloped subjec of surface-field metrology for 'open' microstrip and other related 'open' plaiiar transmission structures. Early measurements on microstrip lines were aimed at determining the dispersive properties of the medium using a number of different techniques, some of which are listed below: (a) Measurements on open-circuited and short-circuited resonant microstrip

lines (6) Ring-resonator techniques

(c) Variation of phase shift of a line with frequency ( d ) Nodal-shift techniques None of these methods, however, provide much insight into the detailed field distributions that actually reside on the conductors. Liquid crystals have been employed to render mode patterns and regions of high electric field 'visible' to the unaided eye, but the spatial resolution and general applicability of the technique is very limited. The growing need for reduction in the size, weight and cost of millimetric guidance and radar equipments has stimulated the design of circuits with a much higher degree of component integration than is possible with the modular approach to circuit construction. With the growing complexity of circuit-integration techniques, both fault location and test procedures become increasingly difficult. The accessible R F input and output ports provide little information about the detailed internal operation of the system, and the conventional network analyser, much valued for the assessment of isolated modular components, is of limited use as a diagnostic for large-scale circuits. The use of a greater degree of component integration not only makes circuit evaluation difficult, but can also create severe problems owing to unwanted electrical coupling between components.

1194

Microstrip field diagnostics

Microstrip field diagnostics

21.2 Surface analytical techniques To the author's knowledge there have been at least two prior experimental investigations of possible surface diagnostic techniques for microstrip, namely the work of Dahele and Cullen [I] and also that of Ladbrooke [2]. The detailed plots of the near-field radiation pattern of a polyrod antenna obtained by Neumann [3, 41 are also of interest in the context of field-plotting techniques. In the work of Ladbrooke, a special jig was constructed which enabled the top microstrip conductor, defining the circuit pattern, to be moved independently of the ground plane and the 50R microstrip feed line. The ground plane contained a small disc probe 0.1 mm in diameter, separated from the surrounding region by an annular gap. The thin dielectric sheet which supported the microstrip circuit was pressed into contact with the ground plane and feed line. The probe disc was connected to the inner conductor of a miniature coaxial cable whilst the outer conductor was grounded. Connection of the microstrip feed and probe output signal to a vector network analyser enabled the circuit transmission (amplitude and phase) to be measured over a wide frequency range. The measurements presented in Ladbrooke's paper appear to be restricted to longitudinal distributions on open-circuited microstriplines. Evidence for the excitation of surface waves beyond the edge of the open microstrip termination was discussed in a later paper. It is interesting to note that a distortion of the standing-wave pattern similar to that discussed in the books by Ginzton [5] and MOI'-ornery [61. due to probe reactance, was actually observed, but accredited by Ladbruoke to a mismatch of the feed line. The investigation by Dahele and Cullen was more concerned with evaluating, the response of a small coaxial probe with an extended inner conductor to a calculable RF electric-field distribution produced by a boxed cylindrical conductor. A wire, 1.6 mm in diameter was supported along the axis of wide rebate (of rectangular section) cut in a metal plate. The rebate was closed off by a movable plate which also supported the coaxial probe. The inner probe conductor protruded about 2mm into the waveguide region and the probe tip was 6.4 mm from the surface of the wire. The experimentally determined VSWR pattern agreed well with theoretical predictions, and the experiment was subsequently repeated after replacing the cylindrical wire by a flat microstrip line. In a more recent paper accredited to Schwarz and Turner [7], a co-planar waveguide probe is discussed which uses a miniature bismuth bolometer for the direct detection of the microwave signal at the probe tip. Although the bolometer can be made very small, it suffers from the disadvantages of being restricted to scalar measurements and also the need to be specially constructed for each width of co-planar waveguide under investigation. Co-planar waveguide probes have been investigated in our own laboratory where a beam-lead Schottky barrier diode was employed for detection purposes. In order to avoid over-coupling the probe to the co-planar waveguide circuit, it was necessary to employ a very thin low-permittivity substrate for supporting

1195

the probe circuitry. A highly resistive probe circuit was also considered desirable in order to reduce the possibility of internal probe resonances and reflection of the microwave signal from the probe metallisation.

Fig. 21.1

Scanning-nework probe-plotting table

21.3 Scanning-network probe The scanning network probe was originally intended for use as a circuit diagnostic of high frequencies above the normal working range of commercially available network analysers. With this application in mind, a mechanically stable, high-precision two-axis transport mechanism shown in Fig. 21.1 was constructed. A conventional leadscrew drive was employed which had a minimum incremental step size of 0.5pm. Owing to the extreme fragility of the probe sensors necessary at frequencies above 100GHz the majority of the data presented in this Chapter was obtained over the frequency range 26-40 GHz with the coaxial probe shown in Fig. 21.2. The probe is very simply constructed from a rigid single-bore alumina tube of 0.5 mm external diameter. The alumina is metallised on its outer surface and the inner conductor extends approximately 0.2mm beyond the end of the tube. The other end of the probe is terminated in an adjustable cylindrical post, which, in conjunction with a tunable backshort, effectively launches a TE,, waveguide mode. The coupled signal from the probe is fed to a dual-channel homodyne (phase and amplitude) detection system. In order to eliminate the need for soldering the ground plane to a flat rigid backing plate, a vacuum clutch was employed, which had the additional facility for mounting coaxial microstrip launchers anywhere around its periphery. Since the

7 796

Microstrip field diagnostics

probe shown in Fig. 21.2 is axisymmetric, it may be used for recording the distribution of electric field over any irregularly shaped planar circuit configured in open microstrip, slotline, co-planar waveguide or co-planar stripline. The completely automatic data storage and processing facility is extremely versatile in so far as it provides a range of options such as monochrome and colourcontouring routines or a three-dimensional representation of the measured data. The contours may also be sectioned so as to generate a plot of the voltage-standing-wave ratio. An axis of symmetry would normally be selected for this purpose so as to ensure (a) the probe-strip capacitance remains sensibly conat stant along the line of measurement and (b) the magnetic coupling c a n c e ~ ~the VSWR maxima and minima.

Microstrip field diagnostics

7 197

on the two surfaces of the top microstrip conductor are different. It is significant, however, that the edge conditions for the two surfaces are identical, which leads to a common axial periodicity of the charge and current densities on a microstrip line. for, example. z

Fig. 21.3 Probe geometry for deriving near-field pattern of a monopole from an equivalent azimuthal magnetic current M+

Fig. 21.2 26-40 GHz monopole probe

21.4 Theory of the monopole probe

When the tip of the probe approaches an edge discontinuity, the capacitive coupling to the top conductor rapidly decreases. The recorded field intensity, however, does not fall off as rapidly as might be expected, owing to a local enhancement of the surface charge and current densities due to the skin effect. Close to an edge, the recorded distribution can only be regarded as a qualitative indication of the true excitation. However, this apparent failure of the technique does not seriously detract from the physical insight into high-frequency circuit behaviour that is revealed by the tutorial nature of the contour maps. For many purposes it is irrelevant that the magnitude of the charge and current densities

An exact theory for the near field coupling between a short monopole and a narrow conducting strip does not exist at the present time. A realistic theory for the charge and current-density distributions on the top microstrip conductor would need to take into account the lateral skin effect and the proximity effect due to the ground plane. Reference 8 and Fig. 21.3 show that if the probe were considered to be a transmitter located in free space, it would generate both radial and axial electric-field components in the near field. Expressions for these components may be calculated in terms of an equivalent azimuthal magnetic current density k , / ~flowing within the annular aperture of the monopole.

7 198

Microstrip field diagnostics

Microstrip field diagnostics

Expressions for the field components are given in eqns. 21.1 and 2 1.2. Conversely, in reception, the monopole will respond to the net radial and axial field components generated by the microstrip line.

1799

In the majority of practical applications of the probe technique, the surface fields arise from a standing-wave distribution rather than a simple travelling wave, so it is more appropriate to calculate the contributions to A: from each half-period zone along the axis of a narrow strip as given in eqn. 21.6 and shown in Fig. 21.4, where 0 is confined to the Y Z plane:

When the monopole is located above the symmetry axis of the microstrip line it will respond not only to the vertical component of the electric field but also to the surface-field gradient taken in the direction of the symmetry axis. The latter form of coupling alternatively may be considered magnetic in origin, as shown in Fig. 21.5. The total coupling to the probe arises from both the conservative and non-conservative sources of electric field, which may be expressed in terms of the vector magnetic potential A , given by

The derivation of an expression for the magnetic vector potential at a height h above a flat conducting strip of finite width and length is straightforward for the case of a steady axial current I;. The appropriate expression is given by

Strictly, the derivation of this expression assumes the presence of a coaxial return circuit of infinite radius. In the case of a high-frequency current in the form of a travelling wave, a number of additional phenomena need to be taken into account. The most improtant of these is the rapid variation of phase over the dimensions of the strip and also the lateral non-uniformity of the surface current due to the skin effect. Owing to the close proximity of the probe tip to the surface of the flat conductor, the effect of electrical-image charges should also be considered in any realistic calculation of the probe response. When the lateral skin effect is neglected and only the axial phase variation associated with a uniform travelling wave is taken into account, the resulting integral equation 21.5 for the axial component of the magnetic vector potential cannot be solved analytically in the near field: cos (kh tan 8) sec 8 exp (- jkh sec 0) dB

(2 1.5)

Fig. 21.4 Geometry for computing the magnetic vector potential at a height h above an isolated conducting strip

In the case of a large VSWR on the strip, the computation of A, is modified to some extent by the fact that the phase varies discontinuously along the length of the line, increasing rapidly by n at the current maxima and remaining almost constant at the voltage maxima. Since the amplitude of the probe signal falls off rapidly with increasing height h, the slow variation of phase at the voltage maxima could be neglected. However, the rapid phase variation at the voltage minima rather implies that the spatial resolution or radius of the probe 'footprint' will be a function of the standing-wave ratio and frequency, and not purely a constant geometrical factor dependent on the probe diameter. By developing the idea of a combined response to the vertical component of the electric field and transverse component of the magnetic field, a simple phenomenological theory for the probe coupling has been derived. Reference to Fig. 21.5 shows that a quasi-static contribution to the probe signal is visualised in terms of more electric lines of force terminating on the central conductor than the sheath owing to its proximity to the charged microstrip. Increasing the length of protrusion h will cause more lines of force to terminate on the central conductor and a reduction in the number of lines terminating on the sheath, which results in a larger potential difference V being induced on the open-circuited coaxial line. The voltage V can be expressed in terms of line integrals around the contours a-b-a and a'-&-a' in a vertical

1200

Microstrip field diagnostics

Microstrip field diagnostics

section through the probe taken along the symmetry axis of the microstrip. Thus

v

=

r ~ . d i +J : , ' ~ . d i

(21.7)

For any other probe location, the line integrals should be replaced by surface integrals over the probe aperture and tip. The circuital EMFs (5,) from the non-conservative sources-may be found from a similar contour integration. Under the assumption that the probe capture area is determined by the sheath radius b and the probe height h, the circuital E M F may be expressed in terms of the mean phase error 4, ( 4 = b&) as given by

120 1

not on the symmetry axis, there will be a net magnetic contribution to the total measured electric field. The analysis of lines in terms of the voltage standing wave ratio implicitly requires that the probe sensor responds either to the conservative electric field or the magnetic field, but not a combination of both. Under these circumstances the vertical component of electric field close to the surface is proportional to the local surface charge density, whereas the-local transverse component of the magnetic field is proportional to the axial current density. Figs. 21.6 and 21.7 give some indication of the probe size necessary for a particular frequency range. In high-permittivity lines the magnetic coupling is relatively large and is proportional to the effective permittivity.

outer conductor radius b dielectric Inner conductor, rad~us a

X

I

Fig. 21.5 Schematic of coaxial monopole probe (2 figs.)

re

If the electric coupling is taken to be predominantly due to the vertical component of the potential gradient E,h, the magnitude of the total coupled electric field k;, and associated phase angle A are given by eqns. 21.9 and 21.10:

I ~ =, I~ , h { l- ( b ~ , ) ~ ) A z tan-'

I

10

I'

frequency IGHz

Fig. 21.6

Travelling-wave amplitude error against frequency (e,,

= 7.7)

(21.9)

2Bej

{1

The second term in eqn. 21.9 represents the magnetic contribution to the total measured electric field associated with a travelling wave, and may be regarded as an error arising from unwanted coupling. The variation of the amplitude and phase errors as defined above are plotted in Figs. 21.6 and 21.7 as a function of increasing frequency for three different probe diameters. If the probe is used to measure the voltage standing wave ratio of a mismatched microstrip line, the magnetic contribution cancels at both the current and voltage maxima owing to the symmetry of the tangential magnetic field along the axis of the microstrip. At some intermediate axial position or a some point

The extension 6 of the central probe conductor beyond the dielectric tube and co-axial screen has a significant effect on the voltage sensitivity and spatial resolution of the probe. Whereas the sensitivity is easily seen to be proportional to 6, the resolution cannot be readily quantified. As shown in Fig. 21.4, the electric coupling must be determined by summing contributions from an area of line equivalent to the probe 'footprint'. Although this area is difficult to calculate, it may be investigated experimentally by comparing data obtained with progressively smaller-diameter probes. A more tractable approach to the problem of obtaining a quantitative validation of probe technique is by detailed comparison of experimentally measured and theoretically computed surface distributions. For example, resonator geometries possessing high symmetry generally have a calculable field distribu-

7202

Microstrip field diagnostics

Microstrip field diagnostics

tion and mode structure. The book by Bahl and Bhartia [9] contains many references to resonant discs, rings and triangular patches, all of which possess high symmetry and are suitable for comparative studies.

Fig. 21.7

Travelling-wave phase error against frequency

(E,

=

1203

The boundary condition at the magnetic wall, [aEpe]',, requires that the azimuthal component of the magnetic field should vanish at the boundary. The roots of the equation J:,(ka) = 0 determine the TM,,,,, resonant modes of the

1.7)

21.5 Resonant microstrip discs

The four disc resonators shown in Fig. 21.8 were constructed on a proprietary substrate of relative permittivity 2.2. Each disc was excited from a 140Q microstrip line which was tapered up so as to match a 50Q ridged waveguide transformer. Provided that the substrate thickness is much less than the guide wavelength, the system can be treated as a T M cavity bounded by perfect magnetic walls. The solution to the wave equation in cylindrical co-ordinates results in the following equation for the vertical component of electric field E2 inside the cavity: where J,(ke) is the Bessel function of order n and k = wJpo~,. The components of the magnetic field are given by

Fig. 21.8 Microstrip disc resonators

cavity. The integer n represents the order of the Bessel function describing the electric field, and physically corresponds to the number of half wavelength changes around the edge of the disc. The integer rn represents the m th zero of

1204

Microstrip field diagnostics

J,(ka) and corresponds to the number of minima in the range 0 resonant frequency of the nm th mode is given by:

Microstrip field diagnostics

< Q < a. The

where c is the velocity of light, K,,, = m th zero of the first derivative of the Bessel function of order n. An expression for the effective radius a, of the disc is given in Reference 9. Eqn. 21.14 was plotted as a function of Q in order to determine the physical radius necessary to tune each mode to a centre frequency of 35 GHz. The comparative theoretical and experimental plots for the T M , ,, TM,, and TM,, modes given in Figs. 21.9-21.11 generally show a striking resemblance to each other except for obvious differences at the feed point. It is evident from eqn. 21.11 that the cavity modes have the same intensity and are spaced in azimuth by (360/2n) degrees. Table 21.1 lists the experimentally determined excitations and angular location of the maxima for each of the three modes investigated. The 'corrugated' edges seen in the theoretical plots are due to the finite size of the sampling grid used for the computations. Since the theoretical model assumes 'perfect' magnetic walls, there are no fringe fields leaking out of the sides of the cavity, which explains why the surrounding ground plane is completely free of detail. The model is incapable of giving the surface field just above the top conductor, but since the two surfaces share the same boundary, it is assumed that the two distributions are identical to within a constant scale factor. In reality, the side walls are imperfect and the field lines leaving the upper surface of the disc must eventually return to the ground plane. Phase plots have shown that a local ground-plane feature is n out of phase with the corresponding feature on the upper surface of the disc as expected. The lack of nodal symmetry seen in Fig. 21.1 1, arises where a particular voltage node in the upper surfack is locally diminished and the corresponding feature on the ground plane is enhanced. This effect is commonly observed, and will be referred to again in the context of microstrip lines. An enhanced ground-plane feature implies either an enhanced leakage of electric-flux lines out of the cavity, or for some reason the distribution within the cavity is not exactly 'mirrored' on the upper surface of the disc. It is encouraging to note from the data given in Table 21.2 that there is very good agreement between the return-loss figures deduced from slotted-line measurements made in the waveguide feed and those deduced from the VSWR in the microstrip line. The VSWR on the line was deduced from a computergenerated axial section taken through a region of the map corresponding to the parallel-sided section of the line which exists between the stepped ridge transformer and the microstrip taper leading to the disc feed point. The good agreement between the two sets of data suggests that the transformer was well matched at the frequency of operation and that the scanning-network probe yields quantitatively accurate data.

1205

7206

Microstrip field diagnostics

Microstrip field diagnostics

1207

7208

Microstrip field diagnostics

Microstrip field diagnostics

7209

21.6 Resonant microstrip triangles

Equilateral triangular patch antennas also possess high symmetry and support a readily calculable TM-mode structure which is discussed in a paper by Helszajn and James [lo]. The electric-field distribution within the microstrip cavity is given by eqns. 21.15 and 21.16 for a triangle centered at the origin with one of its sides normal to the x-axis: where

+ cos

+ cos

[(g+ q) [26;~ r n ] cos

[(z q) +

'1 y ]

rz] cos [ 2 x ( 1 ~m, y

]

(2 1.16)

Table 21.2 Comparison of scalar network analyser and scanning-network probe return-loss measurements for the microstrip disk resonatnrs

Mode

Waveeuide return loss (dB)

SNP return loss (dB)

A,,, is the amplitude of the mode described by the integers m, n, I which must n 1 = 0. Clearly, the integers cannot all be simulsatisfy the conditions rn taneously zero. The patch geometry and resonant frequencies are determined by

+ +

Patches were constructed on low-permittivity substrates (e, = 2.2) with the edge dimension scaled so that each mode was nominally resonant at a frequency of 35 GHz. The E: distribution within the microstrip cavity and the experimental distribution for the upper surface were determined for the TM,,, TM,,, TM,,, TM,, and TM,, modes. The input impedance of the corner feed point generally increased with increasing complexity of the mode structure. The TM,, mode achieved the best match to the tapered 140R feed line and exhibited a VSWR of approximately 1.4. In order to investigate the mode intensity distribution, the signal levels were determined from the area scan data at six equi-spaced test

Table 21.3

Test-point (TP) data for triangular patches

Mode

TP I

TP2

TP3

TP4

TP5

TP6

2:

TM,, Theory Expt.

1.O

+ 0.2

0.0 0.0 0.02

0.25 0.27 0.03

0.0 0.0 f 0.02

0-25 0.34 +_ 0.05

0.0 0.0 $_ 0.02

$ 2

TM,, Theory Expt.

1.O 1.0 $ 1

0.25 0.25 0.03

1 .O

+ 0.1

0.25 0.25 $_ 0.03

2

0.7

TM,, Theory Expt.

1.O 1.0*0.1

0.25 0.14&0.02

0.25 0.14+0.02

0.25 0.05

0.25 0.31 0.04

TM,, Theory Expt.

1.0

+ 0.1

0.0

0.0 0.02

0.25 0.69 0.07

+

0.19

TM,, Theory Expt.

1.O 1.0 f 0.1

0.37

1.O 1.1 f 0.01

0.48

1.0

+

+

1.O

+

1.O

+ 0.04

+

1.O

+ 0.14

0.1

0.25 0.05

+

1.O 1.1 f 0.1

0.0

+ 0.03

1.O

+ 0.05

1.0 0.4

+

+

0.25 1.1 0.1

+

0.0

1.O 0.79 & 0.07

0.48

0.0 $_ 0.02 1.O

+ 0.05

scale X,Y =2.Ommldivision Z~ZdBlievel

Fig. 21.128

Theoretical (E,I2 for TM,, triangular patch mode

Fig. 21.1 2b Experimental IEJ2 for TM,, triangular patch mode

m, Q

5

72 72

Microstrip field diagnostics

Microstrip field diagnostics

points. The measured intensities were normalised with respect to the feed-point intensity and then compared with the theoretical values calculated from eqn. 21.15. The results of this investigation are summarised in Table 21.3 for the five different modes. The theoretical and experimental distributions for the TM,, mode are given in Fig. 21.12. The TM,, mode has particularly high symmetry owing to the equality of the indices n, rn and also the equality of the intensities at the six test points. However, in practice there is considerable variation between the testpoint intensities, and some asymmetry is observed between features on opposite sides of the feed-point axis. It is of interest to note that, among the five modes investigated, the asymmetry maxima, for example, d o not always occur on the same side of the feed-point axis. Furthermore, there are neither observable blemishes in the etch-back process nor irregularities in the flatness of the substrates. Owing to the rather long recording time necessary for some of the plots, frequency drift could possibly account for some of the asymmetries that have been observed. As a result of the foregoing studies, the potential use of the network probe for mode analysis and in situ circuit diagnostics has been demonstrated. The various test pieces have also shown beyond any reasonable doubt that the distributions observed on the upper surface of the metallisation closely resemble those inside the microstrip cavity.

72 7 3

the outer edges of the line is less pronounced in narrow lines and is not observed experimentally because of the overriding influence of the reduction of the probe-coupling capacitance near an edge discontinuity. However, the depression of the axial current density by the skin effect is more pronounced in the wider lines and is clearly resolved by the probe, as shown in Fig. 21.14. Furthermore,

21.7 Open-circuited microstrip lines In order to investigate the mode structure supported by wide microstrip lines and the frequency dependence of the open-circuit terminations, a series of lines were constructed on 0.254mm-thick PTFE glass-fibre-reinforced substrates with a relative permittivity E, = 2.2. The lines were linearly tapered over a distance of 10 mm to a feedpoint impedance of 50 R. Stepped ridge transformers were used to couple the lines to waveguide WG22, and the overall line length of 60 mm was accommodated on a substrate of dimensions 40mm x 80 mm. The area scans for line impedances of 50 and 22 R given in Figs. 21.13 and 21.14 have been optimised to show the overall field distribution, which inevitably results in an apparent loss of detail on the conducting strip. In order to obtain the VSWR pattern, the contours can be sectioned along the symmetry axis of the microstrip line. If the area scan is not required, it is only necessary to record a single axial scan in order to obtain the VSWR. Although the practising engineer will be pleased to learn that high-impedance lines possess relatively simple field distributions, the wider lines exhibit features which are difficult to explain mathematically. In spite of the overall complexity of the mode structure, the distributions have a number of features in common. For example, both the sectioned axial plots (not shown) and the area scans exhibit a long-wavelength periodicity of the VSWR along the length of the line. The tendency for the lateral skin effect to concentrate the current density along

normal to str~p-lmelrnm

Fig. 21.13

50n open-circuited microstripline at 36GHz

there are complicated periodic longitudinal shifts between the VSWR maxima on the strip and those on the ground plane. These shifts are particularly large close to the open-circuit termination. Another striking observation is the lack of radial symmetry of the features over the ground plane owing to a pronounced curvature of the contours, which periodically alternates from concave to convex along the line. This effect is associated with the waxing and waning of the intensity maxima along the microstrip conductor. It will also be observed that a strong feature over the microstrip is generally correlated with a weak feature over the ground plane. It should be noted that the VSWR maxima and minima

72 7 4

Microstrip field diagnostics

observed along a section through the symmetry axis are equi-spaced for sufficiently narrow lines with characteristic impedances greater than about 4 0 0 . This observation demonstrates that the probe susceptance causes a negligible distortion of the measured data in these lines.

normal to str~p-llnelmm

Microstrip field diagnostics

at the input port. However, when the network probe area scan data is correlated with measurements of the return loss, the E-plane, H-plane and cross-polar radiation patterns, a very detailed understanding of the performance of the system is obtained. Area scan analysis is particularly useful for studying the mutual coupling between parasitically coupled array elements, the voltage standing wave ratio on the feed lines, and the relative excitation of directly coupled elements in an array.

scale

X,Y =l.Ornmldivision

Fig. 21.14 22R open-circuitid microstripline at 35GHz

72 75

Z=l.OdB/level

Fig. 21.1 5 Rectangular patch antenna excited at resonance, F = 3 0 5 G H z

21.8 Antenna diagnostics

One of the most important applications of the scanning-network probe technique is to the analysis of the mode structure supported by planar microstrip antennas. Antennas are necessarily open structures and are therefore generally accessible to probing. Knowledge of the surface charge-density distribution, both in amplitude and in phase, reveals a considerable amount of information about the mode of operation of the antenna, which cannot in the case of multi-element arrays be deduced simply from S-parameter measurements taken

21.8.1 Rectangular patch A return-loss sweep for the isolated patch antenna depicted in Figs. 21.15 and 21.16 showed that the principal resonance at 30.6GHz was associated with a return loss of 18dB. The bandwidth for a lOdB return loss was k415MHz. The fringing effects associated with microstrip open circuits are usually considered to be limited to a few substrate thicknesses distant from the edge; yet here there is evidence for an effect extending over more than 10 substrate thicknesses beyond the edge discontinuity. Another consistent feature of these

12 16

Microstrip field diagnostics

plots is the appearance of a weak 'mushroom shaped' maximum which is located over the ground plane almost a quarter wavelength away from the discontinuity. This feature is particularly large at resonance. As the frequency is raised, the VSWR maxima move along the microstrip line towards the antenna feed point owing to overall shrinkage of the mode pattern supported by the patch. The shift in the positions of the VSWR maxima and minima along the feed line is particularly rapid close to the resonant frequency of the patch. The variation of guide wavelength with increasing frequency can be accurately measured by the probe technique, and generally is in excellent agreement with the theoretically predicted values. Movement of the first feed-point maximum with respect of the edge of the patch may also be used to investigate the change of input impedance of the patch with increasing frequency.

Microstrip field diagnostics

7217

lateral splitting of the patch mode. At somewhat higher frequencies than shown here, all four corners of the patch become relatively strongly excited. The network probe has also been of immense value in clarifying the mode structure supported by simple self-oscillating microstrip patch antenna systems which incorporate a Gunn or Impatt diode. Space does not permit inclusion of this material here, but further information can be found in References 1 1 and 12.

scale Z. Zd Bllevel X,Y=Z.Ommld~v~s~on

Fig. 21.17 I E , I ~distribution for linear four-element array, F = 3 3 . 8 ~ ~ 1 '

21.9 Linear four-element patch array

scale X,Y =l.Ornm/divislon

Z = l OdB/level

Fig. 21.16 Rectangular patch antenna just above resonance F = 31.2GHz

As the frequency of excitation is raised above resonance there is evidence for the excitation of the cross-polar TM,, mode, as shown in Fig. 21.16. Further 'mushrooms' appear on the ground plane and are clearly associated with the

A striking example of the application of the technique to arrays is given in Fig. 21.17. The four-element array was constructed on a low-permittivity substrate (E, = 2.2) and has return-loss dips at 33.8 and 37.8 GHz. The main advantage of the T-junction splitter is its wide bandwidth and simple design, but it does suffer from the disadvantage of being non-isolating. Since the patch feed-point discontinuity produces a substantial reflection, each element in the array directly interacts with every other element owing to the back-reflected waves. However, owing to the high overall symmetry of the array and also a measure of good fortune, each element receives approximately the same excitation in this design. In order to avoid the problem of etching very narrow 200R lines, the output arms of the primary splitter were tapered to 50R and then split again into two

12 18

Microstrip field diagnostics

Microstrip field diagnostics

IOOR outputs. Contrary to the normal practice of avoiding the use of sharp microstrip bends, the corporate feed was laid out using parallel or perpendicular sections of line in order that the position of the VSWR maxima and minima could be determined more precisely for analytical purposes. The array elements exhibit a mode structure similar to that found with the isolated element discussed in the previous Section. One striking observation is that the locus of the current maxima along the width of the array is curved in such a way that the two outer elements appear to be excited below resonance, whereas the two inner elements appear to be excited above resonance. The observed curvature of the phase front suggests that there might be significant mutual-coupling effects between the elements.

I

scale X.Y = Z.Ornrn/divlsion Z=66.66pV/level

Fig. 21.1 8

IEzIZdistribution for four-element circularly polarised array, F

=

34.9GHz

21.10 Circularly polarised patch antennas Two possible methods for generating circularly polarised radiation are shown in Figs. 21.18 and 21.19. It was not immediately apparent, at the outset, what problems might arise with these designs, and they were originally constructed with a view to using them as antenna test pieces purely for demonstrating the two-dimensional field-plotting capability. However, it was clear from Reference 13 that the circularly polarised pentagonal patch mode had been successfully employed by Weinschel in a practical antenna array operating in the UHF frequency band.

12 19

7220

Microstrip field diagnostics

In the case of the four-element array shown in Fig. 21.18 the corporate feed network generates a progressive phase lag of n/2 between adjacent elements, starting with the top right-hand patch, in a clockwise direction~aroundthe array. The primary power splitter contains an additional 112 section in the left-hand output arm so that each of the secondary power splitters is excited with a relative phase of n. The secondary power splitters are of identical design and incorporate an additional 114 section in one output arm in order to generate the required progressive lag. This arrangement by no means represents an optimum solution for the generation of circularly polarised radiation owing to the impedancetransformation properties of the 114 sections of line. Nevertheless, it does provide an opportunity for examining an array in which the mutual coupling between adjacent elements should be quite small, and also for studying the behaviour of a T-junction splitter whose output arms are asymmetrically loaded. The return-loss sweep exhibits four strong resonances at 28.9, 31.8, 34.9 and 39.8 GHz, respectively. The principal resonance occurs at 39.8 GHz and minor resonances also appear at 30.9 and 37.4 GHz. The area scan shown in Fig. 21.18 measured at 34.9GHz corresponds to the only frequency at which any of the patches were strongly excited. This plot was thresholded lOdB above the noise floor of the detector in order to enhance the visibility of the regions of high excitation. It can be seen that only the top right-hand and bottom left-hand patches are strongly excited and also that both appear to be operating slightly below their natural resonance frequencies owing to the shift of the voltage null on the patch towards the feed point. From the slight asymmetry in the position of the VSWR maxima along the vertical arms of the primary splitter, it was found that the relative phase was close to 0,9n, and therefore 10% in error. Since the patches are grossly mismatched to the feed lines, the return-loss dips are probably caused by feeder resonance. This view is confirmed by Fig. 21.18, where it can be seen that the route between the two more strongly excited patches contains an integer number of voltage maxima and forces the primary T-junction to become a voltage minimum. The area scan corresponding to the resonance at 28.9GHz also showed that the route between the top left-hand patch and bottom right-hand patch was resonant at this frequency, whilst the primary T-junction became a voltage maximum in this case. The two patches are more weakly excited at 29.8 GHz because the natural patch resonance is much closer to the original frequency of 34.9 GHz than 28.9 GHz. The area scans (not shown) measured at 31.8 and 39.8 GHz suggest that line resonance can also occur between the pair of patches coupled by either the left-hand or the right-hand secondary splitters. Since the effective length of a patch is 112 at the natural resonance which occurs at approxmately 35.8 GHz, the patch element is physically shorter than 112 at 31.8 GHz and longer than 112 at 39.8 GHz. At frequencies greater or less than the half-width of the fundamental resonance, the edge discontinuities are no longer strongly coupled and can participate independently of one another in generating two additional

Microstrip field diagnostics

122 1

resonances in conjunction with some other discontinuity located elsewhere in the network. In the present example, the resonance at 31.8 GHz is associated with the relatively strong excitations observed at the feed-point edge of the lower lefthand patch and also the more distant edge of the upper left-hand patch. The principal return-loss dip at 39.8 GHz, however, is associated with the relatively high cross-polar T M , ,-mode excitations observed at the feed-point edge of the lower left-hand patch and the upper right-hand patch at this frequency. Furthermore, re-examination of Fig. 21.18 suggests that the return-loss dip observed at 34.9 GHz is also closely associated with the resonant length of line connecting the more distant edges of the lower left-hand patch and the upper right-hand patch as well as the proximity of the natural patch resonances to this frequency. Owing to the complexity of the observed resonance phenomena it would be quite difficult to design an array which exhibited only a single return-loss dip. Nevertheless, the physical insight gained by studying the mode patterns obtained at the various resonances of the structure does clearly identify which line lengths might profitably be adjusted in order to reduce the total number of resonant frequencies present in the system. The basic reason for the failure of the array geometry is due to the mismatch at the feed point of the patch elements, which leads to an imbalance of power division at the secondary splitters. The effect could, in principle, be compensated for by making the secondary feed line an integral number of half wavelengths long at the natural resonance frequency of the patch, and displacing the Tjunction one-eighth of a wavelength from the mid-point between the patches. Under these conditions the two branch lines form a parallel resonance circuit which should result in an equal division of power. Having established the probable cause of failure, the measurement procedure is repeated on the revised array geometry in order to confirm the original diagnosis. The entire process of empirical optimisation is repeated until the required performance has been achieved. In the hands of a skilled microwave engineer, a single one-dimensional scan along the axes of the feed lines could provide sufficient information for the optimisation of an array once the problem areas have been physically identified by a two-dimensional scan of the complete antenna. The pentagonal patch was designed by scaling the dimensions of the circularly polarised VHF antenna discussed in Reference 13 to a nominal frequency of 35 GHz. The return-loss sweep within the frequency range 26-40 GHz indicated the presence of three resonances, one of which was very weak. The strong resonances at 31.35 and 29.5 GHz exhibited return-loss dips of 3OdB abd 14dB, respectively. Area scans for the I E , ~ ' and relative phase distributions corresponding to these frequencies are shown in Figs. 21.19 and 21.20, where it may also be seen that the vertical microstrip feed line is offset a short distance from the apex of the pentagon. Examination of Fig. 21.19a indicates the presence of three voltage maxima of equal intensity which are equidistant from a deep

1222

Microstrip field diagnostics

minimum located at the centre of the patch. The large voltage gradients that exist in directions perpendicular to the edges of the patch suggest that this mode of excitation is not linearly polarised. The phase plot given in Fig. 21.19b indicates that the position of the voltage minimum also corresponds to the 'phase centre' of the antenna, which is the point from which all phase contours appear to diverge. In this particular example the phase levels are at 30" intervals and the software operates in the 180" phase boundary is range from - 180" through zero to + 180'. The represented by the broad contour that spirals out from the phase centre at the top of the Figure, and the small zigzag irregularities on it have no physical significance. It can be seen that the narrow basal edge of the pentagon has an almost constant relative phase of - 180" with respect to the feed point, which was arbitrarily set to zero phase. The intensity contour plot indicates the presence of three voltage maxima located at the vertices of an equilateral triangle inscribed within the pentagonal patch, and the fringe fields in the immediate vicinity of these maxima suffer a progressive phase shift of approximately 120". The phase gradient is particularly large along the two side edges of the pentagon. Viewed along the direction of radiation propagation, the lefthand rotational sense of the contours clearly indicates that this mode of resonance does, in fact, correspond to the left-hand circularly polarised mode discussed in Reference 13. The phase plot given in Fig. 21.20 for the resonance at 29.5 GHz shows that the basal edge has a constant phase of - 180°, whilst the two edges meeting at the apex now have a constant zero phase. The maximum phase gradient occurs approximately midway between the apex and base in a direction parallel to the axis of symmetry of the pentagon. This mode of resonance corresponds very closely to a simple linearly polarised rectangular patch mode. 21.11 Microstrip travelling-wave antenna

The final example of antenna analysis using the scanning-network probe is to a rampart-line array similar in type to that discussed in References 14 and 15. The rampart line is an interesting slow-wave structure because it radiates in the backward direction. The particular design shown here consists of ten meander sections which radiate a principal lobe at an angle of about 140" to the plane of the substrate. The width of the transmission line was increased towards the centre of the array so as to achieve a tapered aperture distribution as suggested in Reference 14. The principal return-loss dip for this antenna occurred at a frequency of 16.7 GHz and the area scan recorded at this frequency is shown in Fig. 21.21. Inspection of Fig. 21.21 shows that half of the structure receives little or no excitation, whilst the other half exhibits a significant standing-wave pattern. Theoretically, of course, this array should support a smoothly tapered voltage distribution which is larger at the two ends owing to the reduced width

Microstrip field diagnostics

1223

1224

Microstrip field diagnostics

Microstrip field diagnostics

of the transmission line. A colour-coded version of the same area scan also clearly shows an enhanced excitation at alternate corners of the rampart line. This rather unexpected result may be due in some way to the existence of mutual coupling between the relatively closely spaced parallel-line sections. The rampart-line antenna gives a very clear indication of the value of the area-scan technique in microstrip antenna diagnostics. A single two-dimensional scan has provided, in this instance, a considerable degree of physical insight into the problem areas of the design geometry. Comparable information could not possibly have been obtained from network-analyser measurements.

Fig. 21.21 IEZl2distribution for rampart-line antenna at 16.7GHz

21.12 Acknowledgments The author wishes to thank the SERC for the provision of a research grant which made this work possible. The Marconi Company is also gratefully acknowledged for supporting a CASE studentship award during the early stages of the programme. Finally, the author is much indebted to his research students,

1225

Dr. J. Whitehurst, Mr. A. Leggetter, and Mr. N. Piercy, for many hours of painstaking effort, and also to Mr. J. Taylor and Mr. L. Ellison for constructing the probe-transport mechanism.

21.13 References 1 DAHELE, J. S., and CULLEN, A. L.: 'Electric probe measurements on microstrip', IEEE Trans., 1980, MTT-28, p. 752 2 LADBROOKE, P. H.: 'A novel standing wave indicator in microstrip, Radio Electron. Engin., 1974,44, p. 273 3 NEUMANN, E. G.: 'Radiation from the free end of a dielectric rod transmission line', Z. Angew Physik., 1967, 24, p. 1 4 NEUMANN, E. G.: 'The electric field near a curved dielectric transmission line', NTZ, 1969, 3, p. 161 5 GINZTON, E. L.: 'Microwave measurements' (McGraw-Hill, 1957), pp. 249-271 6 MONTGOMERY, C. G.: 'Technique of microwave measurements' (McGraw-Hill, 1947) p. 485 7 SCHWARZ, S. E., and TURNER, C. W.: 'Measurement techniques for planar high frequer,cy circuits', IEEE Trans., 1986, MTT-34, pp. 463-467 8 HARRINGTON, R. F.: 'Time harmonic electromagnetic fields' (McGraw-Hill, 1961) 9 BAHL, I. J., and BHARTIA, P.: 'Microstrip antennas' (Artech House, 1980) 10 HELSZAJN, J., and JAMES, D. S.: 'Planar triangular resonators with magnetic walls', IEEE Trans., 1978, MTT-26, pp. 95-100 11 FRAYNE, P. G., and RIDDAWAY, C. J.: 'Resonance in self-oscillating antennas', Electron. Lett., 1986, 22, pp. 1269-1270 12 FRAYNE, P. G., and RIDDAWAY, C. J.: 'Resonance in an active millimetric conformal array antenna with quasi-optical feedback'. 5th Int. Conf. on Antennas and Propagation, York, ICAP 1987, p. 177 13 WEINSCHEL, H. D., and CARVER, K. R.: 'A medium gain circularly polarised microstrip UHF antenna for marine DCP communication to the GOES satellite system'. IEEE AP-S Symp. Digest., 1976, p. 391 14 HALL, P. S., WOOD, C., and JAMES, J. R.: 'Recent examples of conformal microstrip antenna arrays for aerospace applications'. 2nd Int. Conference on Antennas and Propagation, York, ICAP 1984, p. 397 15 HALL, P. S.: 'Microstrip linear array with polarisation control', IEE Proc., 1983,13OH, p. 215

Chapter 22

Microstrip antennas on a cylindrical surface E. V. Sohtell

22.1 Introduction Owing to their ability to conform to the underlying structure, microstrip antennas have a variety of applications to objects with a curved surface. The utilization can be, for example, on aircraft, missiles, ships, satellites etc. In many cases, where the radius of curvature is large, a planar theoretical approach is sufficient. However, when the radius of curvature is small, the curvature of the surface cannot be neglected. The purpose of this Chapter is to describe how theoretical design models, previously developed for planar structures, are extended to the cylindrical case, and to verify the theory with experimental results. A theoretical treatment of a microstrip patch on an infinitely long circular cylinder is presented in Section 22.2. The theory is used in the analysis of a single patch in Section 22.3. Measured results are shown for comparison. Section 22.4 describes the design of a complete phased array consisting of 32 patches. Input impedance, radiation patterns and mutual-coupling coefficients are displayed. The feed network for the array was designed and built by Dr. J.P. Starski, Division of Network Theory, Chalmers Univ. of Technology, Gothenburg.

22.2 Theoretical models for a patch on a cylinder This Section desciibes two theoretical models of the rectangular patch. They are useful both in calculating the input impedance and in finding the radiation pattern from the antenna. The description will concentrate on the radiation pattern from a cylindrical structure. The input impedance can in most cases be found very successfully by applying a planar theoretical approach [I]. An investigation of the influence of the curvature on the resonant frequency and the

1228

Microstrip antennas on a cylindrical surface

input inpedance was made by Luk et al. [2]. It was found that both the resistance and the susceptance of circumferentially polarised square patches vary with the cylinder radius. For axially polarised patches, on the other hand, only the resistance varies. In the cavity model, the patch is considered as a cavity bounded by two electric and four magnetic walls [3-51. From the modes set up in the cavity by the feed, the field distribution in the four magnetic wall are deduced. These field distributions are then used as sources for the radiation from the patch. The cavity model is developed for a rectangular patch on a cylinder in Section 22.2.1. The effect of the substrate surrounding the patch can be taken care of by solving the entire boundary-value problem, in which case the patch may be represented by a surface current on the substrate. When the appropriate integral equation is solved, with the feed probe or a microstripline as the source, the radiation patterns, as well as the input impedance, can be found [6]. Ashkenazy et al. used assumed surface currents in solving the boundary-value problem on a cylinder [7]. The latter description is what will be called the surface current model of the patch. This model will be discussed in Section 22.2.2. The two approaches described here are suitable for cylinders with a radius of up to 4 or 5 wavelengths. For larger cylinders the numerical evaluation becomes very time consuming and ray-tracing techniques are preferable [8].

Microstrip antennas on a cylindrical surface

where

*,(4,

z) =

aces (2) (y) COS

22.2.1 Cavity model of the patch The rectangular patch is modelled by two axial and two circumferential slots. The field distribution in the slots may be found by solving the boundary-value problem inside the cavity, with the feed as the source. The solution is described by a number of modes, which then gives rise to a set of field distributions in the side walls. These distributions are used as sources for the radiation from the patch. Special cases of radiation-pattern calculations are described in References 9 and 10. Internal fields The rectangular patch described by Fig. 22.1 is considered. The antenna is fed via a probe, which sets up a field underneath the patch. When the substrate is thin, we can assume that the E-field underneath the patch has only a p-component. Following the procedure for the planar case [3, 41, we derive the following expressions for the E- and H-fields:

2 C, Fig. 22.1 Axially polarised patch on a circular cylinder

and G~~ = sinc

(2)(e) sinc

p and q are the modal numbers: 0, 1, 2, - - - ;ko = 2n/Lo; E, is the relative dielectric constant of the substrate; +/, zfis the feed location; and A,, A, are the probe extensions in 4 and z for a rectangular probe (planar approximation). 6, = d/2R, z, d and R are given by Fig. 22.1. The effective loss tangent defl is incorporated to take care of all the losses in the cavity. Radiation losses and losses due to finite conductivity of the conductor, as well as losses in the

7230

Microstrip antennas on a cylindrical surface

Microstrip antennas on a cylindrical surface

7231

substrate, can be estimated using the procedure described for the planar case in Reference 11. Another way of describing the losses in the cavity is to use an impedance-boundary condition at the surrounding wall [4]. External fields Next, we want to find the radiation from the lossy cavity. The E-field in the cavity walls can be replaced by equivalent magnetic currents M, and MZ. When the substrate is thin compared to the wavelength, the magnetic currents are narrow and can be approximated by collapsed currents on the conducting cylinder. We may now replace the magnetic currents by flush-mounted slots in the cylinder. We thus end up with two axial and two circumferential slots in the ground plane. The field distribution along the four slots are considered to follow the distribution in the cavity (eqn. 22.1) [12]. The theoretical calculations carried out in this Chapter are all based on the assumption that the cylinder extends to infinity in both axial directions. A two-dimensional Fourier transform can therefore be applied in solving the boundary-value problem. In doing this we will have to make a suitable expansion of the field outside the cylinder and match to the known aperture distribution of a slot in the cylinder. The field from the aperture of a slot can be obtained from two orthogonal components of the vector potentials [13]. These components can be chosen as, for example, A, and F,. A denotes the magnetic and F the electric vector potential. The expressions for the axial components of the vector potentials are found by expanding both the field in the slot and the radiated fields outside the cylinder in cylindrical modes. The radiation condition at infinity indicates that Hankel functions of the second kind are to be used for an ep' time dependence. The tangential E-fields are matched in the slot and are set to zero on the rest of the cylinder. The following expressions are obtained for A, = - Azsin 0 and F, = - F. sin 0 in the far field when an asymptotic formula for the near-field/ far-field transformation is used [13]:

f

A, = exp(-jk0r) koV

"=-a

F, = exp ( -jko r) konr

,,-,

-

E$(n, k, cos 9) w y ( k oR sin e)

ejnbjn

where q is the free-space impedance. An appropriate Fourier transform is defined [I21 and the Fourier-transformed aperture fields are inserted into eqns. 2 2 . 8 ~and b. The radiated far field from each mode in the axial slots will now be given by

E

r

e

=

5

exp (- jkor) kocos O[exp (jkoz, cos 0) cos (qn) ZnZrR ( q n / ~ , ) ~- cos2e e-,kocos8~/2

z0

" &!J"cOs[n(4

-

11

* 4011

Hi2y(koR sin 9)

where the upper and the lower terms within the bracket are used for slots positioned at 4 = - 4, and 4 = 4,, respectively, and - z,/2 < z < zJ2.

+

The circumferential slots give rise to both components of the E-field. For each

P, we get

4 ( n . k0cose) HA2'(koR sin 0) sin 0 cos enEi(n, kocos 8) k,R sin20HA2y(ko R sin 0)

I

where g:(n, k:) and E$(n, kz) are the Fourier transforms of the slot fields Ei(q5) and E$(z). HA2)(z)is the Hankel function of the second kind and nth order, and HA2"(z) is the derivative with respect to the argument of the Hankel function. The radiated electric and magnetic fields are then found from the far-field approximations

where the upper and the lower terms within the bracket are used for slots positioned at z = + zd/2 and z = - zJ2, respectively, and - 4, < 4 < &. The origin in 4 and z is located in the centre of the patch in the expressions

7232

!

Microstrip antennas on a cylindrical surface

kOcod8-tqn/z,,,*

I

bpl(240)12 - n2

11

-10

where the H-field is given by eqns. 2 2 . 2 ~and b. The current densities on the patch are then represented as follows

J:pq

z, q = O zm/2 9 Z 0

240 n and P = 0 n = o , p + o

=

) (2) (y) (2)

H4,pq(4,Z) = - I,, sin - cos

J;,pq= - H q ( z) =

If z, is smaller than L/2, which is always the case for half- wavelength resonant patches, the only zero of the denominator will be for the combination q = 0, 0 = 90". A similar problem is encountered in eqns. 22.1 l a and b when both p and n are zero. A limiting value exists for these functions also. This is given in eqn. 22.13:

- jn[cos(pn) exp (-jn24,) -

7233

the interior fields in the cavity. This is a very crude approximation when the metal thickness is much larger than the skin depth of the metal. We only present an outline of the current method, the details can be found elsewhere [7, 121. Calculated results with an assumed current distribution will be shown in the next Section. The relation between the interior H-field and the surface current will be

given by eqns. 22.10 and 22.1 la, b. We add the contriubtions from the four slots and make a summation over all the cavity modes p, q to find the total field. All the above expressions contain an infinite summation, which is a sum of cylindrical modes in which the fields have been expanded. The number of cylindrical modes necessary for the summation to converge is dependent on the cylinder radius, the 0 angle and the 4 angle. In the circumferential slots there is also a dependence on the excitation mode. The number of terms is usually less than or around 2 kR. The coding of the formulas is fairly straightforward. However, at certain angles and for n = 0 care must be taken. In eqn. 22.10 special attention must be given for 0 angles where cos 0 = q1/2zm,since the denominator will be zero. The expression will have a limiting value, since the numerator also has a null for the same angle 0. It is found that jk, cos 0[exp (jkoz, cos 0) cos (qn) - 11 ( q n / ~ , ) ~- ~ C O S ~ B

Microstrip antennas on a cylindrical surface

cos

sin

(22.150) (22.156)

b is the cylinder radius including the substrate. The radiated far field from the patch is:

(22.13) and

Since the cylinder is considered infinite in the axial direction, the formulas are not valid for angles coinciding with the cylinder axis. The limit to as how close to the axis they can be used is actually set by the accuracy of the computer. A small-argument approximation for the Hankel function is needed for very small 0 angles, but the formulas are still valid as long as 0 is not precisely 0' or 180". Calculated radiation patterns can be found in Sections 22.3 and 22.4, where comparisons are also made with practical results. 22.2.2 Surface-current model We consider an infinitely long cylinder coated with a substrate. The patch is represented by axial and circumferential surface currents that have to be found by a solution of the integral equation for the problem. The fields in the substrate and in free space outside, as well as the currents on the patch, are expanded in cylindrical modes. The proper boundary conditions are satisfied and the resulting currents and fields are found. Alternatively, the cavity modes as deduced in the previous Section may be used to obtain the tangential H-field on the inside of the metal patch. When the 'metal is considered infinitely thin, the surface currents can be directly related to

E4(r74 , 0) = ko

where I

I:[

= M-'[:]

exp(-jk,r) nr

=

.

sin 0

1

j"ejn4 C,(n, kocos 0) (22.163)

n=-m

I:[]: :-

L[

M22

(22.17)

det(M) - M,,

J: and J; are the Fourier-transformed z-directed and 4-directed currents. The ekpressions for the elements in the M-matrix are given by Ashkenazy et al. [7]. The summation of cylindrical modes is similar to the summation for the expressions in the cavity model. However, the expressions are naturally more complicated since the substrate effects are included in the model. For every 0 angle, the Hankel function for three different arguments is necessary, from order zero up to as many modes as are required. It is also desirable to include a

1234

Microstrip antennas on a cylindrical surface

complex dielectric constant to take into account the dielectric losses. The pattern will otherwise show unnaturally large ripples in a 0 cut. A complex dielectric constant, however, leads to a complex argument in the Hankel functions. Routines with such facilities are unfortunately not available in all standard sub-routine packages. 22.3 Single-patch application

A study of the radiation performance of a single patch mounted on a circular dielectric-clad cylinder is described in this Section. Two different frequencies are applied, 2.615 GHz and 5.7 GHz. The element is oriented for axial as well as for circumferential polarisation. Radiation patterns in both 0- and &cuts are studied and measured patterns are compared to theoretically derived curves. Cross-polarisation levels are also of interest. Additional comparisons can be found in Reference 12.

1

Microstrip antennas on a cylindrical surface

1235

22.3.3 Radiation-pattern comparisons The cavity model (eqns. 22.10 and 22.1 la, b) and the surface-current model (eqns. 22.15-22.17) have been used in the theoretical calculations. Two patch sizes are examined here: one patch is 35 x 35 mm2and has a resonant frequency of 2,615GHz, and the other patch is nominally 15.2 x 15.2mm2 with a resonant frequency of 5.7 GHz. In the lower-frequency case, the cylinder has been covered with substrate all around in order to investigate the pattern behaviour in a complete q5 cut. Axially polarised patch at 5.7 GHz The H-plane radiation patterns for an element oriented for axial polarisation are shown in Fig. 22.2. The E,-field is the co-polar component in this diagram and

22.3.1 Mechanical design The cylinder radius is 0.1495m for all experiments described in this Section (1.3 1 and 2,851 at 2.615GHz and 5 7 G H z , respectively). The length of the cylinder is 0.635 m. The element is etched on a substrate which is easily curved about the cylinder. The substrate has a dielectric constant of 2.32 and a thickness of 3.18mm (118"). The loss tangent is given by the manufacturer, Tellite Co., to be 0.00015. The material is sensitive to heat, and, in applications where soldering is required, a low-temperature solder is recommended. This was tested for the soldering of the feed probe in this study. It was found, however, that the strength of the solder was not adequate for the kind of application where the antennas were connected and disconnected several times. A careful soldering with ordinary Pb/Sn solder was therefore made. An alternative feeding of the patch, e.g. microstrip feeding, could have been applied to avoid the soldering problem. In that case the radiation from the microstrip feed line has to be taken into account. 22.3.2 Measurements An anechoic chamber was used for all far field radiation-pattern measurements. The measurement room is equipped with standard instrumentation and has a measurement length of approximately 6 m. In this application, where the radiation pattern is broad, there are problems with reflections from objects nearby. The edge radition from the substrate caused additional difficulties. This radiation was reduced as much as possible by placing microwave absorbers as caps on the ends of the cylinder. An evaluation of the measurement room gave a peak-to-peak variation of the amplitude of around 1.6 dB at a level of - 10 dB, which indicates that the reflectivity level is about - 32 dB.

angle ?) Fig. 22.2 H-plane radiation pattern for an axially polarised patch at 5.7GH.z -measured 0 0 0 0 cavity model ( 5 modes) - - - surface-current model ( p , q = 0 , 1 and 2 , 0 )

the E+-field is the cross-polar component. The solid lines show the measured coand cross-polar levels. The broken lines are the computed fields with the surface-current model and the circles give the cavity-model prediction. The cavity model was used with five modes included, of which the p, q = 0, 1 and

7236

Microstrip antennas on a cylindrical surface

2, 0 modes dominate. The same two modes, with the level of the p, q = 2, 0 mode 40% of the dominant mode level, were also included in the surface-current model calculations. Both co-polar and cross-polar predictions agree very well with the measured curves. In the E-plane, i.e. in a 4 = 0' cut, we do not predict any cross-polarisation. The results of the measurements and calculations are given in Fig. 22.3. The measured cross-polar level is very low. The measured co-polar curve shows a

Microstrip antennas on a cylindrical surface

7237

models. The computed cross-polar curve derived via the surface-current model has used the excitation 1.0 and 0.4 for modes p, q = 1 , 0 and 0,2, respectively (the p, q = 0, 2 mode is the main contributor). The level is correct as it cuts through the measured edge-radiation ripple. We can observe in this measurement cut that the cross-polar-component ripples much heavier than the copolar-component ones. This is due not only to the lower power level, but also to the stronger E-plane field excitation. (This is the E-plane for the cross-polar component.) The cavity model has used five modes, but only two give a significantcontribution, the q = 1, 0 and 0, 2 modes.

b,

Fig. 22.3 E-plane radiation pattern for an axially polarised patch at 5 . 7 GHz -measured 0 0 0 0 cavity model (5 modes) --- surface-current model ( p , q = 0, 1 and 2. 0 )

ripple due to substrate edge radiation. This radiation also prevents the pattern from dropping down in the 0 = 0" and 0 = 180" directions. The same excitations as in the H-plane were used. Note the behaviour of the cavity-model prediction close to the cylinder axis. These peaks are caused by the sin 0 factor in the denominator of eqn. 22.1 l a for the 0:th cylindrical mode. Circumferentially polarised patch at 5.7 GHz Fig. 22.4 shows a comparison between the measured and computed curves for a circumferentially polarised patch in the H-plane (4 = 0'). The E6-component, i.e. the co-polar component, agreement is good for both theoretical

Fig. 22.4 H-plane radiation pattern for a circumferentially polarised patch at 5 7 G H z -measured 0 0 0 0 cavity model (5 modes) - - - surface-current model ( p, q = 1 , 0 and 0, 2)

The E-plane cut for the same patch is displayed in Fig. 22.5. Since the cylinder was not entirely covered with substrate, the measurements are not relevant outside an angle of approximately 100'. The surface-current model curve has a small ripple caused by circling waves around the cylinder. The shapes of both computed curves are symmetrical, whereas the probe excitation makes the measured curve slightly asymmetrical. The cross-polar level is low, which is expected.

7238

Microstrip antennas on a cylindrical surface

I

Circumferentially and axially polarised patches at 2,615 GHz Fig. 22.6 shows a complete 4 cut at 0 = 90°, i.e. in the E-plane for an element oriented for circumferential polarisation. It is interesting to note how well both theoretical models predict the interference from creeping waves circulating

Microstrip antennas on a cylindrical surface

around the cylinder. The amplitude of the interference is much higher when the patch is oriented for circumferential polarisation, compared to what is noted when the patch is rotated 90" (Fig. 22.7). An explanation for this is that the patch creates a stronger field along the ground plane in the E-plane compared to the H-plane. The asymmetry is due to the asymmetric probe location in 4. The cross-polar level is low, around - 35 dB, in the measured curve. This indicates that the probe is located exactly centered in the z-direction.

angle t)

angle

Fig. 22.5 E-plane radiation pattern for a circurnferentially polarised patch at 5.7GHz measured 0 0 0 0 cavity model (5 modes) - - - surface-current model ( p, q = 1 , 0 and 0 , 2)

Fig. 22.7

-

7239

t)

H-plane radiation pattern for an axially polarised patch at 261 GHz

-measured 0 0 0 0 cavity model (6 modes) ( p , q = 0, 1 )

- - - surface-current model

The co-polar component in the H-plane of an axially polarised patch is shown in Fig. 22.7. Only the dominant p, q = 0, 1 mode contributes visibly. The predicted 'back'-lobe, which is caused by the constructive interference from two waves travelling in opposite directions around the cylinder, only reaches a level of -47dB, as compared to - 18 dB in the circumferentially polarised patch case.

22.4 Array application

angle t) Fig. 22.6 E-plane radiation pattern for a circurnferentially polarised patch at 2.61 GHz measured 0 0 0 0 cavity model (6 modes) - - - surface-current model ( p, q = 1 , 0 and 0 , 2 )

-

0

22.4.1 General Microstrip antennas are very well suited to conformal array applications, and several projects have been reported in the literature [14-251. Sanford [I41 describes a phase-steered array, while References 15-21 report omnidirectional applications. A conical beam is produced by the cylindrical array in Reference 22, and a high-gain spherical array was studied by Dubost and Vinatier [23]. Various microstrip conformal arrays are briefly described by Munson [24] and a conical circularly polarised array with monopulse was reported by Newham

1240

Microstrip antennas on a cylindrical surface

Microstrip antennas on a cylindrical surface

[25]. Conformal printed dipole arrays have been analysed theoretically in References 26 and 27, and dipoles above a cylinder were investigated in terms of their active radition pattern in Reference 28. A bibliography of the recent literature on conformal antennas in general has been compiled by Hansen [29]. 22.4.2 Theoretical treatment ofjinite and injinite arrays A cylindrical-array antenna may be treated theoretically as an infinite array in the axial direction and an infinite periodic array in azimuth. As an alternative, an element-by-element approach may be used. When the number of elements is large, the infinite model is preferable, since.all the calculations may be performed by considering a single unit cell [28]. When the array is finite, the elements close to the edge behave differently from the centre elements, owing to the difference in mutual coupling. These edge effects must be taken into account in the design of small and moderately sized arrays, and also when very low sidelobes are required from a large array. Steyskal used an element-by-element approach for the analysis of a finite array of circular waveguides on a cylinder [30]. The same approach was also adopted by Pozar in a study of planar arrays of microstrip elements [31]. The radiation-pattern calculations of a finite-array antenna, using an element-by-element approach, involves the modelling of the antenna element and the incorporation of the mutual coupling. The modelling of the patch antenna was treated in the previous Section. A theoretical model for the mutual coupling between microstrip elements on a cylinder is not yet available; so in the array design described in this Section the measured S-matrix was incorporated to account for the mutual coupling. Since the measurement of the entire S-matrix is a very time-consuming, procedure and the accuracy is limited, an approximation is used. The idea is to assume that elements located similarly will couple the same way. For instance,. the two centre elements in one band are assumed to couple the same way as the two centre elements in another band, which might not be a bad approximation. However, when this reasoning is extended to be valid for the corner element and its closest neighbour in the same band, we have reason to believe that it is a poor approximation. Still, it will be shown that the approximation is acceptable in this application, where a sidelobe level of - 20 to - 30 dB is investigated. 22.4.3 Design of a phased array on C-band , In this Section we will describe the design of a microstrip antenna array on a cylindrical surface. The array is described in more detail in Reference 12 and the entire project was briefly reported by Sohtell and Starski [32]. The frequency of operation was set to 5.7 GHz. Beam steering f 30' was desired in azimuth, but as an extension of the program the possibility to steer the beam in elevation was also desirable. Another option was the incorporation of circular polarisation. The sidelobe level was to be controlled by using variable attenuators. The

1241

number of phase shifters and attenuators was limited to 8 in the first configuration. As in the design of a planar array, the size of the antenna, the element pattern, the type of element grid and the element separation will govern the characteristics of the far-field radiation pattern. Since the elements are placed on a curved surface, it is not possible to separate the element pattern from the array factor, which complicates the synthesis. In a beam-steering situation it is also essential to beware of the limits of the active angle of the array. The element pattern, the element grid and the active angle will be discussed below. The design will focus on the azimuth plane, since no restrictions were set on the radiation pattern in the elevation plane.

'

Antenna element According to the specifications, circular polarisation was required for a possible continuation of this project. There are several types of microstrip antennas that produce circular polarisation [5]. In this project, however, we wanted to be able to predict the radiation patterns theoretically as accurately as possible. An element which could easily be described in a cylindrical geometry was therefore wanted. In addition, we did not want any radiation from the feed network to interfere with the desired radiation. Consequently, a square-shaped probe-fed element was chosen. The dimensions of the element were predicted using standard methods available. The following simple formula for the resonant frequency of a patch on a curved surface is very useful [2]:

where 2R4, = 2R4, + h/& is the effectivecircumferential length of the patch and z, = z, h/& is the effective axial length. The actual dimensions of the patch are z, and 2R4,. R is the cylinder radius,pq is the mode number, h is the substrate height and E, the dielectric constant of the substrate. In our case we found that with E, = 2.32 and h = 3.18 mm, for a TM,, mode at 5.7 GHz, the length z, should be 15.18 mm. The dimensions of the microstrip element designed here are: axial length measured on the etched board is 15.10 0.05mm, and the width is 15.20 0.05mm. The measured return loss for this element is given in Fig. 22.8. The resonant frequency is 5.725GHz, which is exactly what eqn. 22.18 predicts. The bandwidth is -4.7% for a VSWR of 1.5.

+

+

+

Active angle The active angle of the cylinder can be seen from Fig. 22.9 to be limited by the beamwidth of the constituting elements. Beam steering to 0' and 30' is illustrated. Since the elements that were chosen for this array are a little smaller than 4 2 , a fairly broad beam was expected. To get an approximate idea of the beamwidth, a measured radiation pattern for a single element on a cylinder was

.

7242

Microstrip antennas on a cylindrical surface

Microstrip antennas on a cylindrical surface

studied. The element at one end of the array should not be too much out of phase when the beam is steered 30' in the other direction. The usable angle of the element studied was about 130" for 22' phase error and lOdB power loss.

0

5.2

I

I

I

I

I

I

I

I

5.7 Frequency (GHz)

Fig. 22.8 Measured return loss for an isolated probe-fed square patch

I

1

6.2

1243

An active angle smaller than 70" thus seemed necessary if all elements were to contribute to the main lobe for all steering angles without phase compensation. Element grid The specifications asked for beam steering _f 30' in elevation and azimuth with eight phase shifters. Steering of the beam in elevation requires more phase-shifters than beam-steering in azimuth, owing to the non-separable geometry. The array was therefore arranged to be steered in azimuth, in a first configuration, because of the limited number of phase shifters. The difference in beam steering in the two planes is discussed further in Section 22.4.4. The array was designed to allow for beam steering in both planes at the same time. A triangular-element lattice was chosen with a total of 32 elements. The elements were arranged in eight columns of four elements each. The power was thus first split into eight channels, each channel containing a phase shifter and an attenuator. The four elements in each column were uniformly fed with equal phase. The element separation was the next parameter to be found. On a planar surface, the discussion would proceed as follows. The largest separation between elements can be found in adiagonal plane. To be able to steer to 30" in this plane without introducing grating lobes, we would need an element separation smaller than 0.62. We do, however, know that the grating lobes are not as high and distinct in the azimuth cut, owing to the non-uniform element spacing [29]. The element separation in a diagonal plane was chosen to be 0.581, which gave a column/band separation of 0.4141 in q5 and z. The above considerations led to the choice of a cylinder diameter of approximately 0.3m. The actual radius of the cylinder used in the following measurements was 0.1495m (2.842 at 5.7 GHz) excluding the substrate. This resulted in an active angle of 63" when the substrate thickness was 3.18 mrn. A photograph of the array is shown in Fig. 22.10. 22.4.4 Measured performance

Fig. 22.9 Active angle in azimuth of a cylindrical array

Input impedance The cylinder with the array was placed in a small anechoic chamber built up by four walls covered with absorbers. The roof and the floor were not shielded. The room was examined for this application by moving the cylinder about in the room to find the in-and-out-of-phase interference of the reflections. An HP 8409B semi-automated network analyser was used to perform the measurements. The total error in the return-loss measurements was around f0.4dB and f 3" at the 25 dB level. All the neighbouring elements were terminated in matched loads during the measurements. The loads were all better than 20dB in return loss. Fig. 22.1 1 shows the return loss measured at all 32 input ports. The design centre frequency of 5.7 GHz is clearly demonstrated. A bandwidth of 100 MHz

1244

Microstrip antennas on a cylindrical surface

for a VSWR < 1.5 for all the elements was achieved. The variations in return loss are due to the etching, the probe locations, and the mutual coupling between the elements. Considering this, the result is very good. A tendency towards lower return loss was noted for the elements in the centre of the array.

Microstrip antennas on a cylindrical surface

7245

coupling heavily. The errors caused by surface-wave reflections at the edges of the board are not included in the estimations above. Fig. 22.12 gives the amplitude and phase of the measured mutual coupling at 5.7 GHz from a centre element to all the other elements and Fig. 22.13 shows the coupling from a corner element. A study of Figs. 22.12 and 22.13 gives the following information:

I

5.5

5.6

57 58 frequency (GHz)

5.9

Fig. 22.11 Measured return loss for 32 active elements

Fig. 22.10 32-element phased-array antenna

This is caused by the mutual coupling between the elements, since the patches were designed for optimum matching as isolated elements. Mutual co~~pling hetnwn rlw elements The same provisional anechoic chamber described previously was also used for the mutual-coupling measurements. The measurement error for these measurements was found to be less than f 0.4dB and 3" at a 20dB level. It was noted that the surface-wave radiation along the cylinder axis influenced the mutual

+

The coupling upwards from the centre element is stronger than the coupling downwards, except for the closest elements. The reason for this can probably be found in the second-order mutual-coupling effects, which are different owing to the asymmetric location of the element in the array. The E-plane coupling is stronger than the H-plane coupling for both elements, except for the centre element's coupling to the closest elements. The difference is very pronounced for the corner element. It is striking to see the difference in phase between the two planes. There are quite clearly two types of coupling involved. The surface-wave coupling is strongest in the E-plane. The radiation coupling, on the contrary, is probably stronger in the H-plane (cf. dipoles). This is also verified by far-field radiation-pattern computations made for single elements oriented for circumferential polarisation and elements oriented for axial polarisation (Section 22.3.3). It is shown that the surface wave radiated off the edge of the substrate is much stronger when the element is oriented for axial polarisation.

1246

Microstrip antennas on a cylindrical surface

A comparison between Figs. 22.12 and 22.13 shows that there are large differences in the measured amplitude and phase values for two-element combinations located similarly, which means that the mutual coupling is not only

t

%-vector

1

amplitude phase

Microstrip antennas on a cylindrical surface

1247

Feed network A block diagram of the feed network is shown in Fig. 22.14. The first power divider splits the power equally into eight channels, corrresponding to the eight columns of the array. In each channel there is a phase shifter, an attenuator and

1

amplitude phase

Fig. 22.12 Amplitude and phase of the measured mutual coupling from a centre element

Fig. 22.1 3 Amplitude and phase of the measured mutual coupling from a corner element

a function of distance and direction between the elements. The second-order coupling effects result in this difference. This should be remembered when the mutual coupling is included in the radiation-pattern calculations.

finally a 1:4 power splitter. The phase shifter can control the phase in steps of 45' between 0" and 360". The attenuator has an attenuation range of 0-40 dB continuously. The final power divider splits the power equally and with equal phase to the four elements in a column.

7248

Microstrip antennas o n a cylindrical surface

The computer-controlled phase shifter and attenuator are described by Starski and Albinsson in References 33 and 34, respectively. In order to be able to predict the radiation patterns of the array, it was important to know the total resulting phase and amplitude at each element. A

4 k?' Computer

-.

1:8

..

45'

90"

180'

0 -40 dB

Fig. 22.14 Block diagram of the feed network

thorough measurement of the complete feed nework was therefore made. The phase and amplitude at each one of the 32 ouput ports were measured as a function of phase-shifter setting and attenuation. These data were then recorded by a HP9816 computer and could be displayed during the antenna measurements. The values were used as input to the computer program for the prediction of the radiation patterns (see below). However, excitation errors due to reflections at the antenna elements were not compensated for. A discrepancy between the displayed values and the actual output values could also be expected owing to the fact that the semi-rigid cables after the measurement had to be bent to be attached to the elements. The total difference in phase and amplitude in the displayed values and the output values from the feed network is roughly f0.5dB and 7".

+

Antenna gain The antenna gain was measured in the anechoic chamber described in Section 22.3.2. The reflectivity level of the room is around - 40 dB for the entire array measurement. The feed network was set to give a main lobe in 4 = 0". The average power level at the elements was -25.0dB. An ideal power division would give - 15 dB, which means that 10 dB was lost in the feed network including the cables. This loss is mainly due to the phase shifters, which were not in their 0" state during the gain measurements. An increase in phase shift in the phase shifters results in an additional attenuation, and since the attenuation was not equal in all the channels, a compensating attenuation was applied in the leastattenuated channels. The measurements gave an antenna gain of 13.1 (k0.8)dB. Neglecting the feed loss, the antenna by itself has a gain of 23.1 dB. It should be pointed out that a constant amplitude over the aperture would give an equivalent taper which can be described by a function I/cos (4,) x g(4,,). The first term is due to the increased density of elements towards the edge, in a projected aperture plane. 4, is the 4 angle of the m th column, as measured from 4 = 0". g(4) is the

Microstrip antennas on a cylindrical surface

7249

element pattern, which can be approximated by cos(4) for small 4 angles. Consequently, we wanted an excitation with equal amplitudes to the elements during the antenna-gain measurement. An antenna gain of 23.1 (k043)dB gives an effective aperture A, of 16.3 [+3.3/-2.7]A2, using G = 4 ~ A , / 1 ~This . can be compared to the physical projected aperture of the array, which is 9.66A2. The actual aperture with a 112 margin around the printed array is 17.541'. The effective aperture of the array is thus approximately equal to the area of the array, including 142 around the printed pattern. Radiation patterns The cylinder was covered with substrate to a total height of 595 mm. In azimuth the substrate covered 620mm, corresponding to an angle of 230". Radiationpattern recordings outside the range 100" could therefore have been influenced bv the substrate edge. The calculated radiation patterns were all computed using the surface-current model of the patch (Section 22.2.2). The mutual coupling was incorporated using the mesured coupling coefficients from the centre element. In patterns where a cross-polar level is predicted, mode p, q = 2, 0, with an amplitude of 40% of the dominant mode (p, q = 0, 1) amplitude, was included.

-

+

Beam steering Let element number nm be excited by the current I,, = I(+,, z,,), where z, is the z-co-ordinate of then th band and 4, is the 4 angle of them th column. In order to steer the beam in a direction O0, 4,, the element excitation should be

I

- j k R ~ i n B ~ c o -&) s ( ~ ~ -jki,casOo

e (22.19) when the element phases are neglected. When we analyse this expression, we find that, to steer the beam in elevation 0, we need to calculate and change by individual amounts the phase of every element in the array. It is thus not possible to use one band as an entity, a so-called 'row and column' beam steering, the same way as in a planar array. A beam steering in azimuth only (0, = 90°), on the other hand, involves the phasing of the columns. Inrn

=

nm

Active-element patterns When a single element was excited, the surrounding elements were terminated in matched loads. The active-element patterns of a centre element and a corner element were recorded. Fig. 22.15 gives the predicted and measured radiation patterns for the centre element and Fig. 22.16 shows the radiation pattern for the corner element. The former is also compared to the radiation pattern of an isolated patch. Array patterns For the entire array, beam steering was performed in azimuth only. Fig. 22.17

7250 0

,

shows beam steering to 0°, 17O, 34", 55" and 63'. The element phases have been compensated for in the two latter diagrams. The recordings were made with the intention of putting as much power as possible into the main beam, but still keep a constant amplitude taper. None of the columns was therefore attenuated, although this would have helped to reduce the sidelobes.

I

I

-40

,

120

7251

Microstrip antennas on a cylindrical surface

Microstrip antennas on a cylindrical surface

I

I

I

90

60

30

I

I

I

0

30

60

I

I

90

120

I

I

I

I

angle (7

Fig. 22.15 Measured and predicted active radiation pattern for a centre element -measured - - - surface-current model, mutual coupling included . . . surface-current model, isolated element

angle Fig. 22.17 Beam steering to O", 7 7 , 344 55 and 6 3 in azimuth

-401

I

I

I

I

90

60

30

0

I

I

I

30

80

90

angle (7

I

I

120

150

Fig. 22.16 Measured and predicted active radiation pattern for a corner element -measured - - - surface-current model, mutual coupling included

The co- and cross-polar diagrams for a beam pointing in 0" are shown in Fig. 22.18. The sidelobe level for a constant-amplitude distribution is found to be - 13dB, which is also predicted. The cross-polar level is measured to be - 24 dB. The calculated results lie 3 dB below this value. The discrepancy is due to the fact that the cross-polar coupling has not been considered in the theoretical calculations and also because of the inaccurate feeding of the patches. The elements are sensitive to cross-polar components, since mode p, q = 1, 0 is resonant at the same frequency as the p, q = 0, 1 mode. A displacement of the feed probe only slightly will therefore cause cross-polarisation. Fig. 22.19 shows the co- and cross-polar curves when the beam is steered to 36". The patterns are predicted quite well with the theoretical model. The columns are all fed with equal amplitude. Pattern synthesis A good synthesis method is difficult to find for conformal arrays. The projected aperture method is the most commonly used [29, 351. Matrix inversion

-

7252

Microstrip antennas on a cylindrical surface

procedures were reported by Ziehm [36] and James [37] and an iterative method was developed by Guy [38] (also in Reference 39). We will show here the results of a projected aperture synthesis procedure. The sidelobes were reduced in an azimuth cut by using a sampled continuous Taylor distribution [40].

Microstrip antennas on a cylindrical surface

I

7253

the case of constant excitation and 0" beam steering. It should be pointed out that the reduced antenna gain is mainly due to the attenuation in the feed network, since the power in the outer channels is attenuated. A constant total power output would theoretically result in a loss of antenna gain of 0.1 dB for a 20 dB, and 1.4 dB for a 30 dB Taylor distribution, as compared to a constant distribution.

angle (7

Fig. 22.18 Measured and predicted rad~attonpattern with the mutual couplmg mcluded for a beam pointmg ~n0" measured co- and cross-polarlsatlon - - - surface-current model, co-polarlsatlon x x x surface-current model, cross-polar~sation

-

As mentioned earlier in this Section, the increased element density towards the edge of the array is approximately compensated for by the reduced element gain. As long as the angle is small, this is a reasonable approximation. A 30 dB Taylor distribution was applied, in order to reduce the sidelobes. The recorded and predicted radiation patterns are displayed in Fig. 22.20. The predicted pattern uses the excitation delivered by the feed network with the desired phases approximated the best that could be done with the 3 bit phase shifters. The mutual coupling is also included. Theoretical and measured curves agree very well in this diagram. A considerable sidelobe reduction was gained at the cost of lobe width and directivity. A reduced sidelobe level of a beam steered to 10" requires a new projection. The new projection leads to an asymmetrical element distribution. Consequently, a 'new calculation of element currents has to be done. A 20dB Taylor distribution applied to a beam steered to 10" gives the pattern shown in Fig. 22.21. The OdB level in both tapered diagrams is the level of the main lobe in

Fig. 22.1 9

Measured and predicted radiation pattern with the mutual coupling included for a beam pointing in 3 6 -measured co- and cross-polarisation - - - surface-current model, co-polarisation x x x surface-current model, cross-polarisation Source: E.V. Sohtell, 'Microstrip patch phased array on a cylinder', IEEE Int. Symp. Digest Antennas and Propagation, Vol. 111, 1988, pp 1152-1 155. @ (1 988) IEEE

22.5 Summary

Two theoretical models for the microstrip patch on a cylinder have been investigated in this Chapter. Both the cavity model and the surface-current model give a good description of the radiation properties of the patch. Apart from effects occurring for infinite-length cylinders in the theoretical models, and radiation off the substrate edge in the measurement case, the agreement between measured and theoretical curves is good. The cavity-model calculations require much less computer time than those performed with the surface-current model, and the higher-order modes are found quite easily with the cavity model. The

1254

Microstrip antennas on a cylindrical surface

Microstrip antennas on a cylindrical surface

1255

surface-current model does, however, give a better prediction of the radiation pattern for angles near the cylinder axis. It has been shown that the patch antenna is very well suited for application in a cylindrical phased array. The ease of fabrication and low cost make this type of array very attractive. Beam steering & 70' in azimuth is possible without commuting the active region. A three-step commutation will then provide coverage of 360" while maintaining a high antenna gain. It has also been shown that a theoretical model where the measured mutual coupling is included gives a good picture of the electrical performance of a patch array. Pattern synthesis may thus be performed with reasonable accuracy.

- - - - - - rO

22.6 References I 2 Fig. 22.20 Measured andpredicted radiation patterns with the mutual coupling included f o ~ a 3 0 dB Taylor distribution with the beam pointing in O'

-measured - - - surface-current model

Source: E.V. Sohtell. 'Microstrip patch phased array on a cylinder', IEEE Int. Symp. Digest Antennas and Propagation. Vol. 111. 1988, pp 1152-1 155. @ (1 988) IEEE

3 4 5 6 7

8

9

10 II 12

13 14 Fig. 22.21

Measured and predicted radiation patterns with the mutual coupling included for a 20dB Taylor distribution with the beam pointing in 1O'

-measured

- - - surface-current model

IS 16

KROWNE, C. M.: 'Cylindrical-rectangular microstrip antenna', IEEE Trans., 1983, AP-31, pp. 194-199 LUK, K. M., LEE, K. F., and DAHELE, J. S.: 'Input impedance and Q factors ofcylindricalrectangular microstrip patch antennas'. IEE Int. Conf. on Antennas and Propagation, Part 1, York, June 1986, pp. 95-98 LO, Y. T., SOLOMON, D., and RICHARDS, W. F.: 'Theory and experiment on microstrip antennas', IEEE Trans., 1979, AP-27, pp. 137-145. CARVER, K. R., and MINK, J. W.: 'Microstrip antenna technology', IEEE Trans., 1981, AP-29, pp. 2-24 JAMES, J. R., HALL, P. S., and WOOD, C.: 'Microstrip antenna theory and design' (Peter Peregrinus, 1981) NEWMAN, E. H., and TULYATHAN, P.: 'Analysis of microstrip antennas using moment methods', IEEE Trans., 1981, AP-29, pp. 47-53 ASHKENAZY, J., SHTRIKMAN, S., and TREVES, D.: 'Electric surface current model for the analysis of microstrip antennas on cylindrical bodies', IEEE Trans., 1985, AP-33, pp. 295-300 PATHAK, P. H., and KOUYOUMJIAN, R. G.: 'An analysis of the radiation from apertures in curved surfaces by the geometrical theory of diffraction', Proc. IEEE, 1974, 62, pp. 14381447 WU, KUANG-YUH, and KAUFFMAN, J. F.: 'Radiation pattern computations for cylindrical-rectangular microstrip antennas'. IEEE Int. Symp. Digest Antennas and Propagation, Vol. 1, 1983, pp. 39-42 JAKOBSEN, K. R.: 'The radiation from microstrip antennas mounted on two-dimensional objects', IEEE Trans.,1984, AP-32, pp. 1255-1259 PENARD, E.: ' ~ t u d ed'antennes imprimkes par la method de la caviti. Application au couplage'. D.Sc. Thesis, University of Rennes, 1982 SOHTELL, E. V.: 'Microwave antennas on cylindrical structures'. Technical Report 173, Ph.D. Dissertation, School of Electrical and Computer Engineering, Chalmers University of Technology, Sweden, Sept. 1987 HARRINGTON, R. F.: 'Time-harmonic electromagnetic fields' (McGraw-Hill, 1961) chap. 3 SANFORD, G. G.: 'Conformal microstrip phased array for aircraft tests with ATS-6'. IEEE Trans., 1978, AP-26, pp. 642-646 MUNSON, R. E.: 'Conformal microstrip antennas and microstrip phased arrays', IEEE Trans., 1974, AP-22, pp. 74-78 WEINSCHEL, H. D.: 'A cylindrical array of circularly polarized microstrip antenna'. IEEE Int. Symp. Digest Antennas and Propagation, 1975, pp. 177-180

1256

Microstrip antennas on a cylindrical surface

17 AGRAWAL, A. K.: 'Cylindrical array'. IEEE Int. Symp. Digest Antennas and Propagation, 1986, pp. 549-552 18 JAYAKUMAR, I., GARG, R., SARAP, B. K., and LAL, B.: 'A conformal cylindrical microstrip array for producing omnidirectional radiation pattern', IEEE Trans., 1986, AP-34, pp. 1258-1261 19 DUBOST, G., SAMSON, J., and FRIN. R.: 'Large bandwidth flat cylindrical array with circular polarisation and omnidirectional radiation', Electron. Lett., 1979, 15, pp. 102-103 20 OSTWALD, L. T., and GARVIN, C. W.: 'Microstrip command and telemetry antennas for communications technology satellite'. IEE Int. Conf. on Antennas for aircraft and spacecraft, London, 1975, pp. 217-22 21 WEINSCHEL, H. D., and WATERMAN, A.: 'Cylindrical microstrip array - C-band beacon antenna array with 48 rectangular radiating elements fed in phase'. Report AFGL-TR-830218, AD-A135 14414, July 1983 22 HALL, P. S., WOOD, C., and JAMES, J. R.: 'Recent examples of conformal microstrip antenna arays for aerospace applications', IEE Int. Conf. on Antennas and Propagation, York, 1981, pp. 397401 23 DUBOST, G., and VINATIER, C.: 'High gain array at I2GHz for telecommunications'. Int. URSI Symp. on Electromagnetic Waves, Munich, 1980, pp. 213A1-4 24 MUNSON, R. E.: 'Conformal microstrip communication antenna', IEEE Military Communications Conference, Monterey, 1986, pp. 23.3.14 25 NEWHAM, P.: 'Monolithic patch array antenna for small missile applications'. Military Microwaves, Conf. Proc. Brighton, England, 1986, pp. 335-340 26 LEE, K. S., and EICHMANN, G.: 'Elementary patterns for conformal dipole arrays mounted on dielectrically clad conducting cylinders', IEEE Trans., 1980, AP-28, pp. 81 1-18 27 ALEXOPOULOS, N. G., USLENGHI, P. L. E., and UZUNOGLU, N. K.: 'Microstrip dipoles on cylindrical structures', Electromagnetics, 1983, 3, pp. 31 1-326 28 HERPER, J. C., HESSEL, A,, and TOMASIC, B.: 'Element pattern of a cylindrical phased array. Part I: Theory', IEEE Trans., 1985, AP-33, pp. 259-272 29 HANSEN, R. C. (Ed.): 'Conformal antenna array: Design handbook'. AD A1 10091, Jan. 1982 30 STEYSKAL, H.: 'Analysis of circular waveguide arrays on cylinders', IEEE Trans., 1977, AP-25, pp. 610-616 31 POZAR, D. M.: 'Finite phased array of rectangular microstrip patches', IEEE Trans., 1986, AP-34, pp. 658-665 32 SOHTELL, E. V., and STARSKI, J. P.: 'Cylindrical microstrip patch phased array antenna - Chalscan C'. Military Microwaves Conf. Proc., Brighton, June 1986, pp. 317-322 33 STARSKI, J. P., and ALBINSSON, B.: 'Coupled transmission line as a DC isolating phase shifter network'. TR8407, Division of Network Theory, Chalmers Univ. of Technology, Sweden, Sept. 1984 34 STARSKI, J. P., and ALBINSSON, B.: 'An absorptive attenuator with optimised phase response'. TR8402, Division of Network Theory, Chalmers Univ. of Technology, Sweden, May 1984 35 RISZK, M. S. A. S., MORRIS, G., and CLIFTON, M. P.: 'Projected aperture synthesis method for the design of conformal array antennas'. IEE Int. Conf. on Antennas and Propagation, Coventry, 1985, pp. 48-52 36 ZIEHM, G.: 'Optimum directional pattern synthesis of circular arrays', Radio Electron. Engr., 1964, 28, pp. 341-355 37 JAMES, J. R.: 'Conformal antenna synthesis using spherical harmonic wavefunctions', Proc. IEE. 1975, 122, pp. 479486 38 GUY, R. F. E.: 'A synthesis technique for array antennas of general shape with various aperture constraints'. IEE Int. Conf. on Antennas and Propagation, Coventry 1985, pp. 35-39 39 GUY. R. F. E.: 'Power pattern synthesis of conformal arrays'. Military Microwaves, Conf. Proc., Brighton, 1986, pp. 341-346 40 BALANIS, C. A,: 'Antenna theory, analysis and design' (Harper & Row, NY, 1982)

Chapter 23

Extensions and variations t o the microstrip antenna concept P. S. Hall, A. Henderson, J. R. James

23.1 Introduction A large number of contributions to this handbook have described analytic or design aspects relating to single microstrip elements or their use in large microstrip arrays. This reflects a response to an important need for engineering developments in the communications, radar and navigation areas, where many of the ultimate uses of microstrip will be found. The number of ways of configuring a microstrip patch antenna, let alone the different array topologies, is seemingly vast, yet the fundamental performance limitations discussed in Chapter 1 are intrinsic in any microstrip antenna design. There we have cited bandwidth extension, radiation pattern control, efficiency and feeder architecture, substrate technology and manufacture etc., as major fundamental issues in design. Any one property can generally be optimised to a large degree, but only at the expense of the others, and copious illustrations are given throughout the Handbook. It is perhaps a sign of maturity in the microstrip antenna field that ways of combining microstrip printed technology with other constructional methods are now attracting attention. The central idea here is to sacrifice to some degree the manufacturing simplicity or the low profile or the choice of substrate materials and so on, in order to relax one or more of the above limitations fundamental to established microstrip technology. The concept of mixing technologies is well known in engineering design and is best described by considering specific examples. The purpose of this Chapter is to report various examples with which we have had particular design experience. Section 23.2 deals with two arrangements for exercising greater control of radiation patterns whilst maintaining the presence of simplistic microstrip patch antennas. First, in Section 23.2.1, the microstrip radiator is used as a feed element for a large - reflector antenna, thus combining the simplicity of the microstrip concept with the high efficiency and good sidelobe and cross-polarisation control properties of the reflector. Similarly the combination of dielectric spheres with patches (Section 23.2.2) is also seen to lead to improvements in pattern control with novel sparse array facilities, and a possible beam-switching

7258

Extensions.and variations to the microstrip antenna concept

technique is also realisable. Ways of satisfying multi-octave bandwidth demands are presented in Section 23.3, and the log-periodic concept in Section 23.3.1 is a particular demonstration of a significant improvement being made in one parameter, namely bandwidth, at the expense of another, in this case the physical area of the array; from this point of view, it is compatible with the findings elsewhere in the Handbook relating to the bandwidth-size trade off, but is, of course, an extreme case. A very new technique (Section 23.3.2) utilises the frequency-selective properties of a printed mesh and the fact that at low frequency a microstrip antenna can be composed of such a surface without impairing its performance. The outcome is a composite structure containing two sandwiched microstrip arrays, one radiating through the other and offering a dual-band aperture with multi-octave frequency separation. The problem of microstrip-line loss and its increase at millimetre wavelengths is noted in Section 23.4, and a hybrid dielectric/microstrip antenna is described to reduce feeder loss. The merits of this antenna structure, which combines the best properties of microstrip technology with dielectric-line technology, is discussed in the wider context of overall losses, which includes that associated with launching waves into the feeder. Finally in Section 23.5 we discuss the use of extreme values of substrate permittivity and also magnetic materials to create a multiplicity of engineering devices with quite different applications. In Section 23.5.1 we note the results of an investigation into the use of expanded-foam polystyrene substrates to reduce the cost of a large array for direct broadcasting reception from satellites. A novel robust electronic beam-scanning element for satellites using a magnetic overlay is described in Section 23.5.2. In contrast, the use of very high-permittivity substrates enables a reduced-size patch antenna to radiate into human tissue for cancer therapy, as described in Section 23.5.3.

23.2 Radiation pattern control 23.2.1 Reflector feeds Reflectors are well known for their good radiation pattern control, and when combined with high-precision horn-type feeds lead to low-sidelobe envelopes and low cross-polarisation over significant bandwidths. The horn is, however, considered to be the point of greatest complexity in a reflector antenna, and the need for simple antennas makes the implementation of the microstrip reflector feed attractive for many reasons. Their lightweight properties make them suitable for satellite multiple-beam applications [I] and the ease of circuit integration has resulted in investigations into their use as monopulse guidance antennas with integrated comparator systems [2]. Simple microstrip disc elements have been used to feed circularly symmetrical reflectors [3]. Small ground-plane sizes have to be used to reduce feed blockage. This results in some equalisation of the E- and H-plane feed patterns as shown in Fig. 23.1, and a consequent improvement in efficiency and cross-polarisation

Extensions and variations to the microstrip antenna concept

w

N

w

\O

-

0

I

N

G-

e a

f

B ob l o b N VN

'

I

7259

1260

Extensions and variations to the microstrip antenna concept

compared with that expected from patches on large ground planes. Table 23.1 indicates typical results obtained after optimisation of the ground-plane size. The need for a circularly symmetric feed pattern [4] implies a balanced magnetic

Extensions and variations to the microstrip antenna concept

1261

where

Em

=

E,

=

+ cos 8 cos 44 cos 0 sin 40 + cos 44 40

sin

(23.2)

where Em and E, are the radiation fields from the magnetic and electric sources, respectively, and the polarisation is in the y-direction. Substituting eqn. 23.2 into eqn. 23.1 and converting to reference and cross-polarised fields Ed and Em, respectively, gives E,~, EC,,

-90

-60

\30( 0

-30

, 30

= 1 =

+ cos e

(23.3)

0

- A-.

/ y

\.)

60

90 8 ldegl

(01

\

Fig. 23.2

1-120 0

I

-90 Ibl

-60

-30

Small magnetic dipole Small electric dipole

Geometry for calculation of fields due to magnetic and electric sources

--. .-.,

,

I

30

60

90

8 ldegl

Fig. 23.1 Measured radiation patterns of microstrip disc on circular ground plane Patch diameter = 16.4 mm; frequency = 5.89 GHz; substrate diameter = 32.8 mm, thickness = 3.18 mm, (hll, = 0.06). e, = 2 . 5

--

H plane

-.-.----

I

H plane plane

cross-polar Fig. 23.3 Patch and ring feed

and electric source as indicated in Fig. 23.2. The radiated field is given by E

=

Em

+ E,

(23.1)

which indicates zero cross-polarisation. Circular polarisation can be generated by a further pair of sources orthogonal to the first and excited in quadrature. However, for microstrip radiators the source is primarily magnetic. The ideal

1262

Extensions and variations to the microstrip antenna concept

Huygens source can be approached by various practical adaptations such as the finite ground plane noted above. A further example is to surround the disc by a quarter-wavelength-deep short-circuited annular ring [3, 41 as shown in Fig.

Extensions and variations to the microstrip antenna concept

7263

Feed-pattern symmetry can also be achieved by using small patch arrays [5], and the narrower beamwidths are more appropriate to feeding larger F/D reflectors or offset reflectors. Fig. 23.6 shows a typical four-element feed with a co-planar corporate feed circuit. A 4% bandwidth is achieved and typical patterns are shown in Fig. 23.7. The sidelobe asymmetry is primarily due to radiation from the feed lines. Reflector performance of between -20 and - 30 dB cross-polarisation level and about 66% efficiency are indicated in Table 23.1. Fig. 23.8 shows computed reflector patterns of this feed. Use of overlaid feed networks, although resulting in increased constructional complexity, reduces feed-line radiation and hence cross-polarisation, as shown in Fig. 23.9 and Table 23.1.

Fig. 23.4 Measured peak cross-polarisation of microstrip feeds -Disc on circular ground plane (Fig. 23.1) -- Patch and ring feed (Fig. 23.3) ---- Co-planar fed patch array (Fig. 23.6) Overlaid patch array (Fig. 23.9) f = f, is patch or array resonant frequency

€3 deg

Fig. 23.5

Measured radiation patterns of patch and ring feed Patch diameter d = 19.5 mm. gap width g = 2.25mm, ring width r = 9.0mm frequency = 5.2 GHz, substrate thickness h = 3.18mm ( h l l , = 0.06),E, = 2.5 H plane ---- E plane, upper curves co-polar; lower curves cross-polar

-

23.3. Fig. 23.4 indicates that the peak cross-polarisation is reduced by about 7 dB. Coupling to the slightly off-tuned annular resonant section also increases the feed bandwidth by up to 50%. A typical feed radiation pattern is shown in Fig. 23.5.

Fig. 23.6

Co-planar-fed patch arrays For F / D = 0.8reflector, patch size = 9.7 mm x 7.2mm, patch spacing = 17 mm, a = 45 mm, b = 60 mm, substrate h = 1.59mm ( h l l , = 0.06).E, = 2.32,frequency = 12.2GHz

It is clear that microstrip can be combined with reflectors to give antennas with good radiation pattern control and high gain over restricted bandwidths. The above examples illustrate the capabilities of this hybrid microstrip reflector antenna using mainly conventional microstrip concepts to realise the feed. There is no doubt much further scope for innovation and improvement, perhaps in the

1264

Extensions and variations to the microstrip antenna concept

Extensions and variations to the microstrip antenna concept

7265

forming of hybrid feeds. An illustration of this is the dielectric-sphere and patch feed [6], described in the next Section. An example of optimised use of basic patch elements within a dielectric-filled cylindrical cavity has also been given in

Fig. 23.8 Calculated radiation patterns of prime-focus-fed axi-symmetric reflector with linearly polarised patch array of Fig. 23.6 ( a ) E-plane ( b ) H-plane

Progress is also likely in the use of optimised array structures using the sequential rotation technique. Fig. 23.10 shows a 16-element array [q suitable for use as a feed for a high FjD reflector. The patches are circularly polarised and arranged with sequentially rotated feeding [8].A simplified feed structure compared with the conventional corporate network (Fig. 23.6) results in lower feed radiation. The close grouping of the patch input points means that four bends are obviated and the 180' phasing at the T-junction results in this source of unwanted radiation being directed into the main beam, hence reducing spillover and increasing efficiency. The changes in the feed-network radiation characteristics are illustrated in Fig. 23.1 1. Fig. 23.12 shows that array sidelobe levels are reduced by up to 10 dB by the new feed network, and that reductions can also be obtained by thinner substrates albeit at the cost of reduced bandwidth. Reductions in cross-polarisation are similar to those for sidelobes. Improvements in bandwidth are also noted using sequential rotation, with the higher-order modes associated with low-Q patches being suppressed, leading to the possibility of reflector feeds with bandwidths in excess of 10%.

1266

Extensions and variations to the rnicrostrip antenna concept

Extensions and variations to the rnicrostrip antenna concept

1267

23.2.2 Spherical dielectric overlays A truncated dielectric sphere is attached to a microstrip patch antenna as shown in Fig. 23.13. The composite structure is no longer of low profile and its manufacture is more complicated, but an additional dimension in radiation pattern control is achieved [6,9, 10, 1I]. The spherical-lens action occurs in the near field of the microstrip patch and can be approximately analysed [I I] by representing the patch radiator by Hertzian dipole elements at its perimeter and involving equivalent current sources on the sphere surface. The effect of the sphere on the patch resonant frequency and input impedance is of second order and readily allowed for. An example of the theoretical and measured radiation patterns are given in Fig. 23.14. As expected, the sphere tends to focus the broad patterns of the patch, with the resulting gain of the structure increasing with sphere diameter until a threshold diameter is reached. For spheres having relative permittivities of 2.3, the threshold was reached for a sphere diameter of about three free-space wavelengths and a gain of about 16.5 dBi. At larger diameters the field distribution over the sphere aperture departs from the illumination required for low sidelobes and narrow main beam. This is also confirmed by the analysis which allows for the dissipative losses in the sphere and the degree of truncation; progressively increasing the truncation also reduces the gain.

Fig. 23.9 Radiation patterns of overlaid patch array FID = 0.8, patch size = 1 2 . 0 mm x 8.0 mm, patch spacing = 1 8 mm. a = 5 6 mm, b = 5 0 rnm, patch height = 1.59 mm ( h l l = 0.06). feed height = 0.79 mm, 8, = 2.32, frequency = 10.6 GHz

-co-polar cross-polar

I

measured

I

-- co-polar ---- cross-polar the'w

Fig. 23.1 0 Silhouette of disc array for circular polarisation using sequentially rotated feeding Array details: E, = 2.32, substrate thickness = 1.59 mm = 0,05&, frequency = 12.0 GHz. patch spacing = 0.7&.

This new composite element offers greater freedom of design with regard to the equality of the E- and H-plane beamwidths, and there is also some suppression of the cross-polarisation levels of the patch antenna. These aspects are

1268

Extensions and variations t o the microstrip antenna concept

Extensions and variations to the microstrip antenna concept

II

1269

Fig. 23.13 Sketch of dielectric sphere overlaid on a microstrip patch antenna showing truncation of sphere

o', degrees

Fig. 23.1 1

Computed radiation patterns of feed network of array of 4 x 4 elements with disc radiation suppressed a Sequentially rotated feed b Conventional feed as Fig. 23.6 -co-polarised ---- cross-polarised 4 = 0' Patterns are normalised to peak radiation of array and feed together

array

as Fig. 23.10

/

-401 0

0.05

I

0.1

hlh, Fig. 23.1 2

Computed peak sidelobe level of feed radiation of 4 Array details as Fig. 23.6 and Fig. 23.10 -e,= 1.06---e,= 2.32

x

4-element array

Fig. 23.14 H-plane pattern of a rectangular patch element with overlaid sphere at 15.4 GHz Sphere radius a = 25 mm. 8, = 2.2. tanS, = 0.0003; microstrip substrate e ,, = 2.3, rand, = 0.0001. height = 0.79 mm, patch size = 5.9 mm x 5.9 mm -co-polar measured -.-.- co-polar, theory ---- cross-polar measured . . . . . co-polar pattern of patch alone, theory

1270

Extensions and variations to the microstrip antenna concept

0

9,' degrees

-90

-60

-30

0

30

60

I

L

Fig. 23.1 5

90 I

b

Measured radiation patterns of circular microstrip patch with overlaid truncated sphere at 1 1.98 GHz Sphere radius a = 11.1 mm. truncated sphere height h' = 0.92 x diameter, E,, = 2.2, tans, = 0,001; microstrip substrate E , ~= 2.3, tans2 = 0.001, height = 0.79 mm. patch radius = 8 . 5 mm, patch probe = 3.2 mm from centre. Element gain = 10.8 dBi. H -plane co-polar ---- H-plane cross-polar E-plane co-polar . . . . . E-plane cross-polar

-

a Amplitude b Phase centred at z = 7 mm from substrate groundplane

Extensions and variations to the microstrip antenna concept

1277

1272

'

I

Extensions and variations to the rnicrostrip antenna concept

,

,

I

t

,

,

Extensions and variations to the rnicrostrip antenna concept

1273

illustrated in the design [6] of a feed for a reflector antenna. The spherelpatch feed element was required to illuminate the reflector with E- and H-plane patterns of similar beamwidths over a bandwidth of 11.7-12.5 GHz. Crosspolarisation levels were maintained below - 15 dB while the phase deviation over the reflector illumination sector of 50" is small (Fig. 23.15). In another development of this antenna, orthogonal feeds were attached to the patch to facilitate circular polarisation. The weight of the spherejpatch exceeds that of a small microstrip array having the same gain, although the pattern control of the former is superior and is an attractive alternative to a horn feed. The deployment of the spherelpatch antenna in large arrays has some significance at millimetre wavelengths because the spheres can be constructed as a moulded planar radome. For arrays with moderate sidelobe levels sparse array techniques can be used, and an example is shown in Fig. 23.16. This arrangement offers a simplified feeder system for the patch antennas. When smaller spheres are overlaid on an array with conventional element spacing, there is some improvement in the cross-polarisation levels. These properties are summarised in Table 23.2. Another application of the dielectric overlays concerns a way of beam scanning by placing several microstrip patches beneath the sphere. Computations [ll] show the effect on the radiation patterns when three isolated quarterwavelength patch radiators are switched on and off. A beam swing of 25" is achieved which, without the sphere, would require many more microstrip patches plus a phase-shifter system. It is expected that the spherical dielectric overlay technique will find use in special applications demanding additional pattern control, and Dubost has subsequently described a cylindrical implementation using a dielectric-rod lens and a linear array [12].

23.3 Wide-bandwidth techniques

Fig. 23.1 6 Sparsely distributedpatch array with overlaidspheres at 90 GHz, with no truncation of spheres a Photographs of arrays with 6 4 and 16 elements b E-plane radiation patterns of 64-element array Element spacing = 2a = 6.35mm. h'12a = 1 .Or E,, = 2.2. tan 6, = 0.001, E,) = 2.3, tansr = 0.001. h = 0.127 mm, patch size = 1 .O mm x 1 .Omm. co-polar measured ---- co-polar theory . . . . . cross-polar measured

-

23.3.1 Log-periodic structures Microstrip antennas and arrays have bandwidth limitations that have been extensively documented. Owing to the inherent resonant action, patch antennas have bandwidths typically less than 10% [13, 311. Increases on this can be achieved by the use of thick patches with probe inductance compensation [14], stacked patches [I51 or the use of coplanar parasitic elements [16]. Even in these cases bandwidths are usually less than 30% but the use of log-periodic scaling of arrays of microstrip patches allows bandwidths of up to two octaves (120%) to be achieved. Applications of such wideband arrays include electronic warfare and wideband radar and measuring systems [17] in those cases where the low profile is an important system consideration. The log-periodic principle applied to microstrip patches [la, 191 is illustrated in Fig. 23.17, where the patch size and spacing increases along the array by a

1274

Extensions and variations to the microstrip antenna concept

Extensions and variations to the microstrip antenna concept

7275

region and the array or element pattern should have a null in the direction of the wave propagating along the array. These conditions can be met by most microstrip arrays. However, to ensure wideband action the propagation characteristic of the array should have no stop bands below the resonant frequency.

factor z, where:

where I, w and dare defined in Fig. 23.17 and the subscripts refer to the nth and (n f 1)th patches. In addition, the substrate thickness for each patch should be similarly scaled, effectively producing an array on a tapering substrate as shown in Fig. 23.17~.Such scaling will ensure that the array characteristics vary periodically with the logarithm of the frequency, provided certain conditions relating to the patch connection to the feed line are observed. This arrangement is the microstrip analogue of the log-periodic dipole array [20]. In both cases the elements close to resonance form an active region, giving rise to strong radiation, and hence attenuation of the travelling wave on the array.

ty L

-

H plane

x

input

feed

,patches

U I 0 2

.z

0

-1

pd lradsl

1

u,d

lnepers)

(b)

Fig. 23.17 Log-periodic electromagnetically coupled overlaid patch array a With scaled feed line and substrate b With uniform patch displacement p, substrate thicknesses h, and h, and feedline width w,

Criteria for successful log-periodic operation of series-fed arrays have been deduced. To prevent excitation of higher-order mode resonances in the lowfrequency elements beyond the active region, the array should be fed from the high-frequency end, should have high attenuation within and beyond the active

Fig. 23.18

( a ) Equivalent circuit of single overlaid patch as shown in Fig. 23.17 ( 6 ) Propagation characteristic of uniform overlaid patch array -calculated with mutual coupling--- calculated without mutual coupling 0 measured points I = 1 0 m m . w = 8 m m . p = 1 . 2 5 m m , d = 9 4 2 m m , w , = 2 . 5 m m , h,= 1,586 mm, h, = 0.793 mm, 8, = 2.32

The complex propagation constant 8' =

+ jy,, -sin kd 2 yo K Z kd 1 - j-sin r,

cos kd cos /?'d

=

fi

+ ju of a uniform array is given by

1276

Extensions and variations to the microstrip antenna concept

where adjacent-cell mutual coupling only is assumed. d is the array period length, Y,and k are the feed-line admittance and wave number respectively, and Y , , and Y,, are the self and mutual admittances of the array elements. Fig. 23.18 shows the equivalent circuit of the overlaid patch and the propagation characteristic of a uniform array of such patches, deduced using eqn. 23.5. k,, = 2~f/c is the free-space wave number. The normalised propagation constant pd is -a at zero frequency (kod = 0) due to the alternation in patch feeding. pd rises smoothly from - T to the resonant region at kod = 1.7, where heavy attenuation takes place owing to strong radiation. On the other hand, a stop band is noted in the propagation characteristic of a quarter-wavelength-line coupled patch array (Fig. 23.19). Similar characteristics have also been noted 1191for the

i

I 1

Extensions and variations to the microstrip antenna concept

1277

Fig. 23.20 shows the input return loss and gain of a 36-element overlaid patch log-periodic array designed for a near-broadside beam. Return loss is less than - 10 dB and the gain is greater than 8 dB over the bandwidth 4-16 G H z The

1

8

12

16

20 Freq.(GHz)

Fig. 23.19 Calculated propagation characteristic of quarter- wavelength line coupled patch array Array configuration and equivalent circuit of single period shown inset at top right and left, respectively I = 10mm. w = 8 m m t d = 9 ~ 8 2 m r n .w , = 2.5mm.h= 1.586mm.e, =2.32. w, = 0.5 mm, I, = 7.0 mm

comb-line array and the series-connected patch array [21], and it has been concluded that, for good log-periodic action, the patches need to be electromagnetically coupled to the feed line in some way. This introduces a series resonance into the element equivalent circuit which simulates that of the successful dipole log-periodic element. Such conclusions are, however, deduced from heuristic reasoning, and it may well be that other forms without coupling gaps may be discovered which also produce good log-periodic action.

(cl Fig. 23.20 36-element overlaid patch log-periodic array a Array silhouette b Measured input return loss IS,, I and transmission loss IS,, I measured --- calculated c Array gain -measured x calculated I, = 3.67 mrn, w, = 2.92 mm, dl = 3 6 7 mm, r, = 1.05. h, = 0.793mm, h, = 1,586mm. p = 1.25.8, = 2.32, T, = 1 .O Overall array size = 340 mm x 50 mm

-

calculated efficiency ranges from 85% to 70% across this band. Array analysis is based on an equivalent-circuit model of the array and reasonable agreement with theory is noted. Fig. 23.21 shows radiation patterns in the H-(longitudinal) plane. Significant narrowing of the beamwidth occurs at high frequencies. This

1278

Extensions and variations to the microstrip antenna concept

is believed to be due to the increased electrical thickness of the active-region patches at high frequencies, which reduces feed-line patch coupling, and hence increases the active-region length. The high cross-polarisation is also believed to be due to this effect. The lack of tapered substrate thickness is noted as the main limitation on the overall bandwidth of this log-periodic array.

Extensions and variations to the microstrip antenna concept

1279

Figs. 23.22 and 23.23 show results for the quarter-wavelength line coupled log-periodic array, the so-called quasi-log-periodic array [22], shown inset in Fig. 23.19. The array is constructed on a single uniform-thickness substrate. Fig. 23.22 shows input return loss and gain, and Fig. 23.23 shows E- and H-plane radiation patterns. A bandwidth of 22% was obtained for a practical antenna with five elements. frequency

2.6

2.8

3.0

, GHz

3.2

3.4

frequency, GHz Fig. 23.22 Performance of quasi log-periodic antenna; antenna shown inset in Fig. 2 3 . 1 9 a Measured and computed return loss as a function of frequency measured - - computed b Measured power gain in broadside direction as a function of frequency

-

Fig. 23.21 H-plane patterns of array of Fig. 23.22 ( a ) 4 GHz; ( b ) 16 GHz

-measured co-polar

--- calculated co-polar

-.-.-

measured cross-polar

The log-periodic principle can be also applied to microstrip to form endfire arrays [23], in contrast to the broadside-beam types described above. Applications here include mounting on nose cones of aerospace vehicles for a range

7280

Extensions and variations to the microstrip antenna concept

Extensions and variations to the microstrip antenna concept

n"

I

1281

of electronic-warfare functions. The key features in design are choice of element spacing and phasing and choice of element. The necessary close element spacing [24] and strong element radiation in the endfire direction are achieved by using quarter-wavelength shorted patches as shown in Fig. 23.24. These are parasitically coupled by tabs to the feed line to avoid stop bands [19]. Fig. 23.25 shows freq IGHzI

transrniss~on loss

frea IGHzI

return Loss Id01 N)

15

Fig. 23.23

dB Measured and computed co-polar radiation patterns of quasi log-periodic anten. na ( a ) E-plane pattern at 2.81 GHz ( b ) E-plane pattern at 2.87 GHz ( c ) H-plane pattern at 2.8 GHz -measured --- computed

short-circuit Fig. 23.24

Silhouette of endfire log-periodic microstrip patch array

Fig. 23.25 Performance of endfire log-periodic microstrip patch array a Transmission loss ---- measured --- computed b Measured return loss c Measured radiation patterns respectively, at: -4.25 GHz; --- 4.5 GHz; 4.75 GHz, . . . . .5.0 GHz.

the performance of an array which was designed for a 25% bandwidth. Similar performance trade-offs to those for the broadside log-periodic array are expected. as are limitations in overall bandwidth due to the use of flat substrates.

7282

Extensions and variations to the rnicrostrip antenna concept

23.3.2 Dichroic dual-function apertures There is a growing interest in apertures that can be used at different frequency bands, and for microstrip arrays this is most readily achieved by embodying dual-frequency patch elements in the array. The resulting band separation is generally small, but a multi-octave separation is now possible using the new dichroic microstrip concept [25-271 which permits two microstrip arrays to be sandwiched together as in Fig. 23.26. The innovation rests with array B composed of a printed mesh, which at f, is found to function as a conventional microstrip antenna. At frequency f,(> f,) the frequency-selective properties of the mesh render it 'transparent' to the radiation from array A. Typically f H f L

Fig. 23.28

Extensions and variations to the rnicrostrip antenna concept

1283

23.31 is a photograph showing its application. Many variations of the dichroic microstrip concept have been exploited including a rectangular mesh with integral-array feeders [29] and a novel window antenna [27l whereby both the ground plane and patches of a microstrip array are composed of frequency

Geometry of the dual-band dichroic array showing the frequency-selective surface array 6 superimposed on a microstrip array A

will be about 8 : l . The measured and computed radiation patterns of a mesh patch on a low-permittivity substrate are shown in Fig. 23.27, and apart from a higher input impedance the co- and cross-polar patterns are very similar to those of a conventional solid patch. A key issue is the degree of transparency experienced because the mesh patch is of limited size and furthermore is in the near field of the radiation sources. Computations using the NEC program 1281 and measurements establish, however, that the resulting transparency is surprisingly good, as the measurements in Fig. 23.28 show. A scattering analysis [29] gives further insight into the transparency, and establishes that the mesh perimeter has a significant effect, causing the ripple-interference pattern (Fig. 23.28). In the practical deployment of the dichroic concept there are many effects to consider which differ with the application, and numerous examples have been studied. The effect of a mesh on a 4 x 4 microstrip patch array is illustrated in Fig. 23.29, and the extension to higher-gain arrays in Fig. 23.30, which also shows an increase in sidelobe level due to scattering from the feeders of array B. The technique has been applied at millimetre wavelengths, and Fig.

Fig. 23.27 NEC-programme computations and measurements of square-mesh microstrip patch antennas. H-plane radiation pattern of a mesh patch with transmission-line feed (inset) a = 5.6cm; c = 1 cm, t = 0.1 cm, h = 0.06cm, frequency = 2.3GHz

}

I

measured

6,

---- computed E,

= I .05

= 1.0

(i) co-polar (ii) cross-polar

selective mesh, thus allowing the arrays to be used as an electromagnetic window at fH and as a conventional array at f,. Having introduced the dichroic microstrip concept, it is clear that much further exploitation remains using different geometries of mesh and substrate permittivities. The use of high-

7286

Extensions and variations to the microstrip antenna concept

Extensions and variations to the microstrip antenna concept

7287

has established several issues:

I

The increase in microstrip-line loss with frequency is not as excessive as originally contemplated. Travelling-wave dielectric antennas have lower loss than the microstrip counterparts, but control of radiation patterns is a problem. The lower transmission loss of dielectric antennas is negated by their incompatibility with waveguide feeds because of launcher radiation losses. Microstrip technology is the most attractive option up to 140 GHz, but there are some merits in the hybrid dielectric/microstrip linear array that combines the best features of microstrip and dielectric technologies. We will outline here the main features of the hybrid antenna, but first recapitulate briefly on the level and source of the increased microstrip-line loss at

Fig. 23.31

Photograph of 16 array removed.

x

16, 90 GHz array showing superimposed 2

waveguide Iaunc

Fig. 23.30 Measured H-plane radiationpatterns of a comb array A under a mesh-parch array, 6; mesh patch has a size a x a a = 7.95 cm, c = 1.1 1 cm. t = 0.48 cm, frequency = 17 GHz, E,, = 2.32, e, = 1.05, h, = 0.08 cm, h, = 0.6 cm, comb array size = 28 cm x 28 cm. (i)co-polar (ii) cross-polar without mesh-patch array --- with mesh-patch array

-

Fig. 23.32

Hybrid dielectriclmicrostrip antenna array

x

2, 9 GHz

1288

Extensions and variations to the microstrip antenna concept

millimetre wavelengths. A factor that has previously obscured the accurate measurement of microstrip loss at these higher frequencies is the leakage of radiation from the transitions attached to the line. A key contribution in the investigation [30] was the quantification, and hence separation, of the radiation from the dissipative loss. It was found that for RT Duroid substrates the loss at 90 GHz was 0.13 dB/1,, as opposed to 0.1 dB/L, at 20 GHz where 1, is the microstrip-line wavelength. Experiments and computations indicated that some loss reduction could be achieved by polishing the printed conductors to decrease surface roughness, but the practical implementation was unrealistic. Even less realistic in manufacture is the process of thickening the conductor so that its edges can be rounded. The hybrid dielectric/microstrip-antennaconcept aims at replacing the microstrip line in a linear array with an insular guide feeder; the practical arrangement is illustrated in Fig. 23.32. The microstrip patches electromagnetically couple to the insular guide feeder, and analysis and measurements establish that the array distribution is controlled by the feeder-patch separation. A summary of the array performance is given in Table 23.3 and a photograph of the structure in Fig. 23.33. The radiation pattern control is superior to that of a planar dielectric antenna, yet the low-transmission-loss qualities of the latter are preserved. The hybrid antenna only retains its advantage over a microstrip array when used in a compatible dielectric-feeder arrangement, and the test set-up in Fig. 23.32 with a waveguide/insular guide transition will lower the system efficiency owing to increased launcher loss. 23.5 Novel use of materials

23.5.1 Foam substrates for Iarge direct-broadcast-satellite domestic receiving arrays The use of expanded polystyrene foam for microstrip substrates is well known, and for a patch antenna it is generally beneficial in terms of the bandwidth and efficiency [31]. The use of a foam substrate in a large array appears to offer the outstanding advantage of a low-cost substrate, and this has recently been investigated [32,33]. Fig. 23.34 shows the laminar construction technique of the foam array. A distinct problem concerned the design of triplate corporate feeds for this electrically large array because the foam did not confine the feed fields as well as a plastic substrate and a significant radiation loss was experienced at the transition region between the corporate feed and antenna. The array specification was complicated by the requirement for a squinted beam and cikular polarisation, the latter being achieved using a polariser grid. Fig. 23.35 shows the measured radiation patterns. The pattern and bandwidth specifications were difficult to meet with a good margin, and the corporate feed loss contributed somewhat to the noise performance of the receiving system and increased the physical size of the array. A detailed comparison with conventional dish anten-

Extensions and variations to the microstrip antenna concept

1289

Table 23.3 Power budgets of 9 0 GHz hybrid linear microstrip patch antennas

(9

I

(ii)

Beamwidth, deg. (theory) (measured) Squint angle, deg (measured) Sidelobes, dB (measured) Cross-polar, dB (measured) Directivity*, dB Gain, dB (measured) Launcher loss, dB (theory) Mismatch loss, dB (measured) Feeder loss?, (theory) Resonator lossg*, dB (measured) Load loss*, dB Element spacing, mm Efficiency §, % (assuming no launcher or load loss) Efficiency" of microstrip array of same physical size, % ' Directivity = 10 log ( A / & cos (squint angle) dB; A = aperture area

t Calculated using 0.05 dB/& over 40 wavelengths '' From measurements on patch-resonator Q-factors '(i) Load loss = 24.2 - (17 + 2 + 0.04 + 2 + 0.97)

= 2.19 dB (ii) Load loss = 23.6 - (18 + 2 + 0.04 + 2 0.97) = 0.59 dB 5 (i) Efficiency = 24.2 - (17 + 2 + 2.19) = 3.01 dB = 50% (ii) Efficiency = 23.6 - (18 + 2 + 0.59) = 3.01 dB = 50% " Microstrip feeder of same physical length (39 wavelengths), loss = 0.1 3 dB/&, patch loss = 0.97 dB

+

1

1

1

1

1

CMs 1

1

1

1

E~

1

= 2, Z , = 50 R, line

1

Fig. 23.33 Photograph of 80-element 90 GHz hybrid dielectric/microstripantenna array

1290

Extensions and variations to the microstrip antenna concept

Extensions and variations to the microstrip antenna concept

7297

nas [33] is given in Table 23.4, illustrating the relative effects of noise due to antenna loss and the receiver noise. The conclusion for this particular application is that the use of a foam substrate leads to low costs but there is a compatibility problem with the feed arrangement, and the specification could be

H-plane

Fig. 23.35

Measured circularly polarisedradiationpatterns o f foam array at 17.9 GHz for four 33-finger combline sub-array with metal-plate polariser

Table 23.4 Comparison of antenna types and projected carrierlnoise ratios ( C I N ) at 17.9 GHz: NF = noise figure Fig. 23.34 Laminar construction o f foam microstrip array 1 Metal ground plane 2 Foam substrate 3 Combline array elements 4 Foam spacer 5 Polarising grid 6 Waterproof cover

more readily met using a higher-permittivity substrate and perhaps some lowerloss waveguide feeders for the longer lengths of feed. The feasibility then rests with manufacturing a substrate capable of robust stable operation at low cost. The array size, however, is very dependent on the noise performance of the receiver, and recent developments in semiconductors make possible a smaller

Large microstrip array

0.9 m dish

0.6 m dish

0.5 -4.56

- 8.07

5.2 -4.50

14.0 17.5 20.7

10.5 14.0 17.2

9.0 12.2 14.9

0.5

Antenna dissipation, dB Aperture capture area, dB m2 Total C/N, dB: 8 dB NF receiver 5 dB N F receiver 2.5 dB NF receiver

These figures assume: (a) 1.4 dB rain loss (b) 0.3 dB galactic noise (c) 160 W transmitted power (4 Antenna is modelled as a simple attenuator situated before receiver For C-MAC system, picture qualities are 'fair' for C / N > 9 and 'good' for C / N > 12

1292

Extensions and variations to the microstrip antenna concept

more efficient array, thus endorsing the feasibility of a flat plate DBS antenna. This research project [32, 331 has been a milestone in the development of a low-cost DBS array and clearly demonstrates the trade-offs between performance and cost. The additional difficulties of electronic beam scan are also highlighted.

Extensions and variations to the microstrip antenna concept

1293

23.5.3 Use of very-high-permittivity substrates in hyperthermia applicators Microstrip structures have also proved useful in the design of applicators to dispense high-power electromagnetic waves into human tissue in cancer

quor ter wavelength

section X - X Fig. 23.37 Hyperthermia applicator using quarter- wavelength microstrip patch

Fig. 23.36 Scanned microstrip patch antenna using thick ferrite slab a Construction of ferrite microstrip antenna showing co-ordinates b H-plane patterns of antennas e, = 10. e, = 13.8.p, p2 2. 1, 2a = 6 mm, frequency = 8.6 GHz

-

(ii) h, = 3 mm (iii)h2 = 3 mm magnetised Field strength of magnet was measured as 0.04 T in free space

23.5.2 Magnetic materials and beam scanning Magnetised substrates have been used as substrates for patch antennas [34]. More recently [35] a thick ferrite superstrate with an applied magnetic field, as shown in Fig. 23.36a, was devised and led to the creation of a beam that could be scanned between 15" (Fig. 23.366). An approximate analysis of the element illustrates the fundamental non-reciprocal action of the ferrite, but the precise behaviour embraces many effects including leaky-wave and surface-wave action in the ferrite slab. This type of element is of interest in certain communication applications demanding a robust construction, and the use of modem magnetic materials with temperature compensation will lead to a compact assembly.

*

Fig. 23.38 Photograph of microstrip hyperthermia applicatol

therapy. This fairly recent use of electromagnetic waves [36] necessitates the design of applicators that are well matched to the impedance of the human body and are compact in size for clinical convenience. An annular microstrip-loop

1294

Extensions and variations to the microstrip antenna concept

radiator has been devised [38] using plastic substrates, but the more recent compact applicators [36, 371 use a very high substrate permittivity. A sketch of a typical compact applicator is shown in Fig. 23.37 and a photograph in Fig. 23.38. In these designs the size reduction is achieved both by the high permittivity and the use of a quarter-wave as opposed to half-wave resonator. Further details are given in Table 23.5 for lower-frequency applicators. The penetration depth is a measure of performance, indicating the distance over which I/e2of the power is dispensed. Focused arrays of these applicators bring about an increased penetration depth. The compact applicator can be designed for a good stable input impedance match in operation without the use of additional matching elements, and further size reductions are possible at low frequencies by inserting ferrite material in the low-impedance regions of the substrate.

Table 23.5 Characteristics and performance of low-profile applicators

Applicator Material: 6, Pr

Element: quarter wavelength, cm Dimensions, cm Thickness, cm: Substrate Superstrate Frequency, MHz Net power for 235 W kg-' Penetration depth, cm (phantom)

A 30 1 7.5 15 x 15 x 4.5 2.2 2.2 200 156 4.0

B ' 30 2.5 7.5 15 x 15 x 4.5 2.2 2.2 120 406 4.3

23.6 Summary comment

The extensions and variations to the microstrip-antenna concept described are vastly different in application, and emphasise both the ingenuity that has already been experienced and the fund of innovative ideas that will continue to be created in future years. It was stated in Chapter 1 that the inspiration for innovation lies in the demands made by new systems, and this is well illustrated by the efforts on one hand to exert more control of radiation patterns, and on the other to increase bandwidth by an order. In each case one parameter is optimised at the expense of the others in a way which is compatible with the system constraints prevailing, but above all it is the microstrip technology that is diluted by other construction techniques to effect the desired optimisation. As already mentioned, it is a sign of maturity in a technology when a designer has learnt just how to exploit selectively its best features with confidence.

Extensions and variations to the microstrip antenna concept

7295

23.7 Acknowledgements

The authors would like to acknowledge the contribution to the work performed at RMCS and described in this chapter, of Dr G Andrasic, Dr C Hall, Dr C Prior and Mr R Johnson.

23.8 References I

I WOO, K.: 'Multiple beam antenna feed development'. IEEE Int. Symp. on Antennas and Propagation, Philidelphia, USA, 8-13 June, 1986, Vol. 1, p. 409-412 2 OLTMAN, H. G., WEEMS, D. M., LINDGREN, G. M., and WALTON, F. D.: 'Microstrip components for low cost millimetre wave seekers' In 'Millimetre and submillimetre wave propagation and circuits'. AGARD Conf. Proc. 245, pp. 27-1 to 27-9 3 HALL, P. S., and PRIOR, C. J.: 'Wide bandwidth microstrip reflector feed element'. 15th European Microwave Conference, Paris, Sept. 1985, p. 1039 4 HALL, P. S., and PRIOR, C. J.: 'Microstrip feeds for prime focus fed reflector antennas', IEE Proc., 1987, 134H, pp. 185-193 5 HALL, P. S., and PRIOR, C. J.: 'Microstrip array for reflector feed applications'. 14th European Microwave Conference, Liege, Sept. 1984, pp. 631-636 6 JAMES, J. R., HALL, C. M., HALL, P. S., and PRIOR, C. J.: 'Dielectric sphere reflector feed with microstrip excitation'. Proc. ISAP 1985, Tokyo, Aug. 1985, pp. 101-104 7 HALL, P. S., and HALL, C. M.: 'Coplanar corporate feed effects in microstrip patch array design', IEE Proc., 1988, 135H. pp. 180-186 8 TESHIROGI, T., TANAKA, M., and CHUJO, W.: 'Wideband circularly polarised array with sequential rotation', Proc. ISAP 85, Tokyo, Aug. 1985, pp. 117-120 9 HALL, C. M., ANDRASIC, G., and JAMES, J. R.: 'Microstrip planar arrays with dielectric sphere overlays', Electron Lett., 1985, 21, pp. 356-357 10 HALL, C. M., JAMES, J. R., and ANDRASIC, G.: 'Microstrip patch arrays with spherical dielectric overlays', Proc. Int. Conf. on Antennas and Propagation, Warwick University, IEE, April 1985, p. 89-93 11 JAMES, J. R., HALL, C. M., and ANDRASIC, G.: 'Microstrip elements and arrays with spherical dielectric overlays', IEE Proc., 1986, 133H, pp. 474482 12 DUBOST, G., and NICOLAS, M.: 'Broad angular coverage and large bandwidth antenna. 17th European Microwave Conference, Rome, Sept. 1987 13 JAMES, J. R., HENDERSON, A., and HALL, P. S.: 'Microstrip antenna performance is determined by substrate constraints', Microwave Syst. News, 1982, 2, pp. 73-84 14 HALL, P. S.: 'Probe compensation in thick microstrip patches', Electron Lett., 1987, 23, pp. 606-607 I5 HALL, P. S., WOOD, C., and GARRETT, C.: 'Wide bandwidth microstrip antennas for circuit integration', Electron. Lett., 1979, 15, pp. 458-460 16 KUMAR, G., and GUPTA, K. C.: 'Non-radiating edge and four edges gap coupled multiple resonator broad band microstrip antennas', IEEE Trans, 1985, AP-33, pp. 173-177 17 BENNETT, C. L., and ROSS, G. F.: 'Time domain electromagnetics and its applications', Proc. IEEE, 1978, 66, pp. 299-318 18 HALL, P. S.: 'New wideband microstrip antenna using log periodic technique', Electron Lett., 1980, 16, pp. 299-318 19 HALL, P. S.: 'Multi-octave bandwidth log periodic microstrip antenna array' Proc. IEE., 1986, 133 H, pp. 127-136 20 ISBELL, D. E.: 'Log periodic dipole arrays' IRE Trans., 1960, AP-8, pp. 260-267 21 DONG, W. R., and SENGUPTA, L. L.: 'A class of broad band patch microstrip travelling wave antennas', IEEE Trans., AP-32, (I), pp. 98-100

7296

Extensions and variations to the microstrip antenna concept

22 PUES, H., BOGAERS, J., PIECK, R., and VAN DE CAPELLE, A.: 'Wideband quasi log peripdic microstrip antenna', IEE Proc.. 1981, 128H, pp. 159-1 63 23 HALL, P. S., and SPARROW, A,: 'Microstrip log periodic antenna array with end fire beam', Electron Lett., 1987, 23, pp. 912-913 24 GREISER, J. W., and MAYS, P. E.: 'The bent backfire zigzag', IEEE Tram., 1964, AP-12, pp. 28 1-290 25 BOND, K., and SHELLEY, M. W.: 'Dual frequency antenna integration using invisible grating structures', IEE Proc., 1986, 133H. pp. 137-142 26 JAMES, J. R., and ANDRASIC, G,: 'Dichroic dual band microstrip array', Electron Letts., 1986, 22, pp. 1040-1042 27 ANDRASIC, G., and JAMES, J. R.: 'Microstrip window array', Electron. Lett., 1988,24, pp. 96-97 28 BURKE, G. J., and POGGIO, A. J.: 'Numerical electromagnetic code (NEC) method of moments', Tech. document 116, Naval Electronic Systems Command, July 1977 29 JAMES, J. R., and ANDRASIC, G.: 'Superimposed dichroic microstrip antenna arrays', IEE Proc., 1988, 135H. No 5, pp. 304-312 30 JAMES, J. R., and HENDERSON, A.: 'Planar millimetre wave antenna arrays' In BUTTON, K. I. (Ed.): 'Infra-red and millimetre waves'. Vol. 14: Millimetre components and techniquesPart V. (Academic Press, 1985), pp. 189-247 31 HENDERSON, A., JAMES, J. R., and HALL, C. M.: 'Bandwidth extension techniques in printed conformal antennas'. Military Microwaves Conference, Brighton, 1986, pp. 329-334 32 HENDERSON, A,, JAMES, J. R., HALL, P. S., STOTT, J. H., and BOARDMAN, D. H.: 'Investigation of a cost constrained 12 GHz flat plate antenna for DBS'. Proc. ICAP, Warwick, 1985, pp. 108-112 33 HENDERSON, A,, and JAMES, J. R.: 'Low cost flat plate array with squinted beam for DBS reception', Proc. IEE, 1987, lMH, pp. 509-514 34 DAS, N., CHOWDHURY, S. K., and CHAlTERJEE, J. S.: 'Circular microstrip antenna on ferromagnetic substrate', IEEE Trans, 1983, AP-31, pp. 188-190 35 HENDERSON, A., JAMES, J. R., and FRAY, A.: 'Magnetised microstrip antenna with pattern control' Electron. Lett., 1988, 24, pp. 45-47 36 JAMES, J. R., HENDERSON, A,, and JOHNSON, R. H.: 'Compact electromagnetic applicators'. In HAND, J. W., and JAMES, J. R. (Eds.): 'Physical techniques in clinical hyperthermia' (Research Studies Press, John Wiley, 1986), pp. 149-209 37 JAMES, I. R., HALL, C. M., and ANDRASIC, G.: 'Angled dual compact hyperthemic applicators', Proc. IEE, 1987, lMH, pp. 315-320 38 BAHL, I. J., BHARTIA, P., and STUCHLY, S. S.: 'Design of microstrip antennas covered with a dielectric layer', IEEE Trans., 1982, AP-30, pp. 314-318

Index

Abberation, 96 Acid, copper, 936 Activation energy, 875 Active angle, 1241 Active element pattern, 701,739, 1249 Active elements in a cylindrical array, 1249 Active impedance, 732 Active patches, 34 Active reflection coefficient, 708, 739 Additives, brightener, 936 Adhesion, 936 Adjustable height patch. 30 Admittance, aperture, 727 Aerospace systems, 1057 Air gap, adjustable, 193 Air-filled waveguide, 858 Airborne antenna, 1139 Airborne phased arrays, 802,810 Alumina substrates, 14, 1025 Aluminium, 93 1, 946 Aluminium foil, 1075 Amplitude distributions, 830 Analytical methods aperture radiation model, 583 cavity model, 458,580,1058,1228 Cohns method, 611 contour integral method, 472 desegmentation, 456,494 direct form of network analogue, 462

EMF,249 Filton Integration method, 285 integral equations, 715 method of moments, 364,708 moments method, 593 multiport network approach, 455 multiport network model, 462 network analysis, 488 plane wave spectrum method, 285 real-space integration method, 286

reciprocity method, 278 Richmonds reaction equation, 597 segmentation, 456,488 spectral domain approach, 590 steepest descent method, 278 surface current model, 1228 synthesis, 361 transmission line model, 456 variational method, 235 Wiener-Hopf method, 478 Angled slot array, 39 Anisotropy, 881, 909, 917 Annealed, 946 Annular ring, 25,879,1262 Annular slot, 111,611,1086 Annular slots attenuation coefficient, 614 guide wavelength, 611 impedance, 611 reflector planes, 617 Antennas conical, 601

DBS,859,861 dielectric, 1287 directly coupled three resonator, 507 hybrid microstrip, 580 integrated, 14 gap coupled multiresonator, 507 millimeter wave hybrid, 1285 multi-terminal, 236 open microstrip, 580 window, 1283 wraparound, 85 Antenna location, received signal fluctuations, 1084 Antennas for portable equipment, 1092 Aperture admittance, 727 Aperture blockage, 96, 104 Aperture coupled patches, 330

lndex

1298 lndex

Aperture coupling, 35, 332, 823 Aperture distribution, 762,821, 822, 825, 851 Aperture distribution Dolph-Chebyshev, 855 Aperture radiation analysis method, 583 Apertures, dichroic, 1282 Applications, 8 Array factor, 829 Array lattice rectangular, 706 triangular, 706, 1243 Array structures, 36 Arrays, 7,35 angled slots, 39 architecture, 745 asymmetric step, 39 bonding, 916 brick wall, 848 cascaded patch, 822 chain, 37, 763, 816 Chebyshev, 774 circularly polarised, 755,765 co-planar, 758 comb line, 37, 766, 822 composite element, 759,770 conformal, 795, 1153, 1227 conical, 1154 constant-conductance, 846 corner fed patches, 647 corporate-fed, 789 crank, 844 crank-line, 777 crank-type, 764 cross fed, 36, 655, 843 cross printed-dipole, 766 cross slot, 766 cylindrical, 34,765, 1227 DBS, 766,790,1288 design of planar, 622 discontinuity, 843 dual frequency, circular polarised, 802 dual polarised, 1073 electronically switched, spherical, 792 finite, 301, 731 flat, circular polarised, 765 four element, 1217 Franklin, 8 16, 848 Franklin line, 38 herringbone, 835 herringbone line, 38 infinite, 698, 731 lattice, 848

linear, 345,449 linear centre fed, 839 linearly polarised, 846 log periodic, 39, 387 microstrip, 443 millimeter wave, 1282 monopulse, 849, 1068, 1153 non uniform, 630 omnidirectional, 39, 382 parasitic, 801 parasitic patch, 825, 833 parasitically coupled, 37, 345 patch, 1263 planar, 345, 776,790 rampart, 816, 844 rampart line, 38,223, 763, 1222 recurrent sequential, 808 resonant, 769,816 scanning, 792 sector beam, 1081 sequential, 759, 788, 805 sequentially rotated, 12 series, 816 series fed patch, 515 series fed patches, 624 series-fed, 789, 8 18 series-fed circular polarised, 770 serpent, 816,833,843 serpent line, 38 sparse, 1273 spherical, 34,793, 1239 square patches, 1073 square-looptype, 764 squintless, 758,841 strip dipole and slot, 39 sub arrays, 655 synthesis, 662 tapered, 650 transposed, 821,822 travelling wave, 755, 762, 765, 769, 816,1222 triangle line, 38 two dimensional, 808 two sided, 746 untransposed, 821 wide bandwidth, 372 wideband, 804 wire grid, 848 Assemblies, 916 Asymmetric feeds, 797 Asymmetric step array, 39 Attachment mode, 433 Attenuation, 1016

Attenuators, 1241 Axial polarisation, 1239 Axial ratio, 723, 787, 1185 Axial-ratio bandwidth, 758,829, 859 Azimuthal modes, 53 Backward firing beams,834 Bag-moulding, 930 Balanced stripline, 1003 Bandwidth, 5, 11, 111, 128,219, 335, 338, 554,743,796,895 Bandwidth, 9 axial-ratio, 829, 859 extension, 9 gain, 823 VSWR, 118,823 Base-station antenna, 1083 Basis functions, 282 entire domain, 429, 437 Maxwell, 282 Maxwell, modified, 282 pulse, 282 subdomain, 282,437 subsectional, 423,440 Beam squint, 758 Beam steering, 1241, 1249, 1273 Beam-forming, adaptive, 862 Beams backward firing, 834 forward firing, 834 Beamwidth, 104 Bend measurement, 976 Bending, 916 Bends, 1168 Beryllia substrates, 1025 Bessel function, 1058, 1204 Bidirectional communications, 1107 Bismaleimide, 95 1 Bismaleimide-triazineepoxx878 Black copper oxide, 880 Blind spots, 336, 729 Blockage, aperture, 96 Boards, printed wiring, 916 Bolometer, 1194 Bonding lead, 952 thermal-compression, 938 thermosonic, 938 wire, ultrasonic systems, 938 Boundary conditions, 49, 115,395 Branch-line coupler, 854 Branching network, 825

1299

Brass, 946 Brick wall arrays, 848 Broadband microstrip antenna, 1083, 1086, 1129,1134 Broadband matching, 558 Built in antennas, 1092 Butler matrix, 855, 860, 1083 Cabin antenna, 1085 CAD, 14, 1031 Acline, 1033 Analop, 1036 Autoart, 1037 CADEC, 1033 CiAO, 1035 computer graphics, 1175 Esope, 1033 LINMIC, 1034 Mama, 1036 Micad, 1037 Micpatch, 1035 Microkop/Suspend, 1036 Micros, 1038 microstrip, 1001 microwave software applications, 1036 Midas, 1034 Multimatch, 1036 photoplots, 1175 Planim, 1036 S/Filsyn, 1037 Supercompact, 1033 techniques, 517 Temcad, 1039 Touchstone, 1032 Transcad, 1037 triplate, 1001 Fringing, 901 Capacitance, 901 Capacitive tuning, 329 Capacitors, 1040 Car telephones, 1079 Carbide, 922 Carbon fibre reinforced plastic, 1075 Cavity feeds, 859 ~ a v i t model, ; 112,458, 580, 884, 1058, 1228 Cavity-perturbation, 884 CCIR-TVRO conditions, 671 Central shorting pin, 85 Centred fed dipole, 287 Ceramic-PTFE, 953

1300 lndex

lndex

Chain array, 37, 763, 816, 940 Chain scission, 940 Chebyschev taper, 774, 1069 Chloride acid cupric, 949 alkaline cupric, 949 ferric, 949 Choke, peripheral, 104 Chokes, 97 Chromic-acid, 950 Circuit, etching, 1028 Circular array, 1127 Circular array feed, 1132 Circular array of slots, 1132 Circular array of strips, 1132 Circular microstrip discs, 1136 Circular patches, 45, 63, 111, 720, 1058, 1202 Circular polarisation, 5, 130, 219, 722, 744, 755,787, 846,848, 1127, 1132, 1261,1273 Circular polarised radiation, 824 Circular polariser, 766 Circulardisc patches, 756 Circular-patch array, 1113 Circular-patch-slot array, 1119 Circularly polarised, singly fed patches, 221 Circularly polarised arrays, 755,765 Circularly polarised circular patches, 232 Circularly polarised composite type patches, 222 Circularly polarised dipoles, 356 Circularly polarised elements, 12 Circularly polarised line antennas, 762 Circularly polarised patches, 27,499,821, 1218 Circulators, 1041 Circumferential polarisation, 1234 Co-axial feeds, 276 Co-planar arrays, 758 Co-planar coupling, 817 Co-planar feeds, 8 15 Co-polymers, 945 Coating, conformal, 950 Coaxial excitation, 432 Coaxial probe, 29, 433, 1194 Cohns method, 61 1 Collected volatile condensable materials (CVCM), 940 Colloidal, 88 1 Comb array, 37, 766, 822, 833 Combined feeds, 839 Comparator, monopulse, 859

Compensating hole transitions, 967 Components, 1039 Composite element, 755, 759, 770 Computational efficiency, 709 Computer graphics, 1175 Conductance edge, 476 radiation, 476, 554, 822, 835, 859 surface wave, 476 Conductivity, 879 Conductor, losses, 788, 790, 815, 1075 Conformal antenna, 1227 Conformal arrays, 795, 1153 Conformal mapping, 1008 Conical antennas, 601 Conical arrays, 1154 Conical beam, 1112, 1127, 1129, 1132, 1239 Conically depressed patch, 29 Connections, 332 Connector characterisation, 962 Connector test fixture, 963 Connectors, microstrip to coax, 1007 Constant-conductancearrays, 846 Contour integral method, 472 Coplanar line probes, 968 Coplanar stripline patch, 31 Copolymer substrates, 679 Corporate feeds, 301 Copper electroless, 935 Copper foil, 1075 Copper-Invar-copper, 946 Comer fed patches, 647 Comer reflector, 1082 Corporate feeds, 13, 35, 757,789, 816, 850, 1069,1288 Correction, end-fringing, 888 Correlation, 905 Corrugated ground plane, 28 Cosecant squared pattern, 671 Coupled triplate lines, 1169 Coupled-resonator, 340 Coupler branch-line, 854 hybrid-ring, 854 Coupling, 817, 887, 895, 897 Coupling agents, 875 aperture, 823 co-planar, 8 17 direct, 822 electromagnetic, 824 factor, 835

!

probe, 822 proximity, 8 18 Coupling gaps, 762 Coupling mechanisms, 816 Crank arrays, 764,777,844,1115 Cross-printed dipole arrays, 766 Cross fed arrays, 36,655,843 Cross patch, 501 Cross polarisation, 68,74,76, 100, 104, 590,1234 Cross slot arrays, 766, 1136 Crossed dipoles, 356 Crossed slot, 28 Crossover level, 793 Crystalline, 873, 878, 942 Current distributions, 112 magnetic, 726 sources, 112 Current sheet model, 731 Current-ribbon, 151 Cyanide, copper, 936 Cycling, wet/dry, 941 Cylindrical antenna, 1227 Cylindrical array, 1109 active-element, 1249 array feed, 1248 design, 1240 gain, 1248 impedance, 1243 mutual coupling, 1244 pattem synthesis, 1251 scanning, 1249 Cylindrical modes, 1230 Cylindrical near field scanning, 981 Cylindrical patches, 1227 Cylindrical wave propagation, 1072 Dantzig algorithm, 662 Data-relay satellite, 1146 DBS antennas, 766,790,859, 1112 De-smearing, 929 Decomposition, thermal, 919 Deformation, 924 Degenerate modes, 756 Dendrites, 879 Dents, 917 Desegmentation method, 456,494 Design procedure, series-feed, 836 Device attachment, 936 Diagnostics, 1159,1193.1214 Diagnostics, liquid crystal, 984

1301

Diagonal slot square patch, 499 Diagonally fed nearly square patch, 499 Dielectric antennas, 1287 losses, 788,815, 1016 Dielectric constant, 790, 897 Dielectric constant, effective, 481 Dielectric filling factor, 790 Dielectric image guide, 822, 858 Dielectric loss, 1075 Dielectric rod array, 39 Dielectric spheres, 3 1 Difference radiation pattem, 1068 Diffraction coefficient, 1069 Diffraction effects, 1069 Diodes, 1041 Dipole centre fed, 287 flat folded, 765 horizontal electric, 276,403 infinitesimal, 276 printed, 765 circularly polarised, 356 crossed, 356 efficiency, 367 EMC, 295 flat, 353 multiple, 299 mutual impedance, 359 parasitic, 759 polarisation, 361 printed, 706,732 stacked, 299 strip, 761 synthesis, 361 variable directivity, 372 Direct coupling, 822 Direct form of network analogue, 462 Direct-BroadcastSatellite, 1288 Directional coupler hybrid-ring, 855 rat-race, 855 Directivity, 127, 372, 554, 831 Directivity, linear arrays, 625 Directly coupled three resonator antenna disc,25,507,843,1258 Discontinuity arrays, 843 Discontinuity radiation, 791 Dispersion, microstrip, 1015 Dissipation, loss, 1285 Dissipation factor, 871, 878, 886, 895 Distribution amplitude, 830

1302 lndex

aperture, 825 Dolph-Chebyshev, 830 Taylor, 830 Dolph Chebyshev distributions, 830, 855 Dose rate, 940 Double tuning, 1064 Doubly diffracted field, 1069 Drills, 922 Dual aperture-fed patches, 823 Dual feeds, 219 Dual frequency circularly polarised arrays, 802 Dual ijarised array, 1073 Dual-fed circularly polarised patches, 220 Dual-frequency patches, 30, 188, 197,200, 312,313,796,802 Dual-polarisation patches, 3 12, 3 18 Ductility, 879, 936 Dust protection shield, 1063 Dyadic Green's function, 284,399 E-H antenna, 1083 Earth stations, 1112 Edge conductance, 476 effects, 1069 equivalent admittance network, 463 ground plane, 12, 731 non radiating, 481 Effective dielectric constant, 481 Effective loss tangent, 461 Effective permittivity two-layer medium, 196 Effective radius, 65, 137 Effective width, 115 Effects, environmental, 939 Efficiency, 5,13, 117,313,346,367,413, 554,781,837,1258 Efficiency computational, 709 measurement, 991 radiation, 9, 598, 734, 872 spill-over, 104 Elastic, 924 Electromagnetically coupled patch, 31 Electric current analysis method, 583 Electric dipole, 403 Electric shielding ring, 803 Electric source, 1260 Electric walls, 113 Electric-current source method, 762,765 Electric-field integral equation, 715, 726, 732

lndex

Electro-etch, 879 Electromagneticcoupling, 207, 797, 824 Electronically switched spherical arrays, 792 Electroplating, 935 Electrostatic charging, 1065 Element endfire, 749 tapered-slot, 751 Element factor, 831 Element grid, 1241 Element pattern, 732 Elliptical patch, 25, 182,235,756, 1129 Elliptical polarisation, 186 EM-field, far-zone, 117 EMC dipole, 295 EMF method, 249 End fringing, 887 Endfire arrays, 1279 Endfire elements, 749 Energy, confonnational, 88 1 Entiredomain basis functions, 429, 437 Environmental conditions, 875 Environmental effects, 679 Epoxy, 878,951 Equitriangular patches, 111 Equivalence . external, 47 internal, 49 Equivalent sources, 112 Equivalent circuit, 237, 728 Eauivalent circuit model., 769.. 776 Equivalent current sources, 114 Eauivalent edne admittance network. 463 ~quivalentmagnetic current, 116 Equivalent slot, 534 Equivalent surface currents, 49 Equivalent waveguide model, 817 Etch plasma, 929 sodium, 929 Etchant, 949 Etching, 1028 Eulers constant, 474 Excitation, coaxial, 432 Excitation field, 396 Excitation voltage, 784 Expansion functions, 53 External equivalence, 47 External matching circuits, 28 Fabric, 922 woven-glass, 935

Far-field approximations, 408 Feed isolation, 320 Feed structures, 35 Feeder of a cylindrical array, 1248 Feeds, 32, 756,767, 1001 3 dB hybrid, 220 architecture, 13 asymmetric, 797 cavity, 859 co-axial, 276 co-planer, 8 15 coaxial probe, 29 combined, 839 corporate, 13, 35, 306, 757, 816, 850, 1069 corporate, triplate, 1288 dual, 219 four point, 28 four-probe, 756 Lecher line, 353 microstrip line, 29 novel, 12 overlaid, 1263 parallel, 335, 757, 816, 825, 828 perpendicular, 747 phased array, 862,1248 radial waveguide, 859 rear, 758 reflector, 96 resonant, 835,1074 sequentially rotated, 36 series, 335,758,767,816,832 series compensated, 36 single, 219 spurious-radiation, 332 squintless, 832 stripline, 353 travelling-wave, 832 two-dimensional, 839 two-line, 276 Ferrimagnetic substrates, 1027 Ferrite superstrates, 1292 Fibres, glass, 922 Field, excitation, 396 Filler, ceramic, 922 Films, barrier, 930 Filton integration method, 285 Finite arrays, 301, 731 Finite ground plane, 12, 1069 Flat dipoles, 353 Flat folded dipole, 765 Floquet modes, 703 Flouborate, copper, 936

1303

Flush mounted antennas, 1092 Foam, 953 Foils adhesion, 875 aluminium, 1075 copper, 1075 electrodeposited, 879 rolled, 879 wrought, 879 Folded slots, 353 Forming rolls, 924 Forward firing beams, 834 Four element arrays, 1217 Four element sub-arrays, 805 Four point feeding, 28 Four-probe feeds, 756 Fourier Transform, 403,406,708, 716, 721,726 Franklin array, 38, 816, 848, 1105 Free radical, 941 Frequency, resonant, 895 Frequency agility, 187 Frequency diversity, 1084 Fringing fields, 113 Full sheet resonance test method, 884,897, 90 1 Fumes, 919 Functions testing, 53 triangular, 54 Future prospects, 1 GaAs substrate, 332 GaAs superstrate, 281 GaAs transitions, 968 Gain, 127, 554, 831 minimum coverage, 793 bandwidth, 823 factor, 104 Gain of a cylindrical array, 1248 Galerkin solution, 284 Gap coupled multiresonator antenna, 507 Gap-wupled patch, 8 17 Geometric optics field, 1069 Giotto spacecraft, 1061 Glass transition temperature, 875 Glossary, 24 Grain structure, 879 Grating lobes, 428, 826, 834, 1183 Green's function, 50, 116, 398, 41 1, 421, 426,462,695,726 dyadic, 399

lndex

1304 Index

planar configurations, 519 spectral domain, 327 Ground plane corrugated, 28 slot, 32 edge, 12,731 GTD, 1183 Guide dielectric image, 822 insular, 822 Gunn diode. 34 H-shaped patch, 26 Half-wave patch, 313, 817 Hand held message communication terminal, 1125 Handbook, 17 Hankel Transform, 406 Hankel function, 264, 473, 1230 Hard boundary diffraction coefficient, 1069 Herringbone array, 38, 835 Higher order modes, 356,787,796, 1058, 1129 Historical development, 1 History mechanical, 874 thermal, 874 Holes, burr-free, 922 Honeycomb substrate, 796 Horizontal dipole, 403 Humidity, 875 Huygens sources, 1262 Hybrid coupler, 1064,1081,1164 Hybrid microstrip antenna, 25, 580 Hybrid sources, 353 Hybrid-ring coupler, 854, 855 Hydrocarbon, 951 Hydrolysis, 875 Hydrophobic, 941 Hyperthermia applicator, 1293 Image, 116 Impedance active, 732 cylindrical array, 1243 input, 9, 118,439, 590, 708 matching, 655, 1190 matrix, 708,716 port matrix, 737,739 surface, 400 transformer, 1064

Incoherent radar, 1073 Indoor communications antenna, 1083 Indoor receiving antenna, 1084 Inductance feed probe, 329 Inductors, 1041 Infinite arrays, 698, 731 Infinite phased arrays, 698 Infinitesimal dipole, 276 Infra-red, 875 Input impedance, 9, 118,238,432,439, 708,875 admittance, 770 conductance, 554 Input resistance o f patches, 324 Inserted connector transitions, 967 Insular guide, 822 Integral equation, 47 Integral equation, electric-field, 715, 726, 732 Integrated antennas, 14 Integrated phased arrays, 742 Internal equivalence, 49 Iris, 906 Isolated power dividers, 852 Isolators, 1041 Junction effects, 1166

K connector transitions, 967 K', thermal coefficient of, 947 Kevlar epoxy, 1075 Land mobile satellite communications, 1127 Lattice arrays, 848 Launchers, 1287 Layer, resistive, 947 Leaky cavity, 119 Lecher line feeds, 353 Light, ultra-violet, 929 Limiting oxygen index, 919 Line analysis dielectric Green's function, 1020 Fourier transform, 1020 integral equations, 1020 TEM models, 1020 variational techniques, 1020 Line antenna, circularly polarised, 762 Linear arrays, 345,449

Linear centre fed arrays, 839 Linear polarisation, 130 Linear slots, 606 Linearly polarised arrays, 846 Lines dielectric, 1285 discontinuities, 762, 1017 losses, 624 open circuited, 1212 parallelaupled, 856 parameters, 971 parameter measurement, 970 synthesis, 1015 width, 943 Liquid crystal diagnostics, 984, 1058, 1159 Loading, reactive, 204, 826 Lobes, grating, 826, 834 Log periodic arrays, 39,387,834, 1273 Longitudinal polarisation, 822, 846 Lorentz's gauge, 398 Loss tangent, 117, 461 Losses, 174,407 conductor, 788,815,942,1075 dielectric, 1016, 1075 dissipation, 1285 line, 624 ohmic, 1016 radiation, 1016, 1075 reflection, 8 16 resistance, 887 resistive, 895 surface wave, 816, 1075 Low cost substrates, 674 Machining, 916 Magnetic current, 116,726,762 materials, 1292 source, 1260 walls, 113 Main beam direction, 781 Mandrel, 931 Manpack radars, 1079 Manufacture, 5,14 Marine radars, 1079 Maritime satellite communications, 1127 Matched terminations, 964 Matching, 5 Matching circuits external, 28 gaps, 28 Mated connector test method, 963

1305

Materials, magnetic, 1292 Mathematical modelling, 14 Matrix Butler, 861 excitation, 58 formulation, 50 impedance, 708,716 Maxson-Blass, 861 Maxon Blass matrix, 860 Maxwell basis functions, 282 Maxwell, modified basis functions, 282 Measurements, 957, 1006 bends, 976 efficiency, 991 line parameters, 970 radiometric, 993 resonant techniques, 976 T-junctions, 977 Melt point, crystalline, 879 Melt viscosity, 928 Metal failure, 934 Metallic ring transitions, 967 Method of moments, 282,295,364,401, 423,708 Metrology, 1193 Microstrip circuit realisation, 1028 impedance, 1013 line, 1004 materials and manufacture, 1023 Microstrip antenna hybrid, 25 frequency variable, 1092, 1101 post loaded, 1O92 quarter wavelength, 1092 window attached, 1092 Microstrip dispersion, 1015 Microstrip field diagnostics, 1193 Microstrip line, 537 Microstrip line feeds, 29 Millimetre wave hybrid antennas, 1285 Minimum coverage gain, 793 Mismatch thermal, 953 Mixed potential integral equation, 400 Mobile communications base stations, 1081 Mobile communications antenna, 1083 Mobile satellite communications, 800, 1142 Mobile systems, 1079 Modal expansional method, 235 Mode ambiguous, 901 Modelling mathematical, 14 Modelling accuracy, 16 Modes

1306

lndex

azimuthal, 53 degenerate, 756 higher order, 356, 787, 796, 1058 orthogonal, 221 parallel-plate, 8 16 resonant, 900 suppressing pins, 1065 transverse electric field, 887 unwanted, 258 Modularity, 744 Modulus, 953 Moisture, 875,941 Moments method, 593 Monopole probes, 1197 Monopulse arrays, 849, 1068, 1153 Monopulse comparator, 859 Moulding vacuum-bag, 926 Multi-terminal antenna, 236 Multibeam antenna, 1083, 1146 Multilayer substrates, 679,944 Multipath fading, 1096 Multiple beam-forming networks, 817, 859 Multiple dipoles, 299 Multiple feed point patches, 262 Multiple frequency patches, 320 Multiple layer patches, 30 Multiple tuning, 341 Multiport network approach, 455 Multiresonator patch, 507 Mutual coupling, 249, 306, 337.445. 561. Mutual coupling in a cylindrical array, 1244 Mutual coupling network, 464,482 Mutual impedance, 237,291,359,378 Narrow pin transitions, 967 Near field mapping 989 Near-field probes, 98 1 Network analysis techniques, 488 Networks multiple-beam-forming, 817 special-purpose, 859 Nitrogen, 930 Nodules, 879 Non radiating edge admittance network, 482 Non radiating edge characterisation, 481 Non uniform arrays, 630 Notched patch, 27,796 Numerical analysis, 16 Numerical techniques, 417

lndex

Off centred pin transitions, 967 Offset fed oatches. 221 Ohmic lo-, 101'6 Omnidirectional arrays, 382, 765 Open circuit end, 534 Open circuited lines, 1212 Open microstrip antennas, 580 Operational factors, 5 Optical modulator probe, 983 Optically tuned patches, 192 Orthogonal fields, 787 Orthogonal polarisation, 30 Overlaid feeds, 1263 Overlaid patches, 35, 1277 Pagers, 1092 Paired elements, 263,270, 758, 788, 804 Parallel feeds, 335, 757, 816, 825, 828 Parallel date resonator test method, 959 ~arallel-bu~led lines, 856 Parallel-plate modes, 8 16 Parallel-plate polariser, 766 Parallel-plate waveguide, 858 ~arasiticrarra~s, 80i Parasitic patches, 29,214,264, 797, 825, 833,1083,1086,1129 Parasitically coupled array, 37 Passivate, 950 Patch arrays, 822, 1263 Patches annular ring, 25, 111 apertureaupled, 330, 723 bandwidth, 111, 554 cavity model, 1228 circular, 45,63, 11I, 232, 580, 720, 1058, 1202 circulardisc, 756 circularly polarised, 27,499, 755, 821, 1218 composite type, 222 conically depressed, 29 coolanar strioline, 3 1 corner fed, 847 cross, 501 cylindrical, 1227 design, 557 diagonal slot square, 499 diaaonallv fed nearly square, 499 directivity, 554 disc, 1258 dual aperture-fed, 823 dual band circularly polarised, 1061

dual-fed, 220 dual-frequency, 30, 188, 197, 200, 312,313,796,802 dual-polarisation, 3 12, 3 18 efficiency, 554 electromagnetically coupled, 31,207, 797 elliptical, 25, 182, 235, 756 equitriangular, 111 gain, 554 Green's functions, 462 H shaped, 26 half-wavelength, 313 input conductance, 554 input resistance, 324 multiple feed points, 262 multiple frequency, 320 multiresonator, 507 mutual impedance, 378 notched, 27,796 offset fed, 221 optically tuned, 192 overlaid, 1277 paired, 263, 270, 804 parasitic, 214, 797 pentagon, 756 pentagonal, 25,505, 1218 piggy-back, 313 polarisation, 378 post-tuned, 3 15 probe-fed, 713,720 quarter wavelength, 313, 1154 rectangular, 111, 224,235,436, 553, 580, 1215,1234 rectangular, comer-fed, 756 rectangular ring, 26 resonant frequency, 324 short circuit, 374 short circuited, 353 short circuited ring, 346 shorted, 1281 singly fed, 221 slotted, 27 square, 25 square ring, 501 stacked, 29,320 stacked circular-disc, 197 star, 26 stepped, 29 strip line, 111 surface-current model, 1232 thick, 253 tilted slot, 756

1307

triangular, 25, 235, 1209 truncated comer, 27 truncated corner square, 499 two port, 51 1 wide, bandwidth, 320 wideband, 28, 796 Pattern, active element, 739 Pattern synthesis of cylindrical arrays, 1251 Peel strength, 937 Peel-test, 878 Pentagon patches, 25,505,756, 1218 Performance trade-offs, 7 Peripheral choke, 104 Permittivity complex, 872 effective, 48 1 relative, 871, 878, 881, 886, 895 very-high, 1293 Perpendicular feeds, 747 Persulfate, 949 Perturbation segment, 224 Perturbation cavity, 914 Phase centre, 96, 106, 1161 Phase constant, 779 Phase shifters, 864, 1081,1241 Phase shifters, Schiffmann, 848 Phased arrays, 378, 741, 802, 810, 862, 1241 Phased arrays infinite, 698 integrated, 742 Photolithographic techniques, 1002 Photomask, 888 adhesion, 9 18 Photoplots, 1175 Photoresist, 1029 Piggy-back patches, 313 Pinholes, 880 Pits, 917 Planar arrays, 345, 776, 790 Planar near field scanning, 981 Planar segments, characterisation by Z matrix, 467 Plane wave spectrum method, 285 Plastic substrates, 14, 1025 Platen-press, 929 Plating holes, 916 Point dipole approximation, 287 Poisson sum formula, 699 Polarisation, 5, 743, 783 Polarisation 45 deg, 821 axial, 1239

1308 lndex

circular, 5, 130,219, 722, 744, 755, 846,848,1261, 1273 circumferential, 1234 cross, 68, 74,76, 100, 104,590, 1234 ellipse, 1187 elliptical, 186 ellipticity, 231 linear, 130 longitudinal, 822, 846 orthogonal, 30 tracking, 755 transverse, 82 1, 846 Poles, surface wave, 697 Polyethylene, 873 Polymer fume fever, 919 Polymer systems, thermoset, 878 Polymerisation, 88 1 Polymides, 951 Polypropylene substrates, 678 Polypropylene-ethylenesubstrates, 679 Polytetraflouroethylene, 873 Post-tuned patches, 3 15 Posts, 235 Potential, 41 1 diffracted field, 397 scalar, 399, 405 vector, 50, 399,403,405 Power combiners, 8 16 Power dividers isolated, 852 rat race, 1069 split-tee, 852 three-port, 852 Wilkinson, 307, 852, 947, 1069 in-line, 850 Precision, 891 Press, platen, 926 Pressure vessel, 929 Printed dipoles, 706,732,765 Probe coupling, 822 Probe-fed patches, 71 3 Probes coaxial, 433, 1194 coplanar line, 968 errors, 1200 monopole, 1197 near-field, 981 optical modulator, 983 scanning network, 1195 short monopole, 982 small loop, 982 split coaxial balun, 982 square law, 983

lndex

wafer, 968 Processing, 916 Proximity coupling, 8 18 F'TFE, 873,881,919 ceramic, 884 glass fibre, 883 woven glass, 884 Pulse basis functions, 282 Pyrophosphate, copper, 936 Q factor, 111, 119, 128, 174, 324, 590, 593,796,887,895 Quarter wave resonance, 353 Quarter-wave patch, 3 13, 8 17 Quasi-log-periodic, 1279 Radar, 1105 Radar reflector, 1107 Radial waveguide feeds, 859 radiated, electric field, 41 1 Radiation circular polarised, 824 conductance, 8 17 cosmic, 940 damage, 941 dose, 941 efficiency, 9, 126, 598, 734 exposure, 939 feeds, 12 fields, 112 high-energy, 940 losses, 788,791, 1016, 1075 nuclear, 940 patterns, 122, 335, 449 resistance, 413 slot, 222 spurious, 353,743,816,824 ultra-violet, 941 unwanted, 787 Radiometric measurement, 993 Radius, effective, 65 Radome, 14,926,945, 1273 Railway antennas, 1087 Rampart array, 38, 763, 816, 844, 1222 Rat race hybrid, 855,1069 Reactance compensation, 761,823 Real space integration method, 286 Rear feeds, 758 Reciprocity method, 278 Rectangular array lattice, 706 Rectangular patch, 7,25, 111, 235,436,

1

553, 1215, 1234 Rectangular ring patch, 26 Rectangular-slot array, 1118 Reflect array, 33 Reflection coefficient active, 708, 739 Reflection losses, 816 Reflector feeds, 96, 1258 Relaxation synthesis, 662 Residue, 278 Resin poly(tetraflouroethy1ene)(PTFE), 879 polycyanate, 878 polyetherimide, 879 polyethersulfone, 879 polyimide, 878 polystyrene, 878 polysulfone, 879 triazine, 878 Resin laminates, 929 Resistance, radiation, 413 Resistive box terminations, 964 Resistive layer, 950 Resistivity, surface, 948 Resistors, 1040 Resonant arrays, 769,816 Resonant cavity, 111 Resonant feed networks, 835, 1074 Resonant frequency, 115,324,593 Resonant peak, 887 Resonant ring test method, 961 Resonant-mode, 117 Resonator microstrip, 914 stripline, 914 Resonator strip test method, 960 Richmonds reaction equation, 597 Rotation, sequential, 12,263, 828, 859 Rotman lenses, 860 Routers, 922 Rutile substrates, 1025 S-matrix, 1240 Safety, 916, 919 Sapphire substrates, 1025 Satellite ERS-I, 1073 ETS-V, 1112 NAVSTAR (GPS),1124 antennas, 1146 communications, 1136 systems, 1079 Scalar potential, 399, 405

1309

Scan angle, 785 Scan blindness, 700,709,719,723,731 Scan range, 743 Scanning a cylindrical array, 1249 Scanning arrays, 792 Scanning losses, 792 Scanning network probes, 1195 Scattering matrix, 702, 783 Scatterometer, 1073 Schartz-Christoffel transform, 1011 Schiffmann phase shifters, 848 Schotky barrier diode, 1194 Secondary su~eillanceradar, 1068 Sector beam array, 1081 Sector patterns, 664 Segmentation method, 456,488 Semi infinite substrate, 731 Semiconductor substrates, 1027 Sequential arrays, 12,36,263, 788, 805, 828,859,1142,1265 Series arrays, 816 Series compensated feeds, 36 Series fed patch arrays, 5 15 Series feeds, 335,758,767,816,832,789, 818 Series-fed circularly polarised arrays, 770 Series-feed design procedure, 836 Serpent array, 38,816, 833, 843 Shear, 937 Shipbourne antenna, 1136 Shock, thermal, 934 Short circuit patches, 25,346,353, 374, 1087,1281 Short monopole probe, 982 Shorting pin, 85 Sidelobe level, 5, 774 Simplex synthesis, 662 Single feeds, 219 Singly diffracted field, 1069 Skin effect, 943 Slot antenna, 1136 Slot combiner, 1084 Slotline transitions, 962 Slots annular, 6 11 crossed, 28 folded, 353 linear, 606 Slotted line measurements, 975 Slotted patch, 27 Small loop probe, 982 Smear, 923,934 Sodium-bisulphite, 950

1310 lndex

Solder reflow, 938 Solvents, 875 Sommerfeld equation, 276,285,407,417 Sources, hybrid, 353 Space diversity, 939, 1084 Sparse arrays, 1273 Spatial phase delay, 805 Special-purpose networks, 859 Specimen, test, 909,907 Spearal domain method, 265,327,404, 590 Spectral domain Green's function, 327 Spherical arrays, 34, 792, 793, 1134, 1239 Spherical dielectric overlays, 1267 Spherical near field scanning, 981 Spill-over efficiency, 104 Spiral, 30 Spiral slot, 33 Split coaxial balun probe, 982 Split-tee power dividers, 852 Splitters, Wilkinson, 356 Spurious radiation, 332, 353, 743,816, 824 Square law probe, 983 Square patch, 25 Square patch array, 1073, 1115 Square ring patch, 501 Square-loop-type arrays, 764 Squintless arrays, 758, 826, 832, 841 Stacked antenna, 312 Stacked circulardisc patches, 197 Stacked dipoles, 299 Stacked patches, 29,320 Stainless-steel, 946 Standing wave distribution, 887, 1199 Star patch, 26 Steepest descent method, 278,408 Stepped patch, 29 Strain, internal, 920 Strain relief, 920 Stress riser, 934 Strip combiner, 1084 Strip conductors, 275 Strip dipole, 761, 1132 Strip line patches, 111 Strip slot, 1132 Stripline, balanced, 1003 Stripline suspended, 8 16,823,857 thickness, 1011 triplate, 816, 823 feeds, 353 transitions, 962 resonator, 884

lndex

St~ctWes array, 36 feed, 35 Subarrays 2*2,759 four element, 805 two element, 804 Subdomain basis functions, 282,437 Subsectional basis functions, 423,440 Substrates, 15 alumina, 14, 1025 bending, 1177 beryllia, 1025 copolymer, 679 effects, 279 environmental effects, 679 ferrimagnetic, 1027 foam, 1288 GaAs, 332 honeycomb, 796 low cost, low loss, 674 materials, 871 measurements, 958 metal deposition, 1028 metallisation, 1027 multilayer, 679 non-woven glass-PTFE, 892 perpendicular, 337 plastic, 14, 1025 polypropylene, 678 polypropyleneethylene, 679 mtile, 1025 sapphire, 1025 semi infinite, 731 semiconductor, 1027 technology, 14 thick, 28, 113,275, 356 thickness, 74, 791 thick metal backed, 678 thin, 112 Sum radiation pattern, 1068 Summary, of chapters, 21 Summary, of topic areas, 18 Superstrate, 275, 597 GaAs, 281 teflon, 28 1 Superstrate effects, 281 Surface charge, 1196 current density, 1196 currents, 441 fields, 67 gradient, 52

resistivity, 117 tangent, 52 wave, 406,407,4 10 Surface analytical techniques, 1194 Surface current model, 1228 Surface currents, equivalent, 49 Surface field metrology, 1193 Surface impedance, 400 Surface resistivity, 815 Surface treatment, 879,929 Surface wave conductance, 476 Surface wave losses, 816 Surface wave poles, 593 Surface waves, 9, 12, 592, 600, 703, 728, 731,734,740,751 Surface waves circle diagram, 706 excitation, 116 loss, 1075 poles, 697 excitation, 127 Surveillance radars, 1079 Susceptance, edge, 479 Suspended stripline, 816, 823,857 Suspension, 881 Switchedelement spherical array, 1132 Synthesis, 361 Synthesis, lines, 1015 Synthesis methods, 662 Synthetic aperture radar antenna, 790, 1146

T junction, 977, 850, 1166 Tab patches, 30 Tapered absorbing film terminations, 964 Tapered arrays, 650 Taperedslot elements, 751 Taylor distribution, 830 Teflon superstrate, 281 Telemetry, 924 Temperature, 875,941 transition, 921 variation of K' with, 942 Terminations matched, 964 resistive box, 964 tapered absorbing film, 964 thin film pad, 964 Test method evaluation, 914 fluiddisplacement, 883 full-sheet-resonance.897

1311

mated connector, 963 microstripresonator, 893 parallel plate resonator, 959 resonant ring, 961 resonant-cavity perturbation, 906 resonator strip, 960 stripline-resonator, 882 stripline resonator test, 886 Testing functions, 53,427 Thermal paint, 1065 Thermalexpansion coefficient, 878, 936 Thermoplastic, 927 Thermoset, 927,941 Thick film, 1031 Thick patches, 253 Thick substrate, 28,275 Thin film pad terminations, 964 Three-faced array, 1111 Three-port power dividers, 852 Throwing power, 936 Tilt angle, 1188 Time-domain-reflectometry,979 TM210-mode microstrip antenna, 1129 Total mass loss (TML), 940 Toxity, 919 Tracking slope, 1188 Train antenna, 1087 Transistors, 1041 Transition, 942 Transition, crystalline, 881 Transition phase, 875 Transitions, 1288 compensating hole, 967 GaAs, 967 inserted connector, 967 K connector, 967 metallic ring, 967 narrow pin, 967 off centred pin, 967 slotline, 962 stripline, 962 thermal, 881 waveguide, 962 Transmission line analysis, 295, 527 Transmission line model, 112,317, 456, 769 Transmission lines, 1001 Transmission-line matrix method, 1023 Transportable earth station, 1125 Transposed arrays, 821 Transverse polarisation, 821, 846 Travelling wave arrays,' 13, 762, 765, 769, 816, 1222

1312 Index

Travelling wave feeds, 832 Travelling-wave array design, 777 Triangle line array, 38 Triangular array lattice, 706, 1243 Triangular functions, 54 Triangular patch, 25,235,1209 Triazene, 95 1 Triplate, 857 Triplate, balanced, 1003 Triplate CAD, 1001 Truncated corner patch, 27 Truncated corner square patch, 499 Tuned circuit, 9 Two element sub-arrays, 804 Two port patch, 511 Two sided arrays, 746 Two-dimensional feeds, 839 Two-line feeds, 276 Two-sided configuration, 332 UHF pagers, 1079 Uniform lines, 1006 Untransposed arrays, 821 Unwanted modes, 258 Unwanted radiation, 787 Unwanted waves, 762 Urban mobile communications, 1086 Vacuum outgassing, 939 Vacuum-bag, 929 Variational method, 235 Vector potential, 50, 399 Vehicle antennas, 1086 Very-high permittivity, 1293 Vim, 945 plated-through hole, 953 reliability of, 953 Visw-elastic, 873,920,924 Voids, 935 Voltage maxima, 88 Voltage vector, 716 VSWR bandwidth, Wafer probing, 968 Walls

electric, 113 magnetic, 113 Waveguide, 906 air-filled, 858 dielectric, 944 model, 817, 1023 parallel-plate, 858,897 simulator, 711,719 transitions, 962 Waves cylindrical, 1072 surface, 406,407,410,592,600,703, 73 1,734,740,75 1 unwanted, 762 Weathering, 941 Welding, 937 electron-beam, 938 laser, 938 parallel gap, 938 percussive arc, 938 resistance, 938 ultrasonic, 938 Wettability, 935 Wheeled vehicles, 1085 Wicking, 875,941 Wide bandwidth arrays, 372 Wide bandwidth patches, 28, 320,796 Widebandwidth, 324, 1273 Wideband arrays, 804 Wideband baluns, 968 Wideband techniques, 253 Wiener-Hopf method, 478 Wilkinson power dividers, 307, 356, 852, 1069 Window antennas, 1283 Wire grid arrays, 848 Wrap around antenna, 34,85 X-ray, 933

Z matrix arbitrary segments, 472 circular segments, 471 from Greens functions, 468 planer segments, 467 rectangular segments, 469