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Handbook of Microwave Technology VOLUME

2

This Page Intentionally Left Blank

Handbook of M icrowave Technology VOLUME

2

Applications

Edited by

T. Koryu Ishii Department of Electrical and Computer Engineering Marquette University Milwaukee, Wisconsin

ACADEMIC PRESS San Diego

New York

Boston

London

Sydney

Tokyo

Toronto

This book is printed on acid-free paper.

Copyright © 1995 by ACADEMIC PRESS, INC. All Rights Reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Academic Press, Inc. A Division of Harcourt Brace & Company 525 B Street, Suite 1900, San Diego, California 92101-4495

United Kingdom Edition published by Academic Press Limited 24-28 Oval Road, London NW1 7DX Library of Congress Cataloging-in-Publication Data Handbook of microwave technology / edited by T. Koryu Ishii. p. cm. Includes index. Contents: v. 1. Components and devices -- v. 2 Applications. ISBN 0-12-374696-5 (v. 1). -- ISBN 0-12-374697-3 (v. 2) 1. Microwave devices--Handbooks, manuals, etc. I. Ishii, T. Koryu (thomas Koryu), date. TK7876.H345 1995 621.381'3--dc20 CIP PRINTED IN THE UNITED STATES OF AMERICA 95 96 97 98 99 00 MM 9 8 7 6

5

4

3

2

1

94-48777

Contents of Volume 2

Contributors Preface

xxi

xxiii

CHAPTER

Klystrons Brian Roach

I. Klystron Characteristics Introduction RF Circuit

I I

Electron Beam System 2. Klystron Applications Linear Accelerator Applications Communication Applications

9

Industrial Heating Applications Radar Applications

12

3. Klystron Specification

12

Electronic Performance Parameters Operating Parameters Environmental Parameters

17 19

14

vi

Contents of Volume 2 Life and Reliability Physical Parameters Miscellaneous Items

20 21 21

4. Design and Fabrication of Klystrons Typical Design Methodology 22 Construction 24

22

5. Noise and Stability Characteristics Noise 25 Stability

27

6. Klystron Protection References

CHAPTER

25

28

30

2

Magnetrons Wayne Love I. Introduction

33

2. Microwaves

35

3. Components of the Magnetron Cathode Anode Output

37 41 43

4. Space Charge

43

5. Magnetic Field

46

6. Power Adjustment Pulsing

36

46

46

Reduction of Anode Current

47

Adjustment of Magnetic Field

48

Attenuation of Microwave Energy 7. Rieke Diagram

50

8. Power Supplies

51

9. Magnetron-System Interface General 53

50

53


vii

Common Problems and Causes Additional Reading

CHAPTER

55

55

3

Traveling-Wave Thermionic Devices Jeffrey D. Wilson I. Introduction

57

2. Cathodes

57

Thermionic Emission

57

Secondary Emission

60

3. Electron Guns Perveance

60

60

Convergence Ratio

60

Electron Gun Types

61

Grids

62

4. Electron Beam Focusing Brillouin Flow

62

62

Confined Flow

63

Periodic Permanent Magnet Focusing Thermal Beams

64

5. Linear-Beam Traveling-Wave Tubes Applications Helical Circuit

65 65

Coupled-Cavity Circuit High-Frequency Circuits Attenuators and Severs

67 70 71

Transitions and Windows

72

Electron Beam Collectors

72

74

6. Linear-Beam Backward-Wave Devices Backward-Wave Amplifiers

77

Backward-Wave Oscillators

78

7. Magnetrons

64

64

General Operation

Simulation

63

79

77

eee

VIII


Applications 79 General Operation 80 Anode Slow-Wave Circuit Strapping 82 Coaxial Magnetrons 83 Simulation 84

80

8. Crossed-Field Amplifiers Applications 84 General Operation 85 Power and Efficiency 85 High-Frequency CFA 86 Low-Noise High-Gain CFA Amplitron 87

84

87

9. Crossed-Field Backward-Wave Oscillators Applications 87 General Operation 88 Frequency Tuning 89 References CHAPTER

87

90 4

Gyrotrons, Magnicons, and Ubitrons Paul Tallerico

I. Introduction

97

2. Gyrotron Principles of Operation 3. Gyrotron Design 4. Gyrotron Structure 5. Gyrotron Fabrication

98

103 104 108 II0

6. Gyrotron Performance

7. Prebunched Gyrotrons and the Magnicon 8. Gyrotron Applications

112

9. Gyrotron Mode Purity

114

10. Ubitron Principles

114

II. Ubitron Structure

115

III


ix

12. Ubitron Performance References

CHAPTER

116

116

5

The Peniotron David Gallagher and Gtinter D6hler

I. Introduction

121

2. The Traditional Peniotron Principle of Operation

123

123

Small-Signal Calculations

124

Large-Signal Calculations

126

Performance of Traditional Peniotrons Traditional Peniotron Design

126

127

3. Nontraditional Peniotrons

130

Square and Rectangular Waveguides The "True" Gyropeniotron Circular Waveguides

130

130

131

The Magnetron-Type Peniotron

132

Other Peniotron and Peniotron-like Devices References

CHAPTER

133

133

6

Thermodynamics of Microwave Devices K. Fricke, V. Krozer, and H. L. Hartnagel

Nomenclature I. Introduction

137 138

2. Conductive Heat Transfer Steady-State Heat Conduction Unsteady-State Heat Conduction

139 139 142

Electrical Equivalent of Thermal Conduction 3. Convective Heat Transfer

145

Single-Phase Convective Heat Transfer Boiling Heat Transfer

149

145

145

x

Contents of Volume 2 4. Heat Transfer by Radiation

151

5. Measurement of the Thermal Resistance IR Measurement

155

155

Liquid-Crystal Measurement Electrical Measurement

155

156

6. Thermal Enhancement Techniques

156

7. Thermal Properties of Electronic Materials References CHAPTER

163

164 7

Microwave Antennas John Hill and Mary Lynn Smith I. Antenna Defined

168

Antenna Requirements and Specifications

168

2. Microwave Integrated Circuit (MIC) and Monolithic Microwave Integrated Circuit (MMIC) Antennas 187 3. Radiation Pattern Synthesis

193

Antenna Patterns with Nulls in Particular Directions Antenna Patterns with Specific Distributions

194

194

Antenna Patterns with Low Sidelobes and Narrow Beams 4. Antennas for Missiles

UHF Antennas

195

196

S-Band Antennas

197

C-Band Beacon Antennas

198

5. Measuring RF Leakage of Test Couplers 6. Materials

201

Conductors

201

Dielectrics References CHAPTER

203 204

8

Propagation at Microwave Frequencies Ernest K. Smith

I. Introduction General Relations

207 207

199

194


xi

Atmospheric Refractive Index Propagation in Free Space

212 213

Carrier-to-Noise Ratio (C/N)

214

2. Attenuation Mechanisms

215

Attenuation Due to the Gaseous Atmosphere Attenuation Due to Rain

215

220

Attenuation Due to Fog and Cloud

227

Attenuation Due to Snow and Ice Crystals Attenuation Due to Sand and Dust

227

228

3. Terrestrial Line-of-Sight Propagation

228

Diffraction Fading Due to Partial Obstruction of the Path Fading Due to a Multipath and Scintillation

230

Fading Due to Variation in the Angle-of-Arrival 4. Propagation beyond the Horizon Diffraction

230

231

Tropospheric Scatter

231

Atmospheric Ducting

232

5. Earth-Space Propagation

232

Geometry for the Geostationary Orbit Ionospheric Effects

234

Tropospheric Effect

237

Mobile Satellite Propagation Effects 6. Mobile Propagation Effects 7. Short-Path Propagation 8. Noise

241

References

242

CHAPTER

230

233

239 240

240

9

Consumer Applications of Microwaves: Microwave Ovens and Accessories Koji Iwabuchi, Ichiro Fukai, and Tatsuya Kashiwa I. Microwave Oven Design Fundamentals [I] Moding Region

249

249

229

oo

Xll

Contents of Volume 2 Arcing Region

251

Overheating Region

251

Low'Efficiency Region

251

Recommended Region

252

2. Microwave Field Visualization Background

252

Formulation

253

Example [I I]

252

254

3. Microwave Leakage Minimization Design Door Structures

256

Radial Line Filters [20, 21]

260

Perforated Plates and Wire Gauzes 4. Operation and Maintenance [24] Operation Procedure Maintenance

256

260 271

271

271

5. Microwave Oven Accessories and Containers Accessories and Their Use

272

Containers and Their Use References

CHAPTER

272

274

10

Industrial Applications of Microwaves T. Koryu Ishii

I. Microwave Heating Temperature Rise

277 277

Approximate Equations for Temperature Rise 2. Microwave Curing Rubber Curing

281

281

Tire and Asphalt Curing

284

3. Microwave Material Processing Microwave Thawing Microwave Drying Microwave Heating

284 285 289

284

280

271

xiii


4. Microwave Applications in Agricultural Industries 5. Microwave Applications on Forest Products 6. Microwave Application on Sensing

293 296

297

7. Microwave Object Identification

300

Microwave Radiometer Technique

300

Microwave Monostatic or Bistatic Radar Technique

300 300

Microwave Reflection or Radiation Pattern Recognition Technique 8. Microwave Data Communications General Configurations Data

301

Modulator

301

Microwave Transmitter Microwave Launcher

301 302

Microwave Transmission System Microwave Catcher

303

Microwave Receiver

303

Data Display References

CHAPTER

300

300

302

303 303

II

Biomedical Applications of Microwave Engineering Joseph H. Battocletti

I. Electrical Properties of Biological Materials

309

2. Heat Deposition in Biological Material, Particularly Man 3. Exposure Guides and Standards

323

4. Microwave Hyperthermia for Cancer Treatment The Bioheat Equation Applicators

327

328

330

5. Microwave Monitoring, Imaging, and Sensing One-Antenna, Active Sensing, Remote Life Detection

332 332

One-Antenna, Passive Scanning, Thermography or Radiometry Two-Antenna, Microwave Imaging References

315

340

337

333

xiv


CHAPTER

12

Chemical Applications of Microwaves Thomas C. Ehlert

I. Microwave Absorption Spectroscopy 347 Introduction 347 Classifications of Molecules 347 Conditions 347 Rotational Energies 348 Resonant Frequencies 349 Probability of Absorption--Attenuation of Microwaves Transition Cross Section 350 Population of the Lower Quantum State 351 Nuclear Statistical Weight 352 Limitations 352 Widths and Shapes of Spectral Lines 352 2. Nuclear Magnetic Resonance Spectroscopy 353 Introduction 353 Nuclear Magnetic Dipole Moment 353 Magnetic Dipole Moment Components 354 Magnetic Dipole Energy States 355 Allowed Transitions between Energy States 355 Details of Spectra 355 Relaxation Processes 357 Power Saturation 357 High-Field NMR 357 NMR Spectra of Solids 358 Fourier Transform NMR 358 3. Electron Spin Resonance Spectroscopy 359 Introduction 359 Electron's Magnetic Dipole Moment 359 Magnetic Dipole Moment Components 359 Magnetic Dipole Energy States 359 Allowed Transitions between Energy States 359 Spectra 360 Relaxation Processes 360 4. Chemical Synthesis and Analysis Using Microwave-Produced Plasmas 360

350


xv

Apparatus 360 Theory 361 Synthesis 361 Analysis 362 5. Thermal Effects Introduction Heating

362 362

362

Reaction Rate Enhancement References CHAPTER

363

363 13

Electron Paramagnetic Resonance James S. Hyde

I. Introduction

365

2. Continuous Wave Bridges: 0.5-35 GHz 368 One-Arm Bridges 369 Reference-Arm Bridges 375 Detection of Dispersion 378 Reference-Arm Bridge with a Low-Noise MicrowaveAmplifier Notes on Advanced Microwave Bridges 383 3. Resonators for EPR Spectroscopy 384 Multipurpose TE~0zCavity 384 EPR Cavity Problems 386 Multipurpose Cavity Accessories 387 Conversion to Other Rectangular TE Modes 391 Other EPR Microwave Cavity Designs 395 Other Types of EPR Sample-Containing Structures 398 References

CHAPTER

399

14

Microwave Navigational Aides G. Stephen Hatcher and Goson Gu

PartA:

THE GLOBAL POSITIONING SYSTEM

I. General Description Space Segment

404

404

381

xvi

Contents of Volume2 Control Segment User Segment

405 405

2. Position Fixing

405

Concept of Position Fixing

405

Satellite-Position Acquisition and Radio Ranging Clocks

407

407

Pseudorangesand Navigation Equations 3. Time Measurement

408

408

4. Velocity Measurement 5. Signal Structure

409

410

6. Navigation Message

410

7. Navigation Solution and Dilution of Precision The Navigation Solution Dilution of Precision (DOP) 8. Error Sources

413

414

Space Segment

414

User Segment

414

Propagation Link

415

9. Differential GPS

415

Concept of Differential GPS

415

Implementation of Differential GPS 10. Summary Part B:

411

411

415

416

DOPPLERNAVIGATION SYSTEM

I. General Description

417

2. Fundamental Principles of Doppler Radar

418

3. Functional Description of Doppler Radar

421

Antenna

421

Transmitter and Receiver Frequency Tracker

422

422

4. Doppler-Radar Performance and Errors Doppler-Radar Performance Doppler-Radar Errors

424

423

423

xvii


425

5. The Navigation Computer Additional Reading CHAPTER

425

15

Microwave Applications for Law Enforcement John Tomerlin and John Fuhrman

I. Introduction 2. Historical

429 431 432

3. Moving Radar 4. Mechanical Errors

433

5. Mechanical Interference 6. Photo Radar

434

435 436

7. Testing for Accuracy Tuning Fork Calibration Tuning Fork Tests

437

438

Microwave Transmission Low-Voltage Supply

438

439

Doppler Audio 439 Electromagnetic Interference Speed Accuracy 440 8. Does Radar Increase Safety? Additional Reading CHAPTER

439 448

448

16

Microwave Radio Communication George Kizer

I. Introduction

449

2. Equipment-Dependent Radio Performance Analog Systems

451

Digital Systems

454

Estimating End-to-End Digital Radio Performance

451

457

3. Transmission-Path-Dependent Radio Performance Transmission Path Loss

466

465

xviii

Contents of Volume 2 Received Signal Variation ("Fading")

472

Atmospheric (Nonrain) Absorption

473

Rain Loss

474

Reflection ("Fresnel Zone") Fading

477

Obstruction ("Diffraction") Fading

478

Power Fading Duct Fading

485 486

Atmospheric Multipath Fading

487

4. Path Availability Calculations 5. Conclusion References

CHAPTER

492

501 502

17

Microwave Instrumentation and Measurements Aksel Kiiss

I. Scattering Parameters

505

S-Parameter Measurements

505

Uncertainties Caused by Adaptor VSWR 512 Uncertainties Caused by the Harmonic Content of the Test Signal Inaccuracies in Transmission Measurements ($2~and S~2) 2. Transmission Measurements

514

Transmission Measurement Magnitude Transmission Measurement Phase 3. Reflection Measurements 4. Electrical Delay 5. Group Delay

514 516

520

525 525

6. Noise Figure/Noise Temperature Measurements Definitions of the Noise Figure/Noise Temperature Noise Figure

512

527 527

528

Absolute Accuracy of Noise Figure Measurements 7. Microwave Power Measurements Thermal-Based Power Detectors Diode-Based Power Detectors Diode-Based Power Meters

538 538

540 540

534

512


xix

Frequency Calibration Factor Peak Power Meters

541

542

Accuracy: How to Calculate Your Measurement Uncertainty RSS and Worst-Case Calculations

542

544

Measurement Techniques for Improved Measurement Accuracy

544

8. Microwave Frequency Measurements (CW and Pulsed) Single-Shot, Precision VCO Characterization HP 5372A Specification Summary Specifications

545

546

550

9. Measurement of Phase Noise Power Spectral Density Short-Term Frequency Stability

558

560

Long-Term Frequency Stability (Figure 21)

CHAPTER

545

568

18

Microwave Mathematics James Richie

I. Preliminary Definitions

569

Phasor Notation and Fourier Transform

569

2. Mathematical Functions for Microwave Engineering Complex Functions

571

Generalized Functions

573

3. Vectors and Matrices Definition

576

Properties

577

Hermitian Adjoint

576

578

Commutator and Anticommutator Tensors and Dyadics Group Theory 4. Vector Spaces Definition

578

579 579

579

Linear Independence Inner Product

580

580

Orthonormality

580

Gram-Schmitt Process Inequalities

581

581

578

571

XX


5. Linear Operator Theory 581 Definition 581 Properties 582 Inverse 582 Similarity Transformation 582 Projection Operators 583 Adjoint Operators 584 Unitary Operators 584 Eigenvalue Problem 584 6. Function Spaces

585

7. Vector Fields 586 Operations 587 Theorems 589 Vector Identities 589 589

8. Differential Equations and Their Solutions Analytic Techniques 590 Numerical Solutions 595 9. Integral Equations and Their Solution Tabulated Solutions 599 Asymptotic Methods 599 Numerical Solutions 600 References CHAPTER

599

602 19

Microwave Materials Hamid H. S. Javadi

I. Introduction

605

2. Dielectric Properties of Compounds

608

3. Properties of Manufactured Special-Purpose Compounds 4. Thin Films

635

5. Electromagnetic Properties of Metals

635

6. Physical and Electromagnetic Properties of Bulk and Thin-Film Superconductors 638 References Index

642 645

626

Contributors

Numbers in parentheses indicate the pages on which the authors' contributions begin. Joseph H. Battocletti (309) Department of Neurosurgery, Medical College of Wisconsin, MCW Clinic at Froedtert, Milwaukee, Wisconsin 53226 Giinter D6hler (121), Tube Research and Development, Northrop Grumman Corporation, Rolling Meadows, Illinois 60008 Thomas C. Ehlert (347), Department of Chemistry, Marquette University, Milwaukee, Wisconsin 53233 K. Fricke (137), Technische Hochschule Darmstadt, Institut ftir Hochfrequenztechnik, D-64283 Darmstadt, Germany John Fuhrman (429), AUTO SCENE, Laguna Beach, California 92615 Ichiro Fukai (249), Department of Electrical Engineering, Hokkaido University, Hokkaido, Japan David Gallagher (121), Tube Research and Development, Northrop Grumman Corporation, Rolling Meadows, Illinois 60008 Goson Gu (403), Summit Design, Inc., Renton, Washington 98055 H. L. Hartnagel (137), Technische Hochschule Darmstadt, Institut fur Hochfrequenztechnik, D-64283 Darmstadt, Germany G. Stephen Hatcher (403), Summit Design, Inc., Renton, Washington 98055 John E. Hill (167), Watkins-Johnson Company, San Jose, California 95131 James S. Hyde (365), Biophysics Research Institute, Medical College of Wisconsin, Milwaukee, Wisconsin 53226 T. Koryu Ishii (277), Department of Electrical and Computer Engineering, Marquette University, Milwaukee, Wisconsin 53233

xxi

xxii

Contributors

Koji Iwabuchi (249), Kashiwa Works, Hitachi Hometech, Ltd., Chiba-ken 277, Japan Hamid H. S. Javadi (605), Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California 91109 Tatsuya Kashiwa (249), Department of Electrical Engineering, Hokkaido University, Hokkaido, Japan Aksel Kiiss (505), MITEQ, Inc., Hauppauge, New York 11788 George Kizer (449), Alcatel Network Systems, Richardson, Texas 75081 V. Krozer (137), Technische Hochschule Darmstadt, Institut ftir Hochfrequenztechnik, D-64283 Darmstadt, Germany Wayne Love (33), Richardson Electronics, Ltd., LaFox, Illinois 60147 James Richie (569), Department of Electrical and Computer Engineering, College of Engineering, Marquette University, Milwaukee, Wisconsin 53233 Brian Roach (1), Varian Associates, Inc., Palo Alto, California 94303 Mary Lynn Smith (167), Watkins-Johnson Company, San Jose, California 95131 Ernest K. Smith (207), Department of Electrical and Computer Engineering, University of Colorado, Boulder, Colorado 80309 Paul Tallerico (97), Los Alamos National Laboratories, Los Alamos, New Mexico 87545 John Tomerlin (429), AUTO SCENE, Laguna Beach, California 92615 Jeffrey D. Wilson (57), Lewis Research Center, NASA, Cleveland, Ohio 44135

Preface

The

purpose of this book is to provide a compact, ready reference tool on practical microwave technology to practicing technicians, scientists, and engineers. Readers may be trained in the field of microwave technology or may be trained in their own field but not necessarily in the field of microwave technology. This book is written with care for the latter category of audience as well as for the former. Consequently, this book is also useful to people in business and industry as well as to science and engineering students who are involved in microwave technology. Not only is this book a ready reference tool at present but it is also a good investment for use in the future. The emphasis of this book is to answer the question of "how to" rather than that of "why so." Chapters are full of useful formulas, charts, graphs, tables, examples, and diagrams for analysis and are designed for daily use. These reference resources are clearly explained and easily applicable to specific practical cases that the readers may encounter in their professional activities. Naturally the field of microwave technology is so vast that, no matter how well covered, it is impossible to include everything in one volume of limited size. For this reason, the Handbook of Microwave Technology is split into two volumes. Volume 1 covers "Components and Devices" used in microwave circuits, and Volume 2 covers "Applications" of microwave technology. This enormously wide area of microwave technology, which spans both fundamentals and applications, is condensed into two, compact, conveniently portable volumes for easy reference. Since both volumes are written independently of each other, the audience may choose one or both volumes depending on their needs. For those who wish to acquire information beyond the materials presented in this book, complete lists of references are provided at the end of every chap. . .

XXIII

xxiv

Preface

ter. The quest for "why so" and further information is realized by making full use of these references. The editor thanks chapter contributors, suppliers of industrial resources, providers of permissions for copyrighted materials, and those who provided clerical assistance. He also acknowledges assistance from the publisher's staff. Without their assistance, perseverance, and patience, this book may never have been completed.

T. Koryu Ishii Editor

Milwaukee, Wisconsin 1995

CHAPTER

Klystrons Brian Roach

I. Klystron Characteristics Introduction 17"

l~xlystrons are linear beam tubes. Although they are available as both oscillators and amplifiers, only amplifiers will be discussed in this chapter. This is because most oscillator applications have been supplanted by solid-state alternatives. Klystrons are inherently narrow-band devices, although some klystrons have some degree of tunability. They have high gain and are capable of operation at high peak and average power. They are capable of either pulsed or CW operation. Table 1 delineates some broad performance capabilities of klystrons. Note that most desirable characteristics of these tubes are enhanced at higher peak power or lower frequency. (This is explored in greater depth under Electronic Performance Parameters.) Figure 1 shows the essential elements of a klystron in a simplified form. As can be seen from the figure, klystrons are divided into two portions; the RF circuit and the electron beam system [1, 2]. (References [1] and [2] are recommended for a more complete description of klystron operating principles.)

RF Circuit Klystron RF circuits are fairly simple, at least when compared with traveling wave tube circuits. The circuit comprises a number (typically

Handbook of Microwave Technology, Volume 2

Copyright © 1995 by Academic Press, Inc. All rights of reproduction in any form reserved.

Brian Roach

TABLE I Klystron Overview

Characteristic

Typical values

Center frequency Peak power output Average power output Bandwidth Gain Efficiency

Focus Electrode

Anode

300 MHz-40 GHz 100 W-150 MW 1 0 0 W - 1 MW 0.1-10% 20-60 dB 20-70%

Input

Electron

Cavity

Beam

Output Cavity

Magnet

\

Collector Cathode

.. ~ t~ I~1~~..r''////'//I~L Electron

I--

Gun

// RF Input

Input Window

Output Window

;~1 RF Output

Figure I. Simplified klystron layout.

between three and six) of resonant cavities. These cavities are disposed around the electron beam and operate in the TM010 mode. The electric fields associated with this mode are depicted for a typical cavity in Figure 2. This figure also shows an electron beam traversing the cavity. As depicted in Figure 1, the RF signal is coupled through a ceramic window into the input cavity. The electron beam is slightly modulated in the input cavity and is remodulated by the intermediate cavities. By the time the electron beam reaches the output cavity, it is highly modulated (strongly bunched). The output cavity couples the amplified signal back into the transmission line to the outside world. This interaction with resonant cavities is the klystron's greatest strength and greatest weakness. The fact that there are no beam-circuit synchronism requirements (as in TWTs and crossed-field devices) means that klystrons are comparatively less demanding to design and manufacture. The lack of backward traveling waves means that klystrons are, for most

I. Klystrons

/ / . . . . _ _ _ _ _Electron __ beam

~

Electric field lines (peek of RF cycle)

i

I

Figure 2. Klystroncavity:TM010 mode.

practical purposes, unconditionally stable. However, the principle of resonant interaction inherently restricts the bandwidth capability of klystrons. From a systems point of view, klystrons are sometimes regarded as narrow-band elliptic filters with gain. Figure 3 shows a gain model for a four-cavity klystron amplifier. An n-cavity tube can be modeled as an ( n - 1)-pole filter. Figure 4 shows a calculated response for a typical five-cavity (four-pole) klystron. Various types of hybrid devices have been built to circumvent the limitations of the resonant circuit [3]. Examples of these devices are the Twystron and the extended interaction klystron (EIK). It is worthwhile to note that some of the same stability considerations that apply to wave tubes also apply to these hybrid tubes.

Figure 3. Klystron small signal gain model.

Brian Roach

.E

50

,

40

'1

3o

"~

Gain poles

20 lO

~

o

~

-10

~

-20

Gain zero

I

+2O0 -200 fo Freq. (MHz dev. from fo) Figure 4. Calculated klystron small signal gain.

The Twystron [4, 5] was invented to address an aggravating fault of klystrons, viz, that it is possible to bunch the electron beam internally over a wide frequency range, but impossible to couple it efficiently to the outside world with a simple resonant output cavity. The Twystron substitutes a wave tube circuit for the output cavity. Electronic bandwidths in excess of 15% have been demonstrated with Twystrons at the 6-MW peak power level. The ElK [6] substitutes sections of shorted wave tube circuits for one or more of the resonant cavities normally present. In one class of applications, the output cavity is treated in this manner. This confers advantages similar to those of the Twystron. It also allows the possibility of higher peak and average power compared with klystrons with simple resonant output cavities [7-9]. In another class of applications, all of the cavities are treated in this manner. This is particularly advantageous in higher frequency ( > 30 GHz) tubes [10]. The RF circuit of most klystrons is entirely within the vacuum envelope. Tubes of this type are called internal cavity tubes. In external cavity tubes, the RF cavities are distinct from the vacuum envelope. They are clamped onto the tube by the user. External cavity tubes can be cheaper to replace, because the RF cavities are reusable. Problems with multipactor on the ceramic and RF arcing, along with the need to tune the tubes in the field, have tended to inhibit the broad application of external cavity tubes. Figure 5 shows a detail of a typical external cavity.

I. Klystrons

/

E~etyna'

Ceramic window

External cavity Figure 5. Klystroncavity:externalcavitytype.

Electron Beam System The electron beam system can be divided into three parts; the electron gun, the magnetic circuit, and the collector. Electron Gun

The electron gun is the source of a klystron's electron beam. It is probably the most critical subassembly of a klystron. Most of the significant properties of linear beam devices are acutely sensitive to the properties of the electron beam. And the properties of the electron beam are highly sensitive to small gun dimensional changes, cathode surface chemistry, etc. References [1, 2, 11-13] discuss the subject of electron guns and cathodes in far greater detail than this chapter. The cathode is the portion of the electron gun which actually emits the electrons. The cathodes of all practical klystrons are thermionic; they must be heated to emit electrons. During operation, the surface of the cathode is maintained at temperatures ranging between 800 and 1100°C by a heater (or filament). Over the years, great effort has been devoted to the enhancement of desirable cathode properties. These properties are high current emission per unit area, long life, operation at lower temperatures, and resistance to poisoning. Table 2 enumerates the more significant types of klystron cathodes along with some miscellaneous comments. References [14-16] explore the subject of cathode materials in greater depth. The heater (or filament) of an electron gun is aptly named. It is the portion of the gun which heats the cathode to its required operating temperature. Differences in cathode size and warm-up-time requirements

Brian Roach TABLE 2 Cathode Types

Comments

Type Oxide Impregnated tungsten Coated tungsten

Pulse width/emission restrictions, easily poisoned Most commonly used Susceptible to damage, high-emission capability

have produced a variety of heater types. Most heaters, though, comprise a coiled tungsten wire which heats the back of the cathode button by conduction or radiation. The remainder of the electron gun provides the electrodes required to initially accelerate, form, and modulate the electron beam. The guns of all practical klystrons are of the Pierce type and are ceramic metal assemblies. The fact that klystrons use Pierce-type cathodes establishes the current-voltage relationship of klystrons, k = i/V3/2,

where i is the beam current, V is the beam voltage, and k is a constant called perveance. The microperveance of a tube is the perveance times 10 6. Note that microperveance is often loosely referred to simply as perveance. The microperveance of most klystrons ranges between 0.5 and 2. Pulsed klystrons normally utilize pulsed electron beams. Although it is possible to simply pulse the high voltage applied to the electron gun, frequently a control electrode is introduced into the gun. This permits the beam to be pulsed with the application of a voltage less than the full beam voltage. The figure of merit/x is the ratio of the beam voltage divided by the control electrode voltage swing. Table 3 describes the common types of control electrodes used in klystrons for pulsing the electron beam.

TABLE 3 Types of Control Electrodes

Type None (cathode pulsed) Mod anode Focus electrode Intercepting grid Nonintercepting grid

Control/x

Comments

1 2 8 50 30

Most suitable for high beam voltage Usable for perveance variation Older type Low duty cycle Mechanical complexity and difficulty of design

I. Klystrons

7

Beam Focusing Once formed by the electron gun, the electron beam must be maintained at a small diameter for a considerable distance while it passes through the RF circuit. Both the space charge of the beam itself and the RF interaction tend to cause the beam to spread. Maintenance of the beam diameter is critical; lost electrons are not able to interact with the RF circuit, contributing to losses of efficiency. More significantly, the power in the electron beam is usually more than that required to damage or destroy the RF circuit. In principle, beam confinement may be achieved with either magnetic fields or electrostatic fields [17]. In practice, however, almost all klystrons utilize magnetic focusing. References [1, 2, 11-13, 18] discuss magnetic focusing methods in greater detail. The minimum amount of magnetic field required to maintain a "pencil" electron beam at a constant diameter is the Brillouin field. The Brillouin field (B b) in gauss is B b = 8.3 × 10-411/2/(V1/4r), where V is the beam voltage, I is the beam current, and r is the beam radius in inches. Because the electron beam becomes highly bunched in a klystron, the actual magnetic field is typically maintained at a multiple of two to three times the Brillouin field. Klystrons can use permanent magnets (PM), periodic permanent magnets (PPM), or solenoids to supply magnetic focusing fields. Permanent magnets are frequently used for the focusing of klystrons below a peak output power level of about 10 kW. This peak power restriction is dictated by the long magnetic gaps which are typical of klystrons of higher peak power levels. (Permanent magnet weight is approximately proportional to the cube of the magnetic gap length.) Note that the SLAC klystrons are a conspicuous exception to this rule. The use of the term "permanent magnet focusing" is somewhat deceptive, in that it refers to klystrons that have a single uniform focusing field in the RF interaction area. Arrays of smaller magnets (PPM focusing) [19, 20] can be used to create a chain of alternating magnetic fields around the electron beam. PPM focusing is used infrequently on klystrons. It is not usable on designs of low peak power (less than about 10 kW) because of the space requirements of the multiple pole pieces and magnets along the beam path. The comparatively poor beam transmission characteristics ( ~ 90%) of PPM focusing tend to restrict the average power output to less than 1 kW. Newer techniques, however, may extend the average power capability of PPM focused klystrons [21]. Progress in higher energy prod-

8

Brian Roach

uct magnets has aided appreciably in the development of lightweight permanent magnet and PPM klystrons. Solenoids are used for focusing klystrons of all power outputs and frequencies. As alluded above, solenoids are usually the focusing method of choice for high peak and average power klystrons. Collector

After the electron beam traverses the RF interaction area, it passes into the collector. Most collectors are rather massive copper cups which serve to dissipate the unused power of the electron beam into heat. A collector must be capable of dissipating the full power of the beam (i.e., no RF modulation plus a safety factor). Almost every imaginable type of heat transfer has been utilized for the dissipation of this heat, including liquid cooling, boiling heat transfer, air cooling, conduction cooling, and radiative cooling [22]. Liquid and air cooling are, however, the most common types of cooling. Collectors are frequently electrically isolated from the RF circuit (which is usually at ground potential). This permits the measurement of body current, that being beam interception on the RF circuit. The application of a negative bias to an isolated collector is called "depressing" the collector. This permits the recovery of some of the beam power that would otherwise be converted into heat. The use of depressed collectors on klystrons is possible, although somewhat uncommon. The high electronic efficiency of klystrons not only reduces the incentive to use depressed collectors, but also makes the design of such collectors difficult. This is because the efficient extraction of energy from the electron beam tends to result in a wide mixture of electron velocities as electrons leave the output gap. This wide spread of electron velocities complicates the design of depressed collectors for klystrons. A depressed collector klystron is described under Communication Applications.

2. Klystron Applications Klystrons are found in linear accelerators, communications, industrial heating, radar systems, and other miscellaneous applications. These applications have typically resulted from good operating characteristics at high power, low noise characteristics, and the comparative low cost of klystrons.

Linear Accelerator Applications The Varian VKS 8252 klystron, used in a medical linear accelerator, not only is a good example of an accelerator application, but also is similar to

I. Klystrons

9 TABLE 4 Klystron Example: VKS-8252 Characteristic Center frequency Bandwidth Peak power output Average power output Drive power Beam voltage Beam current Modulation type Cooling Focusing type Size Weight

Value 2.856 GHz 5 MHz 5.5 MW 5.5 kW 100 W 120 kV 83 A Cathode pulsed Water Solenoid 37 in. long 111 lb (without solenoid)

many tubes that are used in narrow-band radar applications. The operating characteristics are shown in Table 4. It is a five-cavity tube. The input and second cavities are nominally tuned to the center frequency, whereas cavities three and four are tuned above the band. This tuning of cavities above the pass band (inductive tuning) is done to enhance the efficiency of the tube. The output cavity is tuned to the band center. The klystrons used at SLAC have been described many times [23-25]; their detailed performance will not be enumerated here. The performance of the basic S-band tube has been extended to 150 MW. SLAC and Mitsubishi have also made noteworthy progress at the X band, with reports of 30 MW at narrow pulse widths from SLAC and of 4 MW from the Mitsubishi tube at 5 /zS pulse width. The development of useful X-band klystrons for accelerator applications, if not in hand, can be said to be nearly in hand [26, 27].

Communication Applications Tunable CW medium-power klystrons have found extensive use in satellite up-link applications. These applications often require the ability to tune the instantaneous bandwidth across some frequency range. The Varian VKX-7799 (Figure 6) is able to position a 2% instantaneous bandpass across a 6% tuning range. The instantaneous bandwidth is achieved by stagger tuning the driver cavities and by using a double-tuned output circuit. Table 5 shows the characteristics of this tube. The 7799 is somewhat atypical, in that the majority of satellite communication klystrons are actually PM focused. Reference [28] describes a permanent magnet fo-

I0

Brian Roach

Figure 6. VKX-7799 klystron (solenoid not shown).

cused tube for a similar application. Reference [29] describes another PM focused tube and provides detailed performance information. Lower frequency klystrons are used in many UHF TV transmitters. The Varian VKP-7990 is an interesting klystron developed for that application. It is a solenoid focused tube that is fitted with a five-stage depressed collector. Without collector depression, its efficiency in saturated operation is 55%. With collector depression the tubes overall effiTABLE 5 Klystron Example: VKX-7799 Characteristic Center frequency Bandwidth CW power output Drive power Beam voltage Beam current Cooling Focusing type Size Weight

Value 7.9-8.4 GHz (tunable) 175 MHz 10 kW 3W 14.3 kV 2.3 A Water/glycol Solenoid 16 in. long 20 lb (without solenoid)

II

I. Klystrons TABLE 6 Klystron Example: VKP-7990 Characteristic

Value

Center frequency Bandwidth Peak power output Drive power Beam voltage Beam current Cooling Focusing type Size Weight

470-810 MHz (tunable) 6 MHz (8 MHz with lower gain) 64 kW 20 W 26 kV 4.5 A Water Solenoid 62 in. long 300 lb (solenoid weight, 500 lb)

ciency improves to 70% [30, 31]. The 7990 has another feature worthy of note; like most UHF TV tubes, it is an external cavity tube. Table 6 describes the characteristics of the 7990.

Industrial Heating Applications Industrial heating applications take advantage of the high efficiency and high average power capabilities of klystrons [32]. This application has essentially no bandwidth requirement, so that tube performance can be optimized for efficiency. Lein has reported an electronic efficiency (i.e., no collector depression) of 75% [33], although the limit for practical tubes is probably 70%. The Varian VKP-8275 is an example of a tube used in industrial heating. It is used to cure epoxy-wood laminates. Its characteristics are summarized in Table 7. TABLE 7 Klystron Example: VKP-8275 Characteristic Center frequency Bandwidth Average power output Drive power Beam voltage Beam current Cooling Focusing type Size Weight

Value 910-920 MHz (tunable) 4 MHz 100 kW 2W 32 kV 6.5 A Glycol/water Solenoid 70 in. long 325 lb (solenoid weight, 700 lb)

12

Brian Roach TABLE 8 Klystron Example: VKX-7809 Value

Characteristic Center frequency Bandwidth Average power output Drive power Beam voltage Beam current Cooling Focusing type Size Weight

10.0-10.25 GHz (tunable) 50 MHz 2.5 kW 0.3 W 9.5 kV 1.0A Air Permanent magnet 15 in. long 55 lb (includes magnet)

Radar Applications Radar might be called the classic application of klystrons. The low-noise characteristics of klystrons make them attractive for illuminators. The availability of very high peak power makes klystrons ideal for use in search radar transmitters. They also are potential candidates for active seeker transmitters. The VKX-7809 is a good example of an radar illuminator tube. Table 8 delineates its characteristics, whereas its noise performance is shown in Figure 18. Note that gridded tubes of this class are appropriate for use in pulse doppler radars. The Varian VKS-8345 (Figure 7) is a good example of a larger pulse radar tube. It has six cavities plus a two-cavity EIK output. The first four cavities are tuned across the bandpass of the tube for gain. The remaining two are tuned above the upper band edge to promote efficiency. EIKs, as mentioned previously, typically have limits on the allowable range of beam voltage and load mismatch. These limits are imposed by the stability requirements of the output circuit. The beam voltage of this tube must be maintained between 108 and 120 kV, and the load mismatch must be 2 : 1 or better between 2.9 and 3.5 GHz. The 8345 is a cathode pulsed tube. The characteristics of this tube are summarized in Table 9.

3. Klystron Specification Specification of klystrons (as with most devices) is complicated by the fact that most of the desirable performance factors are interdependent. A1-

I. Klystrons

I

~

iii!~

.....C~ii!:ili~dlii

Figure 7. VKS-8345 klystron (solenoid not shown).

iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii

14

Brian Roach TABLE 9 Klystron Example: VKS-8345

Characteristic Center frequency Bandwidth Peak output power Average output power Drive power Beam voltage Beam current Cooling Size Weight

Value 3.0 GHz 200 MHz 4.0 MW 6.7 kW 400 W 117 kV 80 A Water 43 in. long 140 lb (without solenoid)

though some of the more obvious interactions will be discussed, the reader should be cautioned that all of the most desirable performance parameters are not achievable in a single device. The electronic performance, operating parameters, environmental performance, reliability, mechanical envelope, and other miscellaneous items must be addressed when specifying klystrons. Electronic Performance Parameters

One of the more significant klystron performance interactions is between peak power and most other electronic parameters. In general, klystrons with high peak output power tend to display more favorable gain, bandwidth, and efficiency compared with lower peak power designs. Another tradeoff involves the relationship among perveance, efficiency, and bandwidth. High perveance tends to favor broad bandwidth, whereas low perveance tends to favor better efficiency [34]. Figure 8 shows the relationship between bandwidth and peak power for three types of tubes. Tubes with simple resonant output cavities have a lower bandwidth capability compared with those with double-tuned outputs, whereas Twystrons and ElKs are capable of the greatest bandwidth. Although klystrons can operate at arbitrarily low peak power, the poor performance of low peak power tubes, coupled with the availability of viable technical alternatives, tends to limit practical designs to peak power levels higher than a few hundred watts. The upper limit to peak power is not yet entirely clear; the performance of the accelerator tubes under Linear Accelerator Applications is representative of the state of the art. At frequencies below the high X or Ku band, the practical limits seem to

15

I. Klystrons 10,000

1,000

o / o/4,~/

/

1oo

I_O I

/

, ,,I,,,~

I

,,,,,,,I

, ,

10

I

Bendwidth (%) Figure8. KIystronbandwidthcapability,

be RF breakdown in the interaction gaps and electron gun voltage hold-off [35]. At higher frequencies, the limiting factors appear to be available electron beam power and tube efficiency [36]. Klystrons that operate at short pulse widths (less than 1 /~S) will have a higher peak power capability than those that operate at longer pulse widths. The practical available average power output of klystrons is shown in Figure 9. This figure neglects tubes at frequencies below 8 GHz, for which the ultimate performance limits have not yet been established [37, 38]. This is not too surprising when one considers the power supply require,~

250

""

100

Liquid Cooled Q.

0

10

k-

o £3_

Air I

13 ID >

"-

Band I - " " ~ edge

°~ "~ 2

I

I

6160

I

I

I

I

6180 6200 6220 Frequency (MHz)

6240

Figure 12. Typical group delay characteristics.

Figure 12 shows the group delay characteristics of a typical klystron. Group delay varies most rapidly at the band edges of most klystrons.

Operating Parameters Figure 13 and Table 10 show a klystron in schematic form, along with some significant operating parameters. Each of these parameters should be specified at its normal operating level and at some absolute maximum level. An absolute maximum level should be used as a guide for the limitation of peak transients. Note that in many (or most) cases, continuous operation at an absolute maximum level will result in tube failure.

18

Brian Roach

I by

+

Pd

Eb(

Ff

,k

Im

,fTiy

Figure 13. Klystron schematic diagram.

The operating parameters of tubes will affect RF performance. The changes in operating parameters, along with their accompanying effects, are referred to as "pushing figures." These pushing figures are important, because they will dictate the degree of regulation required from the power supply or modulator. Ripple of the beam voltage creates both phase and amplitude modulation of the amplified signal. There are simple relationships which describe this pushing. (These are valid for small excursions--ones that are not large enough to appreciably affect the efficiency or saturation characteristics of the device.) The amount of amplitude modulation is determined by the variation of power into the tube times the tube efficiency. The change of output power is

(AV)(5/2)(P/V), where P is the power output of the klystron and V is the beam voltage. TABLE 10 Klystron Operating Parameters Symbol

Eb /k Ef If /by egk eco Im Pd Po

Description Beam voltage Cathode current Heater current (WRT cathode voltage) Heater voltage (WRT cathode voltage) Body current Grid turn-on voltage (WRT cathode voltage) Grid cutoff voltage (WRT cathode voltage) Solenoid current RF drive power RF output power

I. Klystrons

19

Beam phase pushing is caused by the change in the electrical length of the tube. To calculate this number, the electrical length of the tube must be known. This parameter is typically between 2000 to 5000 °. The change in a klystron's phase length with changing beam voltage is

(AV)~/(2V), where 4~ is the phase length of the tube and V is the beam voltage. Ripple on the heater voltage can induce sidebands on the signal due to magnetic modulation of the electron beam. This effect can be minimized through careful design of the heater windings. Where even a small amount of this modulation is objectionable, the use of DC heater supplies is sometimes required. In extreme cases, a synchronous heater power supply may be used. The source and load impedance presented to a klystron will have an effect on its performance. The situation is somewhat different between narrow-band and broadband tubes. In a narrow-band tube, the effects of source and load impedanc,e variation are small changes in tube gain and bandwidth. It is usually possible to design tubes that will maintain specification across a 1.3:1 variation of impedance. In a broadband tube, variation of the source and load impedance can result in excessive amplitude ripple in the tube's power output vs frequency response. Source and load variations as small as 1.1:1 can be quite significant in this regard. Isolators and circulators are frequently required in demanding applications. Note that in the case of EIKs and Twystrons, an excessive load mismatch (even out of band) can cause oscillations. Environmental Parameters

The environmental performance of klystrons should be regarded from two viewpoints; survival of the device and operation with fidelity while under stress. Generally, within rather gross bounds, temperature does not affect the survival of klystrons. However, temperature, and specifically the temperature of the RF circuit, can have a noticeable effect on electronic performance. This is because of dimensional changes in the resonant cavities, which causes detuning of their resonant frequencies. This effect can be considerably mitigated with cavity and mechanical tuner thermal compensation. In cases in which extreme stability is required under a wide range of ambient conditions, the temperature of the body must be controlled via a small temperature-controlled coolant loop. Klystrons are very susceptible to damage from mechanical stress. Spurious modulations of the amplified signal are also quite possible during periods of mechanical stress. These spurious modulations are commonly referred to as "microphonics."

20

Brian Roach

There is little useful general advice on shock and vibration specification that can be given. Klystrons are capable of operating to demanding specifications under the harshest mechanical conditions. However, the effort required to design a tube for such an application can be very great. The effort to verify tube performance during mechanical stress can also be very great. Pains should be taken to carefully specify the environmental stress that will actually be placed on the klystron. Unrealistic mechanical excitations should not be specified (e.g., sinusoidal sweeps). The difficulty of verifying electronic noise parameters while mechanical stress is applied should not be underestimated. Because klystrons operate at high voltages, voltage standoff and corona are concerns when operation at high altitude is required. As vacuum tubes, klystrons are not affected by radiation exposure (except for degradation of the mechanical properties of the assembly under conditions of extreme long-term exposure).

Life and Reliability The life and reliability of klystrons are highly dependent on system design and maturity. Klystrons are frequently the first component to fail in the event of system malfunction. Poorly designed or new systems can induce large numbers of tube failures. Particular tube sockets will frequently induce disproportionate numbers of failures compared with similar sockets in other locations. Tube failures should always be the occasion for system, as well as klystron, failure analysis [41, 42]. The main end of life mechanism for klystrons is cathode depletion. This mechanism is related to the temperature that the cathode is run at, which, in turn, is a function of gun design and selection of cathode material type. Generally, tube designs at higher frequency and higher peak power tubes will have a shorter life than other tubes. Numerous studies on cathode life have been conducted using various test vehicles [43]. However, these test results are not always strictly applicable to actual klystrons. This is partly due to the fact that operating tubes are not as favorable an environment for cathode materials as the test vehicles typically used in the studies. Fixed station klystrons have recorded lives in excess of 70,000 hr, although klystron lives of 15,000 to 40,000 hr are more the norm. A mechanical wearout mechanism is present in tunable klystrons. These tubes have mechanisms that require a portion of the vacuum envelope to be a deformable wall or bellows. Vacuum leaks can develop after some number of tuner cycles. Depending on the tube design, the average number of permissible tuner cycles is highly variable~from nearly infinite to less than 100 cycles in some designs.

21

I. Klystrons TABLE II Typical Klystron MTBFs

Application

Typical MTBF (hr)

Reliability factors

Airborne

1,000-5,000

Shipboard

5,000-10,000

Ground mobile (operating) Ground transportable

5,000-10,000 10,000-20,000

Ground fixed

20,000 +

Cycling, size, cooling, shock/vibration, temperature extremes Cycling, salt air/humidity, shock/vibration, power surges Cycling, power surges, shock/vibration, dust/dirt Cycling, power surges, shock/vibration, dust/dirt 24 hr/day operation, easy access, controlled/sheltered environment

Another wearout mechanism is present in fast-start guns. Quick-start guns will typically have a finite number of quick-start cycles. Table 11 gives typical MTBF figures for tubes in mature systems. Although this table was developed from data derived from a variety of linear beam tubes, it is quite relevant to klystrons in particular. This table clearly shows the link between environmental stress and tube MTBF. Airborne applications show the poorest reliability for two reasons; the environmental stress of the application and the fact that airborne tube protection schemes are sometimes less elaborate than those used in ground-based applications.

Physical Parameters Klystron size and weight are, to great degree, dictated by the operating requirements of the system. Klystrons of higher frequency, lower peak and average power, and smaller gain/bandwidth tend to be smaller and lighter. The main degrees of klystron design freedom involve the selection of cooling type and magnetic focusing circuits. The tubes described in Section 2 will give the reader some notion of typical klystron sizes and weights. Note that tubes intended for airborne applications can be considerably lighter. This is due to the typical specification of fairly high frequency ( > 8 GHz) and the use of rare earth permanent magnets.

Miscellaneous Items Klystrons require an excellent vacuum (between 10 .7 and 10 .9 T) for proper operation. Unfortunately, gas will evolve from the walls of the

22

Brian Roach

tube, especially during operation. Even a klystron with no leaks will suffer degradation of vacuum while on the shelf due to gas diffusion through the walls of the tube. Fortunately, klystrons will pump themselves to some degree during operation. However, in some cases, ion pumps or getters are specified. They are particularly recommended for large tubes, applications for which a fast turn-on after storage is required, or designs in which internal walls reach unusually high temperatures during operation. The modulation requirements of the system will have a profound effect on the specification and design of the electron gun. The higher the required /z for a gridded tube, the greater the difficulty of gun design. There are similar tradeoffs involved in heater turn-on time. Generally, the shorter the time is, the greater the complexity of the gun. For example, extremely short turn-on times (less than 1-2 s) require elaborate bombarder-type heaters, which, in turn, require a programmed heater turn-on profile and an additional HV supply. It is easier to design fast turn-on guns for physically small tubes without extreme RF performance or long-life requirements [44].

4. Design and Fabrication of Klystrons Klystrons, although more simple than wave tubes, are still complex devices. The RF, electron beam, thermal, and mechanical properties of tubes all tend to be highly interactive. This means that the task of designing klystrons is a complex and iterative one. There is no single design code or methodology that begins with the desired properties of a tube and yields a workable design. Fortunately, the requirement to design a tube from the ground up is infrequent; usually, there is an existent design that needs only to be modified to meet some new requirements.

Typical Design Methodology A scenario for a bottom-up design of a klystron is shown below. Although it is laid out in a linear process, in reality it is highly iterative. As in any design process, the experience of the designer can sharply reduce the number of required iterations. The design of modern klystrons relies heavily on the use of computer modeling [45, 46]. The first task is small signal modeling of the tube. Based on the assumed properties of the electron beam and cavities, this process establishes the required cavity tunings and cavity spacings required to obtain a required gain-bandwidth product. These small signal programs are typi-

I. Klystrons

23

cally proprietary; all of them follow the gain model of Figure 3 rather closely. The next task is large signal modeling of the device [46-48]. Small signal design best models the first portion (buncher section) of the tube; the large signal design addresses itself to the tunings and cavity spacings of the last two or three cavities. The design of the output circuit (simple resonant, double tuned, EIK, traveling wave) is also done at this stage. The next task is realization of the cavity or circuit properties assumed in the previous two steps. This can be done with physical cold test models [49] or with the use of appropriate computer codes (LALA, Superfish, SOS, etc.). The next step is design of the electron beam system. This includes the determination of the electrode geometries of the electron gun and the magnetic field requirements for proper beam formation. Usually, specialized proprietary codes are used for this purpose. In many cases, gun prototyping is done in beam analyzers [50]. These are test stands in which prototype guns can be exercised. Inside the beam analyzer, a small aperture is scanned across the gun's electron beam at various axial positions to measure the beam profile. The design of the magnetic focusing circuit is the next task. There are an increasingly large number of magnetostatic codes available for this purpose. Properly done, the results of this modeling can be extremely accurate. The amount of experimental cut and try should be minimal. Next comes thermomechanical design. There are a variety of inputs to this stage of design: The probable thermal fluxes derived from the electron beam and RF properties of the klystron. The physical requirements of the RF electron beam portions of the tube. The mechanical and environmental requirements of the application. The thermal and cooling design must be done with great care, as collector average power densities of hundreds of W/cm 2 are fairly common, and densities higher than 1 kW/cm 2 are not unheard of. Finite element thermomechanical modeling programs are frequently used in this stage of design. Last comes the layout and design of assemblies and piece parts. Standard mechanical CAD packages are normally used. This is an especially important stage, because the necessary design craftsmanship translates rather directly into high operating reliability and good manufacturing yield. Particular attention must be paid to proper braze joint'or weld joint design.

24

Brian Roach

Construction

Klystrons, like other high-power microwave tubes, are of ceramic metal construction. Most of the materials are chosen with an eye toward high. purity and low vapor pressure. Outside of the electron gun, the metals used are primarily OFHC copper and 300 series stainless steel. Where magnetically soft parts are required, low carbon steel and pure iron are used. High-purity ceramic (mainly alumina, but occasionally berylia) is utilized for voltage standoff purposes and microwave windows. The predominant construction method for smaller tubes is furnace brazing, usually with silver-copper and gold-copper braze alloys. The brazing is generally done in hydrogen. Larger tubes tend to use a greater proportion of welding in their construction. Great pains are taken in tube construction to minimize contamination. This is due to two reasons. First, contamination can inhibit the flow of alloy during brazing, causing leaks. Second, seemingly trivial amounts of contamination inside the vacuum envelope can result in endless amounts of gas during tube processing and operation. Therefore, manufacturers exercise stringent control on materials used in tubes. Most piece parts are subjected to a series of chemical cleaning baths. Assembly operations are often carried out in clean rooms to minimize contamination by dust, finger grease, etc.

Figure 14. Major subassemblies of a K~-band klystron.

25

I. Klystrons

Typically, there will be several levels of assembly before the tube is evacuated in a bake-out furnace. Figure 14 shows a Ka-band tube at the subassembly stage. Several steps of tube dress and RF processing will follow before construction is complete. References [51] and [52] describe the materials and technology of tube construction in great detail.

5. Noise and Stability Characteristics Noise Klystrons are amplifiers that can be represented by the gain and noise blocks that are normally used in system design. Typical noise figures for klystrons range from 30 to 40 dB. The total noise power output (or output per unit frequency) is readily calculable given the noise figure, gain, and bandwidth of the klystron. All calculations of this type start with the assumption of thermal noise at the input of the amplifier. These calculations are appropriate only for in-band noise. Klystrons usually attenuate out-of-band signals, so out-of-band noise is determined by the beam noise figure and the out-of-band response of the output circuit. Reference [2] has examples of typical noise calculations. Figure 15 illustrates typical levels of random noise. Figure 4 shows the out-of-band response of a typical five-cavity tube. Typical klystron intermodulation properties are depicted in Figures 16 and 17. Figure 16 shows the relative power output for a typical klystron. It shows the total output power of a klystron driven into saturation with two equal carriers. This total output power includes all intermodulation prod-

I Typical signal output power level

40 t

N

m 13

0 -40 -80

-120 -160 -200

.f-~- f .

f

/lyplcal

f

f

f

f

f

f

f

f

f

noise power level

f / ~

V l l l l l l l J J J J /

f

,

100kHz

1M~Hz 10MHz A f from fo

100MHz

Figure 15. Typical klystron noise power output,

26

Brian Roach 0

Single carri

o

o •

-5

0 0 O_

o 3

-10

°N

~

0

0

~

m "o

-15

,/

I

I

I

I

-20 -15 -10 -5 RF drive (dB below saturation)

J

0

Figure 16. Typical input- output curves - - one-carrier and two-carrier cases.

ucts and is somewhat lower than the single-carrier saturated power output. Figure 17 shows the relative amplitude of the largest intermodulation product under these conditions. Typical klystron harmonic output levels are - 3 0 dB down from the fundamental for the second harmonic and - 5 0 dB down for higher harmonics. This can be rather difficult to verify, however. This is because harmonic frequencies are in the overmoded frequency range of the waveguide outputs used by most klystrons. Klystrons generally exhibit low AM and PM noise; typical curves are shown in Figure 18 for the VKX-7809. These levels of AM and PM noise can be severely compromised, however, by ion oscillations. Ion oscillations

~

-10

"E -15

E~~

-20

.E

-25

~g ~ -3o

~' ~ -35

_J

m

-40

-o v

"2 "4 "6 "8-10-12-14-16 RF drive (dB down from 2 carrier sat)

Figure 17. Largest intermodulation product (with reference to either carrier).

27

I. Klystrons -6O "-

-80

•

-100

k_ O 0

m

0

_~

-120

m

'~

-140

•0-~

- 160

_

AM noise h

Z

I

10 DeviGtion

from

I

I

100 f o (KHz)

Figure 18. Typical klystron AM and PM noise (VKX-7809, 40-dB gain).

are described in References [12, 53, 54]. Careful attention to magnetic design and meticulous tube processing are required to eliminate these troublesome instabilities. Other sources of noise are actually caused by variation of the power supply voltages. These pushing factors are addressed under Operating Parameters.

Stability Although the basic klystron is usually regarded as unconditionally stable, there are, in reality, some possible instabilities that can occur [55]. RF leakage from the output flange to the input flange can cause oscillations in extreme cases and gain anomalies in less extreme cases. Internal feedback is possible in the form of electrons that have become turned around and propagate toward the gun. This is more likely to occur in tubes with depressed collectors, permanent magnets, or ultra-high-efficiency tubes. Note that these possible gain anomalies are especially significant to applications that have critical intermodulation requirements. Multipactor is a secondary electron discharge that is possible in the presence of strong RF and magnetic fields. It can occur on output drift tube tips, output windows, or the cavity ceramics of external cavity klystrons. Multipactor on drift tubes can manifest itself in the form of gain "clamping" or other anomalies. Multipactor on ceramics can easily cause the thermal shattering of the ceramic. Several stratagems are available to prevent multipactor [56-58]. An excessive mismatch at the output of an EIK or a Twystron can cause oscillations. This is the case both in and out of band. The allowable

28

Brian Roach

mismatch at different frequencies is a function of the particular design. EIKs and Twystrons can also oscillate if an inappropriate beam voltage is applied. The performance of a typical tube is outlined under Radar Applications. Low-frequency gun oscillations and monotron oscillations result from the interaction of a high-power electron beam and structures with RF resonances. They are possible in some extremely high-power designs [59-61]. Grid oscillations can result from the interaction of the low-frequency L and C characteristics of the grid with the power supply. They manifest themselves as an unexpected LF or HF modulation of the amplified signal. In an analysis of this phenomenon, the gun control electrodes should be regarded as the elements of a triode or tetrode.

6. Klystron Protection Tube protection is an area which cannot get enough attention. It presents a very real dilemma to the power supply designer. On the one hand, good tube protection can greatly enhance the reliability of a system. But, on the other hand, the complexity of the schemes required can, of themselves, contribute appreciably to the overall complexity of the supply and the difficulty of its design. However, there is an adage that should be borne in m i n d m t h e tube is the most expensive fuse in the entire system. Reference [62] contains useful information and references for power supply designers. The first level of protection that must be afforded klystrons is physical. Handling damage is a major failure mechanism in most fielded klystron systems. It can be greatly reduced by thoughtful design of the transmitter and the logistic system for supplying replacement tubes. Proper shipping containers, convenient tube lift points or handles, easy socket accessibility, and proper personnel training are keys to the elimination of this mode of failure. High-voltage arcs can occur either inside or outside the vacuum envelope. Wherever the location, a sustained arc can easily damage the tube. Depending on the location of the arc and the size of the tube, as little as a few joules of energy can be enough to cause damage. The power supply design should be such that stored energy is quickly dumped in response to internal tube arcing. Usually a fast acting switch (or crowbar) is required. A possible exception to this rule is a switching power supply. In switching systems with low-energy storage, simply shutting down the inverter can sometimes be sufficient to prevent klystron damage.

I. Klystrons

29

Waveguide RF arcs are not uncommon in high-power microwave systems. Arcs will propagate toward the klystron and will break the output window if no action is taken to extinguish the arc. Arc detection is best done with a photodetector aimed at the output window. The output power must be reduced within 10 ~S to prevent damaging the window. This can be achieved in any number of ways; reduction of RF drive, modulator shutdown, crowbarring, etc. The grid and RF circuit (body) of the tube are susceptible to damage by the electron beam. Peak and average overcurrent sensing must be provided for these elements. The supply should react to overcurrent conditions by shutting down pulsing, crowbarring, etc. The specific trip level and speed of response will be peculiar to the klystron type in question. The supply should be designed so that inappropriate voltages cannot be applied to the tube or applied in the wrong order. The manufacturer's limits on operating voltages and currents should be embodied in a system of interlocks. In gridded tubes, the interlocking of operating voltages is especially important. Operating voltages must be applied in a particular order. First, the specified cutoff (eco)voltage must be applied to the grid. Then, the beam voltage may be applied to the cathode. Grid pulsing should not be enabled until the beam voltage clears a preset level. Supply shutdown, especially in the presence of fault conditions, must be carefully considered. Never apply a positive voltage to a grid when the beam voltage is off [63]. In most klystrons, interruption of coolant flow is speedily followed by tube destruction. Therefore, interlocks are highly recommended for coolant flow. In liquid cooled tubes, coolant quality can be of crucial importance. In tubes with high collector wetted wall temperatures, pH, ion content, oxygen content, sulfur content, and bulk resistivity must be maintained within specified limits [64-66]. The situation is somewhat less critical for air-cooled tubes, for which the dust or salt content of the cooling air can be of concern. Other interlocks are typically used for miscellaneous purposes such as operator safety or ion pump current (tube vacuum level). The temperature of the cathode must be carefully controlled to obtain long life. Practically speaking, this means that the heater power must be appropriately set. Miram curves are the best way to determine the appropriate level of heater power that is required for any given tube. They are also a tool for exploration of other electron gun problems [67]. Heaters usually require protection against excessive current upon turn-on. Heater wire will typically run at a temperature of 1500°C. Therefore, the hot (or operating) resistance will be considerably higher than the

30

Brian Roach

cold resistance. If the operating heater voltage is applied to a cold heater, the resulting surge of current can be enough to damage the heater. The use of a current-limited supply or a ramped application of heater voltage is recommended.

Acknowledgments I thank my colleagues at Varian for their contributions of material used in this chapter. I also express my gratitude to my wife and family for their forbearance and support.

References [1] Chodrow, Fundamentals of Microwave Electronics. New York: McGraw-Hill, (1964). [2] Staprans et al., High power linear beam tubes, Proc. IEEE, Vol. 61, pp. 299-330, Mar. 1973. [3] Faillon et al., Wide band klystrons and TWT's, ITG Vacuum-Electron Displays Meet., Garmisch-Partenkirchen, May 1989; see also Vortrage der ITGnFachtagung 1989. Berlin: VDE-Verlag, 1989. [4] Anon, "Twystron Hybrid TWT's," Varian Assoc., Palo Alto, CA, Mar. 1973. [5] LaRue et al. Multi-megawatt hybrid TWT's at S-band and C-band, IEEE Electron Devices Meet., 1964. [6] Chodrow et al., A high efficiency klystron with distributed interaction, IRE Trans. Electron Devices, Vol. ED-8, pp. 44-55, Jan. 1963. [7] Zhao, Impedance measurement technique for double gap klystron cavity, SLAC-PUB2751; see also IEEE Trans. Electron Devices, Vol. ED-29, pp. 316-320, Feb. 1982. [8] Lee et al., Design and performance of a 150 MW klystron at S band, IEEE Trans. Plasma Sci., Spec. Issue High Power Electron Gener., Vol. PS-14, Dec. 1985. [9] Mann et al., "X Band CW Generator Final Report," USAF Rep., Final Tech. Rep. RADC-TR-69-338, Mar. 1970. [10] Viant, "95 GHz EIA for Airborne High Power Transmitters," U.S. Army Laboratory Command Rep., R & D Tech. Rep. SLCET-TR-83-0399, 1983. [11] Pierce, Theory and Design of Electron Beams, 2nd Ed. New York, Van Nostrand, 1954. [12] Gilmour, Microwave Tubes. Dedham, MA: Artech House, 1986. [13] Gittins, Power Traveling Wave Tubes. New York: American Elsevier, 1965. [14] Cronin, Practical aspects of modern dispenser cathodes, Microwave J., Vol. 22, pp. 57-62, Sept. 1979. [15] Falce, Dispenser cathodes: The current state of technology, IEEE Electron Devices Meet., pp. 448-451, 1983. [16] Green, Modern thermionic cathodes, IEEE Int. Electron Devices Meet., pp. 925-928, 1987. [17] Day, New developments in electrostatically focused klystrons, Microwave J., Vol. 13, pp. 59-63, Apr. 1970. [18] Harrold et al., Permanent magnets for microwave devices, IEEE Trans. Magn., Vol. MAG-4, pp. 229-239, Sept. 1968. [19] Sterrett et al., The design of periodic magnetic focusing structures, IRE Trans. Electron Devices, Vol. ED-5, pp. 35-42, Jan. 1958. [20] Schindler, An improved procedure for the design of PPM assemblies, IEEE Trans. Electron Devices, Vol. ED-13, pp. 942-949, Dec. 1966.

I. Klystrons

31

[21] Legerra et al., A convergent confined flow focusing system for millimeter wave tubes, IEEE Int. Electron Devices Meet., 1983. [22] Scott, Cooling of Electronic Equipment. New York: John Wiley & Sons, 1974. [231 Merdinian et al., High power permanent magnet focused, S-band klystron for linear accelerator use, Proc. 5th Int. Congr. Microwave Tubes, Paris, p. 242, Sept. 1964. [24] Merdinian et al., Klystron for SLAC, IRE Trans. Electron Devices, Vol. ED-14, pp. 700-705, Oct. 1967. [25] Lee et al., 50 MW klystron for the Stanford Linear Collider, IEEE Electron Devices Meet., pp. 144-147, 1983. [26] Hayashi et al., High power X-band klystron, IEEE Electron Devices Meet., pp. 371-374, 1989. [27] Allen, "RF Power Sources," SLAC Rep. SLAC-PUB-4646, May 1988. [28] Faillon, Six GHz earth station klystron, Microwave J., Vol. 23, pp. 57-60, July 1980. [29] Anon, "The VA-936 Klystron Series," Publ. No. 3724A. Varian Assoc., Palo Alto, CA, Sept. 1978. [30] McCune, "UHF TV Klystron Multistage Depressed Collector Development Program," NASA Contractor Rep. CR182190, Sept. 1988. [31] McCune, Klystron performance using multistage depressed collector, IEEE Electron Devices Meet., 1987. [32] Kanavets et al., High efficiency multi-cavity klystrons (optimization of bunching and energy exchange), Elektron. Tekh., Ser. I, Elektron. Svch., No. 11, pp. 33-45, 1976. [33] Lien, High efficiency klystron amplifiers, 8th Int. Conf. Microwaves Opt. Gener. Amplification, Proc., Amsterdam, Conv. Rec. MOGA-70, Sept. 1970. [34] Mihran, The effect of drift length, beam radius, and perveance on klystron efficiency, IEEE Trans. Electron Devices, Vol. ED-14, pp. 201-206, Apr. 1967. [35] Symons, Scaling laws and power limits for klystrons, IEEE Int. Electron Device Meet., pp. 156-159, 1986. [36] Nordquist et al., Performance capability of Ka-band klystrons, IEEE Int. Electron Device Meet., pp. 370-374, 1988. [37] Kojima et al., Super high power klystron for JT-60, IEEE Conf. Plasma Sci., Pittsburg, June 1985. [38] McCune, A 250 KW CW X-band klystron, IEEE Int. Electron Devices Meet., 1967. [39] McCune, Klystrons for present and future lower hybrid resonance applications, Fourth Int. Symp. Heating Toroidal Plasmas, Rome, Mar. 1984. [40] McCune, New developments in high power klystrons for lower hybrid resonance heating applications, 13th Eur. Conf. Controlled Plasma Fusion Heat., Schliersee, Ger., Apr. 1986. [41] Allen et al., Performance of the SLAC Linear Collider klystrons, Part. Accel. Conf., Washington, DC, Mar. 1987. [42] Houts et al., "Microwave Tube Reliability--Actual vs. Predicted--A Realistic Appraisal," E I A / R A D C Rep., Jan. 1991. [43] Shroff et al., Life test results of various dispenser cathode types, IEEE Int. Electron Devices Meet., pp. 643-647, 1987. [44] Treseder et al., Design of quick start, high current density cathodes, IEEE Int. Electron Devices Meet., pp. 453-455, 1983. [45] True, Computers and tubes--Today and tomorrow, IEEE Int. Electron Devices Meet., pp. 436-439, 1983. [46] Kageyama, Large signal analysis of broad-band klystron with design applications, IEEE Trans. Electron Devices, Vol. ED-24, pp. 3-11, Jan. 1977.

32

Brian Roach

[47] Kosmahl et al., Two dimensional evaluation of energy extraction in output cavities of klystron amplifiers, IEEE Trans. Electron Devices, Vol. ED-20, pp. 883-890, Oct. 1973. [48] Drobot, Large scale simulation of electron devices, IEEE Int. Electron Devices Meet., pp. 668-671, 1984. [49] Ginzton, Microwave Measurements. New York: McGraw-Hill, 1957. [50] Miram, Diagnostic techniques with a computer controlled beam analyzer, IEEE Int. Electron Devices Meet., pp. 708-711, 1986. [51] Kohl, Handbook of Materials and Techniques for Vacuum Devices. New York: Reinhold, 1967. [52] Rosebury, Electron Tube and Vacuum Techniques. Reading, MA: Addison-Wesley, 1965. [53] Mihran, Positive ion oscillations in long electron beams, IRE Trans. Electron Devices, Vol. ED-3, pp. 117-121, July 1956. [54] McCune, Ion oscillations in pulsed klystron amplifiers, IEEE Int. Electron Device Meet., pp. 148-150, 1983. [55] Tomiyasu, Spurious output from high power pulsed microwave tubes and their control, IRE Trans. Microwave Theory Tech., Vol. MTT-9, pp. 480-484, Nov. 1961. [56] Preist et al., On the heating of output windows of microwave tubes by electron bombardment, IRE Trans. Electron Devices, Vol. ED-8, pp. 243-251, July 1961. [57] Talcott, The effects of titanium films on secondary electron emission phenomena in resonant cavities and at dielectric surfaces, IRE Trans. Electron Devices, Vol. ED-9, pp. 405-410, Sept. 1962. [58] Vaughan, Multipactor, IEEE Trans. Electron Devices, Vol. ED-35, pp. 1172-1180, July 1988. [59] Tomiyasu, Diode oscillations in high voltage klystrons, IRE Trans. Electron Devices, Vol. ED-8, pp. 243-251, July 1961. [60] Tomiyasu, Method for suppressing diode oscillations in high voltage klystrons, IRE Trans. Electron Devices, Vol. ED-8, pp. 381-386, Sept. 1961. [61] Blotekjar et al. "Optimum RF Field Distribution of Monotron Cavities," USAF RADC Contract AF 61 (052)-264 (RADC TN 61-14), Sept. 1960. [62] Skolnik, Radar Handbook. New York: McGraw-Hill, 1970. [63] Ewell, Protection of medium power pulse klystrons, Power Modulator Symp., San Diego, June 1990. [64] Anon, "Recommendations for Cooling High Power Klystrons," Publ. No. 2071 (AEB17A). Varian Assoc., Palo Alto, CA. [65] Anon, "General Procedure for Flushing and Back-Washing Liquid Cooled Klystrons," Publ. No. 2070 (AEB-17B). Varian Assoc., Palo Alto, CA. [66] Anon, "Cleaning and Flushing Klystron Water and Vapor Cooling Systems," Publ. No. 3364 (AEB-32). Varian Assoc., Palo Alto, CA. [67] Grant, A powerful quality assurance technique for dispenser cathodes and electron guns, IEEE Int. Electron Devices Meet., pp. 334-339, 1984.

CHAPTER

2 Magnetrons Wayne Love

I. Introduction IVlagnetrons are devices which are efficient generators of microwave energy. They were the first device capable of generating high-power microwaves and were instrumental in the development of the first radar systems used in World War II. They are vacuum diodes that are made up of circular resonant cavities around a cathode immersed in a perpendicular magnetic field. This magnetic field results in a force that changes the motion of electrons from a straight path to one that is curved. It is this curved motion that allows for a simple and efficient means of electron bunching that abstracts pC energy from the electrons to the RF field to produce the high-power microwave output. There are two types of magnetrons. Pulsed magnetrons have very high peak output power (kilowatts to several megawatts) of a very short duration. The anode voltage is turned on and off hundreds of to ten thousand times a second, allowing high peak power but maintaining low average or total power over time. Current frequency ranges for pulsed magnetrons are less than 1 GHz to over 5 GHz. Pulsed magnetrons are still used in radar applications, but they will not be specifically discussed in this chapter as this book is on microwave power. Much of what can be said about continuous wave magnetrons are also true about pulsed-type magnetrons. Continuous wave (CW) magnetrons have continuous output power from a few watts to up to 10 kW. The most common application of the CW


33


34

Wayne Love

magnetron is in the home microwave oven. Millions of these magnetrons are made on highly automated production lines every year. Most CW magnetrons oscillate at a frequency of 2450 or 915 MHz, but CW magnetrons have been developed at other frequencies. The field of microwave energy has more applications now than just a few years ago. The reasons to use microwave energy over other methods of heating include lower cost, ease of operation, process cleanliness, environmentally cleanliness, limited space, and it may be the only method of heating the material or process. Applications include the following: Cooking food Removal of moisture Generation of plasma Extruding rubber Destruction of waste

Pasteurizing waste Sintering ceramic Heating of chemical reactions Medical applications Mineral processing.

The consumer oven magnetrons have output power of under 1 kW and typically cost under $150 mainly because of demand and manufacturing techniques. Because of this demand, there is intense competition among the manufacturers that make these magnetrons. These manufacturers also have relatively large expenditures for research and development of new magnetron types and processing. Most of the assembly lines that make consumer-type magnetrons are completely automated. Home cooker magnetrons are generally air cooled and have very short warm-up times before they start to operate. They also have a relatively short life expectancy of under 100 hr, but they are typically used only a few minutes a day. Microwave ovens have different power settings which are achieved by turning the magnetron on and off every few seconds, giving different average output powers. Commercial oven magnetrons are much like their consumer magnetron counterparts but only with higher output power (1 to 2 kW). They are used in catering, cafeteria, and institutional settings, where there is a need for warming or cooking a larger quantity of food. Some of these magnetrons are water cooled because of the higher output power, and some of these higher power magnetrons are manufactured by the cookertype manufacturers. Plasma generation is a field that is growing rapidly. The microwaves are used to excite gas at partial pressure to generate a plasma glow discharge. This glow discharge can be used for deposition or removal of materials at relatively low temperatures. Plasmas can be generated at RF frequencies, but as the frequency increases ion bombardment is less intense. This lower level of ion bombardment causes less damage to the substrate materials that it is being used on. The requirements that are

35

2. Magnetrons

placed on these magnetrons are output power stability and, in some cases, frequency stability. The generation of the plasma glow discharge will cause the output power of the magnetron to change. This change in output power can be a problem if it is too great. Special cooling is required in some cases because these magnetrons are often operated in ultra-clean clean rooms. Industrial magnetrons have output power from over 2 to 10 kW. They almost always operate at frequencies of 2450 and 915 MHz and are almost all water cooled. Some of these magnetrons also have air cooling because of the heat that is generated during operation. Most of the industrial magnetrons are made on labor-intensive production lines because of the relatively small quantity made every year. Their construction is more rugged than the cooker magnetrons, and they typically have a longer life. Because of a wide variation of applications, the equipment manufacturer must ensure that the proper conditions for the operation of the magnetron are in place.

2. Microwaves Microwaves are part of the electromagnetic spectrum with wavelengths much shorter than the wavelengths of the radio broadcast spectrum. They are given by the relationship A = C/f,

where A is the wavelength in meters, f is the frequency in cycles per second (Hz), and C is the speed of light (3 x 108 m/s). Microwaves can be directed, much like water in a pipe, through coaxial lines or waveguides. Coaxial lines are two concentric metallic conductors separated by a nonconductor. They are often flexible but generally cannot transmit large amounts of power. Using common-size coaxial lines and connectors, only a few hundred watts can be transmitted. For many applications, waveguides are the better choice, as they are able to transmit high power. Waveguides are metallic tubes of a circular or rectangular cross section of specific dimensions. It is these dimensions which determine what frequency of microwave radiation a waveguide can propagate. The magnetron can be attached to and inject microwaves down the waveguide. The microwaves propagate down the waveguide as a sinusoidal wave. If the work or load absorbs all of the wave, then there is no reflection. This occurs when the resistive load and the source load have equal impedance. This condition is called matched load.

Wayne Love

36 VS~

f

~METER

/

VOLTAGE- ~ STANDING

v LU

m

c-

E .

m

In

Anode Current (mA) Figure 4. Filament voltage reduction with an increase in anode current. The filament voltage with zero anode current is called the standby voltage.

The cathode has a layer of tungsten carbide on the outside diameter and is said to be carburized. The purpose of this coating is to reduce the temperature that is needed to emit electrons and increase life by retarding the migration of thorium. Thorium is a metal that is added to the tungsten to aid in emission. A by-product of this chemical reaction is the formation

OVER TEMPERATURE ~

\,,

/NOMINALTEMPERATURE

I TIME

Figure 5. Graph showing cathode life with cathode temperature.

41

2. Magnetrons

of CO and C02, both of which are gasses. This gas must be absorbed by getters that are placed inside the vacuum tube. The end shields of the cathode prevent the escape of electrons from the vane tip area, which is called the interaction region. The cathode is in the interaction region and is part of the resonant system. Energy can couple into the cathode and be transmitted by the cathode through the input. Many magnetrons have a filter system at its input to reduce this unwanted microwave radiation. Anode

The anode is usually made of copper to minimize microwave losses and is a set of resonant cavities placed around the cathode. It has an equivalent LC circuit in parallel, as shown in Figure 6. The inductor is representative of the individual cavity that is between two vanes. The capacitance is representative of the area at the vane tips. This LC circuit has a resonant frequency of oscillation that is called the PI mode. The PI mode is the most efficient mode of operation, but there are other modes of oscillation that are unwanted. If the magnetron is oscillating in these other unwanted modes, it is said to be moding. These unwanted modes of oscillation are close to the PI mode, but there are methods to separate the PI mode from the others: the strapping of vanes with a conductor, the use of a rising-sun anode, and the use of the coaxial

Figure 6. LC circuit equivalent for a I O-cavity unstrapped magnetron,

42

Wayne Love

magnetrons. The strapping of the anode is the most common method for continuous wave magnetrons. In the strapping method, conducting straps are attached to alternate vanes. In the PI mode, alternate vanes are at the same potential; thus no additional inductance is introduced by the straps. The straps will change the capacitance, and the PI mode frequency will be separated from the unwanted modes. Moving the position of these straps can shift the operating frequency of the magnetron by changing the capacitance of the circuit. This is one method to set the resonant frequency of the magnetron during assembly. When modes other than the PI mode are present, the alternate vanes are at different potentials from each other and the straps will introduce both inductance and capacitance. Because of the different potentials on the alternating vanes, there are currents that flow through the straps. If the current becomes too great, the straps can burn out. For this reason, it is essential that the magnetron not be allowed to operate while it is moding. The anode must also be able to dissipate large amounts of heat caused by the electrons that strike the vane tips. Some of the industrial magnetrons have to dissipate over 3000 W of power while operating. Most of

Manufacture I

Parts

e°c° Incoming

Parts

Cold Test

Chemical Process

Final Vacuum

eoCo Vacuum

Leak

Check

Carburize

Post Exhaust Process

eoCo Sub Assy.

(inc. welding I and brazing) I

Seal

Catho~

I Sub Assy. I

Assemble

Basing

Magnet Charge

Exhaust and Exhaust Processing

Age & Test

Ship

Figure 7. Flow chart showing the essential processing of CW magnetrons,

43

2. Magnetrons

this energy is at the tips of the vanes, so the design and heat transfer away from the tips must be maximized. Most of the high-power magnetrons are water cooled or cooled by a combination of water and air.

Output The output is the means of coupling the microwave energy from the cavities to the waveguide. It is usually a loop in one of the cavities to extract energy or a coaxial type which is a conductor that is connected to a vane. It is important that the output be hardy enough that it may transmit the energy from the cavity to the waveguide. It must also not change shape or position during handling or processing. All of the CW magnetrons must have the above parts, and most are assembled and processed similarly. Figure 7 shows a flow chart that is typical for industrial types but could also be used for other types of CW magnetrons.

4. Space Charge Without a magnetic field, the magnetron would act as a diode (Figure 8). Electrons emitted from the cathode would travel radially outward in a straight path to the anode. There is a force on the electron due to the electric field of - e E . In the presence of a magnetic field that is perpendicular to the electric field, there is a force of (e/c)v on the electron in addition to the electric field force. This magnetic field impedes the path of

Figure 8. Cathode and anode with an electron path (a) in a diode, (b) in the presence of a high magnetic field, and (c) in a magnetic field at the Hull cutoff voltage.

44

Wayne Love

Region of / Current ] t~ 1===4

o

o

Magnetic Field Figure 9. The Hull cutoff voltage for a magnetron of specific dimensions.

the electron. The path of the electrons is now circular, which provides an efficient means of bunching of the electrons which is the method increasing the power output. There is an anode voltage that in the presence of the magnetic field and electric field of the electrons just reaches the anode and current flow. Below this voltage there is no current flow. This voltage is called the Hull cutoff voltage and is dependent on the magnetic field, the electric potential, the radius of the anode, and the radius of the cathode (Figure 9). In the presence of a PI-mode electromagnetic field, there are alternating positive and negative voltages on the vanes. If an electron leaves the cathode into an accelerating field, the electron will speed up and extract energy from the electromagnetic field. These higher energy electrons will be greatly affected by the magnetic field and will be returned to the cathode. This causes heating of the cathode and is the back-bombardment talked about earlier. As the anode voltage is increased, so this backbombardment and the filament voltage must be reduced to keep the cathode temperature constant. Electrons that enter the electromagnetic field from a decelerating field give up some of their DC energy to the electromagnetic field. If the angular velocity of the electron is such that it is always in a decelerating field, then almost all of the energy is given up to the electromagnetic field and strikes the anode (Figure 10). Because there are regions of electrons that are a decelerating field and not in an accelerating field and because these regions move with an angular frequency proportional to the resonant cavity frequency, there is a

45

2. Magnetrons

___3 Figure 10. Electron a enters the electromagnetic field at time TI into an accelerating field and gains energy, It interacts with the magnetic field and spins back to the cathode. Electron b enters the electromagnetic field at T~ and is decelerated, losing energy to the electromagnetic field. At T2 the electron again is in a decelerating field and the electron loses more energy,

cloud of electrons with spokes like that of a wheel (Figure 11). The number of spokes is ~1 the number of cavities. As the spokes move in a decelerating RF field, the electrons that are toward the negative potential vane are decelerated while the electrons close to the vane with positive potential are accelerated. This causes the electrons in the spoke to bunch even further. The bunching of the electrons in each spoke tends to keep the spokes equally spaced. Electrons that do hit the anode have nearly given up their energy.

Figure II. Electron cloud showing "spokes" of anode current,

46

Wayne Love

5. Magnetic Field The magnetic field causes the circular path of the electrons in the electron cloud. It must be as close to parallel in relation to the axis of the cathode as possible in the interaction region. It is also important that the field not change with time in order to keep the output power constant. The magnetic field can be formed from permanent magnets or electromagnets. Permanent magnets can lose their flux by moving or removing any part of the magnetic circuit or by removal of magnetic charge. The magnetic charge can be removed by bringing the magnetron close to iron, including setting it on a metal shelf for storage. These conditions will change the magnetic field and the magnetron must be returned to the manufacturer to be recharged. The permanent magnet magnetrons are sold with the magnets in the magnetic circuit. This adds to the price of the magnetron but is a small percent of the total cost. No additional cost or equipment is required. The electromagnet version requires a separate power supply for the electromagnet. The electromagnet is not temperature stable as the resistance of the coil will change with temperature. Feedback circuits can be used to adjust the input power to the electromagnet. The electromagnet and most of the magnetic circuit is purchased only once. It is only the vacuum tube that needs to be replaced. Replacement may be a little more difficult as the magnetic field may need to be fine tuned to match each magnetron's characteristics.

6. Power Adjustment There is a need for the output power of the magnetron to be varied. Several methods are used to change the power that is applied to the work or load. They include the following: Pulsing the output power of the magnetron. Changing the anode current. Changing the magnetic field. Adjusting the microwave energy that goes to the load.

Pulsing Pulsing the output power of a magnetron to vary the power to the load is a common method that is used in most home cooker ovens. This is not the same as that employed for pulsed magnetrons that are used in radar

47

2. Magnetrons

systems. These cooker oven magnetrons are pulsed very slowly, sometimes on for 2 to 5 s and then off for 2 to 5 s. In this manner, the average power to the load can be controlled. There must be a timing circuit in the power supply which adds complexity and cost. The power to the load is not continuous, which is not compatible with industrial applications. Highpower industrial magnetrons must follow a filament reduction curve. This means that for most industrial magnetrons there is a typical filament warm-up time of 5 to 20 s at the filament stand by voltage, and then the filament voltage is to be reduced after the anode current is increased. This filament warm-up time is greater than the entire o n / o f f cycle above and virtually rules out the use of this type of power adjustment. The home cooker magnetron has no filament reduction, and the power is not continuous and is not a problem for this application. Reduction of Anode Current The reduction of anode current is another method of adjusting the output power. A change in input power will result in a change in output power. The output power of a magnetron is directly proportional to the anode current. Figure 12 shows the relationship between anode voltage and anode current. Note that as the anode voltage increases initially there is little anode current. This small "leakage" current has not been adequately explained. At a voltage that is determined partially by the magnetic field, current will start to flow and the magnetron will start to oscillate. This voltage is called the Hartree voltage and is dependent on the magnetic

~

~

~

~,, ~ i ' ~ J ~

~ml m

~*~um

~

C~

j" 0

~""'--

Hartree Voltage

I I

0t--

Anode Current (mA) Figure 12. Anode voltage vs anode current, At the Hartree voltage, the magnetron starts to oscillate.

Wayne Love

48

/ Anode Voltage

t~ 0

/

>

0 c-

1000-GHz level [3, 4, 39, 42, 64, 65, 83]. The BWO circuit is the same as that of the BWA except that the RF input is replaced with a passive termination. The beam current is increased from zero by increasing the anode voltage. When the beam current reaches a point termed the starting current, IsT , the tube breaks into oscillation [43, 46, 61]. The state-of-the-art maximum power output for BWOs decreases exponentially from about 10 MW at 30 GHz to about 2 mW at 1000 GHz [7].

7. Magnetrons Applications The multicavity traveling-wave magnetron [10, 17, 25, 41, 43, 44, 66, 87] is a crossed-field microwave oscillator capable of producing megawatts of pulsed power at frequencies up to 30 GHz. Efficiencies typically range from 40 to 70%. Because of their low cost, small size and weight, and low voltage requirements, magnetrons are extensively used in radar systems, microwave ovens, and diathermy equipment.

80

Jeffrey D. Wilson

General Operation A schematic diagram of a conventional magnetron is shown in Figure 13. A cylindrical cathode is surrounded by an anode consisting of a reentrant slow-wave circuit. The region between the cathode and the anode is filled with a uniform magnetic field parallel to the cylindrical axis, which causes the electrons emitted from the cathode to rotate around the cathode in a dense turbulent hub, known as the Brillouin cloud. The slow wave structure of the anode propagates an RF wave around its circumference with a phase velocity equal to that of the outer edge of the Brillouin cloud. In the electron-wave interaction, electrons flow to the anode in "spokes" which rotate in synchronism with the RF field, producing oscillation at a resonant frequency. One of the resonators of the slow-wave circuit is coupled inductively to a loop formed from the center conductor of a coaxial cable. The coaxial cable in turn delivers the RF output signal to the load.

Anode Slow-Wave Circuit The multicavity anode is a slow-wave structure, propagating an RF wave at approximately the same velocity as that of the electrons at the outer edge of the Brillouin cloud. The dispersion curve is shown in Figure 14, with the curve repeating every 2rr radians. For an anode with N cavities and with pitch p between cavities, only those values of the phase constant /3 = w/Up for which ~Np = 2rrm

form=0,1,2,...N/2

(29)

are allowable. These values o f / 3 are represented by the vertical lines in

I

L End hat Figure 13. Magnetron (Gewartowski and Watson, [43]).

81

3. Traveling-Wave Thermionic Devices

o~ N/2

f

¢0 N/2-1

e) N/2-2

e) N/2-3 E

I

I~

I "

o e = ~p

Figure 14. Dispersion curve for a magnetron slow-wave circuit with N cavities with pitch p between cavities. Allowable values of the phase constant are represented by the vertical lines.

Figure 14. It is always desired that the magnetron operate in the m = N/2 or rr mode for which the phase shift per cavity is rr radians. The resulting electric field pattern for an eight-cavity circuit is shown in Figure 15.

Figure 15. Electric field pattern for the ~- mode in an eight-cavity magnetron with pitch p.

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Jeffrey D. Wilson

Strapping The frequency of the desired m = N/2 or 7r mode is much different from the frequency corresponding to the undesired mode m = ( N / 2 ) - 1, as represented in Figure 14. It can be shown [41] that typically the ( N / 2 ) - 1 mode frequency is only 1 to 3% different from the rr mode frequency. To prevent oscillation in the undesired mode, the frequency separation between the two modes is increased by a procedure known as strapping [41, 1121. In a strapped magnetron, two parallel wires or fiat ribbons are mounted on the anode structure ends, making electrical contacts to alternate vanes. This causes the frequency separation between the rr mode and the ( N / 2 ) - 1 mode to be about 25 to 35% in low-power magnetrons and about 10 to 14% in high-power magnetrons [44]. Thus oscillation in the undesired modes can be prevented. At frequencies on the order of 10 GHz and higher, straps become very difficult to fabricate because of the small dimensions of the anode. At these high frequencies, rising-sun anode structures of the form shown in Figure 16 can be used to separate mode frequencies [74].

/-

Anode vane

Cathode slot

Figure 16. Rising-sun magnetron.

83


Coaxial Magnetrons General Operation The coaxial magnetron [44, 66], as shown in Figure 17, contains a multicavity anode similar to that of a conventional magnetron. However, the anode is surrounded by a high-Q coaxial cavity operating in the TE011 mode. Slots in the back walls of alternate anode cavities couple the fields in these resonators to the surrounding coaxial cavity. In the 7r mode, the fields in every other cavity are in phase and couple in the same direction into the coaxial cavity. The coupling with the surrounding cavity stabilizes the magnetron in the desired ~ mode of operation, eliminating the need for strapping.

Characteristics The coaxial magnetron has several important advantages over a conventional strapped magnetron [66]. 1. Because the mode spectrum is controlled by the coaxial cavity, the number of cavities can be larger. This permits a larger cathode to be used, resulting in lower cathode loading and higher possible power. Also the interelectrode spaces are larger, reducing the voltage gradients. These factors provide enhanced reliability and lifetime.

Cathode-~

/-- Anode lot

Electric ./ field line - /

\ ~--

Coaxial cavity

Figure 17. Electric field pattern in a coaxial magnetron,

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Jeffrey D. Wilson

2. The unstrapped resonator system has a higher impedance and a higher Q than its strapped equivalent. Combined with the high Q of the cavity, this results in a higher circuit efficiency. 3. The coaxial cavity greatly increases frequency stability. 4. Tuning the frequency of a coaxial megnetron is more easily accomplished by changing the volume of the cavity with a movable end plate. Tuning can also be accomplished by using rotating dielectric paddles in the high-electric-field region of the coaxial cavity. 5. Spectrum quality is generally improved with reduced spurious output.

Inverted Coaxial Magnetron A version of the coaxial magnetron in which the cathode surrounds the anode is known as an inverted coaxial magnetron [9, 58]. Because of the much larger cathode in the inverted design, much higher power densities, lower cathode current densities, or both can be obtained. A disadvantage is that it is more difficult to suppress spurious modes in an inverted design.

Simulation The accurate numerical simulation of crossed-field devices is considerably more difficult than that of linear beam devices. Computer simulation models for magnetrons and other crossed-field devices are described in References [22, 36, 37, 95, 122].

8. Crossed-Field Amplifiers There are two main categories of crossed-field amplifiers (CFAs): injected beam and distributed emission. Injected-beam CFAs [34, 113] were the first crossed-field amplifiers to be developed and used an electron gun to inject electrons into the interaction region. Although they demonstrated high gain and bandwidth, injected-beam CFAs have since been replaced by other devices and are no longer produced. The rest of this section will be devoted to the distributed-emission CFA [17, 43, 44, 78, 100].

Applications The CFA is a compact, low-weight, high-power, highly efficient amplifier with bandwidths up to 25%. Because of these advantages along with its relatively low-voltage operation, the CFA has found wide application in


85

powerful mobile radar systems. It is commonly used as a final stage in an efficient amplifier chain with a linear TWT or klystron as the driver. Its high phase stability makes it useful in phased array applications. Another advantage is that cold cathode operation is possible, with the current supplied entirely by secondary emission. Peak power can reach a megawatt at a frequency of 10 GHz. Efficiencies are typically 40-70%.

General Operation Both forward-wave and backward-wave circuits are used in distributedemission CFAs. The electrons move in the same direction as the power growth in a forward-wave device and in the opposite direction of power growth in a backward-wave device. The main characteristic difference between a forward-wave and a backward-wave CFA is the bandwidth. In a forward-wave CFA, the bandwidth at a fixed c a t h o d e - a n o d e voltage value is usually about 10-20% for radar applications and can be as large as an octave in ECM applications. In a backward-wave CFA, the instantaneous bandwidth is narrow, but the frequency of operation can vary over about 10% by adjusting the anode-cathode voltage. The CFA geometry is very similar to that of the magnetron oscillator. The major difference is that the anode slow-wave circuit of the CFA is nonreentrant (does not close on itself). Instead, the input and output ends of the circuit are each connected to separate external transmission lines. When the RF input power is above a threshold value, electron bunches in the form of current spokes of nearly constant amplitude rotate around the circuit. Each current spoke induces two circuit waves, one traveling toward the input and the other, toward the input. In a CFA, only the waves traveling toward the output add in phase. Since each spoke induces equal power into circuit, the circuit wave grows, with power increasing linearly with distance. Thus the power gain of a CFA is much less than that of a linear beam TWT in which the power increases exponentially with distance.

Power and Efficiency Provided that the input power exceeds the threshold value for spoke stability, the power generated in a CFA is independent of the RF power input. The power generated can be increased only by increasing the anode voltage and current. Neglecting circuit attenuation, the output power is the sum of the input power, Pin, and the generated power, Pgen" Thus the

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Jeffrey D. Wilson

amplifier gain is a function of the power input:

(30)

G = Pin "+"egen.

Because the CFA is a saturated amplifier, it cannot be used in amplitude modulation and is limited to frequency and phase modulation applications. The overall power efficiency in a CFA is typically 40-70% and is defined as the product of the electronic efficiency and the circuit efficiency, Pout - Pin

97 "-" 97cTle ~--- Va0 Ia0

'

(31)

where Tie is the electronic efficiency, ~7c is the circuit efficiency, Pout is the RF power output, Pin is the RF power input, Va0 is the DC anode voltage, and Ia0 is the DC anode current. The circuit efficiency, neglecting loss due to back-bombardment of the cathode, is given by

'r/c-

Pout-Pin Pgen

__[ -

1

Pin] egen

2al

(1 -

exp-2~l),

(32)

where Pgen is the power generated, a is the circuit attenuation constant, and l is the circuit length in the azimuthal direction. The electronic efficiency, neglecting loss due to back-bombardment of the cathode, is given by

m(.o 2 m

2eVa0/32

T~e = 1+

Iaomfl2K [ G + 1 2/32e

1 G-

,

(33)

1

where m is the mass of an electron, e is the electric charge of an electron, 13 is the RF phase constant, co is the angular frequency, B is the magnetic flux density, G is the power gain, and K is the beam-coupling impedance at the circuit given by

2

Emax K = 2/32P ,

(34)

where Emax is the peak electric field and P is the power flow [43].

High-Frequency CFA Since the rotational velocity of the current spokes is about an order of magnitude less than the velocity equivalent of the DC voltage, the periodic pitch distance of the slow-wave circuit is much less than that of a


87

corresponding linear beam TWT. This allows the CFA to be compact, but limits the power and also makes fabrication of conventional circuits for frequencies higher than about 10 GHz impractical. However, CFA operation has been extended into millimeter-wave frequencies with an axial-gain CFA [78]. This device has an inverted cathode surrounding a staggered-slot structure. A prototype has demonstrated 50 kW of peak output power between 35 and 36.25 GHz with 10 dB of gain.

Low-Noise High-Gain CFA The primary disadvantages of the CFA have been high noise and low power gain. However, dramatic improvements in both of these characteristics have been achieved by incorporating a slow-wave structure into the cathode that is matched to that of the anode. The gain has been increased from a typical value of 10-15 dB to 20-30 dB and the noise, reduced by approximately 30 d B / M H z from a typical value of 45-50 d B / M H z [78]. This development promises even wider applications for CFAs in the future.

Amplitron The Amplitron (Raytheon trademark name) is a distributed-emission backward-wave crossed-field amplifier with no drift region between the RF output and the RF input [14, 35]. The absence of a drift region allows electron spokes to recirculate through the circuit, and this regenerative electronic feedback permits extremely high efficiencies on the order of 60-80%. The most common use for Amplitrons has been in powerful radar systems [17, 99]. Because of their very high efficiency and extremely long lifetime when incorporating pure platinum secondary emitting cathodes, it has been proposed that a large array of Amplitrons could be used to beam microwave energy to Earth from space [15]. Another device that could be used for this purpose is the magnetron directional amplifier, which consists of a magnetron in combination with a passive directional device [16,181.

9. Crossed-Field Backward-Wave Oscillators Applications The crossed-field or M-type backward-wave oscillator (MBWO), also known as the carcinotron, is a voltage tunable oscillator with a broad

88

Jeffrey D. Wilson

bandwidth on the order of 20%, efficiency up to 50%, and CW output power of typically 100-200 W [41, 44]. MBWOs have the advantage over magnetrons of being nearly instantaneously tunable over a wide frequency range. In this respect the MBWO is similar to the linear-beam BWO, but with the advantages of high efficiency, linear tuning, and high frequency stability. However, the MBWO produces considerably more noise [43]. Because of their high frequency agility and high noise, the primary use for MBWOs is as noise-jamming signal sources in ECM equipment.

General Operation Figure 18 shows the typical configuration of an MBWO. A ribbon-shaped electron beam is injected into the region between the sole and the slow-wave circuit. Oscillation occurs as energy is coupled from the electron beam to the RF wave on the circular slow-wave circuit. Because this is a backward-wave circuit, the RF signal grows as it travels from the collector end to the electron gun end, where the RF output connector is located. The cathode is a cylinder with a fiat side from which the electrons are emitted. The electrons move toward the accelerating anode and are

Collector RF attenuator

\

/ r

/- Grid / - Accelerating / anode / / - - Cathode

ou u,

Slow-wave structure

X._ Sole .................. Electron beam RF wave

Figure 18. M-type backward-wave oscillator (Gewartowski and Watson [43]).

89


formed into a beam by the grid. The magnetic field parallel to the axis and the pC electric field between the negative sole and the positive anode (slow-wave circuit) force the ribbon beam to travel in a circle in close proximity to the circuit. The circular slow-wave circuit is of the form of a folded waveguide. This circuit is known as an interdigital delay line and is designed so that the phase velocity of the first backward-wave space harmonic is in synchronism with the beam velocity [84]. Noise in the electron beam initiates the propagation of space harmonic waves in the slow-wave circuit. The electrons congregate in bunches which work their way toward the circuit, giving up energy to the first harmonic backward wave. The operating frequency depends on the beam velocity which in turn depends on the applied anode and sole voltages.

Frequency Tuning MBWOs can be turned over frequency ranges between 25 and 40% by varying the sole voltage, anode voltage, or both. Tuning curves for a typical MBWO in which the cathode voltage is varied with constant sole voltage are shown in Figure 19. The frequency tuning is nearly linear with voltage

350 300 =,.

o~ 250 Q. U. rr 200

150

I m

~4

m

o 2 ,,_

4.8 5.0 5.2 5.4 5.6 5.8 6.0 6.2 Frequency, GHz

6.4 6.6

Figure 19. Tuning curves for a representative M-type backward-wave oscillator (Litton Industries L-3726). These data correspond to fixed values for the sole voltage and cathode current of 2450 V and 300 mA, respectively (Gewartowski and Watson [43]).

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Jeffrey D. Wilson

b e c a u s e t h e e l e c t r o n drift v e l o c i t y is l i n e a r l y r e l a t e d to t h e I~C e l e c t r i c field in t h e i n t e r a c t i o n s p a c e . I n c o n t r a s t , t h e e l e c t r o n v e l o c i t y in t h e l i n e a r - b e a m B W O is p r o p o r t i o n a l to t h e s q u a r e r o o t of t h e t u n i n g v o l t a g e [43].

References [1] A. E. Acker, New techniques vitalize mm-wave CCTWT development and producibility, Microwave Systems News and Comm. Tech., Vol. 16, No. 13, pp. 68-79, 1986. [2] K. Amboss, Verification and use of Herrmann's optical theory of thermal velocity effects in electron beams in the low perveance regime, IEEE Trans. Electron Devices, Vol. ED-11, No. 10, pp. 479-485, 1964. [3] E. A. Ash and J. Froom, Slow-wave structures for millimetre-wavelength backward-wave oscillators, Electron Commun., Vol. 38, No. 2, pp. 264-275, 1963. [4] L. R. Barnett, R. W. Grow, and J. M. Baird, Backward-wave oscillators for the frequency range from 600 GHz to 1800 GHz, IEEE Int. Electron Devices Meet. Tech. Dig., pp. 858-861, 1988. [5] K. F. Bartos, E. B. Fite, K. A. Shalkhauser, and G. R. Sharp, "A Three-Dimensional Finite-Element Thermal/Mechanical Analytical Technique for High-Performance Traveling Wave Tubes," NASA TP-3081, 1991. [6] B. N. Basu, B. B. Pal, V. N. Singh, and N. C. Vaidya, Optimum design of a potentially dispersion-free helical slow-wave circuit of a broad-band TWT, IEEE Trans. Microwave Theory Tech. Vol. MTT-32, No. 4, pp. 461-463, 1984. [7] P. Bhartia and I. J. Bahl, Millimeter Wave Engineering and Applications. New York: John Wiley and Sons, 1984. [8] C. K. Birdsall and T. E. Everhart, Modified contra-wound helix circuits for high-power traveling-wave tubes, IRE Trans. Electron Devices, Vol. ED-3, No. 10, pp. 190-204, 1956. [9] W. M. Black, R. K. Parker, R. Tobin, G. Farney, M. Herndon, and V. L. Granatstein, A hybrid inverted coaxial magnetron to generate gigawatt levels of pulsed microwave power, IEEE Int. Electron Devices Meet. Tech. Dig., pp. 175-178, 1979. [10] H. A. H. Boot and J. T. Randall, Historical notes on the cavity magnetron, IEEE Trans. Electron Devices, Vol. ED-23, No. 7, pp. 724-729, 1976. [11] G. M. Branch and T. G. Mihran, Plasma frequency reduction factors in electron beams, IRE Trans. Electron Devices, Vol. ED-2, No. 4, pp. 3-11, 1955. [12] G. R. Brewer and C. K. Birdsall, Traveling-wave tube propagation constants, IRE Trans. Electron Devices, Vol. ED-4, No. 2, pp. 140-144, 1957. [13] L. Brillouin, A theorem of Larmor and its importance for electrons in magnetic fields, Phys. Rev., Vol. 67, No. 8, pp. 260-266, 1945. [14] W. C. Brown, Description and operating characteristics of the platinotronmA new microwave tube device, Proc. IRE, Vol. 45, No. 9, pp. 1209-1222, 1957. [15] W. C. Brown, Adapting microwave techniques to help solve future energy problems, IEEE Trans. Microwave Theory Tech., Vol. MTT-21, No. 12, pp. 753-763, 1973. [16] W. C. Brown, Status of the microwave power transmission components for the solar power satellite, IEEE Trans. Microwave Theory Tech., Vol. MTT-29, No. 12, pp. 1319-1327, 1981. [17] W. C. Brown, The microwave magnetron and its derivatives, IEEE Trans. Electron Devices, Vol. ED-31, No. 11, pp. 1595-1605, 1984. [18] W. C. Brown, The SPS transmitter designed around the magnetron directional amplifier, Space Power, Vol. 7, No. 1, pp. 37-49, 1988.


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[19] W. N. Cain and R. W. Grow, The effects of dielectric and metal loading on the dispersion characteristics for contrawound helix circuits used in high-power travelingwave tubes, IEEE Trans. Electron Devices, Vol. ED-37, No. 6, pp. 1566-1578, 1990. [20] M. Caplan and C. B. Thorington, Improved computer modelling of magnetron injection guns for gyrotrons, Int. J. Electron., Vol. 51, No. 4, pp. 415-426, 1981. [21] R. G. Carter and L. Shunkang, Method for calculating the properties of coupled-cavity slow-wave structures from their dimensions, lEE Proc., Part H, Vol. 133, No. 5, pp. 330-334, 1986. [22] D. Chernin and A. Drobot, Computer simulations of re-entrant crossed-field amplifiers, IEEE Electron Devices Meet. Tech. Dig., pp. 521-524, 1990. [23] M. Chodorow and E. L. Chu, Cross-wound twin helices for traveling-wave tubes, J. Appl. Phys., Vol. 26, No. 1, pp. 33-43, 1955. [24] M. Chodorow and R. A. Craig, Some new circuits for high-power traveling-wave tubes, Proc. IRE, Vol. 45, No. 8, pp. 1106-1118, 1957. [25] G. B. Collins, ed., Microwave Magnetrons. New York: McGraw-Hill, 1948. [26] H. J. Curnow, A general equivalent circuit for coupled-cavity slow-wave structures, IEEE Trans. Microwave Theory Tech., Vol. MTT-13, No. 9, pp. 671-675, 1965. [27] A. N. Curren, Carbon and carbon-coated electrodes for multistage depressed collectors for electron-beam devicesuA technology review, IEEE Trans. Electron Devices, Vol. ED-33, No. 11, pp. 1902-1914, 1986. [28] A. N. Curren, R. W. Palmer, D. A. Force, L. Dombro, and J. A. Long, High-efficiency helical traveling-wave tube with dynamic velocity taper and advanced multistage depressed collector, IEEE Int. Electron Devices Meet. Tech. Dig., pp. 473-476, 1987. [29] A. N. Curren, K. J. Long, K. A. Jensen, and R. F. Roman, An effective secondary electron suppression treatment for copper MDC electrodes. IEEE Int. Electron Devices Meet. Tech. Dig., pp. 777-780, 1993. [30] M. R. Currie and J. R. Whinnery, The cascade backward-wave amplifier: A high-gain voltage-tuned filter for microwaves, Proc. IRE, Vol. 43, No. 11, pp. 1617-1631, 1955. [31] W. E. Danielson, J. L. Rosenfeld, and J. A. Saloom, A detailed analysis of beam formation with electron guns of the Pierce type, Bell Syst. Tech. J., Vol. 35, pp. 375-420, 1956. [32] J. A. Dayton, H. G. Kosmahl, P. Ramins, and N. Stankiewicz, Analytical prediction and experimental verification of TWT and depressed collector performance using multidimensional computer programs, IEEE Trans. Electron Devices, Vol. ED-26, No. 10, pp. 1589-1598, 1979. [33] H. K. Detweiler, "Characteristics of Magnetically Focused Large-Signal Traveling Wave Ampliferes," Rome Air Development Center Tech. Rep. RADC-TR-68-433, Griffiss Air Force Base, NY, 1968. [34] O. Doehler, Injection Type Tubes, in Crossed-Field Microwave Devices (E. Okress, ed.), Vol. 2, pp. 3-10, 155-164. New York: Academic Press, 1961. [35] G. E. Dombrowski, Theory of the amplitron, IRE Trans. Electron Devices, Vol. ED-6, No. 10, pp. 419-428, 1959. [36] G. E. Dombrowski, Simulation of magnetrons and cross-field amplifiers, IEEE Trans. Electron Devices, Vol. ED-35, No. 11, pp. 2060-2067, 1988. [37] G. E. Dombrowski, Computer simulation study of primary and secondary loading in megnetrons, IEEE Trans. Electron Devices, Vol. ED-38, No. 10, pp. 2234-2238, 1991. [38] A. T. Drobot, C. L. Chang, K. Ko, A. Mankofsky, A. Mondelli, L. Seftor, and P. Vitello, Numerical simulation of high power microwave sources, IEEE Trans. Nucl. Sci., Vol. NS-32, pp. 2733-2737, 1985.

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[39] D. C. Forster, High power sources at millimeter wavelengths, Proc. IEEE, Vol. 54, No. 4, pp. 532-539, 1966. [40] F. Friedlander, A. Karp, B. D. Gaiser, J. S. Gaiser, and B. Goplen, Transient analysis of beam interaction with the antisymmetric mode in a truncated periodic structure using the three-dimensional computer code "SOS," IEEE Trans. Electron Devices, Vol. ED-33, No. 11, pp. 1896-1901, 1986. [41] O. P. Gandhi, Microwave Engineering and Applications. New York: Pergamon Press, 1981. [42] P. Garcin, D. Grauleau, R. Gerber, and L. Teyssier, New technologies used for the 1 THz backward-wave oscillator, IEEE Int. Electron Devices Meet. Tech. Dig., pp 850-853, 1988. [43] J. W. Gewartowski and H. A. Watson, Principles of Electron Tubes. Princeton, NJ: Van Nostrand, 1965. [44] A. S. Gilmour, Microwave Tubes. Norwood, MA: Artech House, 1986. [45] J. F. Gittins, Power Travelling-Wave Tubes. New York: American Elsevier, 1965. [46] R. W. Grow and D. R. Gunderson, Starting conditions for backward-wave oscillators with large loss and large space charge, IEEE Trans. Electron Devices, Vol. ED-17, No. 12, pp. 1032-1039, 1970. [47] G. A. Haas, in Methods of Experimental Physics (V. W. Hughes and H. L. Schultz, eds.), Vol. 4, Part A, pp. 1-38. New York: Academic Press, 1967. [48] K. Halbach and R. F. Holsinger, Superfish--A computer program for evaluation of RF cavities with cylindrical symmetry, Part. Accel., Vol. 7, pp. 213-222, 1976. [49] J. W. Hansen, US TWTs from 1 to 100 GHz, Microwave J., Vol. 32, No. 6, pp. 179-193, 1989. [50] L. A. Harris, Toroidal electron guns for hollow beams, J. Appl. Phys., Vol. 30, No. 6, pp. 826-836, 1959. [51] L. A. Harris, Closely-spaced, aligned grids in vacuum tubes, IRE Trans. Electron Devices, Vol. ED-8, No. 11, pp. 481-488, 1961. [52] J. R. Hechtel, Magnetic focusing of electron beams in the presence of transverse velocity components, IEEE Trans. Electron Devices, Vol. ED-28, No. 5, pp. 473-482, 1981. [53] H. Heffner, Analysis of the backward-wave traveling-wave tube, Proc. IRE, Vol. 42, No. 6, pp. 930-937, 1954. [54] L. A. Hemstreet, S. R. Chubb, and W. E. Pickett, Electronic properties of stoichiometric Ba and O overlayers adsorbed on W(001), Phys. Rev. B, Vol. 40, No. 6, pp. 3592-3599, 1989. [55] G. Herrmann and S. Wagener, The Oxide-Coated Cathode, Vols. 1 and 2. London: Chapman & Hall, 1951. [56] G. Herrmann, Optical theory of thermal velocity effects in cylindrical electron beams, J. Appl. Phys., Vol. 29, No. 2, pp. 127-36, 1958. [57] W. B. Herrmannsfeldt, "Electron Trajectory Program," Stanford Linear Accelerator Center Rep. 331, Stanford Univ., Stanford, CA, 1988. [58] J. F. Hull, The Inverted Magnetron, in Crossed-Field Microwave Devices (E. Okress, ed.), Vol. 2, pp. 291-300. New York: Academic Press, 1961. [59] A. T. Isaacs and S. T. Dangzalan, Broadband BWO's to 50 GHz, Microwave J., Vol. 17, No. 3, pp. 39-51, 1974. [60] B. G. James and P. Kolda, A ladder circuit coupled-cavity TWT at 80-100 GHz, IEEE Int. Electron Devices Meet. Tech. Dig., pp. 494-497, 1986. [61] H. R. Johnson, Backward-wave oscillators, Proc. IRE, Vol. 43, No. 6, pp. 684-697, 1955.


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[62] F. Kantrowitz and I. Tammaru, Three-dimensional simulations of frequency-phase measurements of arbitrary coupled-cavity RF circuits, IEEE Trans. Electron Devices, Vol. ED-35, No. 11, pp. 2018-2026, 1988. [63] S. Kapoor, R. S. Raju, R. K. Gupta, S. N. Joshi, and B. N. Basu, Analysis of an inhomogeneously loaded helical slow-wave structure for broad-band TWT's, IEEE Trans. Electron Devices, Vol. ED-36, No. 9, pp. 2000-2004, 1989. [64] A. Karp, Traveling-wave tube experiments at millimeter wavelengths with a new, easily built, space-harmonic circuit, Proc. IRE, Vol. 43, No. 1, pp. 41-46, 1955. [65] A. Karp, Backward-wave oscillator experiments at 100 to 200 kilomegacycles, Proc. IRE, Vol. 45, No. 4, pp. 496-503, 1957. [66] E. Kettlewell, The Magnetron Oscillator. London: Mills & Boon, 1971. [67] G. S. Kino and N. J. Taylor, The design and performance of a magnetron-injection gun, IRE Trans. Electron Devices, Vol. ED-9, No. 1, pp. 1-11, 1962. [68] R. Kompfner and N. T. Williams, Backward-wave tubes, Proc. IRE, Vol. 41, No. 11, pp. 1602-1611, 1953. [69] R. Kompfner, The invention of traveling wave tubes, IEEE Trans. Electron Devices, Vol. ED-23, No. 7, pp. 730-738, 1976. [70] C. L. Kory, J. D. Wilson, J. W. Maruschek, and D. L. Schroeder, Simulation of cold-test dispersion and interaction impedances for coupled-cavity tube slow-wave circuits, IEEE Int. Electron Devices Meet. Tech. Dig., pp. 763-766, 1992. [71] H. G. Kosmahl and P. Ramins, Small-size 81- to 83.5-percent efficient 2- and 4-stage depressed collectors for octave-bandwidth high-performance TWT's, IEEE Trans. Electron Devices, Vol. ED-24, No. 1, pp. 36-44, 1977. [72] H. G. Kosmahl, Modern multistage depressed collectors--A review, Proc. IEEE, Vol. 70, No. 11, pp. 1325-1334, 1982. [73] H. G. Kosmahl and J. C. Peterson, "A TWT Amplifier with a Linear Power Transfer Characteristic and Improved Efficiency," NASA TM-83590, 1984. [74] N. Kroll, The Rising Sun System in Microwave Magnetrons (G. B. Collins, ed.), pp. 83-117. New York: McGraw-Hill, 1948. [75] L. Kumar, R. S. Raju, S. N. Joshi, and B. N. Basu, Modeling of a vane-loaded helical slow-wave structure for broad-band traveling-wave tubes, IEEE Trans. Electron Devices, Vol. ED-36, No. 9, pp. 1991-1999, 1989. [76] R. H. LeBorgne, C. Goodman, R. R. Hull, O. Sauseng, and G. M. Lee, Development of an 800 watt KA-band ring-bar TWT, IEEE Int. Electron Devices Meet. Tech. Dig., pp. 881-884, 1990. [77] H. C. Limburg, J. A. Davis, I. Tammaru, J. P. Vaszari, and J. D. Wilson, Reducing the gain and phase variation in high power MMW TWTs, IEEE Int. Electron Devices Meet. Tech. Dig., pp. 381-384, 1988. [78] G. H. MacMaster, Current status of crossed-field devices, IEEE Int. Electron Devices Meet. Tech. Dig., pp. 358-361, 1988. [79] E. W. McCune, "UHF-TV Klystron Multistage Depressed Collector Development Program," NASA CR- 182190, 1988. [80] B. J. McMurtry, Fundamental interaction impedance of a helix surrounded by a dielectric and a metal shield, IRE Trans. Electron Devices, Vol. ED-9, No. 3, pp. 210-216, 1962. [81] N. Mahale and S. Pissanetzky, Recent advances in MAGNUS computational technology for three-dimensional nonlinear magnetostatics, IEEE Trans. Electron Devices, Vol. ED-35, No. 11, pp. 2034-2038, 1988. [82] J. T. Mendel, Helix and coupled-cavity traveling-wave tubes, Proc. IEEE, Vol. 61, No. 3, pp. 280-298, 1973.

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[83] S. Millman, A spatial harmonic traveling-wave amplifier for six millimeters wavelength, Proc. IRE, Vol. 39, No. 9, pp. 1035-1043, 1951. [84] R. R. Moats, The Interdigital Line as a Waveguide in Crossed-Field Microwave Devices (E. Okress, ed.), Vol. 1, pp. 69-85, New York: Academic Press, 1961. [85] Y. Morizumi, Computer-aided design of an axially symmetrical magnetic circuit and its application to electron-beam-focusing devices, IEEE Trans. Electron Devices, Vol. ED-19, No. 6, pp. 782-797, 1972. [86] W. Muller, Computational modeling of dispenser cathode emission properties, IEEE Int. Electron Devices Meet. Tech. Dig., pp. 399-402, 1991. [87] E. Okress, ed., Crossed-Field Microwave Devices, Vols. 1 and 2. New York: Academic Press, 1961. [88] S. F. Paik, Design formulas for helix dispersion shaping, IEEE Trans. Electron Devices, Vol. ED-16, No. 12, pp. 1010-1014, 1969. [89] J. R. Pierce, Traveling-Wave Tubes. New York: Van Nostrand, 1950. [90] J. R. Pierce, Theory and Design of Electron Beams. New York: Van Nostrand, 1954. [91] S. Pissanetzky, The new version of the finite element 3D magnetostatics program MAGNUS, in Computational Electromagnetics (Z. J. Cendes, ed.), pp. 121-132. Amsterdam: Elsevier, 1986. [92] J. L. Putz and M. J. Cascone, Effective use of dispersion shaping in broadband helix TWT circuits, IEEE Int. Electron Devices Meet. Tech. Dig., pp. 422-424, 1979. [93] P. Ramins and B. T. Ebihara, Improvements in MDC and TWT overall efficiency through the application of carbon electrode surfaces, IEEE Trans. Electron Devices, Vol. ED-33, No. 11, pp. 1915-1924, 1986. [94] P. Ramins and B. T. Ebihara, Isotropic graphite multistage depressed collectorsmA progress report, IEEE Trans. Electron Devices, Vol. ED-36, No. 4, pp. 817-824, 1989. [95] S. A. Riyopoulos, D. P. Chernin, and A. T. Drobot, Guiding center fluid model of the crossed-field amplifier, IEEE Trans. Electron Devices, Vol. ED-39, No. 6, pp. 1529-1542, 1992. [96] J. E. Rowe, Nonlinear Electron-Wave Interaction Phenomena. New York: Academic Press, 1965. [97] M. J. Schindler, An improved procedure for the design of periodic-permanent-magnet assemblies for traveling-wave tubes, IEEE Trans. Electron Devices, Vol. ED-13, No. 12, pp. 942-949, 1966. [98] A. W. Scott, Why a circuit sever affects traveling-wave tube efficiency, IRE Trans. Electron Devices, Vol. ED-9, No. 1, pp. 35-40, 1962. [99] J. F. Skowron, W. C. Brown, and G. H. MacMaster, The super power CW amplitron, Microwave J., Vol. 7, No. 10, pp. 65-69, 1964. [100] J. F. Skowron, The continuous-cathode (emitting-sole) crossed-field amplifier, Proc. IEEE, Vol. 61, No. 3, pp. 330-356, 1973. [101] A. Staprans, E. W. McCune, and J. A. Ruetz, High-power linear-beam tubes, Proc. IEEE, Vol. 61, No. 3, pp. 299-330, 1973. [102] J. E. Sterrett and J. Heffner, The design of periodic magnetic focusing structures, IRE Trans. Electron Devices, Vol. ED-5, No. 1, pp. 35-42, 1958. [103] R. E. Thomas, J. W. Gibson, G. A. Haas, and R. H. Abrams, Thermionic sources for high-brightness electron beams, IEEE Trans. Electron Devices, Vol. ED. 37, No. 3, pp. 850-861, 1990. [104] P. Thouvenin, D. Henry, and A. Pelletier, New helix tapers boost space TWT efficiency to 55%, broadband, IEEE Int. Electron Devices Meet. Tech. Dig., pp. 477-480, 1987. [105] R. True, A theory for coupling gridded gun design with PPM focusing, IEEE Trans. Electron Devices, Vol. ED-31, No. 3, pp. 353-362, 1984.


95

[106] R. True, Calculation and design of grids in Pierce guns, IEEE Int. Electron Devices Meet. Tech. Dig., pp. 215-217, 1989. [107] R. A. Tuck, Thermionic cathode surfaces: The state-of-the-art and outstanding problems, Vacuum, Vol. 33, pp. 715-721, 1983. [108] J. R. M. Vaughan, Synthesis of the Pierce gun, IEEE Trans. Electron Devices, Vol. ED-28, No. 1, pp. 37-41, 1981. [109] J. R. M. Vaughan, Synthesis of a hollow-beam Pierce gun, IEEE Trans. Electron Devices, Vol. ED-34, No. 2, pp. 468-471, 1987. [110] J. R. M. Vaughan, Corrections to "Synthesis of a hollow-beam Pierce gun," IEEE Trans. Electron Devices, Vol. ED-34, No. 8, pp. 1885, 1987. [111] R. P. Wadhwa and R. A. Harris, Transformation of fluctuations along magnetron injection beams, IEEE Trans. Electron Devices, Vol. ED-12, No. 6, pp. 332-343, 1965. [112] L. R. Walker, The Strapped System in Microwave Magnetrons (G. B. Collins, ed.), pp. 118-166. New York: McGraw-Hill, 1948. [113 R. R. Warnecke, W. Kleen, A. Lerbs, O. Doehler, and H. Huber, The magnetron-type traveling-wave amplifier tube, Proc. IRE, Vol. 38, No. 5, pp. 486-495, 1950. [114] G. Warren, Determining mode excitations of vacuum electronics devices via threedimensional simulations using the SOS code, IEEE Trans. Electron Devices, Vol. ED-35, No. 11, pp. 2027-2033, 1988. [115] W. E. Waters, A theory of magnetron injection guns, IEEE Trans. Electron Devices, Vol. ED-10, No. 7, pp. 226-234, 1963. [116] T. Weiland, On the numerical solution of Maxwell's equations and applications in the field of accelerator physics, Part. Accel., Vol. 15, pp. 245-292, 1984. [117] T. Weiland, On the unique numerical solution of Maxwellian eigenvalue problems in three dimensions, Part. Accel., Vol. 17, pp. 227-242, 1985. [118] J. D. Wilson, "Revised NASA Axially Symmetric Ring Model for Coupled-Cavity Traveling-Wave Tubes," NASA TP-2675, 1987. [119] J. D. Wilson, Computationally generated velocity taper for efficiency enhancement in a coupled-cavity traveling-wave tube, IEEE Trans. Electron Devices, Vol. ED-36, No. 4, pp. 811-816, 1989. [120] J. D. Wilson, P. Ramins, and D. Force, "Spent Beam Refocussing Analysis and Multistage Depressed Collector Design for a 75-W, 59- to 64-GHz Coupled-Cavity Traveling-Wave Tube," NASA TP-3039, 1990. [121] J. D. Wilson, H. C. Limburg, J. A. Davis, I. Tammaru, and J. P. Vaszari, A high efficiency ferruleless coupled-cavity traveling-wave tube with phase-adjusted taper, IEEE Trans. Electron Devices, Vol. ED-37, No. 12, pp. 2638-2643, 1990. [122] S. P. Yu, G. P. Kooyers, and O. Buneman, Time dependent computer analysis of electron-wave interaction in crossed fields, J. Appl. Phys., Vol. 36, No. 8, pp. 2550-2559, 1965.


CHAPTER

4 Gyrotrons, Magnicons, and Ubitrons Paul Tallerico

I. Introduction

As the

operating frequency increases above 10 or 20 GHz, the fundamental mode cavities and circuits for classical electron devices become smaller and more expensive. The cross-sectional area of a microwave cavity is proportional to the square of the operating wavelength, and the skin depth decreases as the square root of frequency. These two effects combine and tend to make the power versus frequency curve for any given type of RF generator decrease a s f-2.5. In addition, as frequency increases, the small size of the circuits makes heat removal difficult and limits both the peak and the average power that are achievable by conventional microwave electron devices. Cavity tolerances are properly expressed as a fraction of the wavelength, so, as the frequency increases, it becomes more difficult and expensive to produce a resonant cavity. As early as 40 years ago, several researchers realized that rather than modulating the cavity or circuit walls, one could modulate the beam in a simple cylindrical circuit and still have a good microwave interaction. Generators based on the periodic modulation of the electron beam within a very simple circuit or waveguide are discussed in this chapter. The devices in the gyrotron are fast-wave devices, since the phase velocities of the simple circuits (such as ordinary waveguide) are faster than the velocity of light, rather than slow wave devices, such as the classical microwave devices.


97


98

Paul Tallerico

The gyrotron or electron cyclotron maser employs electron cyclotron resonance and an interaction with azimuthal electric fields to convert the rotational energy from an electron beam to microwaves. The device was first proposed by Twiss [1] in 1958 with a classical analysis and by Schneider [2] in 1959 with a quantum mechanical analysis. The classical theory was also independently published by Gapanov [3] in 1959. Flyagin and Gapanov wrote an excellent historical review [4] of this subject in 1977. The gyrotron is a very important millimeter-wave generator because it can operate with a higher-order mode interaction cavity that is several times larger both in length and diameter than the fundamental mode cavity used in most competing generators, such as klystrons or travelingwave tubes. The output cavity is typically many wavelengths long since the output interaction is distributed rather than concentrated. Thus the power density on the output cavity walls and the peak fields in the output cavity are significantly lower than those in the classical electron devices. The gyrotron finds uses in electron cyclotron resonance heating and current drive in fusion plasma research, and the devices are actively under development in the United States, Japan, Europe, and the former Soviet Union. The gyrotron family of electron devices includes the gyrotron monotron oscillator that is the usual meaning of the word gyrotron, as well as the gyroklystron, the gyro-backward-wave tube, and the gyro-travelingwave tube. The original gyrotron oscillator is the device that is used in most applications, and it is the simplest and most advanced member of the family. The amplifier version of the gyrotron, the gyroklystron, is under development, and the experimental results are described below. The magnicon is a deflection-modulated amplifier whose output cavity can look similar to that of a gyroklystron, but the interaction between the electron beam and the RF fields utilizes TM, rather than TE, modes. Only a single magnicon has yet been built, but the efficiency is so high, 73%, that it is included in this chapter. Several new projects to produce better magnicons at different frequencies are also under way. The ubitron was the first electron device that utilized a circuit that was several times larger that the wavelength. The ubitron's circuit, like that of the gyrotron, could be a factor of 10 to 100 larger in area than that of a conventional klystron or traveling-wave amplifier; hence its power generation possibilities are also one or two orders of magnitude higher than those of conventional microwave tubes. Ubitrons are not yet commercially developed, and their operation is discussed in Section 10.

2. Gyrotron Principles of Operation The gyrotron oscillator is shown schematically in Figure 1. An electron beam is produced in a hollow-beam electron gun (usually a magnetron-

4. Gyrotrons, Magnicons, and Ubitrons

99

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-

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OUTPUT WINDOW

Figure I. Sketch of a gyrotron oscillator.

injection gun [5]) and then transported in an adiabatic compression system that is designed to produce a very small, intense, hollow, spiraling beam in the interaction cavity with a high ratio of transverse-to-longitudinal energy. This is the principle of the magnetic mirror, and the beam can be reflected if the compression process is too strong for the imperfections of the beam. Upon emerging from the gun region, the hollow beam drifts in a gradually increasing magnetic field to increase the transverse energy at the expense of the longitudinal energy. The beam is then bunched in a TEnm field. The interaction proceeds as follows. The beam is initially unbunched at the entrance to the cavity, and the beam is uniformly distributed azimuthally. Let the axial magnetic field be B0: then the rotational frequency of the beam is given by

fl c = eBo/( moT),

(1)

where 3' is the relativistic factor for the beam and is given by 3' = (1

+

U21/C2)-1/2,

(2)

where v is the electron velocity and c is the velocity of light in vacuum. The basic bunching process is shown in Figure 2: the hollow beam is performing the cyclotron rotation in accordance with Equation (1), and each individual beamlet makes a small circular motion in the plane perpendicular to the beam axis. Assume that there is a TE01 field also acting on the beam and that the cyclotron frequency matches the frequency of the cavity field. The electrons that are accelerated by the azimuthal electric field gain energy (electrons labeled 1 in Figure 2) and, by Equation (1), rotate at a lower frequency and lose phase as they drift,

I00

Paul Tallerico

) E

2

E ~

3 3

4

4 3 ~

3 2 ~ E
1, and a's of about 2 or 2.5 are common for good gyrotrons. It is desired to have very little radial motion on the beam in the oscillator cavity, so the compression and drift operation is performed gradually and adiabatically, resulting in many centimeters of compression space, often 30 to 50 cm. Microwave oscillations are also possible in this drift space, so the space is often loaded with high-power microwave absorbers to eliminate these inadvertent oscillations. Lossy ceramics are used to load the drift spaces, and, in high-power CW gyrotrons, the cooling of these loads is a difficult technical problem.

105


The oscillator cavity need only be a wide place in the drift tube to support an oscillation, but provisions must be made to extract the microwave power. The output cavity is typically a complex open resonator, as shown in Figure 4, rather than a simple cylindrical resonator. The complex cavity is used to produce a variation in the azimuthal electric field in the axial direction, to optimize the interaction. The azimuthal field profile is also shown in Figure 4. Another advantage of the complex cavity is that the narrow part can prebunch the beam and force the main part to oscillate in the desired mode, rather than in competing modes. The cavity starts as an abrupt increase in the drift tube diameter, and this usually is made to resonate with a TE01 mode. The beam is designed to travel along the radius of the maximum electric fields in the cavity. The output end of the cavity often has a larger diameter, corresponding to a TE04 mode, for example, to allow more area for cooling in the CW case. By careful design (in the complex cavity case) one can obtain an inner maximum of an electric field of the TE04 mode to be at the same radius as the TE01 E-field maximum, and, of course, both sections must resonate at the

OUTPUT TAPER TEo3 REGION

TEol REGION

DRIFT TUNNEL

AXIS OF ROTATION

E FIELD AT BEAM RADIUS

J AXIAL DISTANCE

Figure 4. A complex-cavity output resonator and the resulting profile of the azimuthal electric field.

106

Paul Tallerico

desired frequency. An outward tapered section on the output end of the complex cavity is used to couple a portion of the RF energy to the collector. This tapered section must be carefully designed to preserve the mode purity of the oscillation: if it is too abrupt, many modes will be excited, and the desired mode purity will be lost. Thus the beam and the RF radiation leave the output cavity coaxially, but the beam is separated from the output radiation by an abrupt decrease along the axial direction of the magnetic focus field. This loss of the focus field forces the beam to expand abruptly in the radial direction under the influence of its own space charge, and it is intercepted over the collector surface. The output power is often transmitted in a 2.5-in. diameter overmoded waveguide, and a down-taper is also incorporated in the collector area, since the collector diameter is often over 2.5 in. in diameter. The overmoded cylindrical waveguide is used because the fundamental mode guide has too much loss at high frequencies. Once again, this taper must be gradual enough to preserve the output mode purity. Finally, when there is no danger of the electrons hitting the output window, a single- or double-disk window is employed to isolate the gyrotron's vacuum system from the external environment. The double-disk window is required for high average power, and it consists of two ceramic windows, separated by a space through which a coolant flows to carry away the heat produced by the dielectric losses in the ceramics. Thus the entire gyrotron (in the highpower case)will often have a length of about 3 m, although the electron gun and the output cavity are each only a few centimeters long. Several other types of gyrotron oscillators are possible. One such variant, the quasi-optical gyrotron, is shown in Figure 5. Here the gun and collector system are similar to those described above, but the resonator is essentially optical and consists of two confocal mirrors, spaced the correct distance apart to support a resonance at the desired frequency. Output coupling is via a hole in one of the mirrors or a partially transmitting mirror, as in an optical cavity. The resonator and output system are very well decoupled from the electron beam system, except in the region in which they overlap and provide the gyrotron interaction. Gyrotrons with the quasi-optical resonator perpendicular and at other angles to the beam have been built. Unlike conventional cavities, the quasi-optical cavity can be made with high Q well into the submillimeter band. Side-coupling apertures [10, 30] to the gyrotron cavity are practical at the lower microwave frequencies to provide the same decoupling of the RF fields and the collector region. At high CW powers, such as the 1-MW gyrotron at 110 GHz, the power density in the collector region would be above the practical limit of 1.5 k W / c m 2 if the collector had the same diameter as the output waveguide. The novel solution of placing an axial aperture in the output waveguide has been used [11] to separate the spent electron beam


107

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Figure 5. The quasi-optical gyrotron oscillator.

from the output radiation. The collector can then have a larger diameter than the output waveguide. The large-orbit gyrotron, shown in Figure 6, has been one of the most successful harmonic gyrotrons. Here the beam encircles the axis, and it is spun up by a cusp magnetic field. A cavity with a structure similar to that of a magnetron is employed to generate the fields with the proper azimuthal harmonic. GUN COILS

MULTIVANE OUTPUT RESONATOR PLASTIC OUTPUT WINDOW

/

ii F,~,~o-~,ss,o~~ CATHODE

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STEEL POLE PIECE

Figure 6. The large-orbit gyrotron.

108

Paul Tallerico

Although not part of the gyrotron, the focus solenoids and their power supplies are important pieces of auxiliary equipment. For fundamental cyclotron-mode devices, superconducting solenoids are required at about 35 HGz, and these also require some form of helium supply or a helium refrigeration system. Only a few percent of transverse magnetic field are allowed from the solenoid, and the magnetic field tolerances increase with the output frequency of the gyrotron.

5. Gyrotron Fabrication Commercial gyrotrons are fabricated in the same manner as other commercial vacuum tubes: the cavities and collector are made from high-quality, oxygen-free, high-conductivity copper, the insulators are generally alumina, and the output windows are made of alumina or berillyia ceramics. Most of the remaining components are stainless steel, and the components are assembled with high-temperature vacuum brazing techniques, so the completed gyrotron may be baked out at 400 to 500 ° C to result in a vacuum that is lower than 1 x 10 - 7 T after bake out. For high-duty factor, high-average-power gyrotrons, the best construction methods must be used to achieve a decent life. The power densities on the cavity walls and in some areas of the collector are high in high-power gyrotrons, so careful attention to cooling must be paid. Most high-power gyrotrons are water cooled. The temperature-limited MIG generally has an impregnated metal cathode, and the cathode current density is generally below 5 or 10 A / c m 2, even for frequencies above 100 GHz. The geometry of the MIG electron gun is favorable to a modest current density (see Figure 5) as the beam thickness depends on the cathode thickness times the tangent of a small angle, the cathode tilt angle which is typically 10 to 30 °. The MIG is inherently unstable, like its parent, the magnetron, and the shallowest angles make the thinnest beams with the highest current density, but they are generally the most unstable. Therefore, hollow-beam Pierce guns have been proposed as an alternative. Small differences in the beam size or location at the cavity change the operating characteristics, so each gyrotron tends to require more time for factory tests than do conventional tubes. Many gyrotrons are experimental models, and these exhibit a very large variation of fabrication methods. The experimental gyrotrons are typically short-pulse, low-duty-factor devices, and they can tolerate poorer vacuum and a shorter life. The electron gun must be high quality, most U.S. experimenters purchase these guns from commercial suppliers, and gate valves are sometimes used to separate the gun from the main interaction

109


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40

60

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100

120

140

160

180

Frequency, GHz Figure 7. (A) Short-pulse and (B)long-pulse (over 0.3 s) achievements in gyrotron development.

I I0

Paul Tallerico

region. Little cooling is required on either the cavity or the collector, and thin output windows of ceramic or even mica suffice for experiments. The focus solenoids are very important for proper gyrotron operation, and these systems must be carefully fabricated for stable operation. When superconducting solenoids are required for their high fields, the expense and complications of the solenoid system increase due to helium requirements and thermal insulation requirements. For short-pulse gyrotrons, Bitter magnets and even pulsed solenoids have been used or proposed.

6. Gyrotron Performance Many commercial gyrotrons have been developed by leading vacuum tube manufacturers. Figure 7 is a performance map showing power versus frequency for the CW and pulsed gyrotrons now commercially available. The 1-MW CW power limit has been in existence for almost a decade, and it is related to the difficulty in cooling the collector area. These commercial gyrotrons all operate at 80 to 100 kV. The frequency and output power depend on several variables, including cathode current, modulating anode voltage, beam voltage, and magnetic field in the oscillator cavity. The gyrotron's output power or frequency is often mapped out in terms of one of these variables, as is shown in Figure 8. Peak powers up to almost 3

HIGH INTERCEPTION REGION 2+

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"-o

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I

5 ~

2.4

i

x

x

o2. ___L./

x ARCING REGION

I

2 5.6

5.7

5.8

5.9

6.0

CAVITY MAGNETIC FIELD, T

Figure 8. Mode map for a ~rotron.

6.1

6.2

63


I I I

1 GW have been achieved at several frequencies. A few experimental gyrotrons have been optimized for operation at many frequencies, with step tuning when the mode in the cavity changes. For example, in Reference [13] output powers of up to 22 kW were obtained over the frequency range of 301 to 503 GHz with a single gyrotron. In the CW regime, another gyrotron [25, 31] operated from below 100 GHz to over 300 GHz with 20 W of power and up above 500 GHz at the second harmonic. In these wide-range gyrotrons, the device operates in many modes, one at a time, and the output frequency will follow the magnetic field for a while and then jump to a new mode and a new set of realizable frequencies. Thus, not all the frequencies in the range are accessible, but, nonetheless, the gyrotron is a powerful and flexible millimeter-wave generator.

7. Prebunched Gyrotrons and the Magnicon Most gyrotrons produced to date have been oscillators, and the major application is plasma heating, so the question of phase synchronization of many sources has not been important in most applications. For some applications, such as phased-array transmitters and particle accelerators, many separate but phase-controlled sources are required. Many researchers have studied a gyrotron oscillator that is stabilized by injecting an external RF signal into the cavity before the beam enters. With this method, phase locking becomes possible, but the locking bandwidth and gain are both better if the external signal is injected into a separate cavity, which may even be a region of the output cavity. Manheimer et al. [16] have given an excellent review of the methods and limitations of both injection locking and prebunching in gyrotrons. The injection cavity may be much more than a prebuncher. Luhmann et al. [17] use an injected RF signal to both prebunch and accelerate an electron beam, which then excites a higher-frequency output cavity. The acceleration cavity operates as a cyclotron resonance accelerator, and it can transfer a reasonable fraction of the input microwave power into bunched cyclotron motion [26]. The experimental results so far have produced about 6.7 kW at 10% efficiency at 27.7 GHz, and the soundness of the principle has been demonstrated. The magnicon is a deflection modulated amplifier (shown schematically in Figure 9) that transports a solid electron beam in a T M l I 0 mode deflection cavity into an expanding spiral by means of a two-phase excitation of the deflection cavity to achieve a rotating wave and therefore a rotating angle of deflection. The beam is also in a static, but varying with

I 12

Paul Tallerico

I.

DEFLECTION SYSTEM

ELECTRON ' GUN GUN FOCUS COIL

~

1'

OUTPUT

I i / ,, WINVOW

Ii

~

~

>

~

]

OUTPUT CAVITY

COLLECTOR COLLECTOR COIL

Figure 9. Schematic of the magnicon.

distance, magnetic field. After a suitable drift distance that maximizes the radial excursion of the beam, there is a sudden change in the magnetic field, and the radial beam motion is converted to cyclotron resonance motion. This transverse motion then interacts with a TE mode output cavity as in a conventional gyrotron, but of course the output is phase locked to the deflection cavity fields. The theory of the magnicon is reviewed in Reference [27]. The most exciting aspect of the gyrotron is that the first experiments by Nezhevenko [18], the inventor of the device, have yielded overall efficiency of 73% with a very high electronic efficiency of 85%, but at the low frequency of 0.915 GHz. Multiple deflection cavities are required for higher gain, just as in the klystron, and it appears possible to produce higher output frequencies by operating the output cavity at harmonics of the input frequency. Projects on magnicon development have been started at the Navy Research Laboratory [28] and at Los Alamos [29], and the Russian work is also continuing.

8. Gyrotron Applications The major application for the gyrotron is electron cyclotron resonance heating and plasma formation for fusion experiments. Although the fusion budget has been sharply reduced by the U.S. government, fusion research is quite aCtive in other parts of the world. The magnetic fields in tokamaks are in the 4 to 10-T regime, so the appropriate electron cyclotron resonant frequencies are from 110 to 280 GHz. The hybrid ion-electron resonance frequency is also utilized for plasma heating and control, and this frequency is usually between 5 and 10 GHz, well within the range of conventional devices, but gyrotrons are sometimes used because of their higher average power capabilities. Gyrotrons for fusion heating in plasmas


I 13

have been under development for over 10 years, with the power or frequency goals gradually increasing. For example, the U.S. Department of Energy funded research whose goal was 1 MW CW at 28 GHz in 1980 and then 1 MW CW at 60 GHz; the present goal remains at 1 MW CW, but now it is at 110 GHz. As an example of plasma heating, the International Thermonuclear Experimental Reactor (ITER) electron cyclotron wave system will require 28 MW installed at 120 GHz, for gas breakdown, plasma formation and preheating, and plasma current profile control. Also proposed, but not yet approved, is 28 more 1-MW systems at 140 GHz for plasma heating at the center and burn control. Although the ITER fusion reactor [12] has not yet been built, it is a major cooperative effort among Euratom, Japan, the former Soviet Union, and the United States, and it is most probable that it will be built. The ITER reactor is representative of the optimism for the gyrotron in the fusion community today. High-power microwaves simply are excellent for performing a large variety of required functions in fusion experiments. Two gyrotrons have also been developed for the Tokamak Upgrade experiment at Frascati, Italy. These gyrotron oscillators deliver up to 1 MW for 1-s pulses at a frequency of 8 GHz. This requirement would have been a very advanced project for a klystron, but the goals were met rather easily for the gyrotrons. One of the gyrotrons for this project has a rather complicated, 12-way divider to take the output power into 12 WR-137 waveguides and feed a grill antenna, which couples into the plasma. With this method, powers up to 700 kW, and a 1-s pulse length are delivered into a 4:1 mismatch [23]. Gyrotron instability has been proposed as a method of accelerating particles [26], and it has been experimentally utilized, but the particle energy goes into cyclotron motion, which is not very desirable in many accelerators. Another possible application of the gyrotron that takes advantage of the high average power available is RF heating of various high-value products. In particular, the sintering of ceramics at gigahertz frequencies has been proposed, with the expectation being that the heating and cooling cycles can be reduced from hours to minutes, allowing higher throughput. A second advantage of RF processing is that nonequilibrium ceramics may be possible, for components that would react in an ordinary oven may not have time to complete their reaction when rapidly heated by microwaves. Another proposed application of the gyrotron family of generators is their use as drivers for very high power particle accelerators. The next-generation electron-positron linear collider may well require GW total peak powers at frequencies in the 10- to 20-GHz range, and research on gyroklystrons is being pursued for this goal. The initial results have been encouraging, and already over 23 MW of peak power has been produced at 10 GHz [24].

I 14

Paul Tallerico

Pulsed gyrotrons along with pulsed solenoids, have been proposed for millimeter and submillimeter radars [12] that may be able to provide near photographic quality images, but so far such radars have not been built with vacuum electronic devices. Lightweight, compact, harmonic gyrotrons have been proposed as radar drivers, and some work in this area is being done [11]. A gyroklystron amplifier has been designed for the N A S A / J P L Deep Space Radar System [15] at the Goldstone Antenna Facility that would provide 400 kW of CW power at 34.5 GHz. This power level would be very difficult to provide with a klystron, and the intent is to provide better mapping of deep space objects with such an amplifier.

9. Gyrotron Mode Purity In a typical fusion experiment, high average RF power is produced in a gyrotron and transmitted over some tens of meters of overmoded waveguide. Then, near the fusion reactor, the RF energy is sent to an antenna that is designed to radiate a single mode efficiently into the plasma. RF power that was either generated in the gyrotron or converted by the transmission system into other waveguide modes is generally lost in the waveguide walls or reflected by windows or the antenna system. Thus, mode purity is an important issue for most plasma heating experiments. Mode purities of 98% have been achieved at 8 GHz, but the typical mode purity at 50 GHz is more like 90%. In the more recent plasma applications, the mode content at the end of a transmission system is specified to the gyrotron vendor, and the vendor must design the transmission system so as to not degrade the gyrotron mode purity. Gyrotron oscillators can change their operating modes in response to the modulating anode voltage or axial focus field. Thus these parameters must be stabilized rather more carefully than with lower frequency devices to preserve mode purity.

10. Ubitron Principles The ubitron was invented by Phillips in 1957, when he realized that, rather than utilizing a periodic circuit through which a linear electron beam propagates, one could also make an amplifier by utilizing a linear circuit, like a rectangular waveguide, and a periodic electron trajectory. The ubitron is related to the undulator work of Motz [20], which was also the foundation of the free electron laser. The ubitron is like a gyrotron in that the interaction area can be 100 times larger than that in a traveling-wave tube at the same frequency, so much greater output powers are possible

4. Gyrotrons,

115

Magnicons, and Ubitrons

with the gyrotron or ubitron. An excellent historical review of the device is provided by the original inventor, Phillips [11]. A periodic beam at a high voltage, usually over 100 kV, can interact with a fast waveguide mode to make an amplifier or oscillator. The bunching and energy extraction are axial, and the potential efficiency is high, even though the interacting fields and particle motion are transverse. The ubitron is the prototype of the free electron laser, although this fact was not noticed until the free electron laser had been independently developed.

I I . Ubitron Structure A sketch of the first ubitrons is shown in Figure 10. A thin, solid beam travels through an ordinary rectangular waveguide operated in the TE01 mode to a collector. The beam is deflected by a system of permanent magnets that make an alternating magnetic field perpendicular to the beam axis. The beam then describes a sinusoidal motion in the direction perpendicular to both the magnetic field and the unperturbed beam axis. The basic schematic is much like a modern free electron laser operating in an amplifying mode. The electromagnetic radiation enters and exits the waveguide aided by 45 ° reflectors at each end of the interaction region, which have holes in them at the center for the beam. The cavity loading is selected by the output coupling.

,//SOLENOID

i"}

iiii~i[~

-

~

" iiiii -ii " " O ii'::ii

[7 WAVEGUIDF

....P:".,,50, 5,,',:"0,,5,,i:'0,,,5,15.',',:",,, :i'",,ix,b,,:5.:::",,, ::?,

~',~

MAGNETRON INJECTION i GUN

,:,::,:

:

:

J

....t POLEPIECE

~

~'::ii'i:

i

~ -,, LAMINATEDSTEEL AND COPPER INTERACTION CIRCUIT Figure I0. Sketches of early ubitrons.

COOLING OwIUTPUT

I 16

Paul Tallerico

12. Ubitron Performance The original ubitrons were at the S band, and interference between the desired TE01 mode and the TM 11 mode was quickly seen, and overcome, by preferential loss mechanisms to reduce the Q of the undesired mode. Maximum power at the S band was 1.2 MW, corresponding to a 10% efficiency [19]. The highest frequency results obtained by Phillips were 150 kW at 54 GHz and a maximum efficiency of 6%, with only 70 kV of beam voltage [19]. At this frequency, a hollow beam and a slotted slow-wave circuit were used. The magnetic bumps were produced by building the circuit from alternating sheets of copper and iron, so the iron disturbed the focusing field. This device was certainly a parent of the gyrotron, with its magnetron injection gun for the hollow beam, the RF power going through the collector, and its use of an output window located coaxially with the beam, but positioned after the collector. These early ubitrons were designed fro high peak power at 50 to 60 GHz, and, indeed, the ubitron power record lasted for over two decades, until the 1-MW gyrotron was developed. Interest in the ubitron has been renewed because of the bandwidth possibilities of the device. Gains of up to 20 dB over a 25% bandwidth in the 12- to 16-GHz range [20-22] have been achieved with an ubitron.

References [1] [2} [3] [4] [5] [6]

[7]

[8]

R. Q. Twiss, Radiation transfer and the possibility of negative absorption in radio astronomy, Aust. J. Phys., Vol. 11, pp. 564-579, 1958. J. Schneider, Simulated emission of radiation by relativistic electrons in a magnetic field, Phys. Rev. Lett., Vol. 2, pp. 504-505, 1959. A. V. Gapanov, Interaction between electron fluxes and electromagnetic waves in waveguides, Izv. Vyssh. Vchebn. Zaved., Vol. 2, pp. 450-462, 1959. V.A. Flyagin, A. V. Gapanov, M. I. Petelin, and V. K. Yulpatov, The gyrotron, IEEE Trans. Microwave Theory Tech., Vol. MTT-25, pp. 514-521, June 1977. W. Lawson, Magnetron injection gun scaling, IEEE Trans. Plasma Sci., Vol. PS-16, pp. 290-295, Apr, 1988. P. Sprangle and A. T. Drobot, The linear and self-consistent nonlinear theory of the electron cyclotron maser instability, IEEE Trans. Microwave Theory Tech. Vol. MTT-25, pp. 528-544, June 1977. W. W. Destler, E. Chojnacki, R. F. Hoeberling, W. Lawson, A. Singh, and C. D. Striffler, High power microwave generation from large-orbit devices, IEEE Trans. Plasma Sci., Vol. PS-16, pp. 71-89, Apr. 1988. K. Yamanouchi, S. Ono, and Y. Shibata, Cyclotron fast wave tubemThe doubled ridged traveling wave peniotron, Proc. 5th Int. Conf. Microwave Tubes, (Paris), pp. 96-102, 1964.


117

[91 M. E. Read, W. G. Lawson, A. J. Dudas, and A. Singh, Depressed collectors for high-power gyrotrons, IEEE Trans. Electron Devices, Vol. ED-37, pp. 1579-1599, 1990. [lO] L. Ives, K. Felch, C. Hess, H. Jory, R. Pendleton, A. LaRue, M. Chodorow, J. Feinstein, L Zitelli, and R. Martorana, Design and test of an 8 GHz, 500 kW, side coupled gyrotron, Int. Electron Devices Meet. San Francisco, Dec., pp. 152-154, 1988. [lOa] J. Neilson, K. Felch, J. Fienstein, H. Huey, H. Jory, R. Schumacher, and M. Tsirulnikov, Design of a 1 MW gyrotron with b e a m / R F separation, Proc. 16th Int. Conf. Infrared Millimeter Waves, Lausanne, Aug., pp. 120-121, 1991. [11]

R. M. Philips, History of the ubitron, Proc. 9th Int. Free Electron Laser Conf.,

Williamsburg, VA, Sept. pp. 1-9, 1987. [12]

[13]

[14] [15]

[16]

[17] [18] [191 [20] [21] [22]

[23]

[24]

[25]

L. Rebuffi, V. Parail, N. Fujiisawa, H. Hopman, W. Lindquist, H. Kimura, W. Nevins, M. Sironi, D. Swain, and J.-G. Wegrowe, Issues for the development and the design of an electron cyclotron wave system for ITER, Conf. Dig. 15th Int. Conf. Infrared Millimeter Waves, Orlando, FL, Dec., pp. 568-571, pp. 1990. H. Guo, Y. Carmel, and V. L. Granatstein, A compact phase-locked harmonic gyrotron for modern millimeter wave radars, Conf. Dig. 15th Int. Conf. Infrared Millimeter Waves, Orlando, FL, Dec., pp. 4-9, 1990. E. F. Eison, A 35 GHz seeker testbed RADAR, Millimeter Wave Technol. IV Radio Freq. Power Sources, Orlando, FL, May, pp. 109-113, 1987. D. J. Hoppe and A. M. Bhanji, High Power K6 Band Transmitter for Planetary Radar and Space Craft Uplink, Proc. l Oth Int. Conf. IR and MM Waves, Lake Buena Vista, FL, pp. 89-91, 1989. W. M. Manheimer, B. Levush, and T. A. Antonsen, Jr., Equilibrium and stability of free-running, phase-locked, and mode-locked quasi-optical gyrotrons, IEEE Trans. Plasma Sci., Vol. PS-18, pp. 350-367, June 1990. C. S. Kou, D. B. McDermott, N. C. Luhmann, Jr., and K. R. Chu, Prebunched high-harmonic gyrotron, IEEE Trans. Plasma Sci., Vol. PS-18, pp. 343-349, June 1990. O. A. Nezhevenko, The magnicon: A new RF power source for accelerators, IEEE Part. Accel. Conf. Rec., San Francisco, May, pp. 2933-2942, 1991. B. G. Danly and R. J. Temkin, Generalized nonlinear harmonic gyrotron theory, Phys. Fluids, Vol. 29, pp. 561-567, 1986. H. Motz, W. Thon, and R. M. Whithurst, Experiments on radiation by fast electron beams, J. Appl. Phys., vol. 24, pp. 826-833, 1953. C. E. Enderby, and R. M. Phillips, The ubitron amplifier--A millimeter-wave TWT, Proc. IEEE, Vol. 53, p. 1648, Oct. 1965. D. E. Pershing, R. H. Jackson, H. Bluem, and H. P. Freund, Improved amplifier performance of the NRL ubitron, Proc. 15th Int. Conf. Infrared Millimeter Waves, Orlando, FL, Dec., pp. 137-139, 1990. P. Garin, G. Mourier, J. M. Krieg, and A. Dubrovin, Extensive experimental results on a 1 MW, 8 GHz gyrotron and the transmission system, Conf. Dig. 15th Int. Conf. Infrared Millimeter Waves, Orlando, FL, Dec., pp. 768-770, 1990. S. Tantawi, W. Main, P. E. Latham, B. Hogan, H. Matthews, M. Rimlinger, W. Lawson, C. D. Striffler, and V. L. Granatstien, Studies of high-power X-band amplification from an over-moded three cavity gyroklystron with a tunable buncher cavity, Conf. Dig. 15th Int. Conf. Infrared Millimeter Waves, Orlando, FL, Dec., pp. 195-196, 1990. G. F. Brand, P. W. Fekete, K. Hong, K. J. Moore, and T. Idehara, Gyrotron IVA, Conf. Dig., 15th Int. Conf. Infrared Millimeter Waves, Orlando, FL, Dec., pp. 496-498, 1990.

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[26] W. H. Miner, Jr., P. Vitello, and A. T. Drobot, Theory and numerical simulation of a TEal 1 gyroresonant accelerator, IEEE Trans. Microwave Theory Tech., Vol. MTT-32, pp. 1293-1301, Oct. 1984. [27] M. M. Karliner, E. V. Kozyrev, I. G. Makarov, O. A. Nezhevenko, G. N. Ostreiko, B. E. Persov, and G. V. Serdobintsev, The magniconmAn advanced version of the gyrocon, Nucl. Instrum. Methods Phys. Res., Vol. A269, pp. 459-473, 1988. [28] W. M. Manheimer, Theory and conceptual design of a high-power highly efficient magnicon at 10 and 20 GHz, IEEE Trans. Plasma Sci., Vol. 18, pp. 632-645. June 1990. [29] P. Tallerico and D. Rees, Fields and trajectories in the magnicon, Proc. IEEE Part. Accel. Conf., San Francisco, May, pp. 640-642, 1991. [30] K. Felch, T. S. Chu, H. Huey, H. Jory, J. Neilson, and R. Schumaker, Design considerations for a 1 MW CW gyrotron with an internal converter, Conf. 18th Int. Conf. Infrared Millimeter Waves, Colchester, Engl., Sept., pp. 517-518, 1993. [311 K. D. Hong, G. G. Brand, and T. Idehara, Second harmonic operation on GYROTRON V, Conf. Dig., 17th Int. Conf. Infrared Millimeter Waves, Pasedena, CA,

Dec., pp. 390-391, 1992. D. E. Pershing, R. D. Seeley, R. H. Jackson, and H. P. Freund, NRL ubitron performance, Conf. Dig., 17, Int. Conf. on Infrared Millimeter Waves, Pasedena, CA, Dec., pp. 50-51, 1992. [33] T. Kikunaga, T. Shimozuma, H. Asano, Y. Yasojima, and K. Nakashima, Experimental Studies of a 120 GHz megawatt gyrotron, Conf. Dig. 16th Int. Conf. Infrared Millimeter Waves, Lausanne, Aug. pp. 118-119, 1991. [34] K. E. Kreischer, M. A. Bastien, T. L. Grimm, W. C. Guss, and R. J. Temkin, Megawatt power level gyrotrons, Conf. Dig. 16th Int. Conf. Infrared Millimeter Waves, Lausanne, Aug. pp. 116-117, 1991. [32]

[35] Y. Mitsunaka, K. Hayashi, Y. Hirata, Y. Itoh, T. Kariya, M. Komuro, T. Okamoto,

[36]

[37]

[38]

[39]

[401 [41]

Y. Okazaki, T. Sugawara, A. Yano, T. Nagashima, and K. Sakamoto, A high-power 120 GHz whispering-gallery-mode gyrotron with a built-in quasi-optical mode converter, Conf. Dig. 15th Int. Conf. Infrared Millimeter Waves, Orlando, FL, Dec. pp. 318-320, 1990. K. E. Kreischer, T. L. Grimm, W. C. Guss, R. J. Temkin, and K. Y. Xu, "Research at MIT on High Frequency Gyrotrons for ECRH," MIT Plasma Fusion Center Rep. PFC/JA-90-37, Oct. 1990. K. E. Kreischer, M. Blank, W. C. Guss, S. K. Lee, and R. J. Temkin, High frequency, megawatt gyrotron experiments at MIT, Conf. Dig. 18th Int. Conf. Infrared Millimeter Waves, Colchester, Engl., Sept. pp. 515-516, 1993. L. Ives K. Felch, C. Hess, H. Jory, J. Neilson, R. Pendleton, J. Shively, M. Chodorow, J. Feinstien, A. LaRue, and L. Zitelli, Design and test of an 8 GHz, 500 kW, side-coupled gyrotron, Conf. Dig., 14th Int. Conf. Millimeter Waves, Wurtzburg, F.R.G., Oct. pp. 71-72, 1989. V. E. Myasnikov, A. P. Cayer, S. D. Bogdanov, and V. I. Kurbatov, Soviet industrial gyrotrons, Conf. Dig., 16th Int. Conf. Infrared Millimeter Waves, Lausanne, Aug. pp. 127-128, 1991. M. Thumm, Progress in development of high power gyrotrons, Conf. Dig. 18th Int. Conf. Infrared Millimeter Waves, Colchester, Sept., pp. 6-7, 1993. V. A. Flyagin, A. L.. Goldenberg, and V. E. Zapevalov, State of the art gyrotron investigation in Russia, Conf. Dig., 18th Int. Conf. Infrared Millimeter Waves, Colchester, Engl., Sept., pp. 581-584, 1993.


119

S. Alberti, B. G. Danly, G. Gulotta, E. Giguet, T. Kimura, W. L. Menninger, J. L. Rullier, and R. J. Temkin, High-power cyclotron Autorresonance maser (CARM) experiments, Conf. Dig., 17th Int. Conf. Infrared Millimeter Waves, Pasedena, CA, Dec., pp. 128-129, 1992. [43] T. L. Grimm, P. M. Borchard, K. E. Kreischer, and R. J. Temkin, High power operation of a 200-300 GHz gyrotron oscillator, Conf. Dig. 17th Int. Conf. Infrared Millimeter Waues, Pasadena, CA Dec., pp. 190-191, 1992.

[42]


CHAPTER

5 The Peniotron David Gallagher and Gfinter D6hler*

I. Introduction

The peniotron

is similar to a gyrotron in several ways: (a) it is a fast-wave device, there is no slow-wave structure, and the interacting RF wave propagates with a phase velocity greater than the speed of light through a waveguide circuit; (b) the circuit is immersed in a uniform, axial, DC magnetic field; (c) the electrons in the electronic beam orbit around the lines of the magnetic field at the cyclotron frequency; (d) the RF interaction between the RF wave and beam acts primarily to convert the beam's orbiting (or transverse) energy into RF energy; and (e) as in all known fast-wave devices, the bandwidth is narrow. Peniotrons are, however, different from gyrotrons in the mechanism for which this energy conversion takes place. Whereas in the gyrotron the interaction involves a bunching of electrons resulting from relativistic mass effects, the peniotron involves neither and therefore can be a low-voltage device. Also the efficiency is potentially very high. In the peniotron, the electron beam can be a large envelope of orbiting electrons as in the gyrotron. Such a device is called a gyropeniotron and is capable of power levels comparable to those of gyrotrons and has applications similar to those of gyrotrons. However, in many cases the electron beam is simply a hollow, axis-encircling (rotating) beam (i.e., one beamlet of the gyrotron beam). The major peniotron types are

tDeceased November

5, 1993.


121


GallagherandD6hler

m22

illustrated in Figure 1. The circuit for a peniotron can be a ridged or cross-shaped rectangular waveguide operating in the TEl0 mode traditional peniotron or can be one of many other waveguide shapes: rectangular, square, round, slotted (magnetron), coaxial, etc. These single-beamlet devices have the potential to generate or amplify hundreds to thousands of watts of RF power at frequencies up to hundreds of gigahertz and therefore have applications for communications and radar at millimeterwave frequencies at which high efficiency and moderate power levels are desired or required and at which broad instantaneous bandwidths are not needed.

B Hollow ,~.,..., ~ .

. . .

Rotating

~

~

Beam

~// "

i

RF Wave ~ _

_

TEIO

-

C

~ E

F Electron Beam

TE31 Figure I. Peniotron types. (A) Traditional four-ridge peniotron; (B) traditional peniotron with a cross-shaped waveguide; (c) square waveguide peniotron; (D) rectangular waveguide peniotron; (E) "true" gyropeniotron; (F) magnetron-type peniotron.

123

5. The Peniotron

2. The Traditional Peniotron The traditional peniotron, invented in the mid 1960s by the Japanese [1] and revived in the late 1970s in the United States [2], is illustrated schematically in Figure 1A, which shows a four-ridged (double-pair-ridged) rectangular waveguide immersed in a constant axial (longitudinal) magnetic field, B 0, and a thin, hollow electron beam rotating symmetrically between the ridges at the cyclotron frequency toc and drifting with constant axial velocity vz. A transverse electric (TEl0) mode with frequency to is assumed to propagate axially (z-direction)with propagation constant k. The main advantage of the traditional peniotron over nontraditional designs is that the waveguide can be designed so that only the TEa0 mode (the fundamental propagating mode) can propagate at the operating frequency, and so there are no moding problems.

Principle of Operation The principle of operation of the basic peniotron interaction can be seen in Figure 1A. Depending on the phase of the RF wave, the electrons near the ridges are accelerated (decelerated) by the strong electric field between ridges, causing the electron orbit to increase (decrease) in size. Assume now that the RF field of the wave changes by one complete period (or integral multiple thereof) during the time it takes the electron to perform half a revolution to reach the other ridge pair. The electron is now accelerated (decelerated) by a force which is smaller (larger) than previously, because the electron is farther from (closer to) the ridges. Thus, during each complete revolution, the electron loses some energy to the wave regardless of the initial RF phase. As long as the alternating acceleration and deceleration of the electrons remain "in phase," the electrons will continue to lose transverse energy until all energy is converted to RF energy and the orbit size becomes vanishingly small, thus leading potentially to a device with very high efficiency, but narrow bandwidth. Expressed mathematically, the above condition for resonance is to o = t o - k v

z=Sto c

S=2P

P=

1,2,3,...,

(1)

where too is the Doppler-shifted frequency, P is the spatial harmonic number of operation, and the cyclotron frequency is given by to c = ( e / y m ) Bo ,

where e l m is the charge-to-mass ratio of the electron and 7 is the factor

124

Gallagher and DBhler

at which v is the total electron velocity and c is the speed of light. The factor of 2 reduces the magnetic field requirement by a factor of 2, and higher values of P reduce it further. Note that no relativistic effects are involved in the interaction. (1 -- U2/C2) - 1/2

Small-Signal Calculations Small-signal calculations were made by decomposing the TEl0 mode of the four-ridged waveguide (approximated by line charges) in a Fourier series, solving for the small signal displacements, and applying Arnaud's equation to obtain a dispersion equation [3]. In a plane perpendicular to the axis, the functional dependence of the transverse electric field component along the circumference of the DC electron orbit is an expansion of terms of the form exp (-jnq~), so that the field as seen by the moving electron is given by exp j(tOt - kz - nq~) = exp jtOnt, where tOn = tO - - k v z ntOc, n is any integer, and z and q~ are the electron's axial and angular positions, respectively. The peniotron resonance occurs when ton "" -I'- toc :=~ to 0 "-

( n - 1) tOc,

peniotron,

(2a)

(tOn = +tOc leads only to net absorption for RF power), which is when the electrons are alternately accelerated and decelerated at a rate equal to the cyclotron frequency. The peniotron is therefore called a "resonant" device, in contrast to "synchronous" devices such as gyrotrons for which tOn =

0 ~

tOO = F/tOc,

gyrotron (cyclotron maser)

(2b)

and the electrons remain in a relatively constant phase of the RF wave [4]. In the traditional peniotron, only odd values of n yield nonzero coefficients. Thus Equation (1) is retrieved, where P = 1,2,3 (S = 2,4, 6) corresponds to n = 3, 5, 7, respectively. If one introduces the normalized parameters 13 =/3e(1 + jD6)~ o =/3e(1 + Db)

f i e - (tOo- 2PtOc)/Vz, where /3, /30, and /3e are the hot, cold, and at-resonance propagation constants, respectively, the dispersion equation, in the absence of spacecharge effects, becomes

6 ( 6 + j b ) = 1,

115

5. The Peniotron

whose solution, ~ = x + j y , is shown in Figure 2 as a function of b. The gain parameter D is given by D 2 = 1/2(I/V)(v2/vz

2)a2p ,

where I and V are the beam current and beam voltage, respectively, v is the electron velocity, and z2p is the coupling impedance given by Z2 P

2 2 ) - 1 R - Z ( r 0 / R ) 4p F sina((zP + 1)0) , = Z0(1 - COcut/~o

where z 0 is the characteristic impedance of the waveguide at infinite frequency (typically near 200 f~ [3]), ¢.Ocut is the cutoff frequency of the waveguide, r 0 is the beam radius, R is the minimum distance from the waveguide center to the ridges, 0 is the angle made by two rays starting at the center, one extending toward the end of the ridge and the other horizontally, and F is a fudge factor equal to 0.13 to fit large-signal calculations. The cosine factor is an important design consideration for the ridges. The gain per unit length at center frequency is given by G = 8.7/3eD. When space-charge effects are considered, they are found to be negligible under most conditions, particularly for thin beams [5]. The bandwidth is determined by the range of b from - 1 to 1, but is unimportant because the actual bandwidth, as determined by large-signal calculations, is much narrower.

3

N

b

F

x

-1 -2

-3 -3

Figure 2. Normalized velocity parameter b.

-2

-1

1

2

gain and phase velocity parameters

3 x and y versus cold phase

126

Gallagher and D6hler

TABLE I Simulated Sample Results for Vo = 10 kV; I 0 = 0.5 A; v t / v z = 2; and an Ideal Beam of Zero Thickness, Ripple, and Velocity Spread [2]

P

1

2

3

4

r 0 (cm) (at 90 GHz) B (gauss) (at 90 GHz) Gain/orbit (dB) Length (orbits, NO) 3-dB bandwidth (A~o/w) 2 PNo (A~o/¢o) Transverse efficiency

0.019 16,000 1.41 25 0.019 0.95 95%

0.038 8000 1.47 21 0.0104 0.87 77%

0.057 5300 1.18 27 0.0052 0.84 65%

0.076 4000 0.83 34 0.0030 0.82 50%

Large-Signal Calculations Large-signal calculations of efficiency were performed by the Soviets [6, 7]. Also, Northrop has developed a computer code which calculates large-signal gain and efficiency in all peniotron- and gyrotron-type devices. The code employees single-electron ballistics and takes into account beam thickness, velocity spread, beam scalloping, circuit losses, the true RF fields in the waveguide, the growth of the RF wave along the circuit, and any attenuators that might be employed. It can calculate bandwidth by injecting signals of different frequencies. Table 1 shows sample results for four optimized designs (ideal beam) for P = 1, 2, 3, and 4, where V = 10 kV, I = 500 mA, and U t / / U z = 2. Note that the instantaneous bandwidth is a little less than 1 / ( 2 P N ) , where N is the required circuit length in orbits.

Performance of Traditional Peniotrons In the mid 1960s, the Japanese obtained 6% efficiency from a 10-GHz peniotron operating in the P = 1 fundamental and with a 10-kV, 5-mA beam injected off center into the magnetic field by a CRT-type gun. Then in the 1980s, Northrop developed experimental peniotrons at 8 GHz ( P = 1 fundamental) and 16 GHz ( P = 2 harmonic), first as oscillators and then as amplifiers, and finally at 45 GHz (amplifier, P = 1) and 90 GHz (oscillator, P = 2) the later of which is presently in development. Progress is summarized in Table 2 [8].

127

5. The Peniotron TABLE 2 Northrop Peniotron Development

8-GHz oscillator 16-GHz harmonic oscillator 8-GHz amplifier 16-GHz harmonic amplifier 45-GHz amplifier 45-GHz oscillator 90-GHz oscillator (cross-shaped WG) 90-GHz oscillator (rising sun WG) aTransverse efficiency is twice as much

Output power

Efficiency a

2 kW 200 kW 3 kW 156 W 300 W 750 W Nominal 5W

30% 3.7% 36% 1.3% 8-12% 11%

Instantaneous bandwidth

2% 6% 1%

year 1981 1982 1982 1983 1986 1987 1992 1994

( U t ; / U z -- 1).

Traditional Peniotron Design

Basic Design of the 45-GHz Peniotron Amplifier A drawing of the 45-GHz peniotron amplifier is shown in Figure 3. On the left is the electron gun whose purpose, together with the magnetics, is Electron gun Gun pole piece Gun solenoid Field reversal \,

and adiabatic compression pole piece RF input 90° bend and transition Attentuator Circuit Main solenoid Collector

Figure 3. Design of a 45-GHz peniotron amplifier.

128

Gallagher and D6hler TABLE 3 45-GHz Peniotron Design Parameters

Center frequency Beam voltage (V0) Beam velocity ratio (Ut//Uz) Beam current Mean cathode radius (r c) Magnetic field at the cathode

45 GHz 9 kV 1 400 mA 0.162 40 g

Cathode thickness (Ar/r c) Cathode loading Magnetic field in circuit Mean beam radius in circuit Circuit length Circuit cutoff frequency

15% 2.5 A/cm 2 8000 g 0.0114 in. 6 in. 42 GHz

to generate the required thin, hollow, rotating beam, which passes through the circuit. On each end of the circuit are the input and output ports. The output consists of a tapered waveguide transition from the double-pair ridge waveguide to the standard rectangular waveguide, followed by a 90 ° bend in the standard waveguide, which contains a three-quarter wavelength impedance transformer (RF window). Inside the circuit is a short attenuator to suppress rereflection oscillations. A short section of the copper waveguide is replaced by inserts made from lossy material, which provide about 40 dB of attenuation. The electron beam exits the circuit through a hole in the 90 ° bend and is collected by the isolated collector shown on the left. Key design parameters are included in Table 3. Beam Formation

Gun designs to generate a thin, annular axis-encircling electron beam (with low ripple) fall into two categories: nonaxially symmetric (i.e., corkscrew) gun designs and axially symmetric gun designs (which require a field reversal). The convergent (spherical) hollow Pierce gun (with total magnetic confinement) is the gun type used in all the Northrop peniotrons. The gun consists of three stages: (1) a hollow, nonrotating, nonconverging beam is generated from a spherical Pierce-type electron gun with total magnetic confinement; (2) a magnetic field reversal causes the beam to rotate at the cyclotron frequency; and (3) an adiabatic compression of the magnetic field reduces the beam radius as required for entering into the circuit. The physical limitation of this approach is that the area convergence of the Pierce gun can be only about 2, thus placing the burden of beam compression primarily on the third stage. The way around this limitation is the "novel" gun approach [8], in which the beam is still

5. The Peniotron

129

compressing when the field reversal is approached. This approach also reduces beam ripple to a few percent. Electron guns have been developed by Litton [6] and Varian Associates [10], which, in addition to the principles described above, makes use of an iron, flux-concentrating center post so that all emitted electrons enclose the same magnetic flux, thus resulting in reduced velocity spreads. Circuit Fabrication

The problem with achieving a good I/0 match to the circuit depends on achieving good tolerances in circuit waveguide dimensions, particularly at millimeter wave frequencies. This problem was solved at 45 GHz by machining the ridges separately as ribbons and then fixturing and brazing them into a blank waveguide half. However, at 90 GHz, the ribbons could not be fabricated and so a cross-shaped waveguide was developed (see Figure 1B). The simulated interaction strength actually increased slightly over that of the comparable four-ridge design. However, at 90 GHz and higher, the brazing of two waveguide halves becomes a problem because of RF losses at the braze seam. Therefore the latest technique is to braze up a stack of predrilled copper pellets, one of them being graphite to provide for an attenuator, and then wire EDM the stack to any shape waveguide desired [11]. Figure 4 shows such a circuit with a slotted magnetron shape.

Figure 4. Ten-vane magnetron-type waveguide with a graphite section for the attenuator.

130

Gallagher and D6hler

3. Nontraditional Peniotrons The purpose of this section is to discuss briefly the many nontraditional peniotrons (often called gyropeniotrons) that have been proposed, theoretically analyzed, and developed. Experimental work has been reported for square waveguides and magnetron-type waveguides. In any of these devices, the principle of peniotron amplification resides with the alternating acceleration-deceleration of the electrons during any cyclotron period and with increasing electric field strength with increasing radius of the orbiting electrons. In opposite directions, the field strength is either symmetric (i.e., traditional peniotron) or antisymmetric, the interaction frequency being even or odd multiples (S) of the cyclotron frequency, respectively, only odd or even values of n yielding nonzero coefficients (Small-Signal Calculations).

Square and Rectangular Waveguides The Japanese [12] have resumed experimental peniotron development using a square waveguide with the TEl1 RF mode, as shown in Figure 1C. In this configuration, the RF field strength increases antisymmetrically about the center of the waveguide (or beam), and so the resonant frequency is at odd multiples of the cyclotron frequency. An experimental oscillator operating in the fundamental mode (to = coc) was constructed and tested at 10 GHz with a 30-kV, 0.92A beam with v t / v z = 3 and cavity dimensions 2.1 x 2.1 x 15 cm. The output power was 10 kW. Alignment of the beam, circuit, and magnetic field is extremely critical and was accomplished to within 0.002 in. by the use of a laser beam. Another proposed configuration for the peniotron is a rectangular waveguide propagating in the TE20 mode with the beam in the center, as shown in Figure 1D. As in the square waveguide the RF field strength increases antisymmetrically from the center toward the left or right. This device was studied theoretically by the Chinese [13, 14]. Efficiencies of 51 and 11% were simulated for operation near co = coc and to = 3w c, respectively.

The "True" Gyropeniotron Another nontraditional peniotron is what might be called the "true" gyropeniotron, because, instead of an axis-encircling beam, the typical polyhelical gyrotron beam is employed. Ono et al. [15] proposed a device (Figure 1 E ) w h i c h exploits exclusively the peniotron interaction in a

5. The Peniotron

131

gyrotron beam. In the device illustrated here, the beamlet centers are placed on the electric field null of the TE02 mode, so that, as the electrons turn in their orbits, they are alternately accelerated and decelerated by the azimuthal electric fields. The principle of operation is the same as that for the traditional peniotron, except that the electric fields are in opposite directions on each side of each beamlet orbit (antisymmetric). This device was simulated with encouraging results, but for very high beam power. Beam voltage and current ranged from 40 to 80 kV and 20 to 140 A, respectively, whereas beam efficiency was around 50%, for operation at o~0 = 3,, .

Cu

m

> u :D

0

u

Au

"-'-"

~AI-Si

Mg _ Brass

100

~

Mo

E eI---

10

lO0

1000

Temperature [K] 1000 >,

Ag

> u

W E 0

u ~

Zn 100 N, Pb

L

v2 A 10

o

,

2;0

,

J

,oo

,

6;0

,

8;0

,

ooo

Temperature [KI Figure I. Thermal conductivity as a function of temperature. (d) isolators, and (e) gases.

(a and b) metals, (c) semiconductors,

6. T h e r m o d y n a m i c s

of M i c r o w a v e

141

Devices

10000

C

.4..o

1000

•~

GaP

~ -o

100

c - y' E

°) O

GoAs ~

InP

.._o

O

E

...-.

10

InAs

L-.

r"

I(]0

' 200

' 31]0 ' /-,00 ' 500

' 61]0 ' 7(]0

1000

' B00 ' 9(]0

Temperature [K] d

10000

>

1000

.-

Diamond BeO

S-145

E L..

1o

D-Mot

D-450

cl--

,

,

~

Sapphme

~

corning , .,

,

J

,

~

,

quartz

,

I

100

200

300

400

500

600

?00 ' 800 ' 91]0

1000

Temperature [ K]

H2

>

"ID c-

01

u O

.-.

E L_

QJ

c-

0.01 100

,

,

1000

Temperature [K] Figure I.

(Continued)

Equation (5)can be solved analytically for a limited number of geometries, and therefore finite-difference or finite-element methods are commonly applied to solve this equation [6, 10, 16, 26-28, 30, 42, 44, 46, 48, 53, 58, 75, 82, 83, 86], especially utilizing commercial packages such as ANSYS

142

Fricke, Krozer, and Hartnagel TABLE I Approximation of the Thermal Resistivity of Ternary and Quaternary Compound Semiconductors as a Function of Composition [I - 3] 1

Ga l_xlnxAs InASl_xPx

GaASl_xPx Gal_xAlxAs Inx_xGaxP Inl_xGaxAsyPl_ r

K cm

~--V-

Compound

2.27 + 7 3 . 4 3 x - 72x 2 3.7 + 2 7 . 7 7 x - 30x 2 2.27 + 1 9 . 0 3 x - 20x 2 2.27 + 2 8 . 8 3 x - 30x 2 1.47 + 7 1 . 8 3 x - 72x 2 1.47 + 7 1 . 8 3 x - 72.23y - 1.26xy - 72x 2 -

25y 2

[67], PHOENICS, and CAEDS [4]. In the case of temperature-dependent thermal conductivity the exact solution of equation (5) can be obtained by using the Kirchhoff transform technique described by Joyce [36]. Many practical problems of heat transfer can be considered in only two dimensions, for which the heat transfer rate per unit depth is dependent only on the temperature difference on each surface. In this case, the thermal resistance can be evaluated by the simple relation R th = 1/(k S), where S is the so-called conduction shape factor. Table 2 together with Figure 2 indicates various examples of systems for which analytical solutions exist. Further examples can be readily found in Kreith [42] and Holman [33].

Unsteady-State Heat Conduction Transient heat conduction problems commonly occur in pulse-driven microwave systems during thermal cycling, etc. The Fourier equation in three dimensions for this case reads OT

V(kVT) = Cpp Ot

(6)

and for homogeneous thermal conductivity of the material reads

V 2 T = Cpp OT k

at

1

OT

a

at'

= --g--

(7)

TABLE 2 Conduction Shape Factors

Figure

Conduction shape factor (S)

2a

S = 4a]--Jl(X)coth(wx/a) x Jo

2b

$1 =

,.oo

Reference

sin x

4aI 1

1-

fo~ sin x X1 I1 = Jo - - J l ( X ) - - xX2 dx

4aI 1 .

4kl

"

[91

dx

$2 -

I2

[43]

I2 7rk 2

Jo'~ sin x J l ( X ) e x p ( - w l x / a )

I2 =

~

t a n h ( w 2 x / a ) dx;

X2

x~ = 1 + A 1 e x p ( - 2 w l x / a ) ; k2 Y1 = 1 - - - t a n h ( w 2 x / a ) ;

Z 1

-

-

Y2

Y1 Y2

1 - A 1exp(-2WlX/a)

X 2 -

k2 Y2 = 1 + - - t a n h ( w 2 x / a )

k 1

kl

,.~ sinx 2c

S = 2aJo - - ~ J l ( X ) c o t h ( w x / a ) dx

2d

S = 2 Z ~

2e

S = 2 Z - -

2e

4w) S---(rrZ)ln - - • t > 0 rrr

K(p2)

r=a

2f

Pl = sinh ~

K(Pl)

K(P2) K(pl )

1+

" P2

=

_

°

Pl-

2a w- t --

¢ =

Pl

P2

cosh(~'a/w)

2g

-

S _

1

K(Pl) K(P2)"

+0.236 ---

1 1+ r

~/ =

[32a]

[32a]

= ~/1 "

p2

P2

--

7r(2a + s)

Pl

t = 0

10 s

[51, 72]

L a m i n a r flow

[13]

Re d < 2100; Pr > 0.7 3g

See Reference

[79]

Boiling Heat Transfer In this section cooling by vaporization is discussed. The arrangement which is considered consists of the hot plate at the temperature Ts which has to be cooled and which is covered by a liquid. Without any agitation of the liquid, this process is called pool boiling. The cooling properties of this arrangement are strongly dependent on the excess temperature ATx = T s - T s a t above the boiling point. At low ATx pure convection heat transfer is observed. If the temperature is increased individual bubbles due to beginning evaporation are formed. Simultaneously the boiling heat transfer coefficient h b increases because the bubbles have an increasing stirring effect. Additionally the heat transfer by evaporation becomes relevant. This regime is called nucleate boiling. At the critical excess temperature the maximum heat transfer coefficient h b is reached. A further increase of ATx results in coalescing bubbles. A vapor film is formed which covers the plate surface. The thermal resistance of this film causes a decrease of h b. This regime is called the film boiling region. Further information of the pool boiling behavior of liquids is found in the books of Holman [33] and Kreith [42]. For the heat flux per unit area, q b / A , in the nucleate boiling regime Rohsenow [68] proposed an experimentally fitted equation,

hfg

= Csf

~lhf~

g ( p l - pv)

P r ~ "7

(18)

150

Fricke, Krozer, and Hartnagel

b

! e

d

O

,

)

g

H

Figure 3. Schematic drawing of the geometries for the calculation of the convective heat transfer.

where ¢1

h~ /Zl or

g Pl' Pv

Pr~

specific heat of the saturated liquid enthalpy of vaporization viscosity of the liquid surface tension of the liquid-to-vapor interface gravitational acceleration densities of the saturated liquid and vapor Prantl number of the saturated liquid

Ws/kg K W s/kg kg/m s N/m m/s 2 kg/m 3

151

6. Thermodynamics of Microwave Devices

Values of the experimental determined constant, Csf , may be found in the books of Holman [33] and Kreith [42].

4. Heat Transfer by Radiation In contrast to heat transfer by convection and conduction heat transfer by radiation does not require a special medium for propagation. Therefore radiative heat transfer has to be considered especially under vacuum conditions. Radiation is essentially an electromagnetic wave emitted from a surface with a certain temperature. The emitted power per unit wavelength and per area of an ideal black body at a temperature, T, is given by Planck's law,

C1A -5 Eb'x-- e c2/;~7"- 1 '

(19)

c 1 = 3.74 x 1 0 - 1 6 W m 2 and c 2 = 1.44 X 1 0 - 2 K m .

(20)

with

Planck's law results in a spectral distribution of the emitted power with its maximum at the wavelength ~'max,

¢3 '~max- T ' m

(2a)

with c 3 = 2.8978 x 1 0 - 3 K m . Integrating Planck's law over wavelengths from 0 to ~ yields the total emitted power per unit area (Stefan-Boltzmann Law),

E b -- trT 4,

(22)

with tr = 5.67 x 1 0 - 8 W / K 4 m 2. Real surfaces emit less power than the ideal black body. The emitted power per unit area of such a gray body is described using the emissivity e: E

(23)

= e E b.

The emissivity e of various surfaces is listed in Table 6. It depends strongly on surface conditions such as smoothness and chemical content. If radiation strikes a surface, a part of the power is reflected by a factor (reflectivity, p), another part (transmissivity, ~-) is transmitted, and the rest is absorbed (absorptivity, a). Therefore one obtains the balance: ~'+p+a=

1.

For most cases the approximation a = e is valid.

(24)

152

Fricke, Krozer, and Hartnagel TABLE 6 Emissivities of Metals and Nonmetals Material

Temperature

Emissivity

(K) Metals Copper Steel Lead Steel Magnesium Tungsten Aluminum Stee 1 Lead Molybdenum Platinum Aluminum Steel Nickel Molybdenum Aluminum Nickel Copper Gold Gold Silver

Oxidized Rolled Oxidized Oxidized Oxidized Filament Casted P o lish ed Oxidized Filament Polished Rolled Polished Polished Polished Polish ed Polished Polished

430 300 472 300 550-1100 3589 300 300 300 1000-2867 300-900 300 385 385 385 300-450 300 300 530 700 500-900

Polished

0.76 0.67 0.63 0.61 0.55-0.2 0.39 0.3 0.24-0.29 0.23 0.096-0.202 0.05-0.104 0.08 0.074 0.072 0.071 0.04-0.06 0.045 0.03-0.04 0.018 0.022 0.02-0.032

Nonmetals Glass Water

300 273-385

0.94 0.95-0.963 0.3-0.18

A1203, 99.5%

For the exchange of radiation between two surfaces, one enclosing the other, i and j on temperatures Ti and T:, a shape factor F/,: is introduced for complete enclosures. The heat transfer rate between the surface A i and the surface Aj is given by

r;) q(i,j)

1

-

E i

1

1 -

e:

+ ~ - ~ - ~ eiA i Fi,jA i EjAj

"

(25)

In this equation ideal diffuse surfaces are assumed. This means that the


153

TABLE 7 Radiation Shape Factors for Diffuse Surfaces

1)_ 2

cos A 4a

Reference

Radiation shape factor

Figure

F12 =

(l+ t h

2 A + arcsin

[41]

1+~

[11, 20, 66]

3g

See references

4b

El2-- ~ 1 ( 1 + R 2 + R 2 - ¢ ( 1

2 22) + R 2 + R 2 2 ) 2 - 4R1R

[81]

ri

Ri=

x2) 2 E1

A = X 2Y1 arctani -~1

4c

F12 -

Ti'X1X2 ai

~ In

YI=¢I+X

X i = - if"

2"

)

+

1

4 X 2 In

ai

+A

X1Y 2 arctan

Y2=¢I+X

[21,41]

2 1

Xlarctan X---7 + X2arctan X2

Xl = ~ "

4e

1 + X21 + X 2

X~ - X 2 arctan X 2

1

1

F12 = ~ 1

+-

-- X1 arctan

o

~ 1 2 arctan ]/FY12

(1+Y12)X 2 (l+Y12)X 2 1+Y12]) YIY12 + X 2 In YzY12 - In YIY2) [81]

Y12 = X2 + X2;

II1

= 1 +

X 2"

Y2

=

1 +

X2

2 X 3 )2 F12 =2-~1

-

ai

Xi-

b

1+

1+

+

2

2

-

1+

1+

2

2

[21]

radiation is constant in all directions. Especially the radiation of nonconductors is concentrated in the direction normal to the surface, whereas conductors exhibit broader directivity.

154


Because of the geometrical symmetry one obtains the equivalence (26)

Z i f i,j = Z j F j , i.

The shape factor Fi, j is defined by 1

Fi'j=

cos ~i COS ~j- d A i d A y

Aifi[j"A"A

"n'r 2

"

(27)

In this equation ~i is the angle between the normal to the surface of A i and the connecting line between A i and Aj. In Table 7 the shape factors Fi, j for different arrangements (Figure 4) are presented. In all cases ideal diffuse surfaces are assumed. The procedure for the computation of the radiative heat transfer among more than two surfaces is discussed in detail by Holman [33]. A more rigorous treatment of radiative heat transfer can be found for instance in the books of Gray [29], Cheremisinoff [13], Holman [33], Simonson [72], and Kreith [42].

F2

e

°_1_ 2

o2 ~ ~ ~ - ~

a_L 2

Figure 4. Schematic drawing of the geometries for the calculation of the radiation shape factor.


155

5. M e a s u r e m e n t of the T h e r m a l Resistance IR Measurement For the IR measurement [49, 70] the infrared radiation from the surface of a semiconductor chip is detected using an IR microscope. Usually the detector in the microscope is liquid-nitrogen cooled. Since the IR emission of the chip depends on the emissivity of the different materials on the chip surface a calibration has to be performed prior to the measurement. The advantage of this method is that a profile of the chip surface temperature can be measured by scanning the measured spot over the chip surface. The spot is approximately 25 /zm in diameter. The measurement takes place as follows: • The chip is heated uniformly to certain temperatures. The corresponding calibration profiles of the detected IR radiation are measured and stored in a computer. These profiles are a measure of the emissivity of the chip surface at a certain point. • In the measurement step the heat sink is kept at a fixed temperature (generally the ambient temperature). The active device is biased and the IR-radiation profile is measured. Comparison with the data of the calibration step yields the temperature profile.

Liquid-Crystal Measurement The technique of measuring the temperature distribution of a hot surface by liquid crystals [49, 54, 83] uses the fact that the molecules of liquid crystals are aligned if the temperature is less than the isotropic temperature. At higher temperatures the molecules are disordered. For the measurement a thin film of liquid crystals is spun onto the surface to be measured. The film has to be as thin as possible since it improves the thermal conductance. The surface of the sample is illuminated with polarized light. A second polarizer is placed in the path of the light reflected from the device under test. Before the measurement the second polarizer is rotated such that an uncovered surface appears black. A part of the light is passing through the system, if the coated sample is colder than the isotropic temperature. This is accomplished by the liquid crystals which work as an additional polarizer. Spots on the surface above the isotropic temperature appear dark because no additional polarization is produced by the liquid crystals. This technique is useful to detect hot spots on the surface and to determine the thermal resistance of a device. For this purpose the device

156


is biased until the isotropic temperature of the device is reached. The temperature difference between isotropic and heat sink temperatures divided by the dissipated DC power yields the thermal resistance.

Electrical Measurement The temperature of a device can also be determined by an electrical method in which a temperature-dependent characteristic of the device is used as a temperature sensor. This may be the temperature-dependent current-voltage characteristic of a Schottky diode [83] or the resistance of the gate metallization [22a, 23], in the case of a MESFET. For bipolar devices the temperature dependent base-emitter voltage needed to maintain a certain collector current is proposed [3a]. The measurement is performed as follows: • For the calibration the device under test is heated uniformly in an oven to a certain temperature. The temperature-dependent electrical characteristic of the device is measured with short pulses. The data of this measurement are stored. • In the measurement step the heat sink temperature is kept constant and the device is biased for normal operation. This bias condition is interrupted for short periods in which the temperature-dependent electrical characteristic is evaluated. Comparison with the calibration data yields the temperature of the device under operation conditions provided the interruptions for the measurement are short enough. This method can be used to determine the thermal resistance of a device.

6. Thermal Enhancement Techniques A schematic drawing of a microwave device inserted into a package with a conductive, convective, and radiative cooling possibilities is illustrated in Figure 5. Also indicated are the respective conductive thermal resistances of device, solder chip carrier, package, finned heat sink, etc. The total thermal resistance can be obtained by means of the equivalent circuit. For a detailed analysis the interfacial effects among the different materials have to be included: 1. gap between two materials increases Rth and 2. mismatch of energy bands in the momentum space yields an increased R th due to reflection of phonons at the interface even in singlecrystal transitions.


I S7

q Rc chip

Rc solder

Rc pack.

Rcl

Rc2

U U Ta= Temperature of Air

Ta

Ta

To

Figure 5. Schematic drawing of a packaged device with a heat sink and the equivalent thermal circuit for steady-state heat transfer. chip

flip- chip

embedded

A

ftatpack

0

X

1000 ~_

..-

100 8 C 2

10-

~

1

E

0.1

"

,, cooting

-

~ w o t e r ~

"

~,_

= -

'=

~

=

microchonne[ cooting

±

forced air cooting- air s t r e a m vetocity [ m / s ] forced water, cooting, water, vetocity [0.1m/s] micr'ochannet cooting, water" pressure drop[psi] Figure 6. Comparison of calculated thermal resistances of chip devices, flip-chip mounting, embedded mounting, and a flat-pack package for different cooling methods.

The thermal resistances can be calculated according to the following formulas due to conduction, Rcona, convection, Rconv, and radiation, Rrad"

Rc°nd =

1 kS

1 Rc°nv = -

hcA s

T 1 -- T~

Rrad=

o'AF12(T 4 _ T4)

.

(28)

158


The expression for R r a d gives the thermal resistance of a radiating body at temperature T 1 surrounded by a black surface on temperature T2 [42]. T~ is a reference temperature [Equation (10)] which is needed in the equation of the transferred heat:

qrad--

1 W---( T -

1-

T~).

(29)

r'rad

TABLE 8 Thermal and Electrical Properties of Metals at Room Temperature k Material

a

w ) ( 10.6

Ag 430 A1 204-240 Au 315-345 40%Au-60%Pt 26 10%Au-90%Pt 76.3 97%Au-3%Si 27 80%Au-20%Sn 57 Brass, 7 0 % C u - 3 0 % Z n 81-116 Constantan, 60%Cu-40%Ni 22.7 Cr 68.8 Cu 380-398 In 82 Mg 171.3 Mo 130-146 Ni 90 NiFe 15 Pb 30-35 Pb-5%Sn 63 50%Pb-50%Ti 46 Pd 71.2 Pt 73 Sn 30 Steel = 50 Ta 54.4 Ti 22.6 W 150 Zn 113

p

co

pd kg

x g-

( × 10-6~ cm)

18 25 14.3

1.6 2.6 2.4

234 900 130

10.5 2.7 19.3

5.2

385 410

8.5 8.9

385

12.3 15.9 17.5 14 4 17 33 4 13 4.14 29 29 29 11 9 23 12 4.5 9 4 29

13 1.7 8.2

( Ws

4.8 1.75

1013 250 450

8.95 7.3 1.74 10.2 8.9

25

130

11.34

10.66 10.66 13 15.65 47.6 5.5 11.5

180 243 134 230 460 151 489 133 385

12 14-19

16.6 4.5 19.3 7.3

159


In the example of Figure 5 T2 is the temperature of the plane opposite to the finned heat sink. T~ may be chosen as the temperature of the surrounding air (T~ = Ta). Each of these resistances can be individually minimized in order to facilitate the heat flow from the device active region to the surrounding area. An example of the determination of the overall thermal resistance of a similar structure has been developed by Donzelli [18]. Improvement of

TABLE 9 Thermal Properties of Insulators at Room Temperature k

Material

AIN 90% A1203 99% A1203 BeO BN Diamond D- MAT 6 D-450 b Epoxy 70% SiO 2 Epoxy glass Glass Glass/ceramics Polimide P T F E 6002 c Quartz Sapphire SiC (poly) Si3N 4 SiO 2 S-145 b TiO 2 Triazine

(w) 70-320 16.7-20 25-37 150-370 500-1300 2200 8.8 4.18 0.2 2 = 0.76 0.3-5 0.07 0.44 1.4 42 40-270 25-30 1.4 34 7 0.2

a

Cp

pd

10-6) (Ws) (

× ~

k-~

2.56-4.5 6.7 6.3-8 5.4-8.5 4.8 1.0 8.2 2.9 20 15 0.4-0.6 3.0 50 24

736 770 770 1020 498 6200 837 821

3.3 3.9 3.9 2.9 5.4 3.5

837 728

2.71

6 3.4 0.8-30 0.5 12.8 7.5 50

930 780 620 170 1400 967

× 103m-5-

TDLQ a

w) 0.087-0.82 0.067-008 0.29-0.49 0.4-1.55 1.59-4.14 0.036-0.056 0.026

0.004-0.145 0.0014 3.98 3.2

0.41-0.5 0.0002-0.0016

4.24

0.19 0.00017

Note. For details, see Kurokawa [45], Werdecker [84], McGillivray [52], Koba [39], and Miyashiro [55]. aTDLQ is the thermal dielectric loss quotient: T D L Q = [ k ( W / m • K)]/[8.854 ( p F / m ) •r tan ~ • 104]. bRegistered trademark of TRANS-TECH, Inc. CRegistered Trademark of Rogers Corp.

160


the thermal resistance of the semiconductor chip can be obtained by the following: • applications of a substrate material with higher thermal conductivity for example, InP instead of GaAs, or GaAs grown on Si; • thinning of the chip, via holes [15, 25], flip-chip mounting [83], or plated heat sinks [74]; and • appropriate thermal device design [17, 18, 26, 28, 36, 75]. The thermal resistance of the solder can be optimized by increasing the effective contact area and solder thickness. Further discussion is included in the review paper of Fletcher [24] and in the contributions of

TABLE 10 Electrical Properties of Insulators at Room Temperature er Material

AIN 90% m 1 2 0 3 99% A120 3 BeO BN Diamond D - M A T (a) D-450 (a) Epoxy 70% SiO 2 Epoxy glass Glass Glass/ceramics Polimide P T F E 6002 (b) Quartz Sapphire SiC (poly) Si3N 4 SiO 2 S-145 (a) TiO 2 Triazine

8.8-9.1 9.4 8.5-9.8 6.7 7.1 5.5 8.9-14 4.5 3.8 4-5 3.8-7 3.9-7.8 3.5-5 2.94 3.8 9.4-11.6 40 6 ~ 10 10 85 3.1

Emax

p

~ cm

(f~ cm)

( × 10 -4)

0.14-0.17 0.2 0.2 0.1

5.0- 1013-1.0 • 1014 > 1.0. 10 TM > 1.0. 10 TM > 1.0. 10 TM ~ 1.0" 1013 1.0-1020 > 1.10 TM = 1.0- 10 TM 4 • 1016 1.0 • 1011

5-10 3 1 5 5

(Mv)

10 0.08 0.08

tan

< 2 < 4

1 1.0.1016 = 1.0. 101° 10 4 0.0007

0.08

> 1.0 • 10 TM 1.0" 1016 1.0" 1014 > 1.. 10 TM

12 1 500

< 2 40

>__ 1.0. 1013

Note. For details see Kurokawa [45], Werdecker [84], McGillivray [52], and Koba [39]. aRegistered trademark of T R A N S - T E C H , Inc. bRegistered trademark of Rogers Corp.

161


Pavio [63] and Prior [65]. The package thermal resistance has a large influence on the overall thermal resistance as has been indicated by Pence [64], Le Jannou [47], Ohsaki [60], Tummala [78], Wesseley [85], Ortega [61], Ozmat [62], Harkins [32], Estes [22], and Handa [31]. The convective heat transfer can be improved by the following: • • • plate •

forced convection instead of natural convection [32]; optimization of the dimension of the fins [19, 79]; utilizing two-phase convective heat transfer by using heat pipes or pipes [14, 38, 76, 87]; and optimization of the cooling agent (water, liquid nitrogen, etc.)

The heat transfer by radiation can be improved mainly by the proper choice of the surface of the radiator in order to achieve a high emissivity, e. Also the allowance of a higher surface temperature (higher active device temperature) yields a lower thermal resistance.

TABLE II Electrical and Thermal Properties of Semiconductors at Room Temperature

k Material

Bi2Te 3 GaAs GaN GaP GaSb Ge InAs InP InSb PbTe Si a-SiC /3-SIC

W

a

10-6)

•

× ---U0.2 46 150 77-110 33 60 26 70 12 0.4 148 500 500

Emax

c--~

4.5-6.63 5.6 5.3 6.7 5.7 5.19 4.56 5.04

13.1 9.5 11.1

0.6

16 12.55 12.35 17.7

1.0

2.6 5.5 5.5

11.9 9.7 9.7

0.5 4.0 4.0

5.0

Cp

p

ws t 325 487 436 255 310 252 310 207

5.32

710

2.33

5.32

Note. For further details, see Brice [7] (GaAs), Brice [8] (InP), Sze [73], Miiller [56], ( I I I / V compounds), Neuberger [57] ( I I I / V compounds), Johnson [34] (thermal expansion), and Matus [50] (SIC, GaAs, and Si, diamond).

162


10 ,---., oO

E •¢

,--._,

1 ~

>,, th cE]

-

0

2

0.1

0.01 100

1000

Temperoture[K] Figure 7. Density of gases as a function of temperature. TABLE 12 Thermal Properties of Solders T

Solders

Composition

(°C)

Ag Cu Au Ge Au In Au Si Au Si Au Sn Au Sn Au Ti Pb Ag Pb In Pb In Pb Sn Pb Ti Ag Pb Ti Ag Pb Ti Ag Ti Ag

72-28% 88-12% 82-18% 96.4-3.6% 94-6% 80-20% 71-29% 80-20% 97.5-2.5% 95-15% 81-19% 90-10% 92.5-5-2.5% 97-1-1.5% 93-5-2% 96-4%

780 E (a) 356 E (a) 415-485 370 370 280 E (a) 278 280 303 E (a) 292-314 270-280 275-302 300 309 280 221

k W

( 1°-6 t

27

12.3

57

15.9

25.53

(a) E, eutectic temperature.

The simulated results for the thermal resistance for a number of packages are illustrated in Figure 6. It can be inferred from this figure that flatpack packages are efficient for forced air and water cooling, whereas

163


the bare chip exhibits the lowest thermal resistance in the case of microchannel cooling. Pence [64] also gives closed form expressions for the thermal resistance for each cooling method.

7. Thermal Properties of Electronic Materials The thermal and electrical properties of metals, semiconductors, insulators, and substrate materials are summarized in Tables 8-11 for room temperature. The quantity TDLQ in Table 9 determines the measure of suitability of isolating materials for applications in microwave circuits. Insulating materials with high thermal conductivity, low loss, and low capacity yield high values of the TDLQ. From the parameters given in Tables 8-11 and Figure 7 the thermal diffusivity can be determined directly. The thermal properties of solders are given in Table 12 The consideration of the different expansivities (see figure 8) of the various materials is of paramount importance for device design [65, 69], device and circuit attachment [63, 65], material fabrication [35, 69], and package design [12, 55], because of the stress introduced if materials with different expansivities are attached together.

.--.

20 18

~"

16

b

~-x

........-

-"

Cu

.........-

.....-

12 10

BeO

o tO 13. X

i,i

/.,

~ / A l t o y / , " |

100

I

200

i

I

3o0

i

I

~00

2

i

"~ SiC I

,

500

1

600

i

I

|

700

Temperature [K] Figure 8. Expansivity of different materials as a function of temperature.

800

164


References S. Adachi, J. Appl. Phys., Vol. 53, pp. 8775-8779, 1982. S. Adachi, J. Appl. Phys., Vol. 54, pp. 1844-1848, 1983. S. Adachi J. Appl. Phys., Vol. 58, pp. R1-R29, 1985. M. G. Alderstein, and M. P. Zaitlin, IEEE Trans. Electron Dev., vol. ED-38 No. 6, pp. 1553-1554, 1991. [4] D. Agonafer, and S. Furkay, 6th Annu. IEEE Semicond. Therm. Temp. Meas. Symp., SEMI-THERM, Phoenix, AZ, p. 103, 1990. [5] R.A. Baker, and A. Sesonske, Nucl. Sci. Eng., Vol. 13, 282, 1962. [6] J. P. A. Bastos, N. Sadowski, and R. Carlson, IEEE Trans. Magn., Vol. MAG-26, pp. 536-539, 1990. [7] J.C. Brice, in Properties of GaAs, 2nd Ed., pp. 1-25. London: INSPEC, 1990. [8] J. C. Brice, A. D. Prins, S. Adachi, K. Haruna, D. J. Dunstan, and H. Maeta, in Properties of InP, pp. 3-23, London: INSPEC, 1991. [9] R.B. Brooks, and H. P. Mattes, Bell Syst. Tech. J., Vol. 50, pp. 775-784, 1971. [10] R. A Brow, T. A. Kinney, P. A. Sachinger, and D. E. Bornside, J. Cryst. Growth, Vol. 97, pp. 99-115, 1989. [11] L. Buller, and B. McNellis, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-4, pp. 538-544, 1978. [12] R. Chanchani, and P. M. Hall, IEEE Trans. Components Hybrids Manuf. Technol. Vol. CHMT-13, pp. 743-750, 1990. [13] N. P. Cheremisinoff, Heat Transfer Pocket Handbook. Houston, TX: Gulf Publishing Co., 1984. [14] P.V. Ciekurs, and W. D. Brokaw, Microwaves RF, Vol. 27, pp. 83-88, 1988. [15] O. P. Daga, K. Fricke, and H. L. Hartnagel, J. Electrochem. Soc., Vol. 133, pp. 2660-2661, 1987. [16] R. Darveaux, I. Turlik, L.-T. Husang, and A. Reisman, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-12, pp. 663-672, 1989. [17] J. Dell, T. S. Kalkur, Z. Meglicki, A. G. Nassibian, and H. L. Hartnagel, (1984). Int. J. Electron., Vol. 57, pp. 155-160, 1984. [18] P. Donzelli, G. Ghione, and C. U. Naldi GaAs '90, Gallium Arsenide Appl. Symp., Rome, pp. 120-125, 1990. [19] G.N. Ellison, IEEE Trans. Parts Hybrids Packag., Vol. PHP-4, 371-378, 1976. [20] G.N. Ellison, IEEE Trans. Parts Hybrids Packag. Vol. PHP-4, 517-522, 1979. [21] ESA, Spacecraft Thermal Control Design Data, Vol. 1. Nordwijk, Netherlands: ESTEC, ESA Publications Div., 1989. [22] R. C. Estes, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-15, pp. 843-859, 1992. [22a] D. B. Estereich, 5th Annual IEEE Semicond. Therm. Temp. Meas. Symp. San Diego, CA, Feb. 7th-9th, 1989. [23] W. Fallmann, H. L. Hartangel, and P. C. Mathur, Electronl Lett., Vol. 7, pp. 512-513, 1971. [24] L. S. Fletcher, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-13, pp. 1012-1021, 1990. [25] K. Fricke, Die Optimierung des GaAs-Leistungs-MESFET unter Beeriick-sichtigung seiner verteilten Eigenschaften. Diisseldorf: VDI Verlag, 1989. [26] G.-B. Gao, M.-Z. Wang, X. Gui, and H. Morko~, IEEE Trans. Electron Devices, Vol. ED-36, p. 854-863, 1989. [27] G.A. Garfinkel, Circuit Des., Vol. 7, pp. 54-57, 1990. [1] [2] [3] [3a]


165

[28] G. Ghione, P. Golzio, and C. U. Naldi, Alta Freq., Vol. 57, pp. 311-320, 1988. [29] W. A. Gray, and ~r. Miiller, Engineering Calculations in Radiatiue Heat Transfer. Oxford: Pergamon Press, 1974. [30] A. Hadim, A. T. Chang, A. Chu, and A. Yskamp, Trans. ASME, J. Electron. Packag., Vol. 111. pp. 54-60, 1989. [31] T. Handa, S. Iida, and Y. Utsunomiya, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-16, pp. 384-387, 1993. [32] L . E . Harkins, and D. J. Nelson, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-15, pp. 761-770, 1992. [32a] R. K. Hoffman, Integrierte Mikrowellenschaltungen. Springer Verlag, 1983. [33] J.H. Holman, Heat Transfer, 3rd Ed. New York: McGraw-Hill, 1968. [34] R. W. Johnson, Final Rep. Workshop High Temp. Electron., Albuquerque, NM, pp. C3-C18, 1989. [35] A.S. Jordan, and R. Caruso, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-11, pp. 464, 1988. [36] W.B. Joyce, Solid-State Electron., Vol. 18. pp. 321-322, 1975. [37] S. Kaka~, R. K. Shah, and W. Aung, eds., Handbook of Single-Phase Conuectiue Heat Transfer. New York: John Wiley & Sons, 1987. [39] R. Koba, and W. A. Russell, Final Rep. Workshop High Temp. Electron., Albuquerque, NM, pp. C185-C210, 1989. [40] H. Kraussold, Forsch. Ingenieures., Vol. 4, pp. 39-44, 1933. [41] F. Kreith, Radiation Heat Transfer for Spacecraft and Solar Power Plant Design, pp. 204-229. Scranton, PA: Int. Textbook Co., 1962. [42] F. Kreith, Principles of Heat Transfer. New York: Intext Educational Publishers, 1973. [43] V. Krozer, "Verfahren der Kleinsignal- und Grossignalanalyse und Charak-terisierung von Mikrowellenschaltungen und Bauelementen mit Hilfe der Volterra Reihe," Ph.D. Thesis, Darmstadt, Germany, 1991. [44] H. Kuhn, Wiss. Z. Tech. Uniu. Dresden, Vol. 39, pp. 18-23, 1990. [45] Y. Kurokawa, K. Utsumi, H. Takmizawa, T. Kamata, and S. Noguchi, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-2, pp. 247-252, 1985. [46] J.H. Lau, Trans. ASME, J. Electron. Packag., Vol. 111, pp. 312-320, 1989. [47] J. P. Le Jannou, and Y. Yuon, IEEE Trans. Components. Hybrids Manuf. Technol., Vol. CHMT-14, pp. 366-373, 1991. [48] W. Liu, and B. Bayraktaroglu, Solid-State Electron., Vol. 36, pp. 125-132, 1993. [49] H.M. Macksey, in GaAs FET Principles and Technology (J. V. DiLorenzo, and D. D. Khandelwal, eds.), pp. 257-278, Dedham, MA: Artech, House, 1982. [50] L.G. Matus, J. A. Powell, and J. B Petit, Trans. 1st Int. High Temp. Electron. Conf., Albuquerque, NM, pp. 222-228, 1991. [51] W.H. McAdams, Heat Transmission, 3rd Ed. New York: McGraw-Hill, 1954. [52] K. McGillivray, Final Rep. Workshop High Temp. Electron. Albuquerque, NM, pp. C163-184, 1989. [53] Y. J. Min, A. L. Palisoc, and C. C. Lee, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-13, p. 980, 1990. [54] M. Minot, "Auantek Application Note," ATP-1072/7-86, 1986. [55] F. Miyashiro, N. Iwase, A. Tsuge, F. Ueno, M. Nakahashi, and T. Takahashi, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-13, pp. 313-319, 1990. [56] G. Miiller, H. Jacob, in Landolt-B6rnstein, New Series (K.-H. Hellwedge and O. Madelung, eds.), Vol. 17d, pp. 12-17. Berlin: Springer-Verlag, 1984. [57] M. Neuberger, III-V Semiconduction Compounds. New York: IFI/Plenum Data Corp., 1971.

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[58] C.K. Ng, IEPS Proc. Tech. Conf., 9th Annu. Int. Electron. Packag. Conf., San Diego, pp. 530-534, 1989. [59] P . Y . C . , Normington, M. Makalingam, and T. Y. Tom Lee, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-15, pp. 806-814, 1992. [60] T. Ohsaki, IEEE Trans. Components Hybrids Manuf. Technol. Vol. CHMT-14, pp. 254-261, 1991. [61] A. Ortega, and H. Kabir, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-15, pp. 771-777, 1992. [62] B. Ozmat, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-15, 860-869, 1992. [63] J.S. Pavio, IEEE Trans. Microwave Theory Tech., Vol. MTT-35, pp. 1507-1511, 1987. [64] W. E. Pence, and J. P. Krusius, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-13, pp. 245-251, 1990. [65] C.J. Prior, and E. J. Crescenzi, Jr., Microwave J., Vol. 31, pp. 157-164, 1988. [66] S.N. Rea, and S. E. West, IEEE Trans. Parts Hybrids Packag., Vol. PHP-2, 115-117, 1976. [67] C.J. Ritter, Proc. Tech. Program, NEPCON East '89, Boston, 1989. [68] W.M. Rohsenow, Trans. ASME, Vol. 74, pp. 969-975, 1952. [69] B. S. H. Royce, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-11, p. 454, 1988. [70] F. N Seschi, B. S. Perlman, and J. M. Cusack, IEEE MTT-S, Int. Microwave Symp. Dig., p. 143, 1977. [71] E.N. Sieder, and G. E. Tate, Ind. Eng. Chem., Vol. 28, p. 1429, 1936. [72] J. R. Simonson, An Introduction to Engineering Heat Transfer, 3rd Ed. New York: McGraw-Hill, 1967. [73] S.M. Sze, Physics of Semiconductor Devices, 2nd Ed. New Delhi: Wiley Eastern, 1981. [74] G.C. Taylor, D. Bechtle, S. G. Lin, P. Jozwiak, and R. Camisa, Microwaves RF, Vol. 30, pp. 00-00, 1991. [75] G.C. Titinet, P. M. Scalafiotti, CSELT Tech. Rep., Vol. 18, pp. 37-41, 1990. [76] T. Y. Tom Lee, and M. Makalingam, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-15, pp. 778-785, 1992. [77] T.Y. Tom Lee, and J. A. Andrews, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-15, pp. 786-793, 1992. [78] R. R. Tummala, IEEE Trans. Components Manuf. Technol., Vol. CHMT-14, pp. 262-271, 1991. [79] D . W . Van de Pol and K. Tierney, IEEE Trans. Parts Hybrids Packag., Vol. PHP-10, pp. 267-271, 1974. [80] D. van Leyen, Wiirmeiibertragung. Berlin: Siemens AG, 1971. [81] VDI, VDI-Wiirmeatlas. Diissseldorf: VDI-Verlag, 1963. [82] A. Virzi, J. Cryst. Growth, Vol. 97, pp. 152-161, 1989. [83] S. H. Wemple, and H. C. Huang, in GaAs FET Principles and Technology (J. V. DiLorenzo, and D. D. Khandelwal, eds.), pp. 309-349. Dedham, MA: Artech House, 1982. [84] W. Werdecker and F. Aldinger IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-4, pp. 399-404, 1984. [85] H. Wessely, O. Fritz, M. Horn, P. Klimke, W. Koschnick, and K. H. Schmidt, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-14, pp. 272-284, 1991. [86] I. Witte, Wiss. Z. Tech. Univ. Dresden, Vol. 39, pp. 23-26, 1990. [87] S.M. You, T. W. Simon, and A. Barcohen, IEEE Trans. Components Hybrids Manuf. Technol., Vol. CHMT-15, pp. 823-831, 1992.

CHAPTER

7 Microwave Antennas John Hill and Mary Lynn Smith

The

necessary length of this chapter precludes extensive treatment of any one antenna subject. The objective is primarily to direct the reader to sources of detailed theory and design information. Thus this chapter provides a very broad view of microwave antennas. The material is organized to follow the outline of a generic antenna specification. A microwave antenna has been arbitrarily chosen to be an antenna with an operating frequency higher than 1 GHz or with a wavelength of 30 cm (11.8 in.) or less. An upper frequency has not been reached, although the FIRST (far infrared and submillimeter telescope) antenna is being designed for the 300- to 3000-GHz frequency band. The first microwave antenna may have been a cylindrical parabola with a spark-gap-driven dipole at the focal point, built by Heinrich Hertz in the 1880s. Following this, little work was done at microwave frequencies until the 1930s, when the beginnings of World War II created the conditions which fostered the development of radar. By 1947, when Microwave Antenna Theory and Design [1] was published, the principles of most antennas in use today had been established. The 45 ensuing years have seen the refinement of those early designs and the development of the wide-band frequency-independent antennas (spirals and log periodic dipole arrays) and the narrow-band transmission-line antennas (microstrip patch) and the phased array. An antenna engineer given a sleeping potion in 1947 and awakened in 1995 would have little trouble understanding current antennas. He would,


167


168

Hill and Smith

however, be amazed by the test equipment and the amount of antenna literature available. See the bibliography for a list of publications found to be valuable in the daily work of antenna design.

I. A n t e n n a Defined An antenna is a transducer which converts electromagnetic fields in space into current on a transmission line, converts current on a line to an electromagnetic field, or both. The purpose of an antenna is to transmit RF energy in a defined direction or to receive RF energy from a defined direction. Often the same antenna is required to do both.

Antenna Requirements and Specifications For the purpose of this discussion, an antenna requirement is the performance desired by the buyer. An antenna specification is the description of an antenna and its performance for the purpose of selling. Antennas are unique when compared with most other microwave devices. They are one-port reciprocal devices from the point of view of bench testing, for their second port is accessible only with a very special measuring tool, the pattern range. Impedance characteristics and power capability are tested in the transmit mode. Pattern characteristics are usually measured in the receive mode even when the antenna is to be used to transmit. An antenna's performance is determined by its physical structure and by its location. The step-by-step definition of an antenna requirement/specification is a convenient method of introducing antenna principles. An antenna requirement/specification will contain most of the following parameters. Following sections will treat the definitions in more detail. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13.

Frequency Beamwidth Directivity Gain Polarization (of an Antenna) Sidelobes Squint Voltage Standing Wave Ratio (VSWR) Power Handling G/T Site Environment Special Terms

7. Microwave Antennas

169

Each subject will include some or all of the following: a. b. c. d. e. f. g.

Definition Units Related terms Measurement accuracy Significance Comments References

A requirement or specification implies that the parameters defined can be verified by testing and that the test results are accurate enough for the purpose intended. Because the measurements of an antenna's characteristics are often complex, a test procedure is an important adjunct to the specification, and it is the test procedure, rather than the specification, which usually determines an antenna's acceptance. Acceptance criteria are very significant when an antenna is required to perform in a complex environment such as a ship, aircraft, missile, or spacecraft. An antenna requirement should have some basis in reality. It is recognized that advances come about through attempts to meet difficult requirements, but unrealistic expectations lead to frustration on both sides. "A man's reach should exceed his grasp," but not beyond nature's limits. Thus many of the following approximations serve to define the possible and help the system engineer avoid the unobtainable. Frequency

The frequency range over which all of the other parameters apply. Units: Gigahertz Related terms: F h = highest frequency and F 1 = lowest frequency Bandwidth = F h / F 1 = 2 / 1 = octave Percentage bandwidth = ( F h / F 1 - 1)100 Center frequency = C F h X F 1 To divide a frequency range, F~ to F h into rl subbands of equal ratio, 1 . In swept frequency measurements the points within the sweep are usually not critical. Beginning and ending frequencies should be set with care. The number of points in the sweep (when using a synthesized source) should be sufficient to reveal all the peak values. Significance: Frequency is the first antenna requirement to be established and may result from factors external to system design. The performance of broadband antennas, for which bandwidth is 50% or greater, is not particularly sensitive to frequency. Microstrip patch antennas and waveguide slot arrays, however, with a bandwidth of 5% and less, must be tested at exact frequencies.

x" x = '~/F h / F

170

Hill and Smith

Comments: The majority of microwave antennas operate at frequencies of 1 to 18 GHz, with diminishing usage from 18 to 40 GHz. Above 40 GHz the horn is the most practical device, as other types become difficult to fabricate. Any type requiring coaxial lines above 18 GHz becomes impractical, although coaxial connectors to 65 GHz are available. Beamwidth

Usually taken to be the half-power beamwidth, the angle between the two directions in which the amplitude of the major lobe is one half the maximum value. Usually two orthogonal beamwidths (such as vertical/ horizontal and E p l a n e / H plane) are defined, with maximum and minimum values. Figure 1 illustrates beamwidth and other pattern characteristics. Figure 2 is the standard spherical coordinate system used in antenna measurements. Units: Degrees and decibels from peak Related terms" Principal half-power beamwidths, E plane, H plane, radiation pattern, and free space Measurement accuracy: Beamwidth is measured at the two intersections of the pattern trace and the reference level. Two factors are to be considered: the accuracy of the positioning and recording equipment and the accuracy of reading the data. If beamwidth is manually read from a

3 dB BEAMWIDTH

I1|! llll III1! I|1| IIII 1

'~II Ii,,i I

]

'°III11!oJAL,oL ,ll ",olllIII ,R,i~[l:J ii

t

.... ................ .[... I .... I I.... I .... I .... I I.... I .... I ................. ,I"

L

G, UN

t

t 1

ISOTROPIC LEVEL

°i~

~l~!

I~

ill r r!,t.... I/t

_,~,"~ ....=........,,,,~,,~"......[ 11I..l,.v,............ I ..................L.. II~ ................L............!t i -180

-150

-:120

-90

-60

o -30 AZIMUTH

~o

do

CI e g r e e s

Figure I. Pattern characteristics,

90

/...........,t/,,,I t ....

~o

150

|

180

171

7. Microwave Antennas O:O e

Z

0

=

90" 27'0"

" ' ~ ~.

v 0=90" 11, - 90"

0:90" ÷:o"

~

/

o : 180"

Figure 2. Standard spherical coordinate system.

pattern plot, accuracy is about 10% of the beamwidth. If determined with automatic equipment, accuracy may be about 5% of beamwidth. Significance: Beamwidth defines the capability of the antenna in directing transmitted energy in a desired direction or its ability to receive or reject waves from different directions. An antenna of narrow beamwidth and low side lobes may be considered a spatial filter. An antenna with very narrow beamwidth must be pointed accurately in order to derive benefit from the higher gain. Comments: Common beam shapes are pencil beam; fan beam; cosecant squared beam; monopulse beam; conical scan beam; cardiod beam; dipole pattern; isotropic pattern (omnidirectional).

Directivity The ratio of the maximum radiation intensity in a given direction to the radiation intensity averaged over all directions. (In the following discussion it is assumed that an antenna is a reciprocal device; therefore transmitting and receiving cases are interchangeable and equivalent. For further reading on reciprocity, see Reference [2].) Directivity is a measure of an antenna's radiation intensity in a particular direction and is the ratio of that radiation intensity to the average intensity over a sphere. Directivity is usually expressed in decibels

172

Hill and Smith

Figure 3. Directivity defined by power flow. (A) Power flow through a convenient spherical boundary, (B) power flow through a square area of I square degree, and (C) power flow through a circular area of 4 square degrees.

above isotropic and does not include efficiency factors such as ohmic and mismatch losses. Directivity is related to beamwidth. Assuming that a significant amount of radiated power is not diverted into minor lobes, directivity is inversely proportional to beamwidth. A simplified approximation of directivity may be found by considering a spherical boundary at which the power radiated by a directional antenna may be measured. All power may be imagined to flow outward and through the surface shown in Figure 3A. This surface may be divided into areas each occupying 1° in the vertical plane and 1° in the horizontal plane. The total surface of a sphere contains 41,253 square degrees, 360 2 4rr square radians (steradians) = 4rr - ~ = 41,253 square degrees. If all the power radiated flows through 1 square degree, as shown in Figure 3B, the directivity in that direction would be 41,253 times greater than if the power flowed equally through the surface of the sphere, which is the case with an isotropic, or point source radiator. The directivity, D, is then D=41,253/1

and

DaB= 101og10D=46dB.

A somewhat more accurate approximation of directivity from the pattern assumes that all power flows through an area which is circular in cross section, as in Figure 3. The area of a circle inscribed in the square is 4~r of the square area; therefore the resulting directivity is D = (41,253/®1®2)'47r = 52,525/191192,


173

where 1~102 are the measured orthogonal beamwidths of the pattern DaB = 10 log10 52,525 = 47.2 dB.

In practical antennas, the beam is usually circular in cross section with many minor lobes and with the beamwidth measured at the - 3 - d B points. To account for this the assumption is made that 55% of the power radiated flows through the half-power beamwidth of the main lobe. The directivity is now approximated by DdB -- 10 log10 2 9 , 0 0 0 / O 1 0

2.

This is an approximation, but useful for estimation. Table 1 lists other useful approximations relating beamwidth, gain, and directivity for parabolas, horns, and arrays. TABLE I Formulas for Beamwidth and Directivity of Representative Aperture-Type Antennas Aperture

Aperture type

illumination

Beamwidth

efficiency (%)

(from aperture)

Directivity (from aperture)

100

O -

Uniformly i l l u m i n a t e d linear array

100

O1=

a

beamwidth)

10a 2

58A Uniformly i l l u m i n a t e d circular aperture (hypothetical)

Directivity (from

D -

~2

Sidelobes (dB)

52,525 D-

02

-18

,O

51A -13

a

16ab D -

?b,t

A.2

41,253 D-

O10 2

51A 02-

b 56A

Rectangular horn

60

-13

01 aE

E plane

8aEa H

D

/~2

D=

31,000 O102

67A H plane ~-ah--~

60

- 26

0 1 -aH

5a 2

72A Nonuniformly illuminated

55

0 -

a

D -

h2

29,000 D-

circular aperture a>>A Source. Courtesy of Watkins-Johnson Co. [6].

DdB = 10 log10 D

02

- 26

174

Hill and Smith

Directivity, D O

0 = 0°

0 = 90 °

0 - 900

001

~ 0o

0 = 180 ° Figure 4. Broad beamwidth antenna pattern.

For broad-beamwidth antennas, such as satellite terminal antennas, with beamwidths on the order of 100 ° to 280 °, the simple pencil-beam approximations yield pessimistic values of gain. For these antennas, with patterns similar to those of Figure 4, the graph of Figure 5 is useful. The graph was prepared from the equation [3]: {~ -{- COS - 1

[(1

+ k

-

2~Do)~(1

-

k)].

Gain

Gain is simply directivity reduced by antenna dissipation losses. Gain and effective area: Gain, G, to be precise, is defined for the transmitting case and effective area, Ae, for the receiving case. The properties are related by G = 4~'Ae/A 2 or

A e = GAZ/41r.

In practice, the distinction is generally ignored. Units: Isotropic decibels (dBi) for gain with respect to the theoretical isotropic source of like polarization. Frequently, the letter 1 or c is added to dBi to indicate the polarization (i.e., dBic for gain with respect to the

175


Beam SemiAngle 8o

Imllm/limlmml

140° ~1~ 13°°

120°

11o°

.o

Backlobe

• 1O0°

90 °

-20 dB -15d

/

•

-

8o °

70° -10 dB

~ ,

-,,,,

6o °

50°

o

I 1 1

1 I J 1

2

I I 1

3

1 I I

4

1 1 ! I 5

Gain (dB) Figure 5. Directivity versus beam semiangle for broad beamwidth antennas,

isotropic source of circular polarization and dBil for gain with respect to the isotropic source of linear polarization). Related terms" Partial gain, realized gain, directivity, and effective area Measurement accuracy: The measurement of gain is probably the most difficult of all antenna measurements. It is an indirect measurement with a number of variables. With extreme care and attention to detail, + 0.25 dB is achievable. The standard gain antenna substitution method is usually used. The three-antenna method is also used. Refer to References [2] and [4], Microwaue Antenna Measurements, for a more detailed discussion of gain measurement methods. Measuring the gain of circularly polarized antennas adds another dimension of difficulty, for there is no circularly polarized standard gain reference. A method often used is to measure the gain of the antenna with reference to two orthogonal linear

176

Hill and Smith

polarizations, O1 and

~2" Gain

is then

G = (Gol + G o 2 ) / 2 .

Significance: Gain defines the capability of an antenna in a communications link. Directivity defines the antenna's ability to reject waves from other than the desired direction. Comments: "Gain" in a specification usually refers to the gain of the antenna in the direction of maximum radiation for matched polarization, yet the performance of interest is partial realized gain, for a stated polarization, in a stated direction. This is the parameter of interest to the systems engineer. To obtain this value, it is important to specify the point in the system at which the gain is to be defined. This point is usually at the connector nearest the antenna, whereas the gain from the system point of view is at the input to the receiver or output of the transmitter. References: Gain is discussed in most antenna books. Kraus [5] is recommended. For a simplified explanation, with minimum mathematics, see Reference Hill [6].

Polarization (of an Antenna) In a given direction, the polarization of a wave radiated by an antenna or the polarization of a wave which produces maximum power at a receiving antenna's terminals. Units: Decibels for polarization ratios and ' ellipticity; degrees for orientation of polarization ellipse; and right or left hand for sense Related terms: Elliptical, circular, right-hand circular, left-hand circular, linear, vertical, horizontal, slant linear, copolarization, cross polarization, axial ratio, and dual polarization Measurement accuracy: (a) Right-hand/left-hand circular: A right or wrong measurement and easily gotten wrong. The surest method is to test against a circularly polarized antenna of unmistakable polarization such as a spiral or helix. (b) Axial ratio: Easily tested with a rotating linear source antenna. Make sure that the antenna does not spin too fast for the recording system. The source must be truly linear and not elliptically polarized. (c) Tilt of ellipse: A factor of the mechanical accuracy of the positioning system and of the precision with which the plot can be read Significance: Varies with application, but in general the antenna's polarization requirement stems from a system requirement. Comments" Polarization can be the most complex of an antenna's characteristics. In the coupling of energy between antennas the polarizat i o n / g a i n factor is the essence of the link, yet the polarization aspect is often inadequately considered in the procurement requirement. All polarization is elliptical, with major and minor axes. The ellipticity is defined in


177 TABLE 2 Polarization Mismatch Loss Equations

{5

{

Ellipse Ellipse

-101oglo{1/2 + 1/2

4TTTR+ ( 1 - - y 2 ) ( 1 - - T 2 ) ( C O S 2 / 3 ) ] t , (1 + 7 2 ) ( 1 + 7 2 )

]/

0 Ellipse (

)

Linear

+7 2) - 1 0 1 O g l o { 1 / 2 - 1 / 2 [ ( 1-72)(c°s2/3)])(1

(1)

(2)

/

{5

Ellipse {

Circular

-10log10 1 / 2 + 1/2

(1 + y 2 )

(3)

®

\ Linear Linear

-10log m 1 / 2 + 1/2

[ (co~,

(4)

/

\ Linear Circular

{

-10log10 1 / 2 - 1 / 2

O.

® Circular Circular

[°1) ~

= +3dB

= 0 d B when 7T¢ = 7R¢ --1010810{1/2 + 1/2(YTCYRC)} = + ~ dBwhen Yvc = --7RC

(5)

(6)

®

Note: Equations (1) through (6) are from Air Force Test Range Technical Report AF WTR-TR-65-1, by Benhring W. Pike, P. E. 7 = ellipticity ratio, the signed voltage ratio of the major axis of the polarization ellipse to its minor axis, where (1 > 171 > ~); /3 = polarization mismatch angle (0°>/3 > 90°); T, transmitting; R, receiving; E, elliptically polarized; C, circularly polarized. Source. Courtesy of Watkins-Johnson Co. [8].

terms of the voltage axial ratio: ar - Ema x / E m i n

or, in decibels,

AR = 20 lOgl0 (ar).

Table 2, from Reference [5], lists equations for computing polarization mismatch loss.

Circularly Polarized Antennas Circularly polarized (CP) antennas are generally more complex than those designed for linear polarization. CP antennas may be divided into two categories.

178

Hill and Smith

a /

,~

eix

~

Horn with

Dielectric Phasor

Diploe ossed 8lot In Wavegulde

Y

al Spiral

••Horn

with

~ ~

/

M(~:rnidee~ line r Spiral Cavity Back

~"

b

o

~ybpd r Crossed Log-Periodic Dipole Array

I I RH LH Circular Polarization

I Dual-Polarized Quad-Ridged Horns

d ler I

LH RH Circular Polarization

Figure 6. Category I antennas (a). Category II antennas (b),

Category I antennas are those which are circularly polarized by virtue of the structure of their radiating aperture, exemplified by such types as spirals and helices. Their polarization cannot be changed except by changing the structure. A variety of category I antennas are illustrated in Figure 6a. Some of the antennas shown in Figure 6 show a sense of polarization that is obvious from the structure. It is not always obvious from the external appearance of a CP antenna that it is circularly polarized and


179

what is the sense of polarization. However, those antenna illustrations not showing a defined sense of circular polarization indicate that the polarization sense is determined by factors not easily depicted in the diagrams. Category II antennas, illustrated in Figure 6b, usually consist of orthogonal elements, the outputs (inputs) of which are combined in phase quadrature. An example is the dual-polarized horn with an external 90 ° hybrid coupler. This type is capable of producing both right-hand and left-hand circular polarization simultaneously. With additional circuitry, six polarizations can be produced, as illustrated in Figure 7.

90 °

Hybrid Coupler

Ii

II 180 o Hybrid Coupler

o

.-

O3O ~ f-

I

Transmitter or Receiver

Transmitter or Receiver

E V =Vertical

Slant ~ ~ Left ~ , ~ R i g h t

E

R~

Left Circular

Slant

PEH=Horizontal I

Figure 7. Dual-polarized antenna with external circuitry to produce six polarizations,

180

Hill and Smith

Polarization and Space Diversity With complex propagation paths, for which the characteristics of the field at a given point are difficult to assess, a diversity receiving antenna system may be useful for reliable communication. Diversity may be of different types: space diversity, in which two antennas are separated by several wavelengths, and polarization diversity, in which a multimode antenna or two antennas of orthogonal polarization are used. References: For further reading on polarization, see References [7-101. Sidelobes Radiation pattern lobes other than the primary lobe, or the main lobe Special definition: Where the main beam shows slope reversals, a side lobe is presumed to exist if the reversal is 2 or 3 dB deep. Refer to Figure 1. Units: Decibels, usually with respect to the peak of the main lobe Related terms" Minor lobes, shoulder lobes, coma lobes, and back lobe Measurement accuracy: Depends upon the linearity/dynamic range of the measurement system and the test environment. For high-level sidelobes near the main beam, expect _+0.5 to 1 dB of accuracy. For far-out and low-level sidelobes more than 30 dB below the main beam, assume that the levels are essentially undefined unless special care has been taken with the measurement. Significance: In collimating antennas, such as reflectors and arrays, the location and magnitude of the sidelobes reveal phase and amplitude discrepancies. Basically, energy in sidelobes is wasted. In ground-based satellite communication antennas, sidelobes are a source of noise and impacts G~ T. Comments: In directional antennas, sidelobes serve as a figure of merit, because the design and construction are revealed by the sidelobe levels. Sidelobes can be very difficult, and thus costly, to reduce and should not be overly specified if the application does not require low sidelobe levels.

Squint The deviation of the center of a beam from a reference point as a function of the frequency, polarization, or orientation. Usually defined as the variation of the bisector of the half-power beamwidth angle with respect to a mechanical reference. Refer to Figure 1.


I 81

Related terms: Boresight Measurement Accuracy: Same as that for beamwidth Significance: Squint is an important parameter when beam direction must serve a function such as direction finding or when the maximum gain direction must be pointed in a given direction. Comments: Once the antenna has been removed from the pattern range, the mechanical reference provided by the mount or a boresight telescope is the only indication of beam direction.

Voltage Standing Wave Ratio (VSWR) The ratio of incident to reflected voltage at the antenna input. A measure of how well the antenna, as a transducer, matches the impedance of the transmission line to the impedance of space Units: VSWR, a ratio, as n:l Return loss: Decibels Reflection coefficient: A number between 0 and 1 Related terms: Mismatched and matched Measurement accuracy: Variable, depending on the method of measurement. Required accuracy should be to a level which ensures compliance with the requirement. Significance: Depends on the application. A VSWR of 3:1 in a receiving system will cost 1.25 dB in gain loss. The same VSWR in a transmitting system could destroy the transmitter. Loss from VSWR is calculated as follows, mismatch loss = Pm/P -- 1 / ( 1 --Ip] 2) = (S + 1 ) 2 / 4 S , where Pm is the power delivered if matched, P is the power delivered, p is the return loss, and S is the VSWR. Comments: Note that the definition of gain does not include VSWR losses. From the system point of view, such loss must be considered. In coaxial systems, VSWR with respect to an impedance of 50 1) is usually required. In waveguide systems the type of waveguide and VSWR are specified.

Power Handling The power the antenna is capable of accepting at its input terminal and subsequently radiating; for a receiving antenna, the power incident from another source, such as an adjacent radar. (The frequency of the source may be outside the nominal frequency band of the receiving antenna.)

182

Hill and Smith

Units: Watts Related terms: Average power, peak power, duty cycle, pressurization, altitude, critical altitude, ionization, and multipaction Measurement accuracy: The capability of the testing facility to measure power. Usually an indirect measurement by means of a sampling directional coupler Significance: Determines the ability of the antenna to continue to function in the system. Power breakdown is usually not self-healing, except for ionization at altitude. Comments: The power stated in the requirement is generally greater than the power available in the system for which the antenna is intended. Measurement difficulties include obtaining a reliable power source, location of the test, interference problems, altitude, and temperature chambers.

Design of Antennas for High Power Antennas capable of handling high power are not necessarily different, but they must be designed with low conductor and dielectric losses and must avoid high voltage and high current densities. In high-power application, two situations are encountered: high average power and high peak power. For high average power, the common failure mode is excessive heating of the antenna parts. To avoid this, ohmic losses must be kept low and cooling of critical areas may be provided. At high peak powers, failures result from voltage breakdown and arcing. To handle high peak power, voltage gradients within the antenna must be kept below the ionization level. Usually, the power-limiting element in the antenna is the transmission line, because this is where the energy is most concentrated. The limiting factors are voltage breakdown and excessive heating. Waveguides have higher power handling capabilities than coaxial lines. The usual problem with waveguide is voltage breakdown, rather than heating. This is due in part to the fact that an average power exceeding the capability of the waveguide is simply not available. However, peak power that exceeds the capability of the waveguide is available, resulting in voltage breakdown. In a coaxial line, however, for which the diameter must be kept small to avoid moding problems, it is easy to exceed both the peak and the average power capability of the line. Additionally, coaxial lines have an inherent average power limitation, for the center conductor must carry the same current as the outer conductor, and virtually all the current is carried near the conductor surface. Thus the current density and I ZR losses are many times higher in the center conductor, which is thermally isolated from any possible heat


1I]3

sink. Specific techniques in high-power design include the following: Choose metals of high conductivity (copper, aluminum, or silver) and dielectrics of low loss. Minimize abrupt discontinuities and sharp corners. Use low-Q matching structures. Avoid designs of an inherently narrow frequency band. Make circuit elements with generous cross sections and large spacings. Above 8 GHz, try to use a waveguide.

G/T "G over T" is a figure of merit, applied to satellite communications antennas. G is gain as previously defined. T is system noise temperature and includes noise received by the antenna, noise resulting from losses in the transmission line, and the noise figure of the preamplifier. It is measured at the output of the preamplifier or some other specified point. System noise temperature includes antenna noise temperature. Antenna noise temperature is defined in Reference [11]. The antenna noise temperature expressed in kelvins at a specific frequency is equal to the effective temperature of a passive matched load having an equal available noise power output per unit bandwidth. It is defined in the following relationship,

N=kT, where N is the available noise power output per unit bandwidth in watts/hertz, k is the Boltzmann's constant in watts/kelvin hertz, and T is the noise temperature in kelvins. Standard: From Reference [11], "It shall be standard to specify the antenna noise temperature at the feed output flange, including all feed contributions. Any active circuit elements (e.g., amplifiers, detectors) shall not be included. It shall be standard to specify the noise temperature for specific frequencies and polarization at the same point in the antenna as the antenna gain is specified. It shall be standard to specify noise temperature versus elevation angle above the horizon." Comments: To compute G/T, perform the following: [ antenna gain (power ratio relative to isotropic) ]

G~ T = 10 log ~0

(system noise temperature in kelvins)

or

( G / T ) dBK

(antenna gain) dB~ -- 10 log(system noise temperature in kelvins).

184

Hill and Smith

S/te The location of the antenna with respect to structure which can affect the antenna's performance Related terms: Ground plane and radome Measurement accuracy: The characterization of an antenna's performance in its location can be a difficult task. Highly directive antennas such as parabolic reflectors and arrays larger than 20A are little affected by objects to the sides and rear of the aperture, with one important exception: antennas used in satellite communications, in which noise temperature is significant and in which this noise is introduced into the system via the antenna's reception of noise from the Earth or sky. Patterns of broad-beam antennas are more affected by environment and can be rendered nearly useless if the antennas are incorrectly sited. Antennas on aircraft, missiles, and ships should be tested in the location at which they are to function, but this is difficult and can be very expensive. All antennas should be tested in their radomes. Comments: Most antenna requirements define "free-space" performance, yet most antennas are situated in far from free-space conditions. Frequently, a circular ground plane several wavelengths in extent is specified for test purposes. In this case, the edge of the ground plane becomes a significant part of the measured pattern. Ground planes often have rolled edges or attached absorber to mitigate the problem. Scale models are often used to simulate the antenna site. This is especially useful when the antenna location is on an aircraft or a ship. The frequency must also be scaled so that the features of the environment (i.e., the aircraft or ship), measured in wavelengths, are representative. There are two major limitations to this technique: the pattern range's upper frequency capability and its capacity to handle large models. As an example, an S-band antenna operating at 2.2 GHz whose environment is scaled by ~0 would have to operate at 22 GHz. Because of the expense of characterizing the performance of an antenna in its working location either at full scale or with scale models, methods have been developed for calculation of this performance. The following discussion was provided by Plane Avionic Enterprises, Inc. [12].

General Theory of Diffraction (GTD) GTD models calculate reflections and diffractions from canonical structures (cylinders, plates, cones, spheres, and ellipsoids), summing resultant energy from the many paths (phase relative) to provide point-to-point gain. By calculation, vehicles may be assessed if redefined from their real structures into appropriate canonical shapes. Computer models using GTD techniques permit a main


| 85

structure in cylindrical or ellipsoid (single or dual) form, supported by numerous plates, to make up a representative structure, thereby defining the platform. Data are input through mathematical (three-dimensional) coordinates in terms of X, Y, and Z relative to a fixed point (nose or other data). Such a definition is complex and time consuming, being a manual ( m a n / m a c h i n e ) f u n c t i o n . The GTD methodology is reliable in calculating rays via reflective and diffraction paths although somewhat suspect in the transition or border regions existing between the two.

Unified Theory of Diffraction (UTD) The UTD is a method which supplements GTD by providing reliable assessment of energy transfer in those transition regions. Platform Geometry Definition The ALDAS platform geometrical definition consists of cylindrical, rectangular, and ellipsoidal construction, permitting different axis sizes with and without nose cones (truncated or not) together with up to 30 cylinders for other structures, up to 30 plates (each permitting up to 15 corners), and up to 30 four-cornered obstacles. Error checking is included to avoid frequency/geometry inconsistencies, nonplane coordinate definition, etc. Plates and blockages are computer assessed for attachment or edge radiation (wedge or rolled), and surface-mounted antennas are automatically dimensioned and positioned for appropriate phase centering. References: For the complete theory of scale modeling and for the theory of GTD and UTD, see References [13, Chaps. 4 and 32, respectively]. For a brief discussion, see Reference [5]. Environment

The conditions which affect the antenna's survival or reliability Related terms: Temperature, wind, altitude (vacuum), vibration, pyrotechnic shock, acoustic level, sand and dust, humidity, and salt fog Measurement accuracy: The characterization of an antenna's performance in its environment is often difficult, and some combinations may be nearly impossible to measure, such as the recording of patterns at temperature extremes. Frequently only the antenna VSWR is monitored during temperature or vibration testing, and even here the test fixture affects the measurement. Thus a reference in situ VSWR is recorded, and deviations from that reference are evaluated. After testing, normal measurements may be made to test for permanent change or damage. Significance: Designing an antenna to function and survive in extreme conditions can be a difficult problem, in which the electrical design

1116

Hill and Smith

problems are relatively insignificant when compared with the mechanical design problems.

Special Terms Deviation from Omni This specification is used in defining the pattern performance of omnidirectional antennas. Such antennas are actually semidirectional and usually receive or transmit over a hemisphere (such as the pattern of a conical spiral) or omnidirectionally in the azimuth plane (such as the pattern of a biconical antenna). A true omniantenna, which is omnidirectional over a sphere, is not possible for any given polarization. "Any continuous vector field on a Euclidean sphere must have a singularity." (See References [14] and [15]. The ideal omniantenna should receive equally well over the required sector of a sphere. This performance is difficult to achieve and so the performance must be given a tolerance; thus "deviation from omni" refers to this tolerance in terms of gain variations which occur as a function of azimuth angle, elevation angle, polarization, or frequency. The requirement may state "Deviation from omni shall not exceed + 2 dB over 360 ° in azimuth, 0 ° to +45 ° in elevation, for any linear polarization." After the antenna is designed and built, it will probably not meet the specification in its entirety. After negotiation the specification will be modified to add " T h e gain (or axial ratio or deviation from omni) will be met over 90% of the area (or frequency)." Such compromises are necessary because of the difficulty of building a true omnidirectional antenna. To test pattern performance, the antenna would be rotated 360 ° in azimuth, stepped in elevation 5 °, rotated in azimuth 360 °, and so on, whereas the linear polarized source antenna is rotated continuously. The specification is met when amplitude extremes lie within the + 2-dB sector as illustrated in Figure 8. Caution should be used in defining gain for omnidirectional antennas. For some, gain is the mean amplitude, whereas others choose to define it as the peak amplitude. Axial ratio is the variation between the adjacent maximum and minimum amplitudes resulting from the rotating source polarization. Nominal "Nominal" is a favorite word and is used instead of the more appropriate "approximate" when the specification writer (the seller) does not wish to be pinned down to a definite specification. Typical "Typical" in a specification means that the parameter defined is not unconditional. Frequently it means that the performance

7.

Microwave

187

Antennas

MAXIMUM GAIN IIII

.................................................................................................. 1' ........ i' ............. I........

, ,,,! ~ , w ~vv~ ~,~v~v,~w~w~ ~,^ ~gjv ~ WW~Vv~v'!Iv~,v,.~,.. ,~ -v~,;w~ " t

T,O

.....

. . . . . . . . . . . . . . . . . .

1

I. . . .

MINIMUM GAIN DEVIATION FROM OMNI

SPINNING POLARIZATION TRANSMITFER

PATTERN CUT

.uLu~

-180

/

~

.... I .... 1.... 1.... I .... 1.... 1.... I .... 1.... 1.... 1.... 1.... 1.... I .... 1.... I .... 1.... 1.... 1.... I .... 1.... 1.... 1.... 1.... 1.... 1.... 1.... t .... I .... 1.... 1.... 1.... l .......

-150

- t;:)0

-90

-60

-30

Azimuth Figure

8.

Pattern

of an

0

30

60

90

t20

150

t80

degrees elliptically

polarized

antenna.

described is better than the specified value, but that performance will vary from unit to unit.

2. Microwave Integrated Circuit (MIC) and Monolithic Microwave Integrated Circuit (MMIC) Antennas MIC and MMIC antennas are a natural evolution of integrated circuit components in the microwave and millimeter-wave frequency range. Some of the integrated circuit antennas that have been developed are bow ties, cat whiskers, circular slots, dielectric rods, dipole arrays, slots, slot arrays, vees, and Vivaldi antennas [16]. There is an ever-increasing need for monolithic integrated circuits combining amplifiers, antennas, diodes, and transistors on the same substrate. The fastest growing field using MIC and MMIC antennas is the imaging system for military and scientific applications, such as astronomy, atmospheric studies, interferometers, military radar and radiometry, plasma diagnostics, and spectroscopic applications. References [17] and [18] provide a more detailed description of these applications. These imaging systems map the radiation intensity of a distributed source. This radiation intensity is then correlated to the

188

Hill and Smith

various applications. In the past, a single detector has been used in a mechanically or electrically scanned imaging system. This technique has proven to be too slow and inadequate for many applications. A millimeter-wave imaging array consisting of a large number of antennas each with its own detector, placed at the focal plane of an imaging system, would correct these deficiencies. The outputs from the detectors make up the image. Examples of some the detectors that might be used are Schottky diodes, SIS junctions, and microbolometers. This results in a faster imaging system. A monolithic focal-plane imaging array is an even more attractive solution. See Reference [19] for more detail. In these systems, the antennas and detectors are integrated on dielectric substrates. A benefit of using monolithic integrated circuits is that, as the frequency is increased, the advantages of using them tend to increase. The fabrication of the structures becomes easier as more integrated circuit technology can be used. Since more devices can be put on each wafer, the unit cost decreases. Also, as frequency increases, the dielectric losses become less of a problem. Dielectric losses are related to the conductivity of the semiconductor. The relation = o-v//x/e, where o-, /z, and e are the conductivity, magnetic permeability, and electric permittivity, respectively, gives the upper limit of the power loss coefficient. Thus, since the loss per guide wavelength decreases as 1 / f and since a is nearly independent of frequency, the dielectric losses will decrease with increasing frequency. For a thorough discussion of this refer to Reference [20]. However, these advantages are counterbalanced by limited power, low gain, and a very narrow bandwidth. The thermal capacity of the substrate materials limits the power. By arraying the antennas, the gain can be improved. Bandwidth, input impedance, mutual impedance, radiation efficiency, and radiation patterns are effected by the substrate thickness and relative permittivity [21]. The antennas are usually thin-film metal geometries on a substrate. The dielectric substrates commonly used are gallium arsenide, quartz, and silicon. Dielectric substrates are excellent surface waveguides. This is to say that the energy radiated into a substrate at angles larger than the critical angle is completely reflected and becomes a surface wave in the dielectric. This is discussed in detail in Reference [17]. When surface waves come in contact with the integrated circuit, they become shock waves. The electrical charge associated with the surface wave shocks the circuit, causing intermittant disruptions and possible permanent damage. These surface waves have a fundamental mode with no cutoff and can cause cross-talk between adjacent antennas. When placing the antenna on


189

a dielectric substrate, surface waves can be avoided by ensuring that the phase velocity of the guided wave is less than that of the surface waves. If this is not done, the energy will escape from the waveguide and disperse as shock waves in the substrate. Metal antennas cannot be deposited on thick dielectric substrates because the waves in the guide will be faster than the surface waves in the substrate, thus causing shock waves in the substrate. However, metal antennas can be deposited on sufficiently thin dielectric membranes without detrimental shock waves. An example of this is the microstrip antenna. Another alternative would be to sandwich or encase the metal antenna in a uniform dielectric as discussed in References [18] and [22]. Providing that transparent materials are available for the substrate and superstrate, this solution can be used over the millimeter-wave frequency range. Some of the more transparent materials and their absorption coefficients, as discussed in Reference [18], are optosil fused quartz (1.3 d B / c m ) , polyethylene (0.2 d B / c m ) , polypropylene (0.2 dB/cm), silicon (2.~, d B / c m , when the resistivity > 10 o h m / c m ) , and TPX (0.26 dB/cm). By using semiconductor material for the substrate and superstrate, a Schottky diode could be integrated with the antenna. Substrate mode powers can also be reduced by using twin-slot and twin-dipole designs. These designs also improve the patterns. The substrate mode is used by tapered-slot antennas to control the shape of the beam. To eliminate substrate modes, a lens is often mounted on the back of the substrate. Unfortunately, the lens degrades the patterns and increases dielectric absorption losses. However, improvements have been made with a twoelement Yagi antenna with a TPX lens and spiral and log-periodic antennas with quartz substrate lenses. These improvements are discussed in Reference [19]. By integrating the antennas on silicon oxynitride membranes less than a micrometer thick, both the substrate modes and the substrate lens problems can be reduced. Since the membrane is small compared with a wavelength, allowing the antenna to effectively radiate in free space, the free-space antenna design techniques can be used. Figure 9 shows an integrated circuit combining an all-dielectric antenna and waveguide with Schottky diodes. The antenna consists of a tapered dielectric rod etched from a silicon wafer. The guided radiation is fed into the Schottky diode by a V-shaped metallic coupler. The diode is located at the apex of the coupler. In the plane of the V, an electric field is created. Thus, without the use of conventional metal waveguides, efficient in-coupling of radiation is provided by the coupler. This design is discussed in detail in Reference [20]. An example of a two-dimensional monolithic millimeter-wave imaging array is shown in Figure 10. It consists of a two-dimensional array of

190

Hill and Smith

Sil

Membl

E-Fi

Tapered Trapezoidal Dielectric

~un Back)

Antenna

"•..r-.--

Tapered

Dielectric-Rod Antenna

Silicon Membrane

~

V Coupler

~ .... Diode (at Vertex) ~'X~x~'~ - ' - Bonding Pads Figure 9. All-dielectric integrated circuit antenna and waveguide with Schottky diodes.

pyramidal horns etched in silicon. A probe antenna is suspended inside each horn on a 1-~m-thick silicon oxynitride membrane. The energy incident on a resolution cell is collected by the horn which then focuses it on the probe antenna. The interconnections, detectors, and dipoles for the probe are all integrated on the same silicon wafer. The advantage of this approach is that the probe antennas are much smaller than a unit cell. This leaves as much as 75% of the wafer surface for connections and electronics. Reference [19] discusses this design in more detail. A notch radiator (Figure 11) consists of a strip-line input with tapered slot lines forming notches on the ground planes on either side. The perpendicular intersection of the strip line and slot lines couples the energy to the notches. The slot lines are terminated by short circuits, whereas the strip line is terminated by an open circuit. The notch radiation is explained in greater detail in Reference [23].

191

7. Microwave Antennas Contact Pads Front Wafer Back Wafer Nitride Lne

Reflecting Cavity Space for Detection Circuits

Radiated Pattern

Figure I0. Two-dimensional monolithic millimeter-wave imagingarray,

Slot Line

Top Metalization

. . . .

Short Circuit

. /

/

l

Strip Line

Top Dielectric

/

i

-

-

Center Metalization

f

-

/ ' ~ , ~ _ ~ ~

/,/

/

,,~,/~

Circuit Short Circuit

. ~

,

,

~

/ / /

/'~

Slot Line Figure II. Explodedview of a notch radiator.

Bottom Dielectric Bottom Metalization

192

Hill and Smith Air

Slot Antenna \\

Ground Plane

~\\\\\\\\\\\\\\\\\\\~\

Y.

~v'

Air

~v'

o

/

Air Microstrip Dipole I

~

/

/

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h

v'

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,'

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,, :i

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'i',

:!.

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I

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1

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iJ.

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1

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~ ~I:

', ~

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~ i~l

iii,~ ~! !!!i!

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: :::::::--~"~-~_.~~.q~.~.~

i ,

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T _~

11 I

: ; :":~

c~

~,,11~k

' ......

~ ~ ~:~,~,

,,

t tqfiqHll-q,-u, 1 1 ~ ~ ~ ~ : " : 6 t t : ! 1

I __

.

::;:i~

10"1

f ft~m_

i

i i i iliill

'I

10 "2 -~.*-~.~+-~~f-'~IIlll

o

tt

i1 !Illl',l

t1~HittE,e',

.

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~,

I

-

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10

:

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......

°

i}

5 1

! ii

:iti~',I/l I~ I I '.1/J.,,~

--

510 1 2

~

2

5 10 2

I

il

.... 5 102 2 5 1032 Frequency

5 1042

5 105 2

5 106

(MHz)

Figure I. Relative permittivity, er, and conductivity, ~, as a function of frequency (CCIR Rec. 527-2 [21]). (A) seawater (average salinity, 20°C); (B) w e t ground' (C) freshwater, 20°C; (D) medium dry ground' (E) very dry ground; (F) pure water, 20°C; (G) ice (freshwater).

(a is called the attenuation constant, and as shown here is in nepers per meter but will later be represented decibels per kilometer, where 1 Np = 8.686 dB, if the voltage or current is represented); 1 Np = 4.343 dB, if the power is represented, as in certain fields such as remote sensing

210

Ernest K. Smith

radio astronomy [4a], [73]

2/lj2 ]

1/2

13-

~

1 +

~toe

+ 1

rad/m

(8)

(/3 is termed the phase constant). Both a a n d / 3 are positive and real [67].

Reflection and Refraction Reflection and refraction occur at an interface at the Earth's Surface.

Vertical Polarization

The voltage reflection coefficient Pv is e' sin 0 - V/e' - c o s 2 0 "

-

-

Pv

Horizontal Polarization

°

e' sin 0 + V/e' - cos 2 0

(9)

The voltage reflection coefficient Ph is sin 0 - V/e' - COS 2 0

Ph -- sin 0 + V/e' - c o s 2 0 "

(10)

Shown in Figure 2 are the magnitude and phase of the reflection coefficient for horizontal and vertical polarization for seawater and medium-dry ground. If the subsurface m e d i u m is nonconducting ( o - = 0), then a Brewster angle, 0 B, where the signal is totally transmitted and the reflection coefficient Pr = 0, may be defined as in optics by 1)1/2

0 B = tan -1 - -

.

(11)

Er

EXAMPLE" Let ~?r = 81 at 1 GHz and tr = 0. Then 0 B = t a n - l ( 1 / 81) 1/2= 6.3 °. This is the case for (fresh- or salt-)water but due to its conductivity Pv experiences a null but does not decrease to zero. For " m e d i u m - d r y ground," as seen in Figure 2, 0 a = t a n - l ( 1 / 1 5 ) 1/2 = 14.5 °. On the other hand, for very dry ground, E r = 3 and 0 a = t a n - l ( 1 / 3 ) 1/2 = 30 °. In practice these are the two extremes encountered. As can be seen in Figure 2 these estimates are useful approximations. The real part of Pv is negative for 0 < 0 B and positive for 0 > 0 B. The real part of Ph is negative for all 0. In consequence a circularly

211

8. Propagation at Microwave Frequencies

a

b

1.0

E

~

0.8

II II II II II II II II

.~ o.6 "7-, 0.4

0.2

0

'°°f

"~]

I

[[I

] INt 11 I I ~11

1 I~\ N~I II I II\l~J~J/ I I II I%NI~I[[ I II~!A~ I 1 vl~:~/~i~l

120

L,[o-,t~/

II I lit I till II I I I II1 I I 11 Ill

IIII 1111

II o o.1

0.2

0.5

1

2

5

10

Grazing angle, ~o (degrees)

20

50

~11 Y]ll]

I [lllk ~ol I [ III1~ r vlN:~l ~

160

•~

~

-I~~LI[ I1[I [ I I[l~ll[]

90

0 0.1

0.2

0,5

1

2

5

,~

g2LX 10

20

50

90

Grazing angle, ~o (degrees)

Figure 2. Magnitude and phase of the reflection coefficient of a plane surface as a function of grazing angle, ~ for vertical, V, and horizontal, H, polarizations (CCIR Report 1008-1 [27]). (a) seawater, (b) medium dry ground.

polarized wave will be reflected with the same sense of rotation for 0 < 0 B and a reversed sense for 0 > 0~. Note. The effects of ground constants on electromagnetic wave propagation are a classical problem, and the reader is referred to standard texts, for example, References [9, 10, 68, 72].

Penetration Depth The transmitted wave (magnitude, V/1 - p 2 ) is attenuated as it travels in the conducting subsurface medium. The electric field intensity E is given by E ~ e - ~ z , where Z is distance and a is the attenuation coefficient. Penetration depth, 3, is defined [67] as the distance in which E / E o = e-1 or a decrease of 8.686 dB. This decrease is illustrated for a series of media in Figure 3.

212

Ernest K. Smith 103 5 2 102 5

~" 2 .E 0

5

•-~ ~

a.

2 6

g 2

10-1 5 2

10-2 10 -22

510 "1 2

5

1

2

5 10 2

5 1022

5 1032

5 104 2

5 105

Frequency (MHz)

Figure 3. Penetration depth, ~i, as a function of frequency (CCIR Rec. 527-2 [21]): For characteristics of A - G , see Figure I.

Atmospheric Refractive Index

The most widely used expressions good to three significant figures [2, 21, 47-49, 100] are total,

N=(n_

1 ) x 106= -77.6( ~ p + - -4810e --~ ) ,

(12)

dry air, N

= 77.6Pd/T

,

(13)

and water vapor, N-

72e e T + 3.75 × 105 T2 ,

(14)

where n is the index of refraction, N = (n - 1) × 106 is refractivity, T is the temperature in kelvins, p is the total atmospheric pressure in millibars, Pd is the partial pressure of dry air in millibars, and e is the partial pressure of water vapor in millibars.

213


Note. For greater precision and broader scope, the reader is referred to Thayer [108], Hill et al. [63], Liebe [76], and Bevis et al. [8a]. Water vapor density p in g / m 3 is related to e in millibars and T in kelvins, e

p = 216.5--. T

(15)

Substituting Equation (15) into Equation (12)yields a practical form of the S & W relation, namely, U = (n

-

77.6 ~(p T

1)10 6=

+ 22.22p).

(16)

Propagation in Free Space The range equation (also known as the Friis equation [63a]) relates received power Pr to transmitted power Pt as

e r --

PtGrGt A2 (47rR)2 W,

(17)

where G r is the receiving antenna gain above an isotropic antenna in the direction of the transmitter, G t is the transmitting antenna gain similarly defined, A is the wavelength in free space in meters, R is distance between antennas in meters, and Pt is the transmitter power in watts. Path Loss

47rR ) Lfs =

a

Pt =

er

(18)

is the loss if G r and G t are isotropic antennas. Lfs is also called the "free space loss." Another expression of Equation (17) in terms of carrier power C and receiving antenna aperture is C =

PtGtAr (EIRP) A r 47rR 2 = 4,rrR2 ,

(19)

where E I R P = PtGt stands for Effective Isotropic Radiated Power, A r is the effective area of the receiving antenna and is related to gain above an isotropic radiator by GA 2 = Ar 47r = GAi,

(20)

214

Ernest K. Smith

where /~2 Ai--

4rr

(21)

is the effective aperture for an isotropic radiator.

Carrier-to-Noise Ratio ( C / N )

C/N is basic to microwave transmission. If the noise can be expressed in terms of thermal noise, then C

etatGr

(EIRP)G r

-~ ~-- ZfskTsysn = t f s k L y s n

,

(22)

where Tsys is the system noise temperature in kelvins, k = 1.38062 × 10 -23 J / K is Boltzmann's constant, and B is the bandwidth in hertz. It is common practice to express Equations (17)-(22) in terms of decibels. Given in order these expressions are (log, logarithm to base 10)

(Pr)dBw = (Pt)dBw -k- (Gr)dB i q- (Gt)dB i -+- 20log

~

-

20 log

R

-

21.98

(23) (24)

( L f s ) d B = 20 log R - 20 log ,~ + 21.98.

EXAMPLE: Assume R = 38,000 km and ,~ = 3 cm. Lfs = 201og(38 × 106) - 201og0.03 + 21.98 = 151.60 + 30.46 + 21.98 = 204.04 dB ( C ) d B w = (Pt)dBw -+- ( G t ) d B i -+- 10 log A r - 20 log R - 10.99

(25)

10 log A r = (G)dBi + 20 log ,~ -- 10.99 dB above 1 m 2

(26)

10 log A i = 20 log h - 10.99 dB above i m 2

(27)

( C / N ) d B - (EIRP)oBw + ( a r ) d B i -

(Zfs)d B

+ 2 2 8 . 6 0 - 10 log Ts - 10 log B.

(28)

215


EXAMPLE: Assume f = 1 GHz, R = 39,000 km, Pt = 100 W, G t = 25 dB, and G r = 45 dB. Evaluate C/N if Ts = 100 K and B = 100 kHz. c

2.99792458 x 108

f

109

EIRP =

PtGt =

- 0.299792 m

20 + 25 = 45 dBw

Lrs = 20 log39 x 1 0 6 - 20 log(0.299792) + 21.98 = 151.82 + 10.46 + 2 1 . 9 8 - 184.26 dB

C/N

= 45 + 45 - 184.26 + 228.60 - 20 - 50 = 64.34 dB.

2. A t t e n u a t i o n Mechanisms Attenuation at frequencies above 1 GHz occurs almost exclusively in the troposphere for either terrestrial or E a r t h - s p a c e line-of-sight (LOS) paths. Scintillation, ionospheric and tropospheric, can produce serious signal degradation, but as energy is not subtracted from the signal, it is not considered here to be attenuation. Attenuation mechanisms for LOS paths are due to absorption of energy from the wave, or scattering of energy out of the wave, due to atmospheric gases hydrometers (rain, cloud, fog, or hail), dust, or aerosols.

Attenuation Due to the Gaseous Atmosphere Two atmospheric gases produce significant absorption at frequencies between 1 and 300 GHz. These are molecular oxygen and water vapor.

Oxygen Oxygen has modest U H F / E H F absorption and has over 30 absorption lines between 50 and 70 GHz (which merge into a single broad line at sea level pressures) and an isolated line at 118.74 GHz [21, 76]. The specific attenuation, 70 ( d B / k m at NTP: 15°C and 1013.25 mbar pressure), of dry air (due mainly to oxygen) is shown in Figure 4. Analytically, it is represented by [55]

Y0 =

6.09 7.19 x 10 -3 + f2 + 0.227 + ( f -

4.81 57) 2 + 1.50 f2 X 10 -3 d B / k m (29)

9_ 16

Ernest K. Smith 102

!

.

1 1 H20

/

/

02 [/

2

/

r

!

/

5

I

u._.

,(

e~ r.~ --

H20

I!/' I

A

/\

10-1 !

5

I

/

2

/

10"2

/

..

02

I 2

o,/ j

5

1

I I

1

I

/

I

\i I L

'J l

/

/

..,I"

/ ~.''f

I 1

/'

/

/

\~'I

!

1 10 2 Frequency,[ (GHz)

i

o/

i

t ]

!

!J 5

102

2

3,5

Figure 4. Specific attenuation of molecular oxygen and water vapor (Report 719-3 [21]). Pressure, 1013 mbar; temperature, 15°C; water vapor, 7.5 g / m 3.

for f < 57 GHz and by 7o = [3.79 x lO-Tf +

0.265 ( f - 6 3 ) 2+ 159

x ( f + 198)2 X 10 -3 d B / k m

0.028 (f-

118)2 + 1.47

] (30)

8. Propagation at Microwave Frequencies 300 200

217

h

1 I

LI

1

.

I j.~ jdL/ \ Jk J~ J[

100 r \ j k . , i LI ~" L J i ~/1 iii l - I , /! Ik./ IJ~ I v:t\¢ V% l

50 ~" 20

/,Vl~l:V

,./

lO

~

Ik,, 1

IL /Ill IV~I t

\

)"IL ;t ~l ilill ,llJ ;I;I.1 I11

iv

'-

5

/,

.,,..,

~3 F/,

/

E: 2 (b N

1

/

0.1

~

/

|/

50

....

15

ilill

llll,'ll

~l/I

~I /

~

iv~

~

!

1

\

l,v

,Ill II

v I/~I o v l, ~ x v I '~'-'""--" " I i\/~ //l ~ " - . . "-~ " [ ' I "U . . . . "~ [ L

I

I

I

k~

-

.

\ 1

ivi I 11 IV

'-: /]

/ ]

52

J

,/ ~i !i I~i~i I/

j

,y. "

0.2

~

I ~

/

0.5

v

Jl

I

"-~0

20

54

58

56

64

60 62 Frequency, f (GHz)

/

66

M

68

70

Figure 5. Total zenith oxygen absorption, 50 to 70 GHz, for selected initial heights (Report 719-3 [21 ]; [761).

for f > 63 GHz, where f is the frequency (GHz). In the oxygen absorption band (50-70 km) the specific attenuation has a complicated height (pressure) dependence, and the specific attenuation can be estimated from Figure 5 [76]. The total zenith attenuation at ground level is given in Figure 6. Water Vapor For water vapor the specific attenuation, Y~o, reflects the absorption lines at 22.2, 183.3, and 325.4 GHz. An expression, including the quadratic dependence on water vapor density, is given by [21, 55] %, = {0.050 + 0.0021p +

3.6 (f-

22.2) 2 + 8.5

89 (f-

10.6

+ (f-

183.3) 2 + 9.0

}

325.4) 2 + 26.3 fZp10-4 d B / k m

(31)

for f < 350 GHz, where f is the frequency in gigahertz and p is the water vapor density in g / m 3. Conversion of water vapor partial pressure e in millibars into density p is given by Equation (15).

218

Ernest K. Smith

~n

5

..=

o

10 "1

1

2

5

lo

2 Frequency (GHz)

5

10=

2

4

Figure 6. Total zenith attenuation at ground level (Report 719-3 [21]). Pressure, I atm; temperature., 20°C; water vapor, 7.5 g/m 3

Conversion of relative humidity H,o into water vapor density p can be obtained from e

H,o = 1 0 0 - - , e s

(32)

219


where e s is the saturation water pressure over liquid water in millibars [16]. 17.502t e s = 6.1121 exp

t + 240.97

} ,

(33)

where t is T - 263.15 in degrees centigrade. Note. 1.8t(°C) = t(°F) - 32, where t is in degrees F a h r e n h e i t . Hence, p =

2.167Ho~e s T

.

(34)

EXAMPLE: W h a t is the specific a t t e n u a t i o n at 30 G H z of water vapor at sea level if the relative humidity is 50% and the t e m p e r a t u r e is 75°F?

Solution. t(°C) =

75 - 32 1.8 = 23"9°"

F r o m E q u a t i o n (33), 17.502( 23.9) es = 6.1121 exp{

= 6.1121 exp(1.5786) = 29.63 mbar.

23.9 + 240.97

F r o m E q u a t i o n (34), 2.167(50)(29.63) p

292.78

= 10.97 g / m 3.

F r o m E q u a t i o n (31), 3.6 Y~o = {0.050 + 0.0021(10.97) +

(30-

(30 - 22.2)2 + 8.5

10.6 (30-

8.9 ~ (30)2(10.97) 10_4 d B / k m 325.4) 2 + 26.3 )

= {0.050 + 0.023 + 0.052 + 4.5 × 10 -4 + 10-4}(0.9873) = 0.123 d B / k m .

183.3) 2 + 9.0

220

Ernest K. Smith

Note. Figure 4 shows 0.08 d B / k m for p = 7.5 g / m 3 and t = 15°C. Because 7o~ is roughly linear with p to 12 g / m 3 extrapolating the value in Figure 4 would yield a 7,0 of 0.117 d B / k m .

A t t e n u a t i o n D u e to Rain

Rain consists of water droplets with diameters ranging from about 0.2 mm (drizzle) to 7 mm. Small raindrops ( < 2 mm diameter [85a] are largely spherical, but large drops become flattened and acquire a dimple in the bottom side. The best known studies of drop-size distribution as a function of rain rate are Laws and Parsons [74], Marshall and Palmer [78], Joss et al. [69], and Prupacher and Pitter [91]. Below 30 GHz attenuation is due almost solely to absorption. Above 30 GHz scattering becomes increasingly important. A distinction is then made between the absorbed (coherent) signal and the scattered (incoherent) component [86]. Predicting attenuation due to rain is an important but complex problem, and a variety of models have been developed [36, 65]. The principal ones are the Rice-Holmberg model [94] for the percentage of the year in which rainfall exceeds a given rate, the Dutton-Dougherty model [42-44], the global model [34], the two-component model [35], the Lin model [64, 77], the simple attenuation model (SAM) [103, 104], and the CCIR model [22]. The CCIR method will be outlined here. Specific attenuation due to rain is equally applicable to terrestrial and Earth-space (slant) paths.

Rainfall Statistics Specific attenuation due to rain is a function of frequency, rainfall rate, drop-size distribution, fall velocity, and path orientation. Good reviews of the various aspects may be found in Allnutt [2], Boithias [9], CCIR [22], Flock [48], Ippolito [64, 65], and Crane [37]. The CCIR proposes two methods for regions for which local rainfall statistics are not readily available [22]. One method divides the world into 15 rain climate zones and specifies the rainfall intensity exceeded for 0.001 to 1.0% of the year for each zone. The disadvantage of the zonal method is that boundary discontinuities of a factor of 2 may exist. The second so-called contour method is reproduced here. The land areas of the world are contoured for rain rate exceeded 0.01% of the year (52.56 min). The rainfall rates at other percentages of the year are then derived from this single value. This method has the advantage of continuity but does not allow for the variation of rainfall distribution with climate. For example, in

221

8. Propagation at Microwave Frequencies 165 ° 75 ~

150 °

135 o

120 o

105 °

90 o

75 o

60 °

45 °

30 ° 75 °

x.

60 ° ~

v,.._

-"~---_. ~ ,

1...~..5~ _ - - - - - "

15 °

'

.

~

0°

o

15 °

•

60

40

60o

'I ~ K . . ~ . ~ O 0

0°

~,

15 °

10 1 30 °

30 °

80 45 °

'60

30 60 ° 165 °

150 °

135 °

120 °

105 °

90 °

75 °

450

20

60 °

45 °

60 ° 30 °

Figure 7a. Rainfall contours for 0.01% of the time for the Americas (Report 563-4 [22]).

the Midwest of the United States the rainfall is largely convective (thunderstorm related), whereas on the West Coast of the United States the rain is largely stratiform and the cumulative distributions are very differ-

222

Ernest K. Smith

b 30°

15 °

0°

15 °

30 °

45 °

60 °

-

600

4~

4oi"

~

4,))

"--~j

30°

/

"

i

30°

1 30 °

15~'

O'

15°

30°

45"

60°

Figure 7b. Rainfall contours for 0 . 0 1 % of the time for Europe and Africa (Report 563-4 [22]).

ent, although the 0.01% rain rate may be the same. The CCIR rainfall contours for 0.01% of the time are given in Figures 7a, 7b, and 7c. The curve parameter is the rain rate in millimeters of rain per hour with an integration time of i min. The contour maps come from Report 563-4 [22].

8. P r o p a g a t i o n at M i c r o w a v e

C

60 °

75 ~

223

Frequencies

90 ° •

105 °

120 °

135 ° 'xY-.,-'

150 ° "-J

165 °

180 °

,

60 °

165° 75°

y ,e eo

20

45 °

/

,

4 0 ~

.

45 °

,~

J

0°

,o0

~-, " ~

0o

,oo

15 °

30 °

~

30 °

60

~?

40 4o 45 °

60°60°

~j/

75 °

90 °

105 °

120 °

135 °

150 °

165°

450

180 °

I

Figure 7c. Rainfall contours for 0 . 0 1 % o f the t i m e f o r Asia and Australia ( R e p o r t 5 6 3 - 4 [22]),

Step 1. Obtain the rain rate Ro.ol exceeded for 0.01% of the time from Figure 7. Step 2. Compute the specific attenuation "YR ( d B / k m ) from the nomogram given in Figure 8.

224

Ernest K. Smith

Step 3. Determine the specific attenuation A p for the rainfall rate exceeded for the percentage of time P desired by the following relation: YP

= 0.12P-(O.546+0.043 log P).

(35)

")/0.01

This formula gives factors of 0.12, 0.39, 1, and 2.14 for 1, 0.1, 0.01, and 0.001% of the time. For use between 0.001 and 0.1% of the time, this relationship is not bad. EXAMPLE: What is the specific attenuation for rain exceeded 1% of the time for Boulder, Colorado, for horizontal polarization at 30 GHz? METHOD:

Step 1. Obtain the rain rate from Figure 7a for 40°N, 105°W longitude. This is found to be 32 m m / h . Step 2. From the nomogram in Figure 8 we obtain a value of 6.4 d B / k m for 0.01% of the time. Step 3. From Equation (35) we deduce that for 1% of the time the factor is 0.12 of the attenuation for 0.01% of the time. Hence, ")/1.0

:

0.12(6.4) = 0.77 d B / k m .

Path Attenuation

Heavy rain usually occurs in ceils of a few kilometers in extent. Thus, the attenuation applicable for 0.01% of the time at a location should not be multiplied directly by the path length but by a shorter length to account for lighter rain over some parts. The effective path length Le~ is obtained by multiplying the actual path length L by a path reduction factor, r.

r=

I + L /L o

(36)

where L 0 = 35 exp(-0.015R0.01). For example, in the problem above, if a terrestrial path length of 10 km were specified and R0.01 = 32 m m / h , Equation (36)would give L 0 = 21.66, r = 0.684, and Leff = 6.84 km.

225


Terrestrial Paths The rain attenuation for 0.01% of the time is given simply by

(/0.01)path -- "Y0.01Leff"

(37) .

Equation (35) can then be invoked to obtain the percentage of the time desired by

Ap

Tp -

Ao.01

.

(38)

Yo.oa

Earth-Space (Slant) Paths The procedure for Earth-space paths for elevation angle 0 > 5 ° is given in Report 564-4 [22]. A nomogram for computing specific attenuation for vertical and horizontal polarization as a function of rainfall rate and frequency is given in Figure 8.

Step 1. Calculate the effective rain height h R for the station latitude from 3.0 + 0.0284~ hR(km) = 4 . 0 - 0 . 0 7 5 ( 4 ) - 3 6 )

0 < 4) < 36° ~ 2" .////

I

///J

/bJ~U /

70

t..-

2o

x w//

//. ~

~

~

~-~ ~

- o. B

IO

------ -0.6

16 / / ' ~ ~ ~ - ~ - ' ~

i2

13

14

.10dB

-o.4

15

16 17 IB Diameter D(mm)

Ig

20

21

p]

22

-

Figure 22. Recommended sizes of circular apertures for an attenuation of 10-20 dB with a high opening ratio.

Assuming A to be 122 mm, Equations (9) and (10) are illustrated as Figures 18-22.

Square Apertures in a Metallic Flat Plate Arrangements of square apertures corresponding to those of the circular apertures in Figure 17 are illustrated in Figure 23. Assuming that the opening area of a square aperture is equal to that of a circular aperture, an equation relative to both apertures is obtained as follows, 2W D =

a

•

¢~,

(11)

b

o: '/~-P2 w

~:go" IZ] !--1 Fl~yO [-I

w

Y

L_x

L_x

Figure 23. Square aperture arrangements. (a) Staggered aperture arrangement. (b) Square aperture arrangement.

266

Iwabuchi, Fukai, and Kashiwa

Attenuation 50dB ^

T:P1ate thickness (ram)

1.5

~-0.05 0.1 0.15 0.2 0.25 0.5

1.4 1.3

/ ///,/

1.2 1.1 1.0 ...-.

~o.9 CL

i

=O.B

~J¢~

/ //,~~~ / / / ~ ~ ~ / ~ ~ ~ ~

~o ~

~ . ~ ~,o ~~

/.

~.0.7 0.6 0.5 0.4 0.3 0.2

0.2

0.3

0.4

0.5 0.6 0.7 Aperture width W(ram)

O.B

O.g

I

Figure 24. Recommended sizes of square apertures for an attenuation of 50 dB with a high opening ratio.

T: Plate thickness 22

,-T=O. 4mm~ Attenuation < 0.8 20dB ,.- 1.0

20 1B

/~,,~ 0R=45% 50 [Opening 55 60 / r a t i o

~

.~16

B5

"r - 14 •13. ,-, 12 10 B 6

6

7

8 g I0 II Aperture width W(mm)

12

13

Figure 25. Recommended sizes of square apertures for an attenuation of 20 dB.

9. Consumer Applications of Microwaves

267

where W is the square aperture width and D is the circular aperture diameter. The attenuation equation [Equation (12)] for the square apertures is obtained by substituting the right side of Equation (11) for D in the first term of Equation (6) and also by changing the last term of Equation (6) to the attenuation constant inside the small aperture as a rectangular waveguide beyond the cutoff of a TE m mode.

S = 20 logl0

16W3

+ 8.686T

2rr)

-

~

~-

,

(12)

where P and Q are pitches between square apertures in Figure 23. In the case of W < P and Q

b r-

c o o ~) rh-

._~

E

a

O~

oo

-a~=

eJe~ 0!w'eJ80

(].)

O

o

c~

cO

j:: o .,,_,

"o c~

,,--,

cD

.,-q

5=

. ,...q

~o

cO c~

O

cO j : :

,.c:

~o

cO

~: "o o ©

,,.9,o = E

©

"O

cO

cO

274

Iwabuchi, Fukai, and Kashiwa

References [1] Hitachi, Ltd., "Hitachi Magnetrons," CE-E622 0291, Feb. 1991. [2] C. Lorenson, The why's and how's of mathematical modelling for microwave heating, Microwave World, Vol. 11, No. 1, Spring 1990. [3] X. Jia, Experimental and numerical study of microwave power distributions in a microwave heating applicator, Microwave Power Electromagn. Energy, Vol. 28, No. 1, pp. 25-31, 1993. [4] M. De Pourcq, Field and power-density calculation in closed microwave systems by three-dimensional finite differences, lEE Proc., Patt H, Vol. 132, pp. 360-368, Oct. 1985. [5] K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics. Boca Raton, FL: CRC Press, 1993. [6] K. K. Mei and J. Fang, Superabsorption--A method to improve absorbing boundary conditions, IEEE Trans. Antennas Propag., Vol. AP-40, pp. 1001-1010, Sept. 1992. [7] K. McInturff and P. S. Simon, Closed-form expressions for coefficients used in FD-TD high-order boundary conditions, IEEE Microwave Guided Wave Lett., Vol. 3, pp. 222-223, July 1993. [8] I. S. Kim and W. J. R. Hoefer, A local mesh refinement algorithm for the time domain-finite difference method using Maxwell's curl equations, IEEE Trans. Microwave Theory Tech., Vol. MTT-38, pp. 812-815, June 1990. [9] S. S. Zivanovic, K. S. Yee, and K. K. Mei, A subgridding method for the time-domain finite-difference method to solve Maxwell's equations, IEEE Trans. Microwave Theory Tech., Vol. MTT-39, pp. 471-479, Mar. 1991. [10] D. T. Prescott and N. V. Shuley, A method for incorporating different sized cells into the finite-difference time-domain analysis technique, IEEE Microwave Guided Wave Lett., Vol. 2, pp. 434-436, Nov. 1992. [11] T. Kashiwa, H. Naya, and I. Fukai, A new transducer for thermography to observe the electric field distributions in a microwave oven, Microwave Opt. Technol. Lett., Vol. 4, No. 2, pp. 81-83, Jan. 1991. [12] A. Harada, S. Kitakaze, and T. Oguro, Reduction of 5th harmonic electromagnetic interference from magnetrons and microwave ovens, J. Microwave Power, Vol. 22, No. 1, pp. 3-11, 1987. [13] H. Saito and M. Mino, Improved magnetron with very low level harmonic radiation, Proc. 20th Ann. Microwave Symp. IMPI, pp. 133-136, Aug. 1985. [14] K. Kaneko, K. Iwabuchi, and A. Harada, "Waveguide Filter Used in a Microwave Oven," U.S. Pat, 4,749,973, June 1988. [15] K. Iwabuchi, T. Funamizu, and T. Kubota, "Microwave Heating Apparatus with Fundamental and Second Higher Harmonic Chokes," U.S. Pat. 4,475,023, Oct. 1984. [16] K. Iwabuchi, T. Kubota, Y. Sugaya, T. Kashiwa, and I. Fukai, Effect of conductor losses in new-structure filters for suppressing microwave leakage, in Electronics and Communications in Japan, Part II: Electronics, pp. 80-90, 1993. [17] K. Iwabuchi, T. Kubota, Y. Tanaka, and M. Tawada, "Radiation Sealed Door in a Microwave Heating Apparatus," U.S. Pat. 4,868,359, Sept. 1989. [18] S. Kusunoki, T. Nobue, and T. Kashimoto, "Electromagnetic Wave Energy Seal Arrangement," U.S. Pat. 4,584,447, Apr. 1986. [19] J. M. Osepchuk and J. E. Simpson, "Energy Seal for High Frequency Energy Apparatus," U.S. Pat. 3,767,884, Oct. 1973.

9. Consumer Applications of Microwaves

275

[20] K. Iwabuchi, K. Kaneko, and M. Aoyama, New generation of combination microwave oven and automatic bread making function, Proc. 40th Int. Appliance Tech. Conf., pp. 465-484, May 1989. [21] K. Iwabuchi, M. Tawada, N. Kanagawa, M. Aoyama, and K. Yamazaki, "Microwave Oven Having Automatic Bread Making Function," U.S. Pat. 4,845,327, July 1989. [22] T. Y. Otoshi, A study of microwave leakage through perforated flat plates, IEEE Trans. Microwaue Theory Tech., Vol. MTT-20, pp. 235-236, Mar. 1972. [23] X. X. Peyton, Biological Effect of MicrowaL~e Radiation, Vol. 1, p. 32. New York: Plenum Press, 1961. [24] Hitachi Sales (U.K.), Ltd., "Microwave Oven MR-7970 Instruction Manual."


CHAPTER

10 Industrial Applications of Microwaves T. Koryu Ishii

I. Microwave Heating Temperature Rise

The

temperature rise of a sample due to microwave irradiation when there is no melting, no evaporation, no thermal conduction loss, and no thermal radiation loss is given by

T - To = f0 ~--~SP(1 -p2)dt,

(1)

where To is the initial temperature of the sample (°C), T is the temperature of the sample after microwave irradiation for ~- (s), ~- is the microwave irradiation time in seconds at power P (W), P is the irradiating microwave power (W), C is the average specific heat of the sample (cal/°C kg), M is the mass of the sample (kg), p is the microwave voltage reflection coefficient, and ~ is the thermal equivalent of energy, 0.239 cal,/J. The temperature rise of a sample when only melting is involved is given below. In the part of the sample left unmelted, T' -

T o=

f0• C ,1M , ~ P ( 1 -

p

2) ( 1 - ' r / ) d t ,

(2)

where C' is the average specific heat of the unmelted sample (cal/°C kg),


277


278

T. Koryu Ishii

M' is the mass of the unmelted sample (kg), and r# is the ratio of the mass of the melted sample to that of the unmelted sample. In the part of the sample that melted, T" - T' -~ f~, C"M" ~:P(1 - p2)~/dt,

(3)

where T' is the melting point of the sample (°C), T" is the temperature of the melted sample (°C), C" is the average specific heat of the sample ( c a l / C ° kg), M" is the mass of the melted sample (kg), and z' is the time at which the sample started to melt. The temperature rise of a sample when only thermal conduction loss is involved is T-

TO --

f0"

(P(1 - p2) _ G A T ~ ) - ~

dt,

(4)

where G is the thermal conductance between the sample and a heat sink (W/°C) and ATs is the temperature difference between the sample and the heat sink (°C). The temperature rise of a sample when only thermal radiation loss is involved is T-

To - - f o

•(P ( 1 - p 2 ) - SsE A T Ads )'- ~ d t ,

(5)

where E is the emissivity of the sample (W/°C), ATA is the temperature difference between the surface of the sample and the surrounding atmosphere (°C), and S is the surface area of the sample (m2). The temperature rise of a sample when only the thermal conduction loss and the thermal radiation loss are involved is

T-

TO=

So{

CM

-

The temperature rise of a sample when only the thermal evaporation of the sample is involved is • ~:P(1 _ p 2 ) - m h

r-r°=fo

CM

dt,

(7)

where rn is the mass of the sample evaporated in 1 s ( k g / s ) and h is the latent heat of the evaporated sample (cal/kg). The temperature rise of a sample when thermal conduction loss, thermal radiation loss, and sample

279

I0. Industrial Applications of Microwaves

evaporation are involved is r-

To =

P(1 - o 2) - m A - ~ G AT~ + "o

Latent Heat of Vaporization The amount of heat (cal) required to vaporize 1 kg of the sample without a change in temperature ( c a l / k g ) is the latent heat of vaporization.

Emissivity The amount of energy radiated from 1 m 2 of a surface in 1 s for a I°C temperature difference between the surface and the surrounding atmosphere ( J / m 2 °C s and W / m 2 °C) is the emissivity.

Thermal Conductivity The amount of thermal energy flowing across a square meter of a sample cross section in 1 s for 1 m of thickness with a temperature difference of 1°C ( J / ° C s m and W / ° C m) is the thermal conductivity.

Thermal Conductance The amount of thermal energy flowing in 1 s across cross section S (m 2) and distance 1 (m) is the thermal conductance, S

c

=g7'

(9)

where G is the thermal conductance ( J / ° C s and W/°C), g is the thermal conductivity ( J / ° C s m and W / ° C m), S is the cross-sectional area (m2), and l is the thickness of the sample (m).

Specific Heat The amount of thermal energy required to raise 1 kg of sample by 1°C ( J / ° C kg) is the specific heat.

Thermal Equivalent of Energy ] J -

0.239 cal

1 cal = 4 . 1 8 4 J

Induction Heating (Conduction Heating)

/o t

1-p

2) d t = ~

Jo"

Ri 2 dt = M C ( T -

To) ,

(10)

where R is the electrical resistance of the sample ( ~ ) and i is the induced

280

T. Koryu Ishii

microwave current in the sample (A). The temperature rise in induction heating is

T - TO= f ~ P ( 1 - p2) dt MC "o

(11)

M = m c SS,

(12)

where m c is the specific weight of the sample heated (kg/m3), S is the surface area of microwave irradiation (m2), and 6 is the skin depth of microwave penetration through sample surface S (m), 1 8 - - V/,.n.f~o. ,

(13)

where f is the operating microwave frequency (Hz), /~ is the magnetic permeability of the sample to be heated ( H / m ) , and tr is the electrical conductivity of the sample to be heated (S/m). Dielectric Heating ,r to e. " e 2

fo, P ( 1 - p 2 ) d t = L f o , - - - - f - - d t d u = M C ( T - T o ) ,

(14)

where e is the microwave electric field strength in the sample (V/m), u is the volume of the sample (m3), e = e ' - j e " is the permittivity (F/m), jtoee =jwe'e + toe"e is the displacement current density (A/m2), and we"e is the microwave heating current density (A/m2). ~.~ EVVe

tan S -

weVe

E vv

e'

(loss tangent).

Hybrid Heating (Combination of Conduction and Dielectric Heating)

~P(1

So

-

p 2) dt

=

~ (o" + toe")e 2

SSo

2

dt du

= M C ( T - To)

O" -[- t O E "

tan S -

O.}E r

(loss tangent).

(15)

Approximate Equations for Temperature Rise

Solid Heating T-To

-'ll

IIl,d

0

/

i

IIiil

IIIlllo=

ill

Ill

Ill

a Z

o oe~ .-0

•

~

y!

-/i-" "1, -1

,-0

% "

toO

to 1

t0 2

tos"

FREQUENCY (GIGAHERTZ) Figure 2. Conductivity [Equation (8)], loss tangent, and skin depth [reciprocal of c~, Equation (11)] as a function of frequency, for pure water.

plotted in Figure 2. A log scale is used for conductivity and the loss tangent because of their wide variation. A Cole-Cole relationship [20, 56] which closely fits the experimental data has also been derived. It is a single-Debye function, but with ( f / f c ) (1-°~) in Equation (5), in which a = 0.014, e~ = 4.6, e s = 78.3, and fc = 19.7 GHz. For soft tissue, such as muscle, four distinct relaxation frequencies have been identified (Table 1). Figure 3 shows the variation of relative dielectric constant for muscle whose zero-frequency conductivity is 0.02 m h o / m (resistivity, 500 ohm-m). For the delta dispersion, f c 4 = 1.5 GHz and m E 4 --- 15 were chosen. (Figure 4 shows conductivity and loss tangent curves. Figures 3 and 4 are typical for many types of biological

313

II. Biomedical Applications TABLE I Typical Debye Parametric Values for Muscle Tissue

fc

AE

A~r (mho/m)

Mechanism

Alpha

100 Hz

106

0.005

Beta

500 kHz

10 4

0.4

Ionic diffusion; membrane conductance; charging of intracellular membrane organelles Capacitive charging of cellular membranes; dipolar relaxation of proteins Dipolar relaxation of water Dipolar relaxation of water of hydration; rotational relaxation of polar sidechains; ionic effects

Dispersion

Gamma Delta

25 GHz 50 0.1-3 GHz 10-20

70 0.4-0.5

substances. F i g u r e 6, in the next section, shows a g r a p h of e' a n d tr for several types of tissue for t h r e e f r e q u e n c i e s below 1 G H z , at which variation as a function of f r e q u e n c y is not very large.)

IIII IIIIIII IIIIlll J~= h.1

Illlil Illll l llll~~,lillll~ °~_

IIIiil ,1111 IIiill ,~ ~"-~~ ;~ ;

'lJilil II1~ IIIIII1~IIII!11 I~~~111'i1~ III1~!1 ~!111 IIIIII1~ lllJll,~lllllll Irl'llJl°~.~

IIIIF ll[lll ',,llllfll lllllfl~~ flail Ii1111 N--N~.

~ 1

i 0°

101

I 0=

10~

FRF.OUENCY ( GIGRHERTZ ] Figure 3. Relative dielectric constant [Equation (7)], magnitude of impedance [Equation (13)], and relative wavelength [Equation (14)] as a function of frequency, for muscle tissue.

314

Joseph H. Battocletti

mFVf'.n i ItllnlllllllillllllllllF.iBllli

.:-li||.m;iiilll/lllllllEIIIIlillSli; i

lm i i / n l m m : u u u n / m l m m n n n l l n l n l

1

II//lilllnlLlmimilillri/ll imi/illlllllliiillllrniif~lllllllil Inl/iinnilllliilil~lnilrlllllliliii

i

Illiliilllli~lilhllillllllll/~ill

Jennie

l

U

l

l

in l i l l i l i L q l l l i l i i l n l m l / l l l , l l l l l l I l l l I I / / l l l l l l : l / l l l l l l l i F / l l l l i l i l l l l i l

lUmllml/ni

I

il

" I|l/lllllll|Jlilllll|/lllllll| / I / i ~

l

l m i l

i U i i l I I I i m i

i

l e l n n B B I l l l i

i i B l

l I l J i l G F ' r / i l

I n I i

B m I I l l

I I L I l l ~ I I D R l n g L i

o IZ LU CO u~ Z

lll

•

i i l I

l i i l i l l i i l n l l i l l i U J i l l i U i l l i l i i I I I I I I I I I B I I I R I I i l l i l i l i U l i l i n i i i

•

I='-]dllllllililllllllllillllllil|ll

IILlillilP.iilllilillLllllllilllllli InlliP%tllimlllllll&/VllllllllliLll

,~-CO dO _J

! li|llllllliililllll/:llillllliill

! I|/|llllll|/lllllllP'lllllllll|/lI ;d

l l i l b , l i l l l m i l i l l U l i i l / 1 1 l i l U l ~ i l l n l l l l l l l l n i F l i l L ~ I l i i m l l l l i m l l i U l l l l n i u n

I l i l i ~ l l l l l l l l i l l P l

i

l

i

i

n

L

l

i

l

l

l

n

i

n

n

l

d

l

l

n

i

I I I l l l l l K l U i

n

i

L

l i l l i i i l i i l l m l i l i i

q l n l n l l i

|/llp.~lllmilnlllli.~l/ll nli~-illllllllllllll/:U__n

10 0

101

10 2

FREQUENCY (GIGAHERTZ) Figure 4. Conductivity [Equation (8)], loss tangent, and skin depth [reciprocal of function of frequency, for muscle tissue.

a,

Equation ( I I ) ] as a

Space does not permit the inclusion of tables of dielectric constant and conductivity for biological and other materials at various microwave frequencies. References which are identified by an asterisk ( , ) are excellent sources of this information in both table and graph form. The propagation constant, 3/, and wave impedance, Z, can be derived from basic relationships in wave theory.

"y = j Og¢ l~ o % C:r = a -+- j [3

2=~

(9)

~0 EO~r

•

(10)

315

II. Biomedical Applications

Upon substituting for e r from Equation (4) and simplifying, a=

~-

~ ¢l/l+tan2a

- 1

(11)

/3 = ~-

~ ¢l/l+tan2a

+ 1

(12)

^ Z0 Z = g7r

(

cos -~ + j s i n (1 + tan 2a) 1/4 '

(13)

where c is the velocity of light and Z 0 is the wave resistance of free space, equal to 377 ohm. The wavelength in the dissipative medium is given by 2rr//3. By using Equation (12) and substituting Ao for 27rc/o9 (the flee-space wavelength), the wavelength in the material is r

a = a0

~/E

7(v/1 + tan28 + 1).

(14)

Because e' is usually much larger than unity for biological material, the wavelength and wave impedance are much smaller than the free-space values. The skin depth ( l / a ) is plotted in Figures 2 and 4 for water and tissue, respectively. The wavelength ratio (A/A 0) and magnitude of wave impedance (IZI) are plotted in Figs. (1) and (3). The conductivity-related curves for pure water and tissue were drawn to different scales and different axes because of the widely different values of conductivity, loss tangent, and skin depth between them. The loss tangent was better plotted on a linear scale for tissue, whereas a four-cycle log was best for pure water. Skin depth had to have five log cycles for water in spite of eliminating data below 0.125 GHz. These differences are attributed to assuming "zero" conductivity at "zero frequency" for pure water, whereas it is 0.02 m h o / m for tissue.

2. Heat Deposition in Biological Material, Particularly Man Exposure of biological material to electromagnetic fields is of three types depending on the distance, d, from the source of the field, the largest dimension, D, of the radiating source, and the wavelength (a).

Joseph I-I.

316

Battocletti

Far Field: Normal Radiation

The distance, d, is greater than 2D2/A. E and H are perpendicular to each other and to the direction of propagation, given by the vector, E × H. The field is radiative, comprising a plane wave whose power decreases inversely with d 2. E and H are related to each other by the intrinsic wave resistance, Z 0 - 377 ohm. Near Field: Inductive or Fresnel Region

The distance, d, is between h and 2D2/A. E and H, although perpendicular to each other by virtue of OB

VxE=

Ot '

does not yield plane-wave radiation. Wave impedance varies with distance. Radiation decreases inversely with d 4 and d 6. Near Field: Quasistatic or Reactive

The distance, d, is less than A. Most often the E field or the H field predominates, depending on the nature of the source of the field. Although the space variation of the field may be complex, analysis is often made by assuming a uniform field. Only that part of the field which enters the biological material generates heat by eddy currents when the equivalent conductivity of the biological material is nonzero. The energy absorbed depends on many factors, such as the shape, size, orientation, and heterogeneity of the object, as well as the frequency and nature of the excitation source. The frequency of the incident field determines the properties of the conducting medium, as discussed in the previous section. Heterogeneity may lead to localized heating. Polarization relative to the orientation of the object, as well as the free-space and internal wavelengths relative to the size of the object (resonance effect), is a factor to be considered. Although resonance effects do not occur at microwave frequencies for the human body due to the very short wavelength, resonance of parts of the body may occur. The generally accepted measure of heat generation is the specific absorption ratio (SAR) [64]. SAR is defined as the "time derivative of the incremental energy (AW) absorbed by, or dissipated in, an incremental mass (AM) contained in the incremental volume (AV) of a given density (p)." In equation form it is d(AW) SAR = -~- - ~

1 d(AW) = P ~ -~

(W/kg),

(15)

317


the entire mass of the object. Or it can be applied to a local region of the object, in which case AM is the mass of the selected AV volume. In the latter case, Or

SAR = ~plEI 2 ( W / k g ) ,

(16)

where IEI is the peak magnitude of the electric field in AV. The SAR figure can be measured in a smaller volume (animal) and extrapolated to a larger volume (man). The SARs for different-size objects are similar for a constant product of frequency ( f ) and dimension (L) of the object, i.e.,

fiLl =f2L2 .

(17)

Of course, this does not take into account the difference in the material properties at the two different frequencies. The SAR figure can be evaluated in closed form only for simple geometries, such as semi-infinite slabs, cylinders, spheres, prolate spheroids, and ellipsoids [41]. The development involves the solution of LaPlace's Equation by the method of separation of variables in a coordinate system natural to the geometry of the object [45]. Sometimes, a Schwarz-Christoffel transformation can yield a new geometry amenable to a usable coordinate system [35]. Although the closed-form solution of simple geometries yields qualitative insight into the location of heat generation, SAR must be determined by approximate analytical or experimental methods for real-life geometries. A second complicating factor is the necessity to consider the layered and heterogeneous nature of the object. The differing electrical properties of each layer or region often cause a peaking of the SAR inside the object. There is a large amount of literature which treats the many different models which have been used to assess the degree of deposition of heat in biological material caused by electromagnetic fields. For example, see a special issue on "Electromagnetic-Wave Interactions with Biological Systems" in the IEEE Transactions on Microwave Theory and Techniques, Vol. 32, No. 8, August 1984. Here, we will consider only full-scale human models. Models for mathematical analyses are constructed of a large number of blocks, slices, or both. The relative permittivity and conductivity of each block are selected to correspond to those of the tissue being modeled. Over a period of years, a full-scale heterogeneous model of a 162-cmtall man (Figure 5a) was developed by S. S. Stuchly et al. [66, 67]. It was

318


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(Run No. I) [59].

319

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FREOUENC't' (MEGFIHER'I'Z) Figure 6. Dielectric properties of four types of simulated tissue used in the experimental model of Figure 5c at three frequencies (I 60, 350, and 915 HHz). (a) Relative dielectric constant; (b) Conductivity, and (c) Skin depth [67].

constructed of the following: (a) 1-mm-thick fiberglass shell; (b) a simulated skeleton, comprising a skull, spinal cord, rib cage, and all major bones, except for those in the feet and hands, and fabricated from epoxy

320


and potassium chloride (KC1); (c) simulated brain, lung, and muscle, made from mixtures of hydroethyl cellulose, NaC1, and sucrose in such proportions to obtain the desired dielectric constant and conductivity (hollow silica microspheres were added to the lung mixture to simulate air passages); and (d) a semiliquid material having the dielectric properties of muscle. Measured dielectric constants and conductivities are plotted in Figure 6 for frequencies of 160, 350, and 915 MHz; these values fall within the range plotted in Figures 3 and 4 for muscle. Miniature triaxial electric field probes were placed at 38 locations inside the model to measure the electric field and thus the SAR from Equation (16). The locations are shown in a CT scan of the model (Figure 5b). A dipole antenna was positioned in front of the model and far enough away to generate approximate plane-wave radiation. It was oriented either vertically, i.e., parallel to the long dimension of the model (E-polarization), or horizontally (H-polarization). SAR values normalized to 1 m W / c m 2 of incident radiation are plotted in Figure 7 for locations along the central axis of the model ( A - A in Figure 5b), for all three frequencies, and both polarizations. The following are observed in Figure 7: (a) SAR values peak in the neck region, due to a smaller cross section with the accompanying higher current density; (b) SAR values are an order of magnitude less at 915 MHz than at 160 MHz; (c) SAR values for H-polarization are an order of magnitude less than those for E-polarization. Near-field SAR values were measured by M. A. Stuchly et al. [66, 67] in a similar experiment. The antenna was placed a small fraction of a wavelength in front of the model. Curves similar to those in Figure 7 were obtained; however, the SAR values were about one half as large, compared with far-field values, for the same incident power. The same heterogeneous model of man was used to obtain finer SAR measurements in the head, neck, and lung regions [59]. Measurement scans were made from back to front at 350 MHz for E-polarization. In addition, finite-difference time-domain analyses were made of a block model of 128,300 cubical cells. There were 8300 2-cm cubical cells for the body and 120,000 cells for the volume surrounding the body (Figure 5c). Boundary values of the variables computed for this model (called Run No. 1)were used in a finer-model analysis (called Run No. 2). Figure 8 shows the finer model which includes both the head and the neck regions. There was good agreement between the SAR values of the models and those of the experiment for the lung region and between the values obtained from the studies described above. However, measurement SAR values were generally larger than theoretical values for the head and neck regions. Experimental difficulties arose because of the simulated bone in the measurement path.

321

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322


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Guy and Chou [26] obtained SAR values of about the same magnitude in homogeneous models of man, woman, and child. Material electrical parameters were E ' = 51 and ~r = 1.24 m h o / m at 916 MHz. Radiation was obtained from a mobile radio antenna at 835 MHz. Again, maximum SAR values occurred in the neck region. The Biomedical Engineering group at the University of Utah, Salt Lake City, has developed another type of full-scale man mathematical model for analysis using the F D T D method [68, 69]. The model is based on cross sections taken from the classic book by Eycleshymer and Schoemaker [18]. Whereas the book divided the torso into 24 horizontal layers, Sullivan et al. [69] divided the entire body (typically 175 cm tall and 70 kg) into a larger number of cross sections. Each layer was subdivided into cubical cells of one or more of 14 tissue types, each with its own E' and ~r values. Table 2 gives information for two models, one for 100 MHz and the other for 350 MHz. SAR values were calculated on the basis of a density of 1 g / c m 3. Maximum values occur in the narrow sections, such as the neck and ankles. At 350 MHz, maximum SAR values were 160 m W / k g for 1 m W / c m 2 incident power density. All the above examples are for frequencies below 1 GHz. Gandhi and Riazi [22] discuss biological implications of millimeter-wave absorption above 1 GHz, up to 300 GHz. For tissue (see Figures 3 and 4), conductivity increases rapidly in this range, whereas the dielectric constant and skin

323

II. Biomedical Applications TABLE 2 Full-Scale Man Model Parameters for Two Different Frequencies (Biomedical Engineering Group, University of Utah) Item Number of layers Number of tissue cells Cube cell size (cm) Total number of cells (including air)

100 MHz

350 MHz

68 5,889 2.62 23 x 12 x 68 = 18,768

135 40,067 1.31 45 x 24 x 135 = 144,800

depth decrease rapidly. Consequently, most of the heat deposition (largest SAR values) occurs in the skin; thus, there may be thermal sensations similar to those caused by far-infrared radiation (,~ > 3 ~), since heatsensing nerve endings are distributed at depths from 0.1 to 1 ram. Gandhi and Riazi calculated SAR values greater than 15,000 m W / k g for an incident power of 1 m W / c m 2. They state that the threshold of heat perception occurred for incident power of 0.6 m W / c m 2, and sensations of "very warm to hot," at 8.7 m W / c m 2. The cornea of the eye is of particular and continuing concern at millimeter wavelengths as has been true for all microwaves in the past [4, 42]. Paulsen et al. [93] developed three-dimensional finite element analysis (3DFEA) techniques to calculate SAR in anatomically based human models, derived from CT scans. The formulations center on Helmholtz weak forms. With proper choice of algorithms and preconditioning, reliable convergence of the solution was achieved for matrix ranks of 200,000. Reduced instruction set computer (RISC)workstations were used; run times were on the order of hours.

3. Exposure Guides and Standards Concern over the potential deleterious effects of microwave radiation on man did not reach a critical stage until over 10 years after the end of World War II. The invention and use of high-power radar may have first led to occurrences of cataracts in radar operators and repairmen, even though an early study did not find any changes in the eyes of 45 military radar operators [14]. The first identification of cataracts in radar workers was not reported until 9 years later [28]. In subsequent studies, although some possible occurrences of cataracts may have been identified, more often subjects showed no ocular effects from normal activity in the vicinity of radar and other radiation sources [4].

324


The first exposure standard to gain widespread usage was formulated in 1957 at the Tri-Service Conference by the U.S. Armed Forces. This and subsequent standards and guides are listed and briefly described below with some commentary. For details regarding the more recent standards in the United States and in other countries, see Polk and Postow [49] and Stuchly [65]. The first four standards were applicable to the entire frequency spectrum [70]. Gradually, time duration of exposure was introduced. 1. The Tri-Service Conference (1957), sponsored by the U.S. Army, Navy, and Air Force, stated that the incident power density should be less than 10 m W / c m 2. 2. The Bell Telephone Laboratories (1960) stated that for indefinite exposure, the incident power density should not be more than 1 m W / c m 2. For incidental, occasional, or casual exposure, this level could be increased to 10 m W / c m 2. 3. The U.S. Army and Air Force specified a variable incident power density, P (mW/cm2), dependent on the exposure time, T, in minutes per hour of exposure. The following equation for this condition is applicable up to 55 m W / c m 2, since a minimum of 2 m i n / 1 h of exposure is considered to be practicable, T = 6000/P 2 (minutes per hour of exposure).

(18a)

For continuous exposure, T = 60 m i n / h ; so P = 10 m W / c m 2. 4. The U.S.A. Standards Institute (1966) Standard C95.1 set a limit similar to that of Equation (18a), but expressed the time of exposure averaged over 0.1 h. One form of the equation is T = 60/P

(minutes per 6 min of exposure).

(18b)

For continuous exposure, T = 6 m i n / 6 min; so P = 10 m W / c m 2. In addition, it was stated that this standard could be relaxed at extreme cold temperatures, but should be more severe for moderate-to-severe heat stress. 5. The research outlined in Section 2 led to the introduction of a variable incident power density as a function of frequency. For example, Figure 7 shows that SAR values are frequency dependent. Several Eastern European countries had already introduced frequency dependence into .

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325


their standards at the time the American National Standards Institute (ANSI) C95.1-1982 Standard was published [4]. The C95.1-1982 Standard is based on metabolic rates in humans and on a typical-size man weighing 70 kg and having 1.9 m 2 of surface area. Basal metabolic rates (BMR) of various organs and conditions are given in Table 3 [71]. More specifically, this standard is based on a whole body SAR of 0.4 W / k g , which is one tenth of what is considered to be a hazardous level. The frequency variation of incident power density (P), electric field intensity (E), and magnetic field intensity ( H ) is plotted in Figure 9. The ratio, E/H, in this Standard is 400 ohm; the ratio of E/H of a plane wave in free space is 377 ohm. The ANSI C95.1-1982 Standard is applicable for the general public and the workplace. The guidelines may be exceeded if the SAR does not exceed 0.4 W / k g . Time of exposure per 6 min is determined by Equation (18b). 6. Since the above-mentioned standards were not regulatory, being voluntary and advisory, several political entities in the United States passed laws, usually more stringent the ANSI C95.1-1982. The State of Massachusetts ad Multnomah County (Oregon) mandated a maximum SAR of 0.08 W / k g ; the State of Connecticut chose the ANSI standard; New York City ordered a maximum SAR of 0.02 W / k g [17]. 7. Reports and proposals proliferated in the 1980s by various organizations [17], such as the World Health Organization (1982), National

TABLE 3 Basal Metabolic Rates of Humans (W/kg) Averaged over whole body (sleeping) Skeletal muscle Skin Heart muscle Brain Kidney Liver Diathermy equivalent Young men in heat stress studies Noticeable to most individuals, primarily in the skin and skeletal muscle Theoretical values, assuming no thermoregulation Raise muscle 0.00024°C / s Raise muscle 1.5°C Raise head core temperature 0.2°C

1.05 0.7 1 33 11 20 6.7 50 5 1 1 1.4 1.4

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327

Institute for Occupational Safety and Health (1985), Environmental Protection Agency (1986), National Council on Radiation Protection and Measurement (1986), and Committee on Interagency Radiation Research and Policy Coordination (1986). 8. In 1987, the International Non-Ionizing Radiation Committee (INIRC) of the International Radiation Protection Association (IRPA) approved guidelines for both occupational and general public exposure limits. The occupational standard is based on a maximum S A R of 0.4 W / k g , but for the general public was reduced to 0.08 W / k g . Graphs of both standards are plotted in Figure 10 [2]. 9. The ANSI exposure standard of 1982 was revised by the IEEE Accredited Standards Committee No. 28 on Non-Ionizing Radiation Hazards to include guidelines on RF-pulsed power. The new guideline, C95.1-1991, covers exposure to both RF-pulse trains and single pulses. It includes the frequency range from 3 to 100 kHz and divides the balance of the frequency spectrum (up to 300 GHz) into seven frequency ranges. The new standard covers exposure criteria for both controlled and uncontrolled environments [30]. The graph is not very different from that in Figure 10.

4. Microwave Hyperthermia for Cancer Treatment Although not routinely used clinically at the present time, probably the most important and widely known application of microwave energy in medicine is cancer treatment by means of localized hyperthermia. This therapeutic technique involves the use of elevated temperatures in the 42 to 50°C range to hasten the destruction of cancerous tissue. At the elevated temperature, cells lose their ability to divide. However, the temperature limit for healthy tissue is 45°C due to pain and toxicity for the patient [79]. Review articles, with many references, were published by Cheung and A1-Atrash [13], Steeves [81], and Field and Hand [82]. Hyperthermia is often more effective when used in combination with another method of anticancer therapy, such as radiation or drugs. The combination effects may be additive, multiplicative, or complementary. An example of multiplicative effects is that after 1000 rad of X-ray radiation 100 of 10,000 cells survive, whereas only 1 of 10,000 survive when heat is added. An example of complementarity is that hypoxic cells are largely immune to X-ray radiation, whereas heat is equally efficient on both hypoxic and oxygenated cells. The combination of heat and chemotherapy or electrontherapy is additive [83].

328


Three parameters of critical importance in hyperthermia are temperature, time, and focusing of heat. Focusing is dependent on the type of applicator used and will be discussed later in this section. Desirable temperature and time relationships depend on physical and physiological characteristics of the cancerous tissue. For example, for therapeutic effect on a tumor, the period of heating at 42°C should be 45 min. It is important that heating be rapid and that the temperature distribution over the region of the cancerous tissue be as uniform as possible. For microwave heating, this requires that the local SAR be sufficiently large to compensate for thermal dissipation due to both heat conduction and blood perfusion. Hahn [27] identifies two thermal-time effects: Step-down heating: if cells are exposed to 43°C or higher for a short

time, the cells are much more susceptible to subsequent exposure below 43°C. Thermotolerance" if cells are exposed to mild heat or to slow heating. during patient setup, the cells become resistant when later exposed to 43°C or higher.

The Bioheat Equation A general form of the bioheat equation for the approximate modeling of the heating process in tissue is (e.g., [62]) OT

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=

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(19) where each term is identified according to its action in the heating process. The individual parameters in Equation (19) are defined as follows: Pt, tissue density (kg/m3); ct, specific heat of tissue ( W . s / k g / ° C ) [PtCt = 2 × 10 6 to 4 × 10 6 W" s / m 3 / ° C for various tissue]; Pb, blood density (kg/m3); Cb, specific heat of blood ( W . s / k g / ° C ) ; k c, thermal conductivity of tissue ( W / m / ° C ) , 0.20 to 0.64; m, volumetric flow rate of blood per unit mass of tissue (m3/kg/s); Tb, temperature of the blood entering the region (°C); Q ( x , y, z, t), power absorbed from the impinging M-field per unit volume of tissue (W/kg3), cr[E(x, y, z, t)[2;


329

Wm, power generated by metabolism per unit volume of tissue ( W / kg3); and I~72T, Laplacian of the temperature, T. Except for highly vascularized regions, the conduction term is much larger than the perfusion term. The conduction term also governs the time constant of the system, i.e., the time from onset of Q(x, y, z, t) to the steady state. Knudsen and Overgaard [34] solved Equation (19) as the one-dimension model of a semi-infinite homogeneous volume of tissue. They also applied surface cooling by means of circulating water in a plastic bag. This adds another term to the right-hand side of Equation (19), involving a heat transfer coefficient between the cooling water and the tissue. They showed that, by balancing the heat, Q(z, t), deposited by a plane wave traveling into the medium (z-direction)with cooling by all methods, the temperature could be maximized at a prescribed distance, z, below the surface. Strohbehn et al. [60] solved Equation (19) in polar coordinates, approximately applicable to a cylindrical model in which there is no temperature variation in the z-direction. Their model used N identical antennas equally spaced around the circumference of the cylinder. Isotherms were calculated for various conditions: (a) time following the onset of power deposition, (b) blood flow, (c) frequency of the plane wave, (d) number of antennas, and (e) electrical tissue characteristics, i.e., different types of tissue. The following results of the numerical analysis were obtained. (a) Four antennas excited at a frequency of 1 GHz were used to excite a 2.828-cm-diameter cylinder simulating skeletal muscle (e = 50, ~r = 1.3 m h o / m , Pt 1000 k g / m 3, c t = 3500 W . s / k g / ° C , and k c = 0.63 W / m / ° C ) , with a resting blood flow of 2.7 m l / 1 0 0 g / m i n = 0.45 × 10 -6 m S / k g / s . Therapeutic temperatures were obtained over a large portion of the cylinder after 15 min. (b) As blood flow was increased (e.g., by exercise), therapeutic temperatures were obtained only in the immediate vicinity of the antennas. Externally, cooling is often used to reduce the heating near the antennas [34]. (c) Excitation at 1 GHz gave the best hyperthermia for the multiantenna array for the 2.828-cm-diameter cylinder. (d) The uniformity of hyperthermia is improved as the number of antennas in the array is increased. (e) The region of therapeutic heating of tissue depends on the properties of the tissue. With skeletal muscle considered "unity," the volumes of =

330

JosephH. Battocletti

therapeutic heating of brain tissue and fat obtained in a four-antenna array are given in the following table.

Skeletal muscle Brain tissue Fat

e

tr (mho/ m)

Volume ratio

50 42 5.6

1.3 0.9 0.085

1.00 1.44 1.74

Mechling and Strohbehn [86, 87] solved the bioheat transfer equation for three-dimensional steady-state temperature distributions using a finite element method. Homogeneous and nonhomogeneous blood flow models were considered at 915 and 2140 MHz. Applicators

The majority of hyperthermia equipment for the cancer clinic has been of the "magnetic inductive" type, operating at frequencies around and below 100 MHz. Oleson [47] reviewed clinical applications prior to 1984. Most of the systems involved simple coils. One such system is the Magnetrode [61], developed by Henry Medical Electronics (Los Angeles, CA). A one-turn coil formed from a single sheet of copper was excited at 13.56 MHz. In another type, the CDRH Helix-I (Center for Devices and Radiological Health, FDA), the coil acts as a double-wavelength resonant device, operating at about 82 MHz ([25, 50]). A second type of sub-100-MHz applicator is the "annular phased array" (AA or APA). An example is an octagonal structure with 16 apertures, developed by BSD Medical Corporation (Salt Lake City, UT) [24, 61, 76, 77, 85]. Of the higher frequency hyperthermia applicators, the Interstitial Microwave Antenna Array (IMMA) is probably the one which fulfills the requirement of focusing the microwave radiation in the tumor [58]. The first type of IMMA which had practical clinical usage was four individual dipole antennas located at the corners of a square, typically 2 cm on a side [43, 79]. Each was inserted into the diseased tissue through an individual catheter. The antenna is made of coaxial cable, in which the outside portion of the end is detached. Figure l la shows a simple probe [43, 80]. This simple arrangement is not very efficient, having a cold zone near the tip, so that the probe must be inserted beyond the tumor. A better design was suggested by Turner [78] and is shown in Figure llb. Lyons et al. [43] used 915 MHz (A 0 = 32.8 cm), Winter et al. [79] used 2450 MHz (A 0 = 12.2 cm), and Turner [78] used 640 MHz (A 0 = 46.9 cm) for their applicator systems.

331

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Another design, the "ring-slot" applicator (Figure llc), has been proposed by Terakawa et al. [72]. A typical configuration, however, had a cool spot in front of the tip similar to those of the other two probes. Terakawa et al. proposed an equivalent circuit model, which might enable one to design a more efficient applicator. Driving the four antennas simultaneously and coherently yielded the most efficient operation. Although tuning each antenna produced maximum output at the antenna, it also produced unequal phase shifts which reduced the total power deposited in the tissue [80]. A better strategy is to design the antennas to match 50 ohm as closely as possible and then to use attenuators before the antennas to maintain the match. Of course, the effect of the tissue electrical properties must be taken into account in the tuning process. Typical clinical evaluations of the effectiveness of combined hyperthermia and radiation therapy in head and neck tumors are given by Seegenschmiedt et al. [58, 88]. Work is commencing on microwave waveguide applicators [89], in which beam shaping is accomplished by using absorbing saline/gelatin pad boluses. These pads could be designed to yield a uniform heating pattern over a large area or, alternatively, to generate complex heating patterns for specific clinical applications. In a different approach, a multiapplicator array is set up inside a large rectangular waveguide, operating below its cutoff frequency [94]. The human torso is positioned so that it acts as a post inside the waveguide.

332


5. Microwave Monitoring, Imaging, and Sensing Microwave radiation and detection techniques are being developed for the monitoring, imaging, and sensing of biological and physiological function of the human body. Although most of these techniques are being implemented with the transmitting antenna in contact with the body, remote sensing at a distance, even from behind a barrier, has also been accomplished. Some of the applications, which may have overlapping features, are related to the following: (a) (b) (c) (d) (e) (f) (g) (h) (i)

lung water [31], pulsatile blood flow [48], remote life detection [11], thermography or radiometry [37, 90], thermal imaging [7], permittivity imaging [23], breast cancer detection [16], neuronal activity in the brain [29], and cerebral blood flow [21].

Only several of the applications are discussed below, since most of them are based on similar principles and circuitry. Some applications use separate transmitter and receiver systems, whereas others use the same antenna for both transmitting and receiving. For the latter, interferometric techniques are used to obtain the desired information. In these cases, active sources are used. In some radiometric thermographic applications, detection is passive; i.e., the antenna or antenna array detects the electromagnetic energy naturally radiated by the object being scanned. The applications listed above are based on one of three parameters: (1) motion, (2) temperature, and (3) material variability. An example is given for each parameter.

One-Antenna, Active Sensing, Remote Life Detection An example of a one-antenna, active sensing system is described by Chen et al. [11]. They showed an X-band remote life-detection system, which

could detect slight movements of a living being, including respiration and heart beat. It is an interferometric system utilizing phase shift differences to obtain a signal caused by the motion. "Clutter" was canceled by subtracting some of the power applied to the antenna, properly attenuated and phase shifted, from the total signal picked up by the antenna, as

333

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shown in Figure 12, a simplified block diagram of the life-detection system. Clutter has to be random to be cancelable; other moving objects, such as trees and bushes, will deteriorate the signal from the living being. The operation of the system is independent of the polarization of the radiation, and clothing has no effect. Lin [91] reviews the subject of noninvasive detection and monitoring of movement of tissue and organs from outside the body. One-Antenna, Passive Scanning, Thermography or Radiometry All warm objects radiate electromagnetic energy according to Planck's black-body radiation formula, E(u,T)

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where E is the energy per unit volume between v and v + d~, (j/m3); h is the Planck's constant, 6.626 x 10 -34 J/s; c is the velocity of light, 2.997925 x 108 m / s ; k is the Boltzmann's constant, 1.38 x 10 -23 J / K ; T is the temperature (K); and u is the frequency (Hz). [Some books and articles use obsolete units and consequently have 8 r c h / c 3 as the factor in Equation (20).] A graph of E / E m a x as a function of frequency at a body temperature of 37°C is given by the solid curve in

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FREOUENCY ( 818RHERTZ I Figure 13. Normal Planck's black-body radiation spectrum (solid curve) at a temperature of 37°C. The dashed curve is the relative sensitivity from muscle tissue, using the "skin depth" curve of Figure 4. The normal emissivity of the muscle is assumed to be constant over the frequency range.

Figure 13. Note that maximum radiation occurs at about 18 GHz, with one-half energy points at 7.4 and 35 GHz. However, when temperature below the surface of the tissue is to be measured, the solid curve of Figure 13 must be combined with the frequency-dependent attenuation constant, a, and normal emissivity of the tissue. (Normal emissivity is determined by the physical properties of the tissue surface.) The effect of the tissue is taken into account by employing the truism, "a good radiator is also a good absorber." Therefore, the tissue which absorbs microwaves the best is the best radiator. Consequently, the tissue which has the larger a is the better radiator. For example, assuming that the normal emissivity is not frequency dependent, when a, the reciprocal of the "skin depth" curve of Figure 4 for muscle tissue, is combined with Equation (20), the overall relative sensitivity is given by the dashed curve in Figure 13. The optimum

335


sensitivity now occurs at about 25 GHz, with half-energy points at 14.5 and 45 GHz. These frequencies will vary for different tissues, since the attenuation constant varies differently with frequency for different tissue, as seen in earlier parts of this chapter. The attenuation constant, c~, of the tissue affects the overall emissivity of the radiating object, as already described. Carr [9] showed relative experiment emissivities of various materials including muscle and bone phantoms, saline, and water at 4.76 GHz. He pointed out that the emissivity of muscle, with a larger a, is much greater than that of bone. In the application of the black-body radiation phenomenon to microwave thermography, the inverse problem has to be solved. Through the measurement of radiated microwave energy, W(v), from a "warm body," the temperature, or temperature distribution a(T), of the warm body is to be determined uniquely. The radiation power spectrum is given by the equation, 2hv 3 ,.~ a( T) dT W ( v ) - C2 [Jo eTgvTiT5-i"

(21)

Many papers have been written on the subject of inversion of the blackbody problem, including Bojarski [6], Bevensee [5], and Chen and Li [12]. Solutions generally involve the use of the inverse LaPlace transform. Invariably the data which are obtained by W(v) are insufficient to obtain a(T)precisely [5]. To provide medically useful information, however, microwave thermography must have a temperature resolution of about 0.1°C [37]. Direct temperature measurement cannot meet this requirement. But, the requirement can be met by (a) measuring only differences in temperature and (b) using a Dicke-type comparison radiometer, in which the radiation signal is compared with a known thermal noise signal whose temperature is close to the temperature to be measured. A simplified functional block diagram of a microwave radiometer is shown in Figure 14. The temperature resolution, AT, is given by the equation [37]

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where Q is the radiometer constant whose value lies in the range of 4.6 to 6.6, Tre f and Tsig are the reference and signal temperatures, B is the receiver bandwidth (Hz), and r is the response time of the postdetection filter. Frequently, a commercial lock-in amplifier is used as the coherent detector in Figure 14; the filtering takes place in its postdetector filter. For

336

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example, for Q = 5.6, Tre f = 293 K, Zsig = 310 K, BW = 500 MHz, and ~- = 2 s, AT is calculated to be 0.107 K. Three examples of the use of the microwave thermograph follow. 1. Abdul-Razzak et al. [1] described a scanning microwave thermograph operating in the range of 9 to 10 GHz. An 80- x80-cm area was sampled to give a 64- x 64- x 4-bit image. With an integration time of 0.1 s, the time of the scan was 6.5 min. The antenna was located about 1 m from the subject. This system has been applied in a vascular surgery department to determine the best location for amputation of lower limbs. 2. Carr et al. [10] developed a dual-mode microwave system that combined an active transmitter for localized heating at 1.6 GHz and a passive microwave radiometer at 4.7 GHz. Carr [9] described a similar radiometer. A small-size antenna was placed in contact with the subject. The active transmitter, which provided localized heating, enhanced the early detection of cancer. The radiometer was also used in a study of 61 human volunteers for the following conditions: a. variation of temperature due to the menstrual period in women; b. changes of thermal patterns with age; and c. bilateral thermal symmetry between left and right breasts in women. 3. Land [37] built and tested a compact clinical microwave thermography system at 3 GHz. The antenna was placed in contact with the skin of


337

the subject. Temperature profiles have been taken of the following situations: a. across the left and right breasts to verify the presence of a 1.5-cm-diameter carcinoma; b. across the left and right knee joints to show rheumatoid arthritis; and c. across the lower anterior abdominal wall to show the presence of an inflamed appendix. One problem which has been encountered in the design of microwave radiometers for biomedical applications is impedance matching between the antenna and the tissue. Remote measurement (e.g., Abdul-Razzak et al. [1]) is not as good as contact measurement. Land [37] used a low-loss dielectric loaded TEll-mode circular waveguide with a broadband fin-line transition to a coaxial cable. Carr [9] used a simple TEl0 mode with dielectric loading to reduce the antenna's physical size. In studying the sensitivity of microwave radiometry, Cheever and Foster [92] used a dielectric-loaded waveguide antenna in contact with a lossy dielectric.

Two-Antenna, Microwave Imaging The dielectric properties of biological tissue have been measured, in vivo, by means of characteristics of a transmission line. Some of asterisks [ , ] in front of them describe and specifically, refer to the following.

at microwave frequencies the tissue's effect on the the references which have use this technique. More

a. Stuchly et al. [63] used an 8.3-mm Teflon-filled open-ended coaxial transmission line, described by Athey et al. [3], to measure various tissue in a cat up to 1 GHz. b. Kraszewski et al. [36] used an open-ended 3.6-mm Teflon-filled coaxial transmission line up to 8 GHz, also in a cat. c. Burdette et al. [8] used a 2.2-mm coaxial probe at 2.45 GHz to measure permittivity in the brain (both gray and white matter) of dogs. d. Thansandote et al. [73] used an interferometer system with a horn antenna at the end of the X-band waveguide to monitor biological impedance qualitatively at 9.3 GHz. These efforts led to the idea of performing microwave imaging of intact biological systems [32, 38]. See also the publication Medical Applications of Microwave Imaging, edited by Larsen and Jacobi [39].

338


In computed tomography (CT) using soft X rays, the scanning beam is collimated, so that its scattering is well defined. On the other hand, the electromagnetic radiation used in microwave imaging has a finite beam width and a diverging wavefront, resulting in complex diffraction, interference, and scattering patterns. This characteristic of microwave radiation has led to poor results in the images obtained so far, primarily because the same kind of reconstruction algorithms [algebraic reconstruction technique (ART)] used in X-ray CT were employed. This problem has been magnified by the use of the Born approximation, which assumes that scattering acts as only a small perturbation on the illumination, so that the field within the body is approximated by the incident field. This approximation breaks down in biological bodies due to their high contrast characteristics and large size compared with those of wavelength [33]. Datta and Bandyopadhyay [15] have suggested an improved algorithm, called the "simultaneous iterative reconstruction technique (SIRT)"; however, they concede that further work is needed to obtain a more refined algorithm. Resolution is also a problem, since it is approximately equal to one wavelength (inside the tissue); this problem is not as great as it could be since the wavelength in tissue is a fraction of the flee-space wavelength, '~0 [see Figures 1 and 3, and Equation (14)]. However, the wavelength is different in the various organs of the body. Spatial resolution is improved by immersing the body to be imaged in a medium of deionized water. The cylindrical imaging system described here was built and tested by Jofre et al. [33]; both absolute and differential images of tissue-simulating phantoms and of the arms of human volunteers were obtained. A functional block diagram is shown in Figure 15. Each of the 64 water-loaded waveguide antennas is flared in the E-plane to form a sectorial horn, 2.5 cm high by 2.5 cm long. The radiated field is approximated 2 cm high in the vertical plane of the cylinder. The H-plane is nearly omnidirectional, since it is not flared. In operation, one of the 64 horns serves as the emitter, and 32 horns opposite it on the cylinder wall are scanned sequentially. This is repeated 64 times; the measurement time is 3 s for human tests and 45 s for arm and head phantoms, to obtain better resolution. The following results were obtained. 1. In tests on the human arm, the resolution was much better for the imaginary part of the complex permittivity; the real part was unsatisfactory, which was attributed to the limitations of the Born approximation. 2. The resolution of temperature in water flowing through a 3-cm-i.d. rubber tube was 0.5°C.

339


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3. The changing blood flow in the human arm, in a cuffing-release experiment, was imaged in the differential mode. The sequence of images as a function of time showed both the storage of blood in the vascular system distal to the location of the cuff and the outflow at the release of the cuff. The reference image was that of result No. 1. 4. Differential imaging of a phantom head was performed to show changes within the brain, such as simulation of a hemorrhage. The reference was an image obtained by the reconstruction numerically simulated data. Changes of 1% were detectable. Jofre's system is limited in its application because the object must be immersed in water to provide impedance matching between the antennas and the object. Larsen and Jacobi [38] showed that spatial resolution could be improved by a factor of 9 when water immersion was used.

340

JosephH. Battocletti

Acknowledgments This work was supported in part by the Department of Veterans' Affairs Medical Center Research Funds and by the Department of Neurosurgery, Medical College of Wisconsin, Milwaukee, Wisconsin. Appreciation is extended to the Computing Center at Marquette University for the constant availability of its VAX cluster for the data analysis and graph generation used to prepare this chapter.

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[71] R. A. Tell, "An Analysis of Radiofrequency and Microwave Absorption Data with Consideration of Thermal Safety Standards," O R P / E A D 78-2, U.S. Environ. Prot. Agency, Off. Radiation Programs, Las Vegas, NV, 1978. [72] T. Terakawa, K. Ito, K. Ueno, M. Hyodo, and H. Kasai, Design of interstitial ring-slot applicator for microwave hyperthermia, l lth Annu. Conf. Eng. Med. Biol., Seattle, WA, pp. 1147, 1989. [73] A. Thansandote, S. S. Stuchly, A. M. Smith, and J. S. Wight, Monitoring variations in biological impedance at microwave frequencies, IEEE Trans. Biomed. Eng., Vol. BME-30, No. 9, pp. 561-565, 1983. *[74] W. R. Tinga and S. O. Nelson, Dielectric properties of materials for microwave processing-Tabulated, J. Microwave Power, Vol. 8, pp. 24-65, 1973. *[75] E. C. To, R. E. Mudgett, D. I. C. Wang, S. A. Goldblith, and R. V. Decareau, Dielectric properties of food materials, J. Microwave Power, Vol. 9, pp. 303-316, 1974. [76] P. F. Turner, Regional hyperthermia with an annular phased array, IEEE Trans. Biomed. Eng., Vol. BME-31, No. 1, pp. 106-114, 1984. [77] P. F. Turner, Mini-annular phased array from limb hyperthermia, IEEE Trans. Microwave Theory Tech., Vol. MTT-34, No. 5, pp. 508-513, 1986. [78] P. F. Turner, Interstitial equal-phased arrays for EM hyperthermia, IEEE Trans. Microwave Theory Tech., Vol. MTT-34, No. 5, pp. 572-578, 1986. [79] A. Winter, J. Laing, R. Paglione, and F. Sterzer, Microwave hyperthermia for brain tumors, Neurosurgery, Vol. 17, No. 3, pp. 387-399, 1985. [80] T. Z. Wong, J. W. Strohbehn, K. M. Jones, J. A. Mechling, and B. S. Tembely, SAR patterns from an interstitial microwave antenna-array hyperthermia system, IEEE Trans. Microwave Theory Tech., Vol. MTT-34, No. 5, pp. 560-567, 1986. (Spec. Issue Phased Arrays Hyperthermia Treat.) [81] R. A. Steeves, Hyperthermia in cancer therapy: where are we today and where are we going? Bull. N.Y. Acad. Med., Vol. 68, No. 2, pp. 341-350, 1992. [82] S. B. Field and J. W. Hand, An Introduction to the Practical Aspects of Clinical Hyperthermia. Philadelphia: Taylor & Francis, 1990. [83] J. B. Dubois, M. Hay, and G. Bordure, Superficial microwave-induced hyperthermia in the treatment of chest wall recurrences in breast cancer. Cancer (Philadelphia), Vol. 66, No. 5, pp. 848-852, 1990. [84] C. K. Chou, Evaluation of microwave hyperthermia applicators, Bioelectromagnetics, Vol. 13, No. 6, pp. 581-597, 1992. [85] R. J. Myerson, L. Leybovich, B. Emami, P. W. Grigsby, and W. Straube, Phantom studies and preliminary clinical experience with the BSD 2000, Int. J. Hyperthermia, Vol. 7, No. 6, pp. 937-951, 1991. [86] J. A. Mechling and J. W. Strohbehn, Three-dimensional theoretical SAR and temperature distributions created in brain tissue by 915 and 2410 MHz dipole antenna arrays with varying insertion depths, Int. J. Hyperthermia, Vol. 8, No. 4, pp. 529-542, 1992. [87] J. A. Mechling, J. W. Strohbehn, and T. P. Ryan, Three-dimensional theoretical temperature distributions produced by 915 MHz dipole antenna arrays with varying insertion depths in muscle tissue, Int. J. Radiat. Oncol., Biol. Phys., Vol. 22, No. 1, pp. 131-138, 1992. [88] M. H. Seegenschmiedt, R. Sauer, C. Miyamoto, J. A. Chalal, and L. W. Brady, Clinical experience with interstitial thermoradiotherapy for localized implantable pelvic tumors, Am. J. Clin. Oncol., Vol. 16, No. 3, pp. 210-222, 1993. [89] M. D. Sherar, F. F. Liu, D. J. Newcombe, B. Cooper, W. Levin, W. B. Taylor, and J. W. Hunt, Beam shaping for microwave waveguide hyperthermia applicators, Int. J. Radiat. Oncol., Biol. Phys., Vol. 25, No. 5, pp. 849-857, 1993.


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[90] K. R. Foster and E. A. Cheever, Microwave radiometry in biomedicine: a reappraisal, Bioelectromagnetics, Vol. 13, No. 6, pp. 567-579, 1992. [91] J. C. Lin, Microwave sensing of physiological movement and volume change: a review, Bioelectromagnetics, Vol. 13, No. 6, pp. 557-565, 1992. [92] E. A. Cheever and K. R. Foster, Microwave radiometry in living tissue: what does it measure? IEEE Trans. Biomed. Eng., Vol. BME-39, No. 6, pp. 563-568, 1992. [93] K. D. Paulsen, X. L. Jia, and J. M. Sullivan, Finite element computations of specific absorption rates in anatomically conforming full-body models for hyperthermia treatment analysis, IEEE Trans. Biomed. Eng., Vol. BME-40, No. 9, pp. 933-945, 1993. [94] A. Boag, Y. Leviatan, and A. Boag, Analysis and optimization of waveguide multiapplicator hyperthermia systems, IEEE Trans. Biomed. Eng., Vol. BME-40, No. 9, 1993.


CHAPTER

12 Chemical Applications of Microwaves Thomas C. Ehlert

I. Microwave Absorption Spectroscopy Introduction

This section

is limited to molecular gases. Absorption by atomic gases is extremely rare. Absorption by solids and liquids is not amenable to the following treatment.

Classifications of Molecules Molecules can be classified by their relative inertial moments about mutually perpendicular axes a, b, and c. These moments are represented by I A, I B, and I c , respectively. The classes are as follows. Linear molecules: I A -- I B and I c = O. Symmetric top molecules: I A = I B 4: I c (e.g., N H 3 and CHC13 ). Spherical top molecules: I A = I B = I c (e.g., SF 6, U F 6, and CC14). Asymmetric top molecules: I A 4: I B 4: I c (e.g., H 2° and CH 3OH).

Conditions For a molecular gas to absorb microwave radiation, three conditions must be met.


347


348

Thomas C. Ehlert

Resonance The radiation frequency v must satisfy the resonance condition Vtu = ( E u - E t ) / h ,

(1)

where h is the Planck's constant, E u is the upper energy state, and E l is the lower energy state. In all cases of practical import, u and 1 are rotational energy states. Rotational energy states are quantized; only certain energies are allowed.

Transition Probability The u ~ I transition must have a nonzero probability. This probability will be zero unless the molecule has a permanent electric dipole moment (see below).

Population Some of the sample molecules must be in state 1. Each of these requirements is discussed in detail below.

Rotational Energies The molecule's classification determines the formula to be used to predict the energies E u and E l used in Equation (1). Energy formulas are expressed in terms of rotation constants A, B, and C, related to the three inertial moments I A, I n, and I c, respectively, as A = h/(8rr2IAc)

(2a)

B = h / ( 8 7 r 2 I n c)

(2b)

c = h/(8¢%c),

(2c)

where c is the speed of light.

Linear Molecules For linear molecules E is given by E = J(J + 1)Bhc,

(3)

where J is a positive integer having values from zero upward and B ( = A) is a rotational constant for the nonzero inertial moment. Values of B

349

12. Chemical Applications of Microwaves

(rotational constants) for some diatomic molecules are given in the following table. Molecule BrH CN CO CS

B/cm -1

Molecule

B/cm -1

8.4657 1.8989 1.9302 0.8200

CIH FH HI HO

10.5884 20.9557 6.512 18.871

Values are averaged over isotopic varieties.

Symmetric Top Molecules The energy levels are given by

E = J( J + 1)Bhc + KZ( A - B),

(4)

where K is limited to integer values from 0 to J.

Spherical Top Molecules The energy formula is immaterial because these molecules do not undergo electric dipole transitions.

Asymmetric Top Molecules The formula for E is E = 0 . 5 J ( J + 1 ) ( A + C)hc + 0.5(A - C ) f ( E ) ,

(5)

where A is the largest and C is the smallest of the molecular constants A, B, and C. See Reference [1] for a tabulation of values of the function

f(E). Resonant Frequencies

In general, resonant frequencies are given by Equation (1). In some cases, simplifications are possible.

Linear Molecules Absorption occurs only when J increases by 1 so from Equation (1) resonant frequencies are given by ~, = ( 2 J + 2)Bc.

(6)

Symmetric Top Molecules Only transitions in which K does not change are allowed. As a result, resonant frequencies are given by Equation (6).

350

Thomas C. Ehlert

Spherical Top Molecules Under ordinary conditions (see Limitations), these molecules do not undergo electric dipole transitions.

Asymmetric Top Molecules Transitions for which J changes by 0, + 1, or - 1 are allowed. In general, Equation (6) applies. However, symmetry considerations may be important. See Reference [1].

Probability of Absorption---Attenuation of Microwaves Upon passing distance dx through a sample, the radiation intensity at frequency 2'lu, Ilu, decreases by dI~u: -- d i l u

= (Ilu)(absorber number density) ( transition cross section) dx.

(7) The dimensionless product (absorber number density) (transition cross section) dx represents the probability of absorption. The transition cross section and therefore the absorption probability are zero unless two requirements are met. (1) The molecule has a permanent dipole moment. Spherical top molecules cannot have a permanent dipole moment. (2a) For linear and symmetric molecules, Ju = Jl + 1, where Ju and Jl are the rotational quantum numbers for states u and 1, respectively. (2b) For asymmetric tops, Ju -- Jl + 1 or 0.

Transition Cross Section First, quantum mechanical methods are used to calculate the transition moment/Xlu. Then (transition cross section) = (h/c)[87r3tX2u/(127reoh2)]

(me), (8)

where c is the velocity of light and E0 is the permittivity of space. The quantity in brackets is called the Einstein coefficient of induced absorption Blu. EXAMPLE: If /Xlu for a certain transition is 1 × 10 -30 Cm, then Blu

= 8T/'3 X

(1 × 10-3°)2/((3 X 1.11 × 10 -1°) × (6.6 × 10-34) 2}

- 1.9 × 1018 mkg -1,


351

and by Equation (8) the transition cross section is 1.9 × 1018 × 6.6 × 10-34/3.0 x 10 8 = 4 × 10 -24 m 2. With the above relations, the attenuation equation [Equation (7)] can be restated as dllu -'-

Ilu(Nl/V)(h/c)Blu d x .

(9)

Alternatively, the number of times (S -1) that a molecule undergoes absorption transitions per second in a unit volume of a sample and in a frequency band 1 Hz wide at Vlu is rate of induced absorption = (4hv/c)flu (N1/V)Blu.

(10)

If N 1/ V is constant between x = 0 and x, the intensity change is the integral of Equation (10), In( I / I o)~,u = - ( N1 / V ) ( h / c ) ( Blu ) X,

(11)

where I 0 is the intensity at x = 0.

Population of the Lower Quantum State The absorber number density is the number of absorbers in state 1 per unit volume V. Under equilibrium conditions, N 1/ V is given by the Boltzmann equation which for the J t h rotational state is

Nj/V=

(N/V)(2J + 1)giexp(-Ej/kT)/z,

(12)

where N / V is the number of sample molecules per unit volume, g i, called the nuclear spin statistical weight, is discussed below, and z is the partition function. The following expressions for z are valid except when the temperature is very low. Linear Molecules

For linear molecules having a permanent dipole moment z is given by

z = Bhc/(~rkT),

(13)

where ~r, called the symmetry number, is defined to be unity for nonlinear molecules with no axis of symmetry and n for molecules with an n-fold axis of symmetry. Examples include ~r = 1 for CO, 2 for H 2 0 , and 3 for NH 3. In some cases, e.g., H 2 0 , the nuclear statistical weight gi must be included in z (see below).

352

Thomas C. Ehlert

Symmetric Top Molecules Excluding the possible need for the g i factor, discussed below, the partition function is given by J=~ Z

=--

K=J

E E J=O

(2J + 1)exp(-S(J + 1)Bhc/kT + (A - B)K2/kT).

K=-J

(14)

Asymmetric Top Molecules In this case z is given by Z -- " f f l / 2 0 r - l ( 8 ' w 2 k T h

-2]3/2fl/2fl/2II/2 ] *A "B

~C

"

(15)

Special Cases

For molecules in which one part can rotate with respect to another, as CH 3 can rotate relative to CH2C1 in CH3CH2C1, or which can turn inside out like an umbrella, e.g., NH3, see Reference [1].

Nuclear Statistical Weight The weighting factor g i is needed only in certain cases: molecules having symmetrically positioned identical nuclei with half-integral nuclear spins. Examples are H 2 0 , HzS , and NH 3. See Reference [2] for details.

Limitations The above requirements are valid only for perfectly rigid molecules. Real molecules are not exactly rigid; transitions which these rules forbid occur but with low probability. Due to centrifugal distortion, more complicated formulas are required to more precisely describe energy states. Also, "constants" A, B, and C vary slightly with the vibrational state of the molecule. Finally, at increased pressures interactions with neighbors induce dipole moments, obviating the requirement of a permanent dipole moment.

Widths and Shapes of Spectral Lines All transitions between quantum states occur over a finite range of frequencies. The more important causes include the following.

353


Doppler Broadening Translational motion of the absorber causes "Doppler" broadening of a spectral line. The frequency v' of radiation from a source moving at velocity v is v'=

v(a

-

v/c) ×

(1 -

v2/c2) -1/2,

(a6)

where v is the frequency when the source is at rest. Usually v

i,i ~t) d i,, Z

z:~ --LLI

o~ ~-~

>~- z ,~Ow

,,,

> o

..

a

q=

~"

w ~ u.. ~ u~e:o

•

I?

0

z o_

/J *

..J

F

O ~ >-~ ~ I.-. 1_ £9

Zu. Do

~,

:30~ n oo

xL

-

N

>.'-~ 0 (~)

~- ~_~ £::)

W :D

t9 0 ILl ->,,,

¢~l.-

. - I i_.

> Z ~

•LI_

13. Electron Paramagnetic

Resonance

395

Other EPR Microwave Cavity Designs In this section several novel microwave cavity ideas are discussed. Bimodal Induction Cavities

I n this application, one assumes the existence of two microwave modes that are degenerate in frequency with the microwave magnetic fields at the sample orthogonal. Moreover, both fields should be orthogonal to the static magnetic field H 0. Two incoming microwave waveguides are organized with accompanying irises such that microwave power can be introduced or received from each mode independently. Microwave power for excitation of the sample is coupled into one of the modes. If the two modes are perfectly isolated from each other, no power is found in the crossed mode; however, when magnetic resonance takes place, power is coupled to the orthogonal mode and, therefore, to the output waveguide. The sample can be said to induce a signal in the crossed mode. This is the microwave analogy of the Bloch crossed-coil induction experiment [1]. EPR induction was first described by Teaney et al. [67]. Moore has provided a particularly definitive theoretical analysis, including a discussion of isolation between modes [68]. Spurious leakage between modes can be described by a microwave vector of some phase and amplitude. It must be canceled by introducing an equal and opposite signal using suitable perturbing elements. In the author's experience, 30-dB isolation is achieved easily by careful machining, 50-dB isolation can be obtained and held using perturbing elements, and 80-dB isolation can be demonstrated on the microwave test bench, but is too unstable to be the basis of an experiment. Figure 25 illustrates a bimodal cavity designed by the author [66]. In this structure, two TEl03 modes are crossed, but only overlap for two half-wavelengths. The extra half-wavelength sections that are not "shared" contain the iris structures and provisions to tune the two resonant modes to the same frequency. The static magnetic field must be parallel to the long axis (z axis) of the cavity, which necessitates a rather large magnet gap.

Wire-Wound TEon Cavity Figure 26 illustrates a "wire-wound" TE011 cavity [69]. It is effectively transparent to transverse magnetic fields including not only magnetic field modulation at 100 kHz, but also radio frequency fields used in E N D O R (up to about 100 MHz). Microwave cavities based on this design were available commercially from Varian at both X-band, at which the wire diameter was 0.010 in. and the spacing, 0.010 in., and also at Q-band

W -r~W

0~--

1.1.1N

~

,-,~

>..-." ~ z

:ozX

1,1~0

~zDo~

0 i,a I - I.~

if)

W --W

I--_.1 ~0 W~ ~0_

a o

~..o w

~0~ --

(./') r r _

0

r-,% "

/

/

I

/

° d

g z~W~ ~Z~w

w~o~ E

.~n"

E

c'-

>,,, ..0

(D -(D 0 4-0

O ._C '~

tr~ >,,,

---

I--- -

o

0 E ~' 0

(D -[D

s-

U

oE

'0

~z

-o d

c-

>~

(D

0

c-

E

u~ c-

8

~ W

wO "1-0

Z

Dill

/

c~

'[3 (D

~o L

o~

i_

(D

~-- . _ ._u g-

'0

~>® u

cA

0 X

o -o E

E

13. Electron Paramagnetic Resonance

397

Figure 26. Wire-bound TEol~ cavity,

(35 G H z ) w i t h 0.005-in. wire diameter and spacing. The microwave coupling structure as well as sample access stacks were on one end, requiring careful attention to layout. Some microwave leakage was observed, apparently arising from the radiation field associated with the microwave coupling structure. This was reduced by surrounding the structure of Figure 26 by an insulated layer of closely spaced wires parallel to the axis of the cavity.

Large Sample-Access Cavity Figure 27 illustrates an exploded view of the so-called "large sampleaccess" cavity developed by Carrington et al. [70]. It is well known that very large holes can be placed on axis of TE011-mode cavities. The symmetry of this mode is such that the low cylindrical transmission line modes are not excited. The design employed a 2.5-cm sample-access stack. There was then no longer sufficient access at the ends for a coupling structure. Therefore, a TE012 mode was employed; the first half-wavelength along the z axis of the cavity was used for side coupling, and the second was a wire-wound structure as described in Figure 26.

398

James s. Hyde

Figure 27. Exploded view of the large sample access cavity of Carrington and Hyde for use with gas-phase samples.

Other Types of EPR Sample-Containing Structures Hefices

The traveling wave helix was introduced into EPR spectroscopy by Webb [71]. Resonant helices were analyzed by Volino et al. [72]. Sokolov and Benderskii describe the use of a helix for ELDOR [73]. These workers continued their studies of slow-wave structures for EPR spectroscopy as reported in the specialized Russian literature. Hausser and colleagues describe the use of a helix inserted into a microwave cavity for ELDOR experiments [74, 75]. Loop-Gap Resonators

This lumped-circuit device was introduced into EPR by Froncisz and Hyde [76], and numerous variations were subsequently developed. The subject has been reviewed [22]. The bridged loop-gap resonator of Pfenninger et al. [77] was analyzed by full-scale electronmagnetic field calculations. Anderson et al. [78] and Britt and Klein [79] describe experiments in which loop-gap resonators were inserted into TEl02 cavity resonators. Loop-gap resonators consist of discernable capacitances and inductances with overall dimensions of the order of 1/10th of a wavelength. Thus, they are in fact intermediate between distributed and lumped circuits. In the author's judgment, microwave geometries of this kind remain underdeveloped.


399

Slotted- Tube Resonator

This structure was introduced into EPR by Mehring and Freysoldt [80] following a design for use at much lower frequencies by Schneider and Dullenkopf [81]. The microwave magnetic-field pattern resembles that of the TMll 0 cavity mode. However, the entire structure is miniaturized by introducing curved conducting surfaces that are in the electric-field regions. The slotted-tube resonator has been widely used in pulse-EPR spectroscopy. Dielectric Resonators

The earliest use of dielectric resonators for EPR appears to be that by Rosenbaum [82], and this paper is recommended to the reader. Further access to the literature is provided by Poole [5, 6]. Typically, the EPR dielectric resonator oscillates in the cylindrical TE011 mode with a hole on-axis for the sample. A severe criticism of dielectric resonators for EPR usage is that background signals from trace impurities in the dielectric are very objectionable.

References [1] F Bloch, Nuclear induction, Phys. Rec., Vol. 70, pp. 460-474, 1946. [2] G. Feher, Sensitivity considerations in microwave paramagnetic resonance absorption techniques, Bell. Syst. Tech. J., Vol. 36, pp. 449-484, 1957. [3] T. H. Wilmshurst, Electron Spin Resonance Spectrometers, Monographs on Electron Spin Resonance. London: Adam Hilger, 1967. [4] R. S. Alger, Electron Paramagnetic Resonance: Techniques and Applications. New York: Wiley (Interscience), 1968. [5] C. P. Poole, Electron Spin Resonance: A Comprehensice Treatise on Experimental Techniques. New York: Wiley (Interscience), 1967. [6] C. P. Poole, Electron Spin Resonance: A Comprehensive Treatise on Experimental Techniques, 2nd Ed. New York: John Wiley & Sons, 1983. [7] Electron Spin Resonance, Specialist Periodical Reports. London: Chemical Society. [8] C. Daul, H. Fischer, J. R. Morton, K. F. Preston, and A. v. Zelewsky, Magnetic Properties of Free Radicals, Landolt-B6rnstein, Vol. 9. Berlin: Springer-Verlag, 1977. [9] A. Carrington and A. D. McLachlan, Introduction to Magnetic Resonance, with Applications to Chemistry and Chemical Physics. New York: Harper & Row, 1967. [10] G. E. Pake and T. L. Estle, The Physical Principles of Electron Paramagnetic Resonance, 2nd Ed., Frontiers in Physics. Reading, MA: Benjamin, 1973. [11] J. A. Weil, J. R. Bolton, and J. E. Wertz, Electron Paramagnetic Resonance: Elementary Theory and Practical Applications. New York: John Wiley & Sons, 1994. [12] N. M. Atherton, Electron Spin Resonance: Theory and Applications. New York: John Wiley & Sons, 1973.

400

JamesS. Hyde

[13] P. B. Ayschough, Electron Spin Resonance in Chemistry. London: Methuen, 1967. [14] J. E. Harriman, ~n Theoretical Foundations Of Electron Spin Resonance. New York: Academic Press, 1978. [15] S. A. Al'tshuler and B. M. Kozyrev, Electron Paramagnetic Resonance (trans. by Scripta Technica). New York: Academic Press, 1964. [16] W. Gordy, Theory and Applications of Electron Spin Resonance. New York: John Wiley & Sons, 1980. [17] W. Low, Paramagnetic Resonance in Solids. New York: Academic Press, 1960. [18] C. P. Poole and H. A. Farach, The Theory of Magnetic Resonance. New York: Wiley (Interscience), 1972. [19] A. Ehrenberg, B. Malmstr6m, and T. Viinng~rd, eds., Magnetic Resonance in Biological Systems. Oxford: Pergamon Press, 1967. [20] H. M. Swartz, J. R. Bolton, and D. C. Borg, eds., Biological Applications of Electron Spin Resonance. New York: John Wiley & Sons, 1972. [21] G. Feher, Electron Paramagnetic Resonance with Applications to Selected Problems in Biology. New York: Gordon & Breach, 1970. [22] A. J. HolT, ed., Advanced EPR: Applications in Biology and Biochemistry. Amsterdam: Elsevier, 1989. [23] L. R. Dalton, EPR and Advanced EPR Studies of Biological Systems. Boca Raton, FL: CRC Press, 1985. [24] L. Kevan and R. N. Schwartz, eds., Time Domain Electron Spin Resonance. New York: John Wiley & Sons, 1979. [25] L. Kevan and M. K. Bowman, eds., Modern Pulsed and Continuous-Wave Electron Spin Resonance. New York: John Wiley & Sons, 1990. [26] C. P. Keijzers, E. J. Reijerse, and J. Schmidt, eds., Pulsed EPR: A New Field of Applications. Amsterdam: North-Holland Publ., 1989. [27] L. J. Berliner, ed., Spin Labeling: Theory and Applications. New York: Academic Press, 1976. [28] L. J. Berliner, ed., Spin Labeling H: Theory and Applications. New York: Academic Press, 1979. [29] L. J. Berliner and J. Reuben, eds., Spin Labeling: Theory and Applications. New York: Plenum, 1989. [30] L. Kevan and L. D. Kispert, Electron Spin Double Resonance Spectroscopy. New York: John Wiley & Sons, 1976. [31] H. C. Box, Radiation Effects: ESR and ENDOR Analysis. New York: Academic Press, 1977. [32] M. M. Dorio and J. H. Freed, eds., Multiple Electron Resonance Spectroscopy. New York: Plenum, 1979. [33] P. C. Poole and H. A. Farach, Relaxation in Magnetic Resonance: Dielectric and M6ssbauer Applications. New York: Academic Press, 1971. [34] L. T. Muss and P. W. Atkins, eds., Electron Spin Relaxation in Liquids. New York: Plenum, 1972. [35] K. J. Standley and R. A. Vaughan, Electron Spin Relaxation in Solids. New York: Plenum, 1969. [36] A. Abragam and B. Bleaney, Electron Paramagnetic Resonance of Transition Ions. Oxford: Clarendon Press, 1990. [37] J. R. Pilbrow, Transition Ion Electron Paramagnetic Resonance. Oxford: Clarendon, 1990. [38] T. F. Yen, ed., Electron Spin Resonance of Metal Complexes. New York: Plenum, 1969. [39] F. Gerson, High Resolution ESR Spectroscopy. New York: John Wiley & Sons, 1970.


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[401 J. A. Weil, M. K. Bowman, J. R. Morton, and K. F. Preston, eds., Electron Magnetic Resonance of the Solid State. Ottawa: Candaian Society for Chemistry, 1987. [41] G. R. Eaton, S. S. Eaton, and K. Ohno, EPR Imaging and In Vitro EPR. Boca Raton, FL: CRC Press, 1991. [42] W. A. Anderson, Nuclear magnetic resonance spectra of some hydrocarbons, Phys. Rev., Vol. 102, pp. 151-167, 1956. [43] J. S. Hyde, M. E. Newton, R. A. Strangeway, T. G. Camenisch, and W. Froncisz, EPR Q-band bridge with GaAsFET signal amplifier and low noise Gunn diode oscillator, Rec. Sci. Instrum., Vol. 62, pp. 2969-2975, 1991. [44] R. C. Rempel and H. E. Weaver, Low-power microwave reflection bridge, Rev. Sci. Instrum., Vol. 30, p. 137, 1959. [45] J. S. Hyde, "Magnetic Resonance, Relaxation, and Rapid Passage Phenomena in LiF F Centers," PH.D. Thesis, MIT, Cambridge, MA, 1959. [46] J. S. Hyde, "Gyromagnetic Spectrometer Having Separate Dispersion and Absorption Mode Detectors," U.S. Pat. 3,350,633, Oct. 1967. [47] C. Hoentzch, J. R. Nikals, and J. M. Spaeth, Sensitivity enhancement in E S R / E N D O R spectroments by use of microwave amplifiers, Rev. Sci. Instrum., Vol. 49, p. 1100, 1978. [481 G. Grampp, Application of microwave preamplifier to an ESR spectrometer, Rev. Sci. Instrum., Vol. 56, pp. 2050-2051, 1985. [49] S. L. Dexheimer and M. P. Klein, Sensitivity improvement of a Varian E-109 EPR spectrometer with a low noise amplifier, Rev. Sci. Instrum., Vol. 59, pp. 764-766, 1988. [50] R. A. Strangeway, T. K. Ishii, and J. S. Hyde, Low phase noise Gunn diode oscillator design, IEEE Trans. Microwave Theory Tech., Vol. MTT-36, pp. 792-794, 1988. [51] R. A. Strangeway, T. K. Ishii, and J. S. Hyde, Design and fabrication of a 35 GHz 100 mW low phase noise Gunn diode oscillator, Microwave J., Vol. 31, pp. 107-111, July 1988. [52] D. A. Knoll, "Tuning of Microstrip Circulators for Maximum Sensitivity in ESR Bridges," M.S. Thesis, Marquette Univ., Milwaukee, WI, 1989. [53] J. S. Hyde, J.-J. Yin, W. Froncisz, and J. B. Feix, Electron-electron double resonance (ELDOR) with a loop-gap resonator, J. Magn. Reson., Vol. 63, pp. 142-150, 1985. [54] P. B. Sczaniecki, J. S. Hyde, and W. Froncisz, Continuous wave multiquantum electron paramagnetic resonance spectroscopy II. Spin-system generated intermodulation sidebands, J. Chem. Phys., Vol. 94, pp. 5907-5916, 1991. [55] H. S. Mchaourab, T. C. Christidis, W. Froncisz, P. B. Sczaniecki, and J. S. Hyde, Multiple quantum electron electron double resonance, J. Magn. Reson., Vol. 92, pp. 429-433, 1991. [56] C. F. Davis, Jr., M. W. P. Strandberg, and R. L. Kyhl, Direct measurement of electron spin-lattice relaxation times, Phys. Rev., Vol. 111, pp. 1268-1272, 1958. [57] M. Huisjen and J. S. Hyde, A pulsed EPR spectrometer, Rev. Sci. Instrum., Vol. 45, pp. 669-675, 1974. [58] R. W. Quine, G. R. Eaton, and S. S. Eaton, Pulsed EPR spectrometer, Rev. Sci. Instrum., Vol. 58, pp. 1709-1723, 1987. [59] S. S. Eaton and G. R. Eaton, Applications of high magnetic fields in EPR spectroscopy, Magn. Reson. Rev., Vol. 16, pp. 157-181, 1993. [60] R. C. Rempel, C. E. Ward, R. T. Sullivan, M. W. St. Clair, and H. E. Weaver, "Gyromagnetic Resonance Method and Apparatus," U.S. Pat. 3,122,703, Feb. 1964. [61] L. G. Stoodley, The sensitivity of microwave electron spin resonance spectrometers for use with aqueous solutions, J. Electron. Control, Vol. 14, pp. 531-546, 1963. [62] J. S. Hyde, A new principle for aqueous sample cells for EPR, Rev. Sci. Instrum., Vol. 43, pp. 629-631, 1972.

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[63] A. H. Maki and D. H. Geske, Detection of electrolytically generated transient free radicals by electron spin resonance, J. Chem. Phys., Vol. 30, pp. 1356-1357, 1959. [64] D. H. Geske and A. H. Maki, Electrochemical generation of free radicals and their study by electron spin resonance spectroscopy; the nitrobenzene anion radical, J. Am. Chem. Soc., Vol. 82, pp. 2671-2681, 1960. [65] L. H. Piette, P. Ludwig, and R. N. Adams, EPR and electrochemistry. Studies of electrochemically generated radical ions in aqueous solution, Anal. Chem., Vol. 34, p. 916, 1962. [66] J. S. Hyde, J. C. W. Chien, and J. H. Freed, Electron-electron double resonance of free radicals in solution, J. Chem. Phys., Vol. 48, pp. 4211-4226, 1968. [67] D. T. Teaney, M. P. Klein, and A. M. Portis, Microwave superheterodyne induction spectrometer, Rev. Sci. Instrum., Vol. 32, pp. 721-729, 1961. [68] W. S. Moore, The design, analysis, and performance of resonant and nonresonant microwave transmission devices with theoretically infinite rejection, Rev. Sci. Instrum., Vol. 44, pp. 158-164, 1973. [69] J. S. Hyde, ENDOR of free radicals in solution, J. Chem. Phys., Vol. 43, pp. 1806-1818, 1965. [70] A. Carrington, D. H. Levy, T. A. Miller, and J. S. Hyde, Double quantum transitions in gas-phase electron resonance, J. Chem. Phys., Vol. 47, pp. 4859-5860, 1967. [71] R. H. Webb, Use of traveling wave helices in ESR and double resonance spectrometers, Reu. Sci. Instrum., Vol. 33, pp. 732-737, 1962. [72] F. Volino, F. Csakvary, and P. Servoz-Gavin, Resonant helices and their application to magnetic resonance, Rev. Sci. Instrum., Vol. 39, pp. 1660-1665, 1968. [73] E. A. Sokolov and V. A. Benderskii, Binary electron-electron resonance spectrometer with a spiral resonator, Prib. Tekhn. Eksp., Vol. 3, p. 232, 1969. [74] K. Hausser, "Electron Double Resonance Spectrometer with a Microwave Cavity Bridge Arrangement," U.S. Pat. 3,798,532, Mar. 1974. [75] E. Stetter, H.-M. Vieth, and K. H. Hausser, ELDOR studies of nitroxide radicals: discrimination between rotational and translational correlation times in liquids, J. Magn. Reson., Vol. 23, pp. 493-504, 1976. [76] W. Froncisz, and J. S. Hyde, The loop-gap resonator: a new microwave lumped circuit ESR sample structure, J. Magn. Reson., Vol. 47, pp. 515-521, 1982. [77] S. Pfenninger, J. Forrer, A. Schweiger, and Th. Weiland, Bridged loop-gap resonator: a resonant structure for pulsed ESR transparent to high-frequency radiation, Rev. Sci. Instrum., Vol. 59, pp. 752-760, 1988. [78] J. R. Anderson, R. A. Venters, M. K. Bowman, A. E. True, and B. M. Hoffman, ESR and ENDOR applications of loop-gap resonators with distributed circuit coupling, J. Magn. Reson., Vol. 65, pp. 165-168, 1985. [79] R. D. Britt and M. P. Klein, A versatile loop-gap resonator probe for low-temperature electron spin-echo studies, J. Magn. Reson., Vol. 74, pp. 535-540, 1987. [80] M. Mehring and F. Freysoldt, A slotted tube resonator STR for pulsed ESR and ODMR experiments, J. Phys. E: Sci. Instrum., Vol. 13, pp. 894-895, 1980. [81] H. J. Schneider and P. Dullenkopf, Slotted tube resonator: a new NMR probe head at high observing frequencies, Rev. Sci. Instrum., Vol. 48, pp. 68-73, 1977. [82] F. J. Rosenbaum, Dielectric cavity resonator for ESR experiments, Rev. Sci. Instrum., Vol. 35, pp. 1550-1554, 1964.

CHAPTER

14 Microwave Navigation Aids Stephen Hatcher and Goson Gu

Microwave

navigation systems are moving away from systems requiring ground stations which offer variable performance to systems offering worldwide coverage with high performance in all weather conditions. Two such systems utilizing satellite telemetery and Doppler measurements are summarized in this chapter.

Part A: THE GLOBAL POSITIONING SYSTEM

The Gobal Positioning System (GPS) is a satellite-based position-fixing system under development by the U.S. Department of Defense since 1973. The purpose of GPS is to provide any user at any place on or near the surface of the earth with highly accurate three-dimensional position and velocity information and the time. With as many as 21 high-altitude satellites orbiting the earth, the coverage of GPS is worldwide and its precision is on the order of 10 m rms for position and 0.1 m / s rms for velocity in each dimension. Also it is tolerant of nonintentional or intentional interference. Compared with the existing systems like Loran-C or Transit System, GPS has shown its outstanding performance in precision,


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coverage, and user access. There is no doubt that GPS has become the dominating system for land, water, and air navigation.

I. General Description The GPS has three segments: the space segment, the control segment, and the user segment.

Space Segment (1) The Space Segment consists of 21 satellites orbiting the earth with a period of 12 sidereal hours at an altitude of 20,200 km. (2) In addition to 3 active spare satellites, the 18 operating satellites form a constellation of six orbits with 3 satellites equally spaced on each (see Figure 1). (3) Each orbit is inclined by 55 ° with respect to the equatorial plane and is offset from one another by 60 ° in longitude. (4) The 18 operating satellites continuously broadcast navigation messages which include satellite positions, satellite clocks, clock correction parameters, and other navigation information. (5) The number of in-view satellites above the horizon is at least four at any place on earth.

9 3

5

1

8

4 Figure I. GPS satellite configuration: six orbits with three satellites equally spaced on Earth.

405

14. Microwave Navigation Aids

Control Segment (1) The control segment consists of a master control station, an upload station, and four monitor stations (more stations are planned). (2) The master control station completely controls the operation of the control segment. It performs the computations necessary to determine satellite ephemeris and atomic clock errors, generates user navigation data, and maintains a record of satellite navigation processor contents and status. (3) The upload station provides the interface between the control segment and the satellites. It utilizes an S-band uplink to upload data into satellite navigation processors. The monitor stations are unmanned remote data-collection stations under direct control of the master control station. (4) Each monitor station receives a satellite's broadcast signals for processing and collects local meteorological data for tropospheric signal delay correction.

User Segment (1) The user segment includes any GPS user equipment capable of receiving and demodulating navigation signals broadcast from GPS satellites. (2) A GPS user equipment comprises four major components: antenna, receiver, computer, and i n p u t / o u t p u t device. It receives navigation signals from satellites, selects the satellites with the best geometry and computes the pseudoranges to them, and determines its position, velocity, or both.

2. Position Fixing The coordinate system used in this article is the earth-centered inertial coordinate system shown in Figure 2, in which the positive-x axis goes from the earth center through the intersection of the equator and Greenwich meridian, the positive-z axis goes from the earth center through the North Pole, and the y axis completes the right-handed coordinate system. Because of earth rotation, the x and y coordinates change in longitude about 15° per hour.

Concept of Position Fixing (1) By measuring the distance rl to a satellite at position (x ~, y 1, Zl), we can narrow down our position (x, y, z) from the whole universe to a

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Hatcher and Gu

NORTH POLE GREENWICH

Y

Figure 2. Earth-centered inertial coordinate system.

sphere specified by the following equation (see Figure 3a): ¢(X-

XX) 2 -I- ( y -

y l ) 2 -]- (Z -- Z 1)2 = F1.

(1)

(2) By measuring the distances r I and r e to two satellites at (x 1, Yl, Zl) and (x a, Ya, Za) respectively, our position is confined on a circle specified

Position Locus .....................

2

i

Figure 3. (a) One range puts the user on a sphere. (b) Two ranges puts the user on a circle. (c) Three ranges puts the user on two points.

407


by the following joint equations (see Figure 3b):

1,/" x -V

- xI

)2

2+

+ ( ~ - yl)

( z - Zl)

2

-- r 1

(2)

V/(x . x:) :+(y . .

.

/-2.

(3) Theoretically, knowing three satellite's positions and the distances to them, we can locate our position on earth (see Figure 3c). The position is determined by solving the following joint equations (there are two possible solutions, but one would be obviously wrong): V/(x -Xl)

.

2 + (y -yl)2

.+ ( y .

¢ ( x . x3) 2. + ( y .

+ (z - Zl)2

.+ ( z y3).2 + ( z

= rl

r2 z3) 2

(3)

/'3"

Satellite-Position Acquisition and Radio Ranging (1) The GPS satellites continuously broadcast their positions to GPS users. After a broadcast signal is received and demodulated, the position of the broadcasting satellite can be obtained. (2) The distance to a satellite is based on radio ranging. The distance between two points is measured using a radio signal which travels between these two points. Since radio waves travel at the speed of light, c - 300,000 km per second, the distance to a satellite would be r = c × t, where t is the time a radio signal takes to travel from the satellite to us. The distance to a satellite is measured in terms of the radio signal travel time from the satellite to user.

Clocks (1) To precisely measure the signal travel time requires knowing the exact times at which the signal is transmitted and at which time it is received. Since there are two different "times" involved, the timing system has to be unified. (2) The GPS standard time is indicated by the very accurate clocks at the master control station, which is almost equal to Universal Time Coordinated. With highly stable clocks such as cesium or hydrogen laser clocks, a resolution of 1 ns (10 -9 sec) can be reached. (3) The time of a satellite clock is called the "space vehicle time" (SV time). Although each satellite carries four atomic clocks, the SV time may

408

Hatcher and Gu

deviate slightly from the GPS standard time. This deviation is broadcast to GPS users via the satellite clock correction parameters contained in the navigation message. (4) The user clock is normally a quartz clock with lower accuracy than the satellite clocks.

Pseudoranges and Navigation Equations (1) Since the user clock is not accurate enough, the measured signal travel time would be incorrect. For example, a 10-3-s error will result in a distance error of 300 km. (2) To compensate the user clock error requires using four inaccurate satellite ranges called "psuedoranges." (3) Assume the user clock is tbias seconds faster than the GPS standard time. If the i th navigation signal is transmitted from the i th satellite at GPS time tsv i and received at user clock time tusi, the pseudorange to the ith satellite is /~i "- ¢ X (tus i --tsv i) and the true range is ri =

c X ( t u s i - - t b i a s - - tsv i) - - ri - - ¢ X t b i a s .

(4) Consider the following joint equations:

V/ ( x -

Xl) 2 + ( y -

yl) 2 + ( Z -

Z1)~ --/~1--C X tbias

V/(x - x2) 2 + ( y - y2) 2 + (z - z2) 2 = F2 - c X

/bias

(4)

V/(x-x s (X

-- X 4

2

+ (Y-Ys)

)~ -3t- ( Y

-- Y 4 )

2

2

+ (z-zs) -~- ( Z

-- Z4)

2 -- /~3 -- C X t bias 2

= r4 -- C X t b i a s .

Based on the known information, xi, yi, zi, and Fi, the four unknown terms, x, y, z, and t b i a s , c a n be solved. (5) Thus to derive a position a receiver must receive the navigation signals transmitted from four different satellites, get the satellite position information, measure the pseudoranges, and solve the navigation equations [Equations (4)].

3. Time Measurement (1) The pseudorange is determined by the inaccurate signal travel time (tus - tsv)which is measured by shifting and matching pseudorandom (PRN) codes.


409

(2) The GPS satellites broadcast their navigation messages using two data links: Link 1 (L1) at a center frequency of 1575.42 MHz and Link 2 (L2) at a center frequency of 1227.6 MHz. (3) The L1 and L2 signals are modulated by two PRN codes: a coarse acquisition code ( C / A code) and a precision code (P code). (4) The purpose of using PRN codes is for (a) the identification of the satellites, via code division multiplexing, and (b) the measurement of the signal travel time, via phase-shift measurement. (5) The C / A code is a Gold code with a length of 1023 bits and a chip rate of 1.023 MHz. It repeats every millisecond. (6) The P code is a long precision code with a complete cycle of 267 days and a chip rate of 10.23 MHz. Each satellite uses the exact one-week period of the P code which is nonoverlapping with the codes of other satellites. The P code is reset once a week. (7) The C,/A code is short, slow, and easily acquired. The P code is difficult to acquire but provides more precise timing. (8) Usually the C / A code is acquired first and then a transfer to P code is made. The transfer is made possible using the handover word (HOW). (9) Each 6-s navigation data subframe contains a new HOW (see Navigation Message). The H O W multiplied by 4 gives the Z-count at the beginning of the next 6-s subffame, where the Z-count is defined as the number of 1.5-s epochs since the beginning of a week. (10) Knowing the Z-count in the next subffame is equivalent to knowing the incoming P code in the next subframe. (11) The signal travel time is measured by the phase shift of the received signal with respect to the replica of the C / A code, P code, or both generated by the GPS receiver. (12) Although the measured signal travel time is inaccurate, it can be corrected by solving the navigation equations.

4. Velocity Measurement (1) The determination of the user's velocity is based on the measurement of the Doppler shift. (2) The velocity vector of a satellite at any time can be calculated by the user computer. (3) Knowing the position of the user and the position and the velocity of the satellite, the user's computer can determine the satellite's velocity along the direction of the user to the satellite.

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Hatcher and Gu

(4) The measurement of the Doppler shift gives the satellite's velocity relative to the user along the direction of the user to the satellite. The difference between the satellite's velocity and the satellite's relative velocity is the user's velocity along the direction of the user to the satellite. (5) A similar measurement from two other satellites provides the user with two other velocity vectors. (6) However, the signal frequency is not exactly known. Hence, four satellites and four Doppler-shift measurements are necessary to determine the user's velocity.

5. Signal Structure (1) The GPS signal carries information about satellite position, the satellite clock, clock correction parameters, and other components. (2) There are two data links, L1 and L2. Both the L1 and the L2 signals contain the same navigation data stream. (3) The L1 signal has two components: the in-phase component modulated by the P code and the quadrature-phase component modulated by the C / A code. (4) The L2 signal is modulated by the P code. (5) The C / A code is the product of two 1023-bit PRN codes with certain phase offset. It has a chip rate of 1.023 MHz and a period of 1 mso (6) The P code is the product of two long PRN codes with certain phase offset: one has a length of 15,345,000 bits and the other is 37 bits longer. It has a chip rate of 10.23 MHz and a complete period of 267 days. However, each satellite uses only a seven-day period of the P code. (7) Each satellite has it own C / A code and a seven-day period of the P code. (8) The navigation data stream has a bit rate of 50 bps with a subframe period of 6 s and a frame period of 30 s. (9) The spectra of L1 and L2 signals are shown in Figure 4.

6. Navigation Message (1) The navigation message is contained in a data frame 1500 bits long. (2) There are a total of five subframes in each data frame. (3) Each subframe consists of 10 words of 30 bits each. (4) The first two words are the telemetry word (TLM) and HOW, which are generated by the satellite. The remaining eight words of each subframe are user navigation data generated by the control segment.

411

14. Microwave Navigation Aids a L1 Signal dBW i

~

iq

, i,i

-1601-

2.046 MHz

~,,,,,, C/A Code

1575.42 MHz -

20.46 M H z - - - . ~

b L2 Signal

dBW

-166 1227.60 MHz 20.46 MHz

:-

Figure 4. The spectra of the L t and L2 signals,

(5) The TLM contains an 8-bit preamble, 14 bits of TLM message, 2 noninformation bearing bits, and 6 parity bits. (6) The HOW contains 17 bits of Z-count, a 1-bit synchronization flag, a 3-bit subframe identification, 2 noninformation bearing bits, and 6 parity bits. (7) The first subframe contains the satellite's clock correction parameters and ionospheric propagation delay model parameters, which are generated by the control segment. (8) The second and third subframes contain the satellite's ephemeris. (9) The fourth subframe contains a message of alphanumeric characters. (10) The fifth subframe contains the almanacs of all satellites (one per frame). (11) The format of the navigation message is shown in Figure 5.

7. Navigation Solution and Dilution of Precision The Navigation Solution (1) The navigation equations shown in Equations (4) are nonlinear equations of four unknown terms: x, y, z, and tbias.

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Hatcher and Gu

10 30-bitwords,6-secsubframe

Subframe No.

v

TLM

I HOW

I Block l - Clock Correction

TLM

l HOW

[ Block2-Ephemeris

TEa

I HOW I B'°ck3"Ephemen~(c°ntinued)

TLM

I HOW

TLM

HOW

]

l Block4-Message

1 frame 30 seconds 1500 bits

,

I BlockS-Almanac (25 framesto complete) ]

Figure 5. The format of a navigation message.

(2) A linearized version of Equations (4) can be derived, which is shown in the following, (x°-xl) A x + ( y O _ y a ) A y + ( Z 0 -- Z1) A Z + C • Atbias = A r 1 ~ o 0 0 r 0 -- C " tbias r~ o _ c • tbias r- ° -- C • tbias

(xO _

(yO -Ya) Ay +

X2) Ax +

0 ~0 _ C" tbias

(xO_X3)

-" 0 r 0 -- c " tbias

Ax +

~0 __ C" t0ias (X0--X4)

~0

(yO-Y_3_) Ay + ~0 _ C" t bias

Ax +

(yO_

Y4)

-

(Z° --z3) Az + c'Atbias 0 ~0 C " tbias z

Ay +

o

-

~o

r ° -- C" tbias

~O __ C" t0ias

( Z 0 -- Z 2 ) A Z -t- C" Atbias = A r 2 _ _ C . t0ias

= Af 3

z4)

c • t0ias

A Z + C • Atbias = A t 4 ,

(5) where x = x ° + Ax y=y°+Ay z=z°+Az

0

t bias : t bias -t- A t bias ¢

) 2 ( X 0 --

X i

+

(y

0

-

yi)2

+

(z

0

-

z i

)2

-

~ r° -

c

0 "/bias"

.413


(3) A matrix representation of Equations (5) is (6)

A .X=R,

where

A -

0-11

O'12

0"13

C

O'21

0"22

°'23

C

O"31

0"32

0"33

C

0"41

0"42

0"43

C

X=~ [Ax

Ay

Az

R = [A/~ 1

AE 2

AF 3

Atbias] T z~r4] T.

(4) The navigation solution is X=A

-1 . n ,

(7)

which gives the incremental relationship between pseudorange measurements and the user position and user clock bias. (5) The element 0-ij of A is the direction cosine of the angle between the range to the ith satellite and the jth coordinate, which affects the precision of navigation solution. Dilution of Precision (DOP)

(1) The matrix A is determined by the geometry of the four selected satellites. In the worst case, A-1 does not exit, which implies the unique navigation solution does not exit. (2) The covariance matrix of X is COV(X) = [A T. COV(R) -1 "A] -1. By normalizing COV(R) as the unity matrix, COV(X) = [ATA] -1, which implies the error variance of the user position and user clock bias is determined by the geometry of the four selected satellites. (3) The geometric dilution of precision (GDOP) is defined as oooP-

(4) In order to get the best navigation solution with the smallest error variance, the four satellites with the smallest GDOP should be selected.

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Hatcher and Gu

(5) Other DOP factors are defined in terms of Vx, Vy, Vz, and Vt, where V~, Vy, Vz, and Vt are the diagonal elements of COV(X). (a) Vertical dilution of precision (VDOP): VDOP = fVz(b) Horizontal dilution of precision (HDOP): HDOP = CV x + Vy. (c) Position dilution of precision (PDOP): PDOP

CV~ + Vy + V~.

(d) Time dilution of precision (TDOP): TDOP = ~ t -

8. Error Sources The errors of GPS are primarily from three major sources: the space segment, the user segment, and the propagation link.

Space Segment The errors coming from the space segment include satellite ephemeris error, satellite delay, and satellite clock error. (1) Ephemeris error: The satellite position error results from the difference between the actual satellite positions and the ephemeris data contained in the navigation message received by the user. (2) Satellite delay: The satellite delay is the signal propagation time delay caused by the processing and passage of the signal through the satellite equipment. (3) Clock error: The individual satellite clock may deviate as much as 976 /xs from GPS standard time. The deviation is corrected by transmitting the clock correction coefficients to the user as part of the navigation message.

User Segment The errors coming from the user segment include user receiver measurement error and user mechanization error. (1) Receiver measurement error: This error primarily is contributed by the receiver noise and the receiver quantization error. (2) Mechanization error: The mechanization error is due to finite resolution of user computers, mathematical approximation, algorithm uncertainties, and execution/computation timing delays.

415


Propagation Link The propagation link errors have been identified as being due to ionospheric delay, tropospheric delay, and multipath. (1) Ionospheric delay: The propagation delay of radio signals passing through the ionosphere is due to a reduction in speed and the bending of the ray. The overall delay in the signal is nearly inversely proportional to the square of the signal frequency. (2) Tropospheric delay: The tropospheric delay is the propagation delay of the signal when it passes through the troposphere, which is independent of signal frequency. (3) Multipath: Multipath error results from the combination of data from more than one propagation path that distorts the signal characteristics. This error depends on the environment and the specific location of the user.

9. Differential GPS Concept of Differential GPS (1) The concept of differential GPS is derived from the fact that the measurement errors are highly correlated among different GPS users in the same local area. (2) This correlation is because the satellites are so high up that the paths of satellite signals to different users in the same local area and the signal propagation delays will almost be the same. (3) By canceling the common errors experienced by different users in the same local area, the measurement accuracy can be increased to the order of centimeters.

Implementation of Differential GPS The implementation of differential GPS is shown in Figure 6. (1) A reference receiver at a known location is set up in the area in which greater accuracy is desired. (2) The reference receiver measures the correlated errors which are common to all users in the same local area. (3) The reference receiver broadcasts an error correction message to GPS users in the same local area. (4) The GPS users receive the error message and use it to correct their navigation solutions.

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Hatcher and Gu

ReferenceReceiver

~

H

/

Figure6. ConfigurationofdifferentiaGPS. l I0. Summary (1) The GPS is a satellite-based position-fixing system which provides the user with highly accurate three-dimensional position and velocity information and the time. (2) The GPS has three segments: the space segment, the control segment, and the user segment. (3) The space segment of the GPS consists of 21 satellites orbiting the earth at a high altitude. (4) The control segment of the GPS consists of a master control station, an upload station, and several monitor stations. (5) The position fixing is based on measurements of pseudoranges. It needs four satellites to get four navigation equations in order to solve four unknowns: three-dimensional position plus time. (6) The pseudorange is determined by the signal travel time which is measured via shifting and matching PRN codes. (7) The velocity measurement is based on the measurement of Doppler shifts. It needs four satellites to determine the user's threedimensional velocity vector. (8) The GPS navigation message is broadcast through two data links: L1 and L2. The L1 and L2 signals are modulated by the P code and the C / A code. (9) The C / A code is short, slow, and easily acquired. The P code is fast and difficult to acquire, but provides more precise timing. (10) The GPS navigation message contains the satellite's ephemeris, the clock correction parameters, the satellite's almanacs, and other components.


417

(11) The precision of navigation solution is determined by the geometry of the four selected satellites. This factor is called GDOP. (12) The best four satellites to be selected for solving the navigation solution are the four with the smallest GDOP. (13) The errors of GPS are primarily from the space segment, the user segment, and the propagation link. (14) With the operation of differential GPS, much more accurate measurements can be obtained.

Part B: DOPPLER NAVIGATION SYSTEM

A Doppler navigation system, or Doppler navigator, is a completely self-contained, dead-reckoning system requiring no ground stations. It is an all-weather system (except in certain conditions of rain) and can provide continuous position and velocity information anywhere on earth. The Doppler navigator obtains the velocity information from a Doppler radar and the direction information from a directional sensor. By combining these two pieces of information, the quantities such as along-heading velocity, cross-heading velocity, vertical velocity, ground speed, and drift angle can be determined. The Doppler navigator continuously integrates the velocity information into the distance traveled from the point of departure and resolves the present position. With the information of points of departure and destination or desired course and distance, the Doppler navigator can provide the autopilot information such as bearing to destination, distance to destination, track-angle error, and cross-course deviation.

I. General Description (1) A complete Doppler navigation system has three major components: the Doppler radar, the heading reference and vertical reference, and the navigation computer. The block diagram of a Doppler navigation system is shown is Figure 7. (2) The Doppler radar measures the aircraft velocity with respect to its antenna frame coordinate system.

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Hatcher and Gu Departure position & destination or desired course & distance

Doppler Radar

Velocity ~__

Pitch Roll and

Vertical Reference

Track-angle

Computer

Heading

-..__

~

CurrentBearinposition g Distance error Cross-course deviation

Navigation

1

To displays and to autopilot

1

Heading

Reference

Figure 7. Diagram of the Doppler navigation system.

(3) The heading reference and vertical reference fix the direction of the antenna frame with respect to the navigational coordinate system. (4) The navigation computer accepts the velocity information from the Doppler radar and the heading information from the heading reference, continuously integrates the velocity information into the distance traveled from the point of departure, and resolves the present position. By comparing the information of the current position with destination coordinates, the quantities such as bearing to destination, distance to destination, track-angle error, and cross-course deviation can be continuously computed. These quantities can be output to displays and to the autopilot.

2. Fundamental Principles of Doppler Radar (1) The Doppler effect is a phenomenon in which, when there is relative motion between a wave source and an observer, the observed frequency is different from the transmitted frequency. This change in observed frequency is called the Doppler shift, which can be expressed by

vRf fD=

C

vR -- h '

(1)

where fD is the Doppler shift, f is the wave frequency, c is the wave speed (speed of light for Doppler radar), VR is the relative velocity between the source and the observer, and h - c / f and is the wavelength.

419


(2) Consider an aircraft moving with a horizontal velocity, V~, and radiating a beam at an angle, 4~, with the velocity vector, as shown in Figure 8. The Doppler shift observed after the beam bounces back to the aircraft is 2f

2

f~' = - 7 V. cos 4' = 7 V. cos 4,.

(2)

If ~b and fD are known, V~ can be determined by v~ =

c .f,, a .fo = . 2 f cos & 2 cos ~b

(3)

Equation (3) is the fundamental expression for the measurement of velocity by means of Doppler radar. (3) Since velocity is a three-dimensional vector, it contains three orthogonal components. Therefore, a minimum of three noncoplanar beams are required to measure these three velocity components. A beam configuration, called a Janus configuration, is designed to accomplish this. It has both forward- and rearward-looking beams. A Janus configuration with four beams is shown in Figure 9 in which the beam Doppler frequencies f~ and the velocity components Vi have the following relationships. fA=

2f c[Vx cos 6

+ v, cos 0 - v~ cos 12 ]

f~=

2f 7[Vx cos 4,

- v,, cos 0 - v~ cos a ]

fc=

2_f [-Vx cos 6 - vy cos 0 - Vz cos a ] c

f~

2f = c[-Vx

cos 4, + v,, cos o - v~ cos a ]

c

D -I~ Vx = 8 f cos q5 (f°A + fB

-,"2)

c

v~ = 8 l c o s 0 ( f A - I ~ -

f~ +I5)

--c

v~ = 8 f c o s a ( f ~ +fF, + f c

+f~).

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Vx

Figure 8. Basic Doppler radar beam.

VZ

Vx

Vy

•

-\

Figure 9. Four-beam configuration.

42 I


(4) Since three noncoplanar beams are enough to measure the velocity components, we can drop beam D from Figure 9. The remaining configuration is a three-beam Janus configuration in which the beam Doppler frequencies f~ and the velocity components V/ have the following relationships. foA = 2 f f~=

c[Vx c o s

4, +

Vyc o s 0

2f c[Vx cos

4, -

Vyc o s

fDc = --~2 f [ -- V x

C O S (~ -

Vy

-

Vz

cos f~ ]

0 -

v~

cos f~ ]

cos

0 -

V z cos f~ ]

c

Vx = 4 f cos 05 ( f ~ - fc°) C

Vy = 4 f cos 0 ( f ~ - f ~ ) --C

V~ = 4 f cos f~ ( f DA + f cD) "

3. Functional Description of Doppler Radar A typical Doppler radar consists of four major units: the antenna, transmitter, receiver, and frequency tracker. The diagram of a Doppler radar is shown in Figure 10.

Antenna (1) From stabilization consideration, there are two types of antennas used for Doppler radars: one is fixed to the aircraft frame and the other is continuously stabilized to the local horizontal. (2) The fixed antenna has the advantage of simplicity. It can be made as an integral part of the aircraft's skin or a rigid assembly. However, extra computation is required to obtain the ground speed and drift angle. (3) The stabilized antenna produces simple velocity data and offers better accuracy at large drift, pitch, or roll angles. (4) From physical consideration, the antennas used for Doppler radars include linear slotted arrays, planar slotted arrays, paraboloids and cut

Hatcher and Gu

422

Antenna

Transmitter

Receiver

>~ FrequenCYTracker

Data

Converter

Velocity

Output Figure I0. Diagram of Doppler radar.

paraboloids, and dielectric and metal-plate-lens antennas fed by horns. Linear slotted arrays produce conically shaped fan beams, and the other types of antennas produce pencil or near-pencil beams. Transmitter and Receiver

(1) The radar signal is generated in the transmitter and radiated via the antenna system toward the ground. The signal is then backscattered by the ground, intercepted by the antenna system, and fed to the receiver. (2) In the receiver, the received signal is mixed with the transmitted signal or the signal generated by a local oscillator, and the resulting Doppler signal is amplified and then fed to the frequency tracker. (3) The basic types of signals generally used for Doppler radars are incoherent pulse, coherent pulse, continuous wave, and frequencymodulated continuous wave. (4) Doppler radars use frequencies in the X-band and Ke-band. Frequency Tracker

(1) The function of the frequency tracker is to track the center frequency of the noiselike Doppler signal output from the receiver. (2) The frequency tracker is a closed-loop system consisting of a frequency discriminator, an integrator, and a tracking oscillator. The block diagram of the frequency tracker is shown in Figure 11. (3) In Figure 11, the frequency discriminator measures the frequency difference between the Doppler signal and the signal generated by the tracking oscillator. The output of the frequency discriminator is fed to the integrator, whose output is used to control the tracking oscillator. Using

423

14. Microwave Navigation Aids Doppler Signal (from receiver)

Frequency Discriminator

Integrator

Tracking Oscillator

Doppler Frequency (to data converter) Figure II. Block diagram of a Doppler frequency tracker.

the frequency difference information, the tracking oscillator generates the feedback signal and outputs the Doppler frequency.

4. Doppler-Radar Performance and Errors Doppler-Radar Performance (1) The performance of a Doppler radar is a function of the Doppler signal-to-noise ratio ( S / N ) and the sensitivity of the frequency tracker. (2) The Doppler S / N per beam for a coherent system in which each beam is separately demodulated is given by

S)

PtGoaLrLaWEA 2

d=

, 16-n-2r2Bd k T ~ + PtQi 7

(4)

cos 0

where ( S / N ) d is the Doppler S / N , Pt is the average transmitted power per beam, G o is the one-way maximum antenna gain relative to an isotropic radiator, a is the scattering coefficient, L r are the losses in the radar transmitter and receiver paths, L a are the losses in the atmosphere, w is the antenna-pattern factor, E is the efficient factor, A is the wavelength of transmission, r is the range to the scattering surface along the beam, B a is the bandwidth of interest, k is the Boltzmann's constant, T is the absolute temperature, • is the noise figure of the receiver, Qi is the

424

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effective transmitter-receiver isolation coefficient, (N/S) t is the ratio of transmitter-generated noise to the transmitter power, and 0 is the central beam incidence angle with respect to a normal to the surface. (3) In most well-designed systems, Qi is SO small that the term PtQi(N/S) t in Equation (4) is negligible. In this case, Equation (4) becomes

(S)

Ptaoagrga WEA2

-N d -- 167r2r2BdkTdp COS 0"

(5)

Equation (5)can be rewritten as S

S

S

if

if

where (S/N)iz is the intermediate-frequency S / N in the intermediatefrequency bandwidth BiT of the receiver, expressed by

(S) -N if

_

PtGoaLrLawA 2 16rc2r2BifkTd# cos 0 '

(7)

and U is called the utilization factor which is the ratio of the Doppler S / N to the intermediate-frequency S/N. (4) The sensitivity of the frequency tracker is usually expressed by two quantities: the acquisition sensitivity and the tracking sensitivity. The acquisition sensitivity is the Doppler S / N with which the Doppler signal can be acquired and tracking begins. The tracking sensitivity is the Doppler S / N with which the signal-to-noise detector is set to cause the frequency tracker to stop tracking.

Doppler-Radar Errors (1) There are two types of Doppler-radar errors: random errors and bias errors. (2) Random errors are defined as those errors that vary during a flight or flight leg. There are two types of random errors: those with relatively long correlation times and the Doppler-fluctuation noise, which has a correlation time of 0.25 to 1 s. (3) The major sources of random errors are Doppler fluctuation, beam direction, transmission frequency, altitude hole, sea current, surface wind water motion, and attitude stabilization. (4) Bias errors are those that are constant for the duration of a flight. Known bias errors can be calibrated out, before the start of a flight, after


425

equipment installation in the aircraft, or even before shipment from the factory. All uncompensated bias errors must be taken into account in an error analysis of a Doppler radar. (5) The major sources of bias errors are beam direction, frequency tracker, land terrain, over-water calibration shift, installation, calibration, and readout.

5. The Navigation Computer (1) The navigation computer, fed with velocity information and the heading reference, can evaluate current position, ground speed and drift angle, course and distance to destination, and other navigation information. (2) If Doppler information is lost, the computer can continue to function on memory, using the latest-stored ground speed and drift angle. (3) The computer is required to allow the human operator to feed in the reliable position information any time during a navigation. (4) The computer can be designed as an integral part of the Doppler navigation system or as a separate unit capable of receiving standard inputs and performing the required computations.

Additional Reading R. J. Milliken and C. J. Zoller, Principle of operation of NAVSTAR and system characteristics, in Global Positioning System Papers Published in Navigation, Vol. I, pp. 3-14. Washington, DC: Institute of Navigation, 1980. J. J. Spilker, Jr., GPS signal structure and performance characteristics, in Global Positioning System Papers Published in Navigation, Vol. I, pp. 29-54. Washington, DC: Institute of Navigation, 1980. A. J. Van Dierendonck, S. S. Russell, E. R. Kopitzke, and M. Birnbaum, The GPS navigation message, in Global Positioning System Papers Published in Navigation, Vol. I, pp. 55-73. Washington, DC: Institute of Navigation, 1980. S. S. Russell and J. H. Schaibly, Control segment and user performance, in Global Positioning System Papers Published in Navigation, Vol. I, pp. 74-80. Washington, DC: Institute of Navigation, 1980. B. G. Glazer, GPS receiver operation, in Global Positioning System Papers Published in Navigation, Vol. I, pp. 81-86. Washington: DC: Institute of Navigation, 1980. E. H. Martin, GPS user equipment error models, in Global Positioning System Papers Published in Navigation, Vol. I, pp. 109-118. Wasl~ington, DC: Institute of Navigation, 1980. P. S. Jorgensen, Navstar/Global Positioning System 18-satellite constellations, in Global Positioning System Papers Published in Navigation, Vol. II, pp. 1-14. Washington, DC: Institute of Navigation, 1984.

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K. P. Yiu, R. Crawford, and R. Eschenbach, A low-cost GPS receiver for land navigation, in Global Positioning System Papers Published in Navigation, Vol. II, pp. 44-60. Washington, DC: Institute of Navigation, 1984. M. A. Sturza, GPS navigation using three satellites and a precise clock, in Global Positioning System Papers Published in Navigation, Vol. II, pp. 122-132. Washington, DC: Institute of Navigation, 1984. R. M. Kalafus, J. Vilcans, and N. Knable, Differential operation of NAVSTAR GPS, in Global Positioning System Papers Published in Navigation, Vol. II, pp. 197-214. Washington, DC: Institute of Navigation, 1984. J. Ashjaee, GPS Doppler processing for precise positioning in dynamic applications, in Global Positioning System Papers Published in Navigation, Vol. III, pp. 54-69. Washington, DC: Institute of Navigation, 1986. E. G. Blackwell, Overview of differential GPS methods, in Global Positioning System Papers Published in Navigation, Vol. III, pp. 89-100. Washington, DC: Institute of Navigation, 1986. D. Klein, The use of pseudo-satellites for improving GPS performance, in Global Positioning System Papers Published in Navigation, Vol. III, pp. 135-146. Washington, DC: Institute of Navigation, 1986. R. W. King, E. G. Masters, C. Rizos, A. Stolz, and J. Collins, Surveying with GPS, School of Surveying, Univ. of New South Wales, 1985. D. Wells, N. Beck, D. Delikaraoglou et al., Guide to GPS Positioning. Canadian GPS Associates, 1986. E. Lassiter and M. Ananda, The GPS overview and navigation system concept, in "The NAVSTAR GPS System" AGARD Lecture Ser. No. 161, pp. 1-1-1-13, AGARD, 1988. M. Ananda, The Global Positioning System (GPS) constellation and coverage, in "The NAVSTAR GPS System," AGARD Lecture Ser. No. 161, pp. 3-1-3-17, AGARD, 1988. M. Ananda, The Global Positioning System (GPS) accuracy, system error budget, space and control segment overview, in "The NAVSTAR GPS System," AGARD Lecture Ser. No. 161, pp. 4-1-4-17, AGARD, 1988. P. W. Nieuwejaar, GPS signal structure, in "The NAVSTAR GPS System," AGARD Lecture Ser. No. 161, pp. 5-1-5-6, AGARD, 1988. R. P. Denaro, Differential operation of Navstar GPS for enhanced accuracy, in "The NAVSTAR GPS System," AGARD Lecture Ser. No. 161, pp. 10-1-10-18, AGARD, 1988. J. Hurn, GPS: A Guide to the Next Utility, Trimble Navigation, 1989. A. Leick, GPS Satellite Surveying. New York: John Wiley & Sons, 1990. T. Logsdon, The Navstar Global Positioning System. New York: Van Nostrand-Reinhold, 1992. B. Hofmann-Wellenhof, H. Lichtenegger, and J. Collins, Global Positioning System: Theory and Practice. New York: Springer-Verlag, 1992. R. R. Hatch, ed., Global Positioning System: Papers Published in Navigation, Vol. IV. Washington, DC: Institute of Navigation, 1993. F. B. Berger, The nature of Doppler velocity measurement, IRE Trans., Vol. ANE-4, pp. 103-112, Sept. 1957. F. B. Berger, The design of airborne Doppler velocity measuring systems, IRE Trans., Vol. ANE-4, pp. 176-196, Dec. 1957. D. J. Povejsil, R. S. Raven, and P. Waterman, Airborne Radar. Princeton, NJ: Van Nostrand, 1961. _

.


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M. I. Skolnik, Introduction to Radar Systems. New York: McGraw-Hill, 1962. W. R. Fried, Doppler navigation, in Avionics Navigation Systems (M. Kayton and W. R. Fried, eds.), Chap. 6. New York: John Wiley and Sons, 1969. E. G. Walker, Airborne Doppler, in Navigation Systems: A Survey of Modern Electronic Aids (G. E. Beck, ed.), Chap. 7. Princeton, NJ: Van Nostrand-Reinhold, 1971. J. L. Farrell, Integrated Aircraft Navigation. New York: Academic Press, 1976. G. J. Sonnenberg, Radar and Electronic Navigation. London: Butterworth, 1988.


CHAPTER

15 Microwave Applications for Law Enforcement John Tomerlin and John Fuhrman

I. Introduction l J o p p l e r - b a s e d radar has been in use for traffic speed enforcement since 1947. This application requires a microwave antenna for sending and receiving, signal-processing circuitry, and an LED display for the target speed. When a signal is transmitted on one of the four frequencies presently assigned to traffic enforcement agencies by the Federal Communications Commission (FCC), a portion of that beam is reflected to the antenna by a moving object (target). In accordance with the Doppler principle, the frequency of the reflected energy will be higher than the energy that was transmitted. This difference is proportional to the speed of the target and can be converted into an equivalent value in miles per hour. There are important differences between radar devices designed for police traffic enforcement and those used by the military and commercial aviation. Whereas the latter employ an omnidirectional signal capable of detecting multiple targets and locating them directionally with great precision, traffic radar focuses energy into a relatively narrow beam~typically from 8° to 26 ° in width--in an effort to isolate individual targets. When only a single target is present in the radar's beam and in the absence of various types of interference, police radar is considered accurate to within + / - 1 mph of the target's speed.

Handbookof MicrowaveTechnology,Volume2

429


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Tomerlin and Fuhrman

Inasmuch as traffic radar measures only the difference in energy between the transmitted signal and the reflected signal, not whether one is higher or lower, it cannot determine whether the reflective surface is moving toward it or away from it, only the speed at which it is doing one or the other. A further difference is that, whereas large commercial radar devices measure changes in frequencies (Doppler shift) directly, police radar interprets changes after they are filtered through a phase-lock loop (PLL). This process is intended to stabilize the signal long enough for an operator to identify its source, but may result in other forms of error. Depending on design, traffic radar can be used in either the stationary or the moving modes, with some units being capable of both. Some moving radar can be operated simultaneously to the front and rear of the patrol car by means of dual antennas. In an attempt to defeat radar-detection devices, most recent radars can be operated in the instant-on mode which suppresses the signal until the last instant before a measurement is taken. When operated in this mode, there is no way for the operator to detect false speed readings due to various types of interference. Modern traffic radar produces an audible tone that varies in pitch according to the speed reading being obtained. This feature is known as "audio Doppler" and is extremely important to determine which of several possible vehicles within the radar's beam is responsible for a given speed reading. When more than one target is available, pointing the antenna does little to ensure the resultant reading. This holds true whether the targets are distributed laterally across several lanes of traffic or longitudinally at various distances along the highway. The signal emitted by the radar leaves the antenna in an expanding cone, like the beam of a flashlight, and grows wider (and weaker) as it spreads. At less than one quarter of a mile, the beam of a typical radar unit will cover all four lanes of oncoming traffic on a freeway. At a half of a mile it will pick up readings from all traffic in both directions. At one mile it will cover an expanse wide enough to land and take off in a small airplane. Because radar seeks out the "best" target in its field of reception, i.e., the best reflector it can find, it will readily ignore vehicles closer to it ~ r e g a r d l e s s of their s p e e d ~ t o fix on one more distant. Tests have shown that a small target may remain "invisible" to radar up to 500 ft from its antenna, whereas a large reflective target, such as a semi-tractor-trailer truck may produce a clear reading for up to a mile and a half. Weather conditions have a strong effect on police radar, with precipitation of any sort rendering it ineffective. Reduced visibility exacerbates target-identification problems, and high temperatures can cause erratic signal propagation. Radar cannot read the speed of targets around corners

15. Microwave Applications for Law Enforcement

431

or over the tops of hills, and its microwave radiation is readily absorbed or deflected by common objects in the highway environment such as trees or signs in the median strip. Such limitations make radar unreliable except along unobstructed roadways with relatively light traffic in good weather.

2. Historical Following the development of radar for military uses during World War II, traffic agencies began using a simpler form of the technology to compute traffic speeds. In 1947, the State of Connecticut employed radar to determine average traffic speeds in order to set speed limits and shortly afterward for enforcement. Several legal challenges ensued, all of which were successfully resolved in favor of the enforcement use of radar. In Dantonio v New Jersey, in 1955, the court determined that an officer needed no special training or proficiency in the use of traffic radar in order to measure traffic speeds and make arrests. Connecticut v Tomanelli, in 1966, established that the accuracy of the radar device could be reliably determined by holding a tuning fork of a known frequency in front of the radar's antenna and striking it. If the speed reading obtained by means of this simulation matched the fork's assigned frequency, the radar was presumed to be functioning properly. Honeycutt v the Commonwealth of Kentucky, also in 1966, added that, when more than one vehicle was present in the radar's beam and when a speed reading higher than the legal limit was obtained, the vehicle "out front by itself" and closest to the radar was responsible for the reading. Although, scientifically and factually, all three decisions were wrong, they remain the legal basis of radar speed enforcement. In truth, traffic radar is subject to many types of false speed readings due to interference. Such interference can be of an electromagnetic (radio) or mechanical type. Radio interference will be more commonly encountered in actual field use than in controlled classroom situations, with the result that police officers often underestimate the probability of such interference. The widespread proliferation of transmitting equipment increases the problem. For example, in the past five years alone, more than five million cellular telephones have gone into use, not counting the necessary base stations to support these mobile units. The problem of interference has become so acute that the U.S. military has assigned a special research and development group to do nothing but study this problem. When traffic radar is subjected to moderate to strong radio energy fields, different makes and models respond in nonstandard ways. Some will

432


boost the indicated speed up or down, whereas others may blank the display. When a mobile radio transmitter is within approximately 200 ft of the radar, false speed readings can be produced. Other sources of interference include CB radios, ham equipment, airport radar, and several types of door opening systems and bank alarms. High-intensity discharge also creates radio interference. Mercury vapor and neon lights, high-tension power lines, and electrical power stations are representative of external sources of interference, whereas police-band radio, air-conditioner fans, radiator fans, and even faulty battery connections inside the patrol car can cause false speed readings on police radar.

3. Moving Radar The use of police radar from a moving patrol car, so-called moving-mode radar, is accomplished by measuring two components of the transmitted signal. One component, referred to as the high beam, is directed at a target vehicle approaching the radar whose speed is determined in the usual way by interpreting the shift in frequency of the reflected signal. A second, "low" component of the beam is read from the ground or pavement ahead of the patrol car; this portion of the beam is taken to represent the speed of the patrol car, and is subtracted from the target speed. The sum of the two readings is taken to be the true target speed. The most common source of error in moving-mode radar results from incorrect readings of the low, or patrol car, portion of the beam. If moving radar locks onto a larger, slower moving vehicle instead of the ground, it will compute a lower-than-actual patrol speed; the difference in this reading will be added to the speed reading in the radar's target-speed display. This is known as "shadowing error." Here is an example of shadowing error. Imagine a typical four-lane highway with average traffic. A patrol car equipped with moving radar is traveling in the No. 1 lane (closest to the center divider). The posted speed limit is 45 mph. In the right-hand lane and slightly ahead of the patrol car is a semi-tractor-trailer truck in the process of slowing to turn right; as its speed decreases to 10 mph, the patrol car's radar locks onto the truck's strong reflective surface instead of the ground reference. In these circumstances, the radar will compute the patrol car's speed as 10 mph slower than it really is (actual speed minus truck speed). At the same moment, an automobile approaching from the opposite direction becomes the target of the patrol car's radar. It is traveling at the speed limit of 45 mph. The patrol car itself is moving 40 mph, so the radar


433

computes a closing speed of 85 mph. It then subtracts the (incorrect) low-beam speed reading of 30 mph and displays a target-speed reading of 55 mph. If the officer fails to observe an incorrect reading in the patrol speed window of his radar during the approximate 4-s interval available to him to (a) observe the target, (b) check its speed reading, (c) check his speedometer, (d) match the speedometer reading with the patrol speed reading of the radar, and (e)verify the correct target by means of a change in Doppler tone as it passes, then there is a high probability that the motorist in question will get a ticket for driving 10 mph above the legal speed. All radar is "line of sight." It cannot display the speed of any vehicle out of its direct "view." However, hills, dips in the road, or shallow valleys can cause difficulties in target identification. First of all, the radar unit must be carefully positioned in, or attached to, the patrol car. The antenna must be aligned in the direction of travel and parallel to the ground. This was easier to do when the antenna was incorporated with the console and operated from the dashboard; but increasing concerns for the harmful effects of stray microwave radiation have led to a preference for externally mounted antennas. Such antennas can reduce the amount of electromagnetic contamination reaching radar operators, but complicates the task of proper target alignment. When the patrol car crests a hill the radar beam does not conform to the ground contour, but instead tends to fall on traffic farther away. To visualize this effect, recall how your car's headlights illuminate the road while being driven in rolling or hilly terrain. Under such circumstances, police radar will not travel to the nearest approaching vehicle, but will overshoot it to display the speed of a vehicle or other moving object in the distance. Curves in the highway present a different problem in that moving radar can add speed to a target that approaches its antenna along an inside arc. This error is due to an increase in the frequency shift caused by reading the target along an angle cotangent to its true direction and is known as cosine error.

4. Mechanical Errors Mechanical interference can be defined as the reflection of a radar signal from any moving object other than the target vehicle that produces a speed reading. Traffic radar is designed to measure the relative motion or velocity of objects. The tuning forks used to perform the most basic field

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testing of a radar device utilize the unit's ability to respond to any moving object included in a non-Doppler reflection. It is important to note that the frequency of the return echo has not in this case been frequency shifted; instead, the radar echo has been phase modulated by the vibrating tines of the fork (the frequency of the return echo itself has not been changed). Thus, there are two mechanisms that can cause a reading in the display, the frequency shifted Doppler return echo and the modulation of the unshifted echo, the latter of which may be caused by any vibrating or rotating object. The tuning fork test, it should be noted, verifies only the operation of the radar unit's counting circuits and its display. Tuning fork accuracy is thus only part of the calibration evidence that must be referenced in order to ensure accuracy. Another source of error in police radar is a change in frequency of the microwave oscillator due to age or mishandling. Although the tuning fork is able to verify the accuracy of the timebase used to convert Doppler frequencies into digital readings, it does not ensure that the microwave generator itself is operating on the correct frequency. Inasmuch as the Doppler difference is proportional to the transmitted frequency, if the transmitter produces a higher frequency than that assigned, the radar unit will read high. Lower frequencies will result in lower speed readings, but in neither case will the error be observed during the tuning fork calibration test. Some manufacturers employ quartz crystals for internal signal verification as a sort of self-test. At least one, however, uses a reed device that is suspected of being sensitive to temperature changes. Such units may give unreliable readings in conditions of extreme heat or cold; indeed, this unit failed government tests under these conditions (see below).

5. Mechanical Interference Police radar is highly susceptible to various types of mechanical interference, the most commonly occurring of which is the patrol car's own A C / h e a t e r fan. Depending on the type of radar unit~single piece or m u l t i p i e c e ~ o r the method of mounting, fan reflection can vary from weak to strong. Operation requires care and knowledge by the operator because the fan location is not obvious in most automobiles. Just placing the antenna away from any vents or ducts is not enough; the operator should perform a test by turning the fan on and off and by operating it at different speeds to ensure that "ghost" readings are not being produced.


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Certain roadside objects may also cause undesirable readings on the radar display. Large ventilating fans, rotating ventilators, signs, or turbines are examples of sources of mechanically induced interference. Not only is radar used in the moving mode susceptible to all these sources of interference, many or most of these sources are difficult to identify due to the transient nature of their occurrence. Another situation in which the target's speed can be misread is when the patrol car carrying radar slows down abruptly while performing a reading. This situation may occur often if the police officer begins to slow down prematurely during the reading in order to turn around to begin pursuit. The resulting effect, which is known as "batching," or target-speed bumping, results because the readout for the patrol car's speed is slightly dampened to avoid random fluctuations. Sudden deceleration may confuse the unit and cause it to add several miles per hour to the target speed (or fail to subtract enough patrol car speed, which is the same thing). Because most moving-radar units are built in two pieces, an antenna and a control console, the antenna can be turned in such a way as to scan its own console. This produces very high speed readings. It can occur accidentally when the officer changes from taking readings in one direction to reading traffic coming from the opposite direction.

6. Photo Radar A variation of the use of radar, so-called "camera radar," or "photo radar," has been in use in Japan and some countries of Western Europe for several years. It has been adopted by several smaller U.S. cities. The system consists of a radar speed gun and a still camera. Positioned along the road, or in some cases suspended directly above a lane of traffic, the radar is set to trigger the camera whenever a higher speed is detected. A photograph is taken to capture the license plate and, in U.S. versions, the face of the driver. The license plate number is then used to locate the vehicle's owner from Department of Motor Vehicle records, and the picture is used for identification in case the ticket is protested in court. Photo radar differs from conventional radar in several ways. Instead of being aimed parallel to the road to pick up oncoming or receding traffic, it is directed across one or more lanes of traffic at a shallow (22 °) angle. Its narrow beam width and low power output make it all but invisible to present-day radar detectors. Some detector manufacturers offer " K a " band (34 Ghz) sensitivity, but as a rule they are useful only to tell the driver when he has been through a stakeout, not to warn him ahead of time.

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TomerlinandFuhrman

The effective range of photo radar is about 120 ft, or approximately three lanes of traffic. This makes it susceptible to registering--and photographingmmore than one car at a time. Distributors of photo radar claim that it can reliably distinguish between vehicles under these conditions, but technically speaking this is untrue. Basic lane discrimination depends on the unit being set up with great precision and kept free from such disturbances as wind gusts from passing cars and trucks. When multiple targets are present, no present type of police radar can be relied upon to tell which is traveling at a particular speed. Photo radar devices are manufactured by several companies in Western Europe and Japan, but none are built in the United States at present. This makes it difficult to ensure performance specifications, and to date none has been tested or approved by the National Bureau of Standards. The film is exposed through an optical matrix containing the time, date, location, and radar speed reading of the target vehicle. A magazine holds enough film for about 800 exposures, which can be taken at a rate of up to 260 frames per hour. Once the film has been retrieved and developed, each photo is examined to make certain that the license plate is legible and the driver's face is recognizable. If either has been obscured for any reason, the evidence is thrown away. Otherwise, the registered owner (not necessarily the driver of the car at the time of the violation) is notified by mail and advised of the amount of the fine. Because photo radar is operated from the side of the road, and directed across it at a fairly sharp angle, it is necessary to correct for cosine error. This is done by calculating the amount of cosine effect included in the reading and correcting to produce the vehicle's presumed actual speed. Unfortunately, this method does not allow for sudden changes in vehicle direction, as when it changes lanes, a circumstance that may result in as much as 5 mph being added to or subtracted from the actual speed. Inasmuch as there is no witness to the act of speeding other than the radar itself and since the equipment is not subject to crossexamination, motorists accused of speeding by photo radar have no means of defense.

7. Testing for Accuracy No federal performance standards for police radar exist, nor is regular testing done to ensure accuracy. However, the National Bureau of Standards (NBS) tested the six most commonly used radars in 1980, and the International Association of Chiefs of Police (IACP) tested all available


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brands and models in 1984. Both programs indicated that the reliability of current police radar technology is inadequate. A total of 24 models were tested for compliance to the Model Performance Specifications for Police Traffic Radar Devices developed for the National Highway Traffic Administration (NHTSA) in the Law Enforcement Standards Laboratory (LESL). The specifications had been adopted by the IACP and the program was conducted under their supervision during the period June 1983 to January 1984. The radar devices were subjected to examination, including documents and accessories, laboratory evaluation, and operational testing. During the period of testing the radar manufacturers were allowed to make minor modifications to their products to achieve compliance with the model specification requirements. Upon the completion of the initial testing it was found that many of the individual radar devices failed to comply with the model specifications because the required manufacturer information was not provided. For example, some devices lacked operating or installation instructions, whereas for others the required tuning fork certificate was either incomplete or not provided. In several instances model specifications were misleading or unrepresentative of actual performance, either exceeding the limits for signal processing sensitivity or claiming nonexistent sensitivity in certain speed ranges. Overall, few of the radar units provided for testing were in full compliance with the labeling and manufacturer-provided information requirements at the time of initial testing. In addition, there were some areas of noncompliance with the requirements of the model specification that required "minor modifications" to the test units to achieve compliance. The most common deficiency was failure to meet the signal processing channel sensitivity requirements. This deficiency was corrected, in most cases, by a change in the values of the filter components. The second most common deficiency was in the display readability capability of the units, i.e., character height and luminance contrast. Other areas of noncompliance included frequency stability under conditions of high and low temperature or of high humidity. After modifications were made to the test units under IACP supervision, all five participating manufacturers were judged to be in full compliance with model specifications. This decision was somewhat arbitrary, as the following summary of test results indicates.

Tuning Fork Calibration This test required measurement of the frequency of the tuning fork to ensure that it was within + / - 0 . 5 % of the frequency specified in the

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certificate of calibration. This could not be accomplished with 12 of the radar units as no certificate was supplied by the manufacturer. Tuning Fork Tests

The tuning forks supplied for use in checking the operating condition of the radar device were tested. If the radar is functioning properly, the speed for which the tuning fork is calibrated should appear in the speed display with a tolerance of + / - 1 mph. With moving radar devices, both the target and the patrol speed displays must show correct speed readings. The tuning fork tests were conducted under standard conditions, specified low- and high-temperature conditions, high-humidity conditions, and high-vibration conditions. All of the radar devices were found to be in compliance at ambient temperature; however, four of the devices failed to comply during the environmental tests. Three radar units did not function properly at low temperature. One of the three also did not function properly under the high-temperature test conditions, and another of the three failed during the high-humidity test. The speed display on one additional unit showed erroneous readings during vibration tests. Microwave Transmission

These tests checked the stability of operation of the radar devices under conditions that could be encountered in the operational environment. The tests were repeated a number of times to record performance data under standard test conditions (68 to 80°F) and under conditions of low temperature (-22°F), high temperature (140°F), and high humidity (90% at > 99°F). All tests were repeated at three voltage levels; nominal voltage (13.6 V), nominal voltage plus 20% (16.3 V), and nominal voltage minus 20% (10.8 V) or any lower voltage specified by the manufacturer. Five of the radar devices did not maintain frequency stability within the allowable tolerances during testing. One failed under all conditions, whereas three others failed the low-temperature test. A fifth device failed during the high-humidity test. Three of the radar units that did not meet the frequency stability requirement also did not meet the input current requirements of less than 10% variation and no change in numerical display under one or more of the test conditions. Three additional units were unstable during the low-temperature tests, whereas four failed at high temperature. Four units failed the high-humidity tests.


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Four units did not maintain radiated power output within + / - 1.5 dB from nominal as required by the standards; two did not comply under low-temperature conditions, and one failed the high-temperature test. Two devices were not in compliance under high-humidity conditions. The maximum horizontal beam width allowed by the model specifications--18 ° for X-band radar and 15° for K-band radar--was initially exceeded by three X-band and one K-band unit, and four radars failed the requirement for near-field antenna power density.

Low-Voltage Supply Radar devices are required to operate to a specific low-voltage point and to have a low-voltage indicator capable of being heard or seen by the operator. Low voltage to the radar device is capable of causing incorrect high target speed readings. The required low-voltage operating point is 10.8 V or the lowest voltage specified by the manufacturer. Seven radar units did not meet the performance standard; five units met the requirement of the model specifications, but not the lower voltage claimed by the manufacturer.

Doppler Audio Radar devices are required to emit a Doppler audio tone that correlates with the received Doppler signal and to have an audio volume control. The audio tone helps the operator correlate a visual observation of a target vehicle with the radar speed display and can warn the operator of the presence of electromagnetic interference. Three of the radar units tested were not in compliance with requirements for audio output and volume control. Two units failed to meet requirements for audio squelch and squelch override. One radar did not meet the auto track-through lock test.

Electromagnetic Interference Operational testing was carried out with the radar device properly installed in a patrol vehicle of the type normally used for law enforcement purposes. The test vehicle had an FM transceiver and antenna and a citizens band transceiver and antenna, each installed in accordance with the manufacturer's instructions. A handheld vM transceiver was also positioned in the vehicle for use by the driver. Although the radar was tracking an acquired target vehicle traveling at 50 mph, audio tones from 500 to 3000 Hz generated by a slide whistle were transmitted via the

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microphone of the FM and CB transceivers. The radar display was observed for any erroneous readings caused by the slide whistle transmission from the transceiver. The tests were repeated similarly with the patrol vehicle in the stationary mode, tracking a target vehicle while another vehicle with the FM and CB transceivers passed within 10 ft, first on one side of the patrol car and then on the other. One radar device was subject to interference from the FM transceiver when it was initially tested, and two others were interfered with by the CB transceiver.

Speed Accuracy Tests were conducted on a half-mile measured course over which the target vehicle was driven at constant speeds of 20, 50, and 70 mph. The true speed of the target vehicle for each test was calculated from the elapsed time to travel the known distance or measured with a fifth wheel speed measuring device. The speed displayed on each radar device during the runs was compared with the true target vehicle speed to determine whether or not the radar-displayed speed was within the allowable variation of + 1 and - 2 mph in the stationary model and of + / - 2 mph in the moving mode. Five radar devices were reported as not complying with the speed accuracy requirements of the model specifications; three in the stationarymode/moving-mode target test and one of these t h r e e - - i n addition to two others--in the moving-mode/approaching target test. The three radar devices that were not in compliance in the stationary-mode/movingmode target test situation at 70 mph were in compliance when tested at speeds of 20 and 50 mph, greatly increasing the probability of false speeding tickets at the higher speeds. Notwithstanding these deficiencies, the IACP found all of the units tested to be in full compliance with the agency's requirements and suitable for use in speed enforcement. Earlier tests by the National Bureau of Standards were less forgiving. These tests were designed to determine whether it was possible to affect target speed measurements in several environments and under several conditions that had been identified as the cause of radar inaccuracy during proceedings before the Eleventh Judicial Circuit Court of Florida in 1979. During these tests there was no observed degradation in the performance of any of the six units tested arising from (1) cosine angle effect, (2) automatic lock, (3) heat buildup, (4) mirror switch aiming, and (5) high-tension power wire interference. Only one of the six units tested was affected by police radio transmission at distances beyond 30 ft from the radar.


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Certain of the units were affected in varying degrees by internal electrical interference from the patrol car's ignition and alternator, as well as interference from air conditioner and heater fans. Although transmission from police radios in the same vehicle as the radar was found to have a limited effect on the radar units, CB transmission in the same vehicle affected nearly all radars. Patrol car shadowing was found to affect all but one of the radars, and target speed bumping was observed to affect half of the units. In all cases, the two-piece radars were affected by panning the antenna beam through the display console. In some instances, the performance of the radar units was not degraded by the environments or use situations described above so long as the target vehicle was present. Specific test results included the following.

Shadowing Shadowing, better identified as patrol speed shadowing, is the tendency of a moving vehicle mode radar to use a slow moving large vehicle rather than the ground to measure the speed of the patrol car. This effect was observed, in varying degrees, for several of the radars during testing.

Radar Unit A (Kustom MR-9) The patrol speed reading went from an actual 26 mph to an indicated 22 mph as a large oil tanker passed the patrol car. Radar Unit B (MPH K-55) A large truck came to a stop 50 yards in front of the patrol car, and the patrol car reading changed from 40 to 28 mph. Radar Unit C (Decatur MV-7125) The actual patrol speed of 25 mph was reduced to 17 mph when the patrol car was following a large truck. The actual patrol speed of 34 mph was reduced to 11 mph for a long time when a pickup truck passed the patrol car. The pickup passing the patrol car decreased the patrol speed reading by 10 mph and increased the target speed by same amount. Radar Unit D (CMI Speedgun 6) This particular unit demonstrated very severe shadowing effects from moving vehicles in the vicinity of the radar. A 44-mph patrol speed momentarily dropped to 11 mph with a pickup truck 100 ft in front of the patrol car. While traveling at actual

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patrol speeds of 30-40 mph, with target speeds of 50-60 mph, the following readings were observed as the patrol car was passed by trucks. Patrol speed (mph)

Target speed (mph)

12 16 20 17

80 72 57 68

Radar Unit E (CMI Speedgun 8) While the patrol car was traveling at a patrol speed of 50 mph, shadowing from passing large trucks caused the following radar readings. Patrol speed (mph)

Target speed (mph)

17 11

74 41

This effect did not occur every time a truck passed. Patrol readings decreased momentarily several times when a passenger sedan passed the patrol car.

Radar Unit F (MPH K-55) While the patrol car was traveling at 35 mph, readings of a 20-mph patrol speed and 76-mph target speed were observed. When a pickup truck passed the patrol car and pulled back into the lane, the actual patrol speed of 47 mph dropped to 35 mph. Radar Unit G (Kustom MR-7)

This unit showed no effects from

passing large trucks.

Batching Batching, better identified as target speed bumping, occurs if the target vehicle speed display varies when the patrol car changes speed. This effect was observed for some of the radars during testing.

Radar Unit A (Kustom MR-9) There was no effect on target speed readout due to acceleration or deceleration of the patrol car. Radar Unit B (MPH K-55) The radar occasionally subtracted 2-3 mph from the target reading when the patrol car was accelerating. This was not consistent. There was no effect from deceleration. Radar Unit C (Decatur MV-715) Acceleration or deceleration of the patrol car had no effect on target readings.


Radar Unit D (CMI Speedgun 6)

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Radar target speeds decreased with

both acceleration and deceleration.

Radar Unit E (CMI Speedgun 8) No effect on target speed reading from accelerating or decelerating of the patrol car could be observed. Radar Unit F (MPH K-55) On rare occasions, target speed readings increased 2-3 mph when the speed of patrol car was increased or decreased. Radar Unit G (Kustom MR-7) No effect on target readings from a sudden increase or decrease of the patrol car speed was observed. Panning Error Panning error occurs when the radar antenna is used to pan through its own display. The two one-piece units used in these tests could not do that; using the two-piece units in this manner always produced an erroneous reading.

Radar Unit A (Kustom MR-9) Panning the antenna across the radar readout console produced 101-mph speed readings. Radar Unit B (MPH K-55) Panning the antenna across the radar readout console produced 75-mph speed readings. Radar Unit C (Decatur MV-715) Panning the antenna across the radar readout console caused readings of over 100 mph. Radar Unit D (CMI Speedgun 6)

This radar unit was not applicable.

Radar Unit E (CMI Speedgun 8)

This radar unit was not applicable.

Radar Unit F (MPH K-55) Panning the antenna across the radar readout console produced various speed readings. Radar Unit G (Kustom MR-7)

Panning the antenna across the radar readout console produced 95-mph speed readings.

Scanning Error Scanning errors can result when the radar operator moves his antenna too quickly. The results obtained by positioning the radar in commonly used positions or pointing it in several directions included the following.

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Radar Unit A (Kustom MR-9)

There was no effect from the A C /

heater fan motor.

Radar Unit B (MPH K-55) The unit picked up the A C / h e a t e r fan intermittently while it was mounted on the dash. When the heater fans were on, scanning the dash with the handheld antenna caused readings proportional to the fan speed. No readings from the fans were detected when the antenna was pointed out the side windows. The unit picked up fan readings when the radar was pointed out the rear window. Radar Unit C (Decatur MV-715) When mounted, the antenna was pointed slightly downward toward the dash with the heater fans on high" stationary modemtarget, 34 mph; patrol, 55 mph. No readings from the fans were detected when the antenna was pointed out the side or rear window. The antenna mounted outside the rear passenger window, slightly aimed at the dash with the fans on picked up readings of 24-25 mph in the stationary mode. Radar Unit D (CMI Speedgun 6) This handheld radar when pointed at the dash picked up the A C / h e a t e r fans. There was no effect from the fans, and no readings were detected when the unit was pointed out the side or rear windows. Radar Unit E (CMI Speedgun 8) This handheld radar antenna pointed at the dash picked up readings from the A C / h e a t e r fans. This unit seemed to pick up the fan extremely easily when the antenna was aimed forward but not mounted on the dash mount; no readings were detected when the antenna was aimed out the side or rear windows. Radar Unit F ( MPH K-55) No fan readings were detected when the unit was dash mounted. When the radar antenna was pointed at the dash, the radar picked up the fan readings. No speed readings were detected when the antenna was pointed out the side or rear windows. Radar Unit G (Kustom MR-7) Scanning the dash with the radar antenna did not pick up the A C / h e a t e r fan. No readings were detected when the antenna was pointed out the side or rear windows with all the fans on. Cosine Angle Effect Cosine error, better named the cosine angle effect, was closely observed during the testing, for this effect is present any time that the radar


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and the target vehicle are not headed directly toward each other. The speed that the radar displays when it is in the stationary mode is equal to the actual speed times the cosine of the angle between the direction of travel of the target vehicle and the radius vector from the radar to the target vehicle. No erroneous readings were noted during these tests due to the cosine angle effect.

Automatic Lock The advantages and disadvantages of the automatic lock feature were observed. The advantage is in enabling the officer to automatically obtain a speed on the display console using a present threshold value. The disadvantages far outweigh this advantage. The primary one is that the automatic lock prevents the radar operator from obtaining a tracking history, i.e., what the vehicle being tracked does after it is detected traveling over the speed limit. Also, the radar may automatically lock on a stray abnormal reading which appeared only momentarily due to an unobserved interference source. Another disadvantage is that use of the automatic lock feature makes it almost impossible to compare the patrol car speed with its radar measured counterpart to ensure that the two agree at the time that the display is locked in or at times of possible interference such as that brought on by patrol speed shadowing.

External Interference Theoretically, defective high-tension wires may affect radar speed measuring devices by causing stray readings or by decreasing the sensitivity of the radar and thereby reducing its range of operation. However, no stray readings were noted by the NBS in testing near and under high-tension wires. Four of the radars did not display false readings due to external police radar transmission, and only one radar was affected by external CB operation.

Radar Unit F (MPH K-55) A CB radio mounted in a pickup caused readings of 60-70 mph at distances of up to 175 ft from the patrol car. The 100-W transmitter caused radar readings at 5 ft from the left rear of the patrol vehicle to 30 ft from the right of the patrol vehicle.

Internal Interference The radar units were operated in their usual configuration in a patrol car, and electrical interference due to the patrol car ignition system, alternator, and air condition and heater fan motors was investigated. Some of the radar units displayed a reading when the air conditioner and heater

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fans were operated with no radar target present, and one type displayed a reading during the ignition and alternator testing.

Radar Unit C (Decatur MV-715) With the radar mounted in a pickup, erratic patrol speed readings from the engine alternator, ignition, or both in the moving mode were displayed. Extreme interference from the heater fan motor in the moving mode was observed. When a CB radio was installed in the same vehicle as the radar unit, operating from the same battery, several of the radar units were subject to interference during CB transmission. Radar Unit A (Kustom MR-9) When the CB radio and the radar were mounted in the same truck and connected to the same battery, interference from the CB radio was evident. Interference from the tone whistled into the microphone caused speed readings to be displayed. Radar Unit B (MPH K-55) When the radar and the CB radio were connected to the same battery, readings were observed on the radar target readout. The magnitude of the readings depended on the frequency of the CB radio. Radar Unit C (Decatur MV-715) The radar and the CB radio connected to the same battery caused readings in the stationary mode. Radar Unit D (CMI Speedgun 6) There was interference from the CB radio when the radar and the CB radio were powered by the same battery. Radar Unit E (CMI Speedgun 8) There was no effect when the radio and the radar were both connected to the same battery. Radar Unit F (MPH K-55) This unit was not tested because the unit was found to be "extremely sensitive to external CB transmission." Radar Unit G (Kustom MR-7) The radar and the CB radio connected to the same battery caused a reading on the radar target speed display. Under these conditions, the radar picked up the correct reading on the passing target car, and whistling in the CB microphone had no effect on the correct reading until the target was out of range. Two of the radars were affected by operating the police radio in the same car as the radar.


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Radar Unit D (CMI Speedgun 6) A 100-W transmitter had no effect on large targets or strong signals, but it boosted target speeds as much as 20 mph for distant weak signals or small targets. Radar Unit G (Kustom MR-7) A 100-W transmitter caused increases or decreases of 10 mph in target speed readings intermittently. Several observations were made by the NBS as a result of its radar test program. 1. Two-piece radars can produce erroneous readings when an antenna is panned through the display console. The radar should not be mounted with the display console in the antenna beam. 2. Air conditioner and heater fans and alternator or ignition noise can interfere with the radar when no bona fide radar target is present. The radar antenna should be mounted so that it is not pointed toward the air conditioner or heater fans. If possible, the antenna should be mounted outside of the patrol vehicle. 3. Patrol speed shadowing can occur during move-mode radar operations. Operators should be aware of this, should recognize its symptoms, and should know its cause and that its effect can best be detected by checking the radar patrol car speed with the patrol car speedometer. 4. Target speed bumping can occur during moving-mode radar operations. Operators should know what it is, how it occurs, and that its effect can be avoided by maintaining a constant speed when making speed measurements. 5. The cosine angle effect can occur during stationary radar operation when the target is off axis within the antenna beam. Operators should understand the cosine angle effect and recognize when it is occurring. 6. Transmission from 100-W VM police radios can produce erroneous speed readings. Operators should be aware of this and not transmit on CB radios while using the radar. 7. Use of the automatic speed lock feature (still found on many older-model police radars) may result in wrong target identification. Operators should be aware of this and not use the automatic lock feature, but instead use the manual lock feature and then only when they have observed a sufficient "tracking history" to ensure that the correct target vehicle is being tracked. 8. When two or more vehicles are in the radar beam, it can be difficult to select the correct target. Operators should continue radar tracking until the proper target is positively identified. It may be necessary to wait until the vehicles pass by the radar source and the one being tracked no longer registers a speed reading on the display console.

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8. Does Radar Increase Safety? Contrary to generally held opinion, police radar has little ability to influence traffic speeds or safety. Studies show that enforcement that is not visible to the motoring public does not affect its behavior; inasmuch as radar is visible, in a sense, only to users of radar detectors, it cannot be considered a safety measure. Studies by the Texas Transportation Institute (TTI) at Texas A & M and by the Highway Safety Research Center (HSRC) at the University of North Carolina have shown that police radar has no measurable influence on traffic speeds or accident experience apart from the effect of the visible patrol car that is employing it. Conversely, hidden enforcement including regular radar and photo radar are effective at entrapping motorists traveling at or near the 85th-percentile speed of traffic. Inasmuch as the 85th percentile speed is generally greater than the national maximum speed limit, the use of hidden enforcement results in large numbers of speeding tickets and generate substantial revenues for agencies of local and state government. In light of the many sources of error affecting police traffic radar, the absence of performance standards for the radar or training standards for its operators, and the secondary role of hidden enforcement in improving traffic safety, it seems probable that the value of radar in traffic enforcement has been generally misunderstood and greatly overrated.

Additional Reading P. D. Fisher, Shortcomings of radar speed measurement, IEEE Spectrum, Vol. 17, No. 12, pp. 28-31, Dec. 1980. U.S. Department of Transportation, "Model Minimum Performance Specification for Police Traffic Radar Devices," No. DOT HS-807-415, May 1989. J. F. Campbell, P. D. Fisher, and D. A. Mansfield, Defense of Speeding, Reckless Driving and Vehicular Homicide. New York: Matthew Bender, 1984. P. D. Fisher, Improving on police radar, IEEE Spectrum, Vol. 29, No. 7, pp. 38-43, July 1992. T. K. Ishii, Analysis of target speed determination with Doppler radar, IEEE Trans. Instrum. Meas., Vol. IM-19, No. 2, pp. 85-91, May 1970. T. K. Ishii, Critical analysis and proposal for improvement of vehicle speed radar telemetry, IEEE Natl. Telemetering Conf. Proc., Los Angeles, CA, p. 37, Apr. 1970. T. K. Ishii, Error of Doppler radar in target speed determination for traffic control, IEEE Trans. Microwave Theory Tech., Vol. MTT-13, No. 3, pp. 389-390, May 1965.

CHAPTER

16 Microwave Radio Communication George Kizer

I. I n t r o d u c t i o n

In

the mid-1930s multiple channel point-to-point radio relay transmission using 12 frequency division multiplexed voice channels on an amplitude modulated (AM) very high frequency (VHF) carrier was introduced. During World War II, this technology was extended to ultra high frequency (UHF). In addition to AM systems, frequency modulation (FM) and digital pulse position modulation (PPM)were used. The first transcontinental microwave radio system was the AT & T TD-2 route from New York to San Francisco. This system employed 100 repeater stations operating in the 4-GHz band using a 20-MHz channel bandwidth to relay 480 voice channels on a frequency modulated radio carrier. This system, eventually upgraded to 1800-channel operation, was the forerunner of the many radio systems in operation today between 2 and 11 GHz. By the middle 1970s many of the major radio routes had reached their capacity of 1800 or 2400 analog channels using FM. Several routes were converted to single-sideband amplitude modulation permitting up to 6000 voice channel operation in a 30-MHz wide radio channel. As the microwave transmission network matured, the switching systems were converting from analog to digital operation. In the early 1960s


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George Kizer

digital cable transmission using pulse code modulation (PCM)was introduced. Shortly thereafter, the introduction of digital switches using this technology for voice circuits was begun. In 1965 the first digital switch, the lESS, was placed in service for local metropolitan use. This worked so well that, in 1976, the first four-wire toll switch, the 4ESS, was introduced. By 1979 the 4ESS was upgraded to handle over 100,000 lines serving over 600,000 calls per hour. This all-digital switch, together with the D4 digital voice channel bank, offered a significant economic advantage to the use of digital transmission systems. By the mid 1970s the conversion of analog transmission systems to digital operation had began. Initially the digital radio systems used the simpler digital modulation methods (e.g., 4 PSK, 8 PSK, or 9 QPRS). What these systems had in common was inefficient use of the frequency spectrum for voice transmission, compared with analog radio systems. Substantial improvements in spectral efficiency have been made over the last decade by the near universal adoption of quadrature amplitude modulation (QAM). The most commonly used criterion, b i t / s / H z , for the spectral efficiency of a digital radio is the number of payload bits per second divided by the 99% transmit spectrum power bandwidth. The first QAM radios used two orthogonal sets of four amplitude states. This 16-QAM signal had a spectrum efficiency of 2.5 to 3.5 b i t / s / H z . Later 64 QAM (4.5 to 5.2 b i t / s / H z ) and 256 QAM (5.5 to 6 b i t / s / H z ) w e r e developed. Using 64 kbit/s PCM, the spectral efficiency of a 256-QAM radio is comparable to that of an analog FM radio. The increasing technical difficulties encountered in the design of digital radios at the higher modulation levels have fostered investigations into the feasibility of cross-polarized cochannel frequency transmission. If this can be made practical, the 256-QAM radio, with frequency reuse, would have a spectral efficiency of 12 b i t / s / H z . Using 64 kbit/s PCM, this would make the radio system nearly as spectrally efficient for telephone circuits as a single-sideband analog radio. Of course, the digital radios are far more efficient for digital circuits than their analog radio counterparts. Microwave system design is a tradeoff of many factors. Some of those are a function of state-of-the-art equipment parameters. Other factors are independent of equipment design. These include interference and radio path fading. Design is complicated by the fact that most systems are designed as multiple transmitter/receiver pairs ("hops") cascaded to provided transmission between two remote locations. The effect of cascading the equipment significantly complicates designing systems to meet specific end-to-end performance objectives. This chapter will overview the major factors.

451

16. Microwave Radio Communication

2. Equipment-Dependent Radio Performance Analog Systems Most analog radio systems are FM frequency division multiplex (FDM) configurations. Detailed analog radio system design is done on the basis of a detailed end-to-end noise performance objective. Final noise performance objectives are determined based on appropriate domestic or CCIR objectives. The performance is determined by the worst-case noise. This noise occurs when one or more of the radio system paths is experiencing a partial loss of the received signal level ("fading"). Therefore, most of the design of analog systems revolves around designing the system to minimize the effects of interference and receive signal level fading. However, the designers must confirm that the system performance is not limited by intermodulation noise on an unfaded end-to-end basis. To ensure this, the system designer takes an equipment specification noise power radio (NPR). That specification is converted to a noise value, N. N (dBm0) = NLR (dBm0) - BWR (dB) - N P R (dB), where N L R is the noise loading ratio, - 1 5 + 10 log (number of voice channels) for CCIR systems and - 1 9 . 6 + 10 log (number of voice channels) for North American systems; BWR is the bandwidth ratio, 10 log ([ fb (kHz) - fa (kHz)]/3.1), where fa is the lowest baseband frequency and fb is the highest baseband frequency; and N P R is the noise power ratio. The calculated noise is the sum of the thermal and the intermodulation noise. Using the radio path and radio parameters the thermal noise for a hop of radios is calculated. A convenient method is to use Figures 1 and 2. Obtain a graph value, Ng, from Figure 1 based on C/N.

C/N

(dB) -- RSL (dBm) + 114.0 - NF (dB) - 101ogB ( M H z ) ,

where C/N is the carrier-to-noise ratio, RLS is the received signal level, NF is the receiver noise figure at the location at which RSL is specified, B is the receiver 3-dB bandwidth prior to the FM demodulator (typically the IF bandwidth), and log(x) is the common logarithm (base 10) of x. The received FM receiver thermal noise N is given from the following formula, N (dBm0) = Ng + 29.6 - 20 log [df (kHz)] + 10 log[B (MHz)] - W ( d B ) -

P (dB),

452

George Kizer

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where Ng is the graph value from Figure 1, df is the per channel RMS deviation (for a 0-dBm0 test tone at the emphasis crossover frequency), B is the receiver 3-dB bandwidth prior to the FM demodulator (typically the IF bandwidth), W is the noise weighting (typically 2 dB), P is the preemphasis value from Figure 2, and f is the baseband test tone frequency of interest. The thermal noise is subtracted (on a power basis) from the total NPR noise (using a chart such as Figure 3) to yield pure intermodulation noise. The end-to-end noise is the power summation of the end-to-end thermal and intermodulation noise components. Thermal noise is generated by each radio receiver front end. Since each receiver is independent of each other, the thermal noise is uncorrelated from radio hop to radio hop. Therefore, the anticipated end-to-end thermal noise caused by N identical radio paths would be end-to-end thermal noise (dBm) = single-hop thermal noise (dBm) + 10 log N. Intermodulation noise is a function of composite baseband voltage level. It would be the same on each hop since the composite baseband voltage

453


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would be identical on each hop. Theoretically intermodulation noise adds on a highly correlated basis. For N identical radio paths the anticipated end-to-end intermodulation noise would be 20log N if all noise was enhanced or 0 if every other hop noise canceled. As a practical matter, intermodulation noise addition will vary considerably. Actual measurements of cascaded systems yield results which vary from 10 to 171og N. Use of 13 log N to 16 log N addition are reasonable practical estimates. Therefore end-to-end intermodulation noise (dBm) = single-hop intermodulation noise (dBm) + 13 log N. This entire process is explained in considerable detail in Reference [24].

454

George Kizer

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Digital Systems The digital signal is called a "bit" which is a contraction of "binary digit." A bit represents the state of a single binary symbol. That state is generally represented as "0" or "1 . , . or. .as. . - . . or . . + . The average transmission capacity of a system is generally expressed as bits per second (bit/s). A symbol or single signaling element represents a single transmission event. The term "baud," the unit of signaling speed, is equal to the number of symbols per second. If a symbol can assume any of "m" states with equal probability, then the number of bits "n" that can be transmitted by that symbol are given by the relationship. m=2

n

or

n = log2(m) = 3.321 loglo ( m ) . The transmission capacity of the system ( b i t / s ) is the baud rate (symbols/ s) multiplied by the average symbol capacity (bit/symbol). The transmitted information (bit) is the transmission capacity ( b i t / s ) multiplied by the transmission duration (s).


455

The design and operation of communication networks and equipment are based on various performance objectives. The introduction of digital transmission has caused new performance criteria to be introduced. The criteria may be grouped into three main categories. The first is absolute transmission delay. This is of particular importance to the telephony service in which significant subscriber difficulties arise as the delay increases. Round-trip transmission delay values in excess of 400 ms are presently considered unacceptable for telephony without special measures. Digital radio systems introduce smaller absolute delays than coaxial cable, optical fiber, and satellite systems. Geostationary orbit satellite systems introduce a round-trip transmission delay of 560 ms. The smaller transmission delay for radio systems is an advantage. For radio systems virtually all delay is introduced by multiplexes and time slot interchangers in electronic digital cross-connects. The second is variation in timing position of each bit from the expected position, as defined by the clock interval. This is normally expressed as wander or jitter. Wander is very low frequency jitter. It is the long-term fluctuation of the significant transition instants of a digital signal (with respect to their ideal time position). Wander is generated by changes in propagation delay of the transmission path. This is usually a function of cable length variation with temperature and clock drift. Jitter is the random phase modulation of a digital signal. It is a measure of the short-term frequency and phase stability of a digital signal. Its two principal sources are digital regenerators and digital multiplexes. Regenerator jitter is introduced by imperfections in the timing recovery period, whereas multiplex jitter is introduced in the pulse stuffing mechanism used to synchronize the low-speed incoming pulse stream. Jitter accumulation through the network is a complicated process because the stuffing-destuffing process interacts with the input jitter in a nonlinear way. The interaction alters the frequency of the input jitter as well as its amplitude. Jitter may introduce a number of impairments such as errors, slips, cross-talk, and distortion to the original signal. Thus, jitter can be a particularly important parameter for the types of digital terminals which may be interconnected to asynchronous circuits because the terminal loop timing circuits must work in the presence of jitter. The third is a series of criteria relating to errors in transmission. These criteria follow. Bit Error Ratio (Rate) The most common measurement of error performance is the bit error ratio (BER), sometimes stated as the bit error rate. The BER is the ratio

456

George Kizer

of the number of measured digital errors to the total number of observed digits. No error detection scheme (short of an out-of-service bit-by-bit comparison) can detect all bit errors. The measurement of long-term BER gives little information about short-term error performance. For example, if errors are occurring in short bursts, the error performance might be acceptable. Single random errors (dribbling errors) leading to the same BER could severely affect data throughput. The terms error-free seconds and errored seconds address this problem. The number of error-free seconds is the number of seconds during a defined measurement period when no errors occurred. Conversely, the number of errored seconds is the number of seconds during the same measurement period when any error occurred.

Errored Seconds (ES) An ES is a second during which at least one error has occurred. An important reason for counting ES is the quality statements in data service tariffs are generally given in terms of percentage of error-free seconds. In addition, by combining the count of ES and the effective BER, a measure of the error distribution can be obtained. Distinguishing between bursty and randomly distributed errors can be important in diagnosing a facility problem. Errored second measurements may be made synchronously or asynchronously. For synchronous errored seconds, an errored second begins with the detection of an error. All errors falling within a 1-s window synchronized to the beginning error are included in that error second. Asynchronous measurements use a free running clock to measure the errored seconds. The asynchronous measurement has the potential to give different readings for different test sets connected to the same digital signal. Synchronous measurements avoid this potential problem. Errored seconds are to be measured only when service is available.

Severely Errored Seconds (SES) An SES is a second which contains more than N coding violations. The value of N will vary with the frame size and bit rate and should be chosen to correspond to a bit error ratio of approximately 10 -3, assuming errors are randomly distributed. This count may be used to ascertain problems for particular types of services. It may also be used as a measure of facility outage duration. In conjunction with ES and effective BER, the SES count yields additional information on error distributions. In the case of ESs, SESs should be measured during available time alone (less than 10 s in duration).


457

Consecutive Severely Errored Seconds (CSES) This is a new performance parameter proposed by AT & T which defines a sequence of SESs lasting from 3 to 10 s. Such interruptions can be very disruptive to customer services because they can cause complete loss of the connection due to initiation of carrier group alarm (CGA).

Unavailable Seconds (UAS) Service is said to become unavailable if 10 consecutive SESs occur. Once the service becomes unavailable, it remains unavailable until 10 consecutive nonseverely errored seconds occur, after which it becomes available. The parameter UAS measures the duration for which the service was unavailable, in seconds. Unavailable time is a service-quality measure used in data service tariff specifications. More detailed information may be needed to adequately describe the performance of a error ratio of 10 -4 for an extended period of time. If there is only a facility alarm at a 10 -3 bit error ratio threshold, the degraded performance may not be detected, although this level of service may not be acceptable to a data customer. In effect, this alarm can be used to determine availability but not quality of service. Quality of service is measured only when the circuit is available.

Degraded Minutes (DMs) Available time, with all SESs removed, is grouped into 1-min. intervals. If the average BER of this minute is worse that 1.0 -6, the minute is counted as a degraded minute. As an in-service measurement, this is typically measured as any such minute with m or more CRC violations. The ~¢alue of m must be defined depending on the bit rate and the number of bits per CRC-protected block.

Estimating End-to-End Digital Radio Performance Typically three parameters are most significant to end-to-end equipment performance. These are jitter, bit error ratio and errored (or error-free) seconds. Jitter takes two forms. The first is RMS phase jitter that builds up on cascaded radio hops between modulators and demodulators. Based on the RMS phase jitter of a transmitter/receiver pair (without a modulator or demodulator) the designer must estimate the composite RMS jitter presented to the demodulator prior to digital signal detection. The composite RMS jitter degradation is typically characterized as a system fade margin

458

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degradation (see Figure 4). Theoretically, if n is the number of cascaded identical regenerators, RMS phase jitter accumulations on a square root of n basis. Figure 4 compares actual data with this theoretical result. For small numbers of regenerators, this is a little optimistic. For a large number of regenerators, this is too pessimistic. For a large number of repeaters, the differences due to manufacturing tolerances begins to become apparent. Figure 5 graphs the impairment (C/I degradation) caused by carrier phase jitter at the input to the radio demodulator. The second form of jitter is the peak-to-peak waiting time jitter introduced into digital signals by asynchronous (plesiochronous) multiplexer/demultiplexer pairs (muldems). This jitter is introduced by the pulse stuffing process of the muldems. This jitter is introduced every time digital radios are cascaded unless the radios are back-to-back digital ("rail") repeaters (without digital detection and remodulation). Although like RMS jitter this jitter builds up on a square root of the number of tandem muldems basis, this process is highly nonlinear; considerable variation will exist from case to case. Figure 6 shows actual averaged results for a nine-DS-3 system (1:2 multiline system employing three DS-3 64-QAM radios) with up to eight switching sections spread out over a 1000-mile system. The system designer must make sure that the end-to-end peak-to-peak jitter does not exceed the input jitter specification of the terminating demultiplexer. All North American standard multiplexes must accept five unit intervals of peak-to-peak jitter and still operate properly [4].

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The next digital quality factor considered is bit error ratio. BER has two interesting properties. Unlike other error measurements such as errored seconds, BER is constant regardless of the transmission rate or

460

George Kizer TABLE I Comparison of Various Digital Modulation Techniques (Based on Equal Data Rates) SYSTEM DESIGNATION

2-PSK 3-QPR 4-PSK, 4-QAM 8-QAM 8-PSK 9-QPR 16-QAM 16-PSK 25-QPR 32-QAM 32-PSK 49-QPR 64-QAM 64-PSK 121-QPR 128-QAM 128-PSK 225-QPR 256-QAM 256-PSK 512-QAM 529-QPR 961-QPR 1024-QAM 2209-QPR 2048-QAM 3969-QPR 4096-QAM

INFORMATION DENSITY (bps/Hz)

SIGNAL-TO-NOISE RATIOS FOR BER = 10 -6 CHANNEL Eb/N o (dB)

DECISION CKT S/N (dB)

10.6 12.6 10.6 13.5 14.0 12.6 14.5 18.6 15.5 17.5 23.8 16.6 18.8 28.8 19.5 21.8 34.3 21.0 24.0 39.8 27.2 24.0 26.0 29.0 29.4 32.5 31.0 34.0

13.6 17.6 13.6 18.3 18.8 17.6 20.5 24.6 22.3 24.5 30.8 24.6 26.6 36.8 28.5 30.3 42.8 30.8 33.0 48.8 36.8 34.3 37.0 39.0 40.8 42.9 43.0 44.8

PEAK TO AVERAGE RATIO (dB) (SQUARE ROOT FILTER PARTITIONING)

0.0 2.0 0.0 1.3 0.0 2.0 2.6 0.0 3.3 2.3 0.0 4.6 3.7 0.0 4.3 3.2 0.0 5.7 4.3 0.0 3.4 5.2 6.3 4.5 5.4 3.6 6.5 4.8

multiplexing level. The BER of the DS-3 input of a (M13) multiplexer is the same at the BER of the DS-1 multiplexer output. This assumes errors occur randomly. However, actual measurements using faded radios (which produce error bursts due to error correction and data scrambling)validate this theoretical result for practical systems. For typical BERs (10 -3 or smaller), the end-to-end BER of cascaded links is the sum of the individual link BERs [25]. These properties greatly simplify BER calculations. BER under faded conditions will be treated later. At that time, Table 1 will be useful to estimate faded BER. If Trellis encoding or forward error correction is used, these coding gains must be added to the results of Table 1. Under unfaded conditions the equipment BER performance is quite good. The typical system engineering problem is not how good the (unfaded carrier or non-RSL dependent) system performance is but how to verify that high level of performance during system signoff. The bit error ratio of a digital circuit is defined as the ratio of measured digital errors to the total number of observed digits. It is assumed that the measurement has been made over a statistically significant period of time. For high transmission rates and relatively large BERs (e.g., 10 -3 to 10-6), many errors are observed in a small period of time.

461


For very small BERs (e.g., 10 -9 to 10-12) e v e n very long periods of time will yield only a few errors. For this situation, the question of measurement accuracy is important. The statistical problem of estimating the ratio of two possible discrete outcomes is called the Bernoulli trial problem. The binomial distribution characterizes the binary outcomes of the Bernoulli trials. For a large number of trials (in our case, a large number of transmitted digits), the discrete binomial distribution may be accurately approximated by the continuous Poisson distribution. Assume that n digits have been transmitted and e digits were found to be in error. For the following assume that n is at least 10,000. The median unbiased maximum likelihood estimator for B E R is BER=

1/(3n)

fore=0

BER =

e/n

for e > 0.

Since the number of observed errors (events) is so small statistically, variation of the result should be expected if the experiment is repeated. To determine the expected range of the measurement with a stated confidence level, one determines the upper and lower confidence limits (e.g., 95%) and determines the upper and lower limits of e based on the Poisson distribution (see Table 1). A confidence level of 95% means that, if the experiment were repeated many times, 95% of the time the results would fall within the upper and lower limits. For example, if 10 l° bits were transmitted, 10 errors were observed, and a confidence level of 95% is desired, the B E R lower (BER l) and upper (BER u) confidence limits would be the following: B E R u (95% confidence) =

eupper/n

= 18.4/101° = 1.84 × 10 .9 B E R (maximum likelihood) =

e/n

= 10/1010 = 1 . 0 0 × 10 .9 B E R l (95% confidence) =

elower/n

= 4.7/101° = 4.7 × 10-1°.

462

George Kizer TABLE 2 Error Confidence Limits Confidence Level Errors (e) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

95%

90% Lower Limit 0.0 0.1 0.4 0.8 1.4 2.0 2.6 3.3 4.0 4.7 5.4 6.1 6.9 7.7 8.4 9.2 10.0 10.8 11.6 12.4 13.2 14.0 14.9 15.7 16.5 17.4 18.2 19.0 19.9 20.7 21.6 22.4 23.3 24.1 25.0 25.9 26.7 27.6 28.5 29.3 30.2 31.1 31.9 32.8 33.7 34.6 35.4 36.3 37.2 38.1 39.0 39.9 40.7 41.6 42.5 43.4 44.3 45.2 46.1 47.0 47.9

Upper Llmlt 3.0 4.7 6.3 7.8 9.2 10.5 11.8 13.1 14.4 15.7 17.0 18.2 19.5 20.7 21.9 23.1 24.3 25.5 26.7 27.9 29.1 30.3 31.4 32.6 33.8 34.9 36.1 37.2 38.4 39.5 40.7 41.8 43.0 44.1 45.3 46.4 47.5 48.7 49.8 50.9 52.1 53.2 54.3 55.4 56.6 57.7 58.8 59.9 61.0 62.2 63.3 64.4 65.5 66.6 67.7 68.8 69.9 71.1 72.2 73.3 74.4

Lower Limit 0.0 0.0 0.2 0.6 1.1 1.6 2.2 2.8 3.5 4.1 4.7 5.4 6.2 6.9 7.6 8.4 9.1 9.9 10.6 11.4 12.2 13.0 13.8 14.5 15.3 16.1 17.0 17.8 18.6 19.4 20.2 21.0 21.9 22.7 23.5 24.4 25.2 26.0 26.9 27.7 28.6 29.4 30.2 31.1 31.9 32.8 33.7 34.5 35.4 36.2 37.1 38.0 38.8 39.7 40.5 41.4 42.3 43.1 44.0 44.9 45.8

99% Upper Limit 3.7 5.6 7.2 8.8 10.2 11.7 13.1 14.4 15.8 17.1 18.4 19.7 21.0 22.3 23.5 24.8 26.0 27.3 28.5 29.7 30.9 32.1 33.3 34.5 35.7 36.9 38.1 39.3 40.5 41.7 42.9 44.0 45.2 46.4 47.5 48.7 49.9 51.0 52.2 53.3 54.5 55.6 56.8 57.9 59.1 60.2 61.4 62.5 63.7 64.8 65.9 67.1 68.2 69.4 70.5 71.6 72.7 73.9 75.0 76.1 77.3

Lower Llmlt 0.0 0.0 0.1 0.3 0.7 1.1 1.5 2.0 2.6 3.1 3.7 4.3 4.9 5.6 6.2 6.9 7.6 8.2 8.9 9.6 10.3 11.1 11.8 12.5 13.2 14.0 14.7 15.5 16.2 17.0 17.8 18.5 19.3 20.1 20.8 21.6 22.4 23.2 24.0 24.8 25.6 26.4 27.2 28.0

28.8 29.6 30.4 31.2 32.0 32.8 33.6 34.5 35.3 36.1 36.9 37.8 38.6 39.4 40.2 41.1 41.9

Upper Limlt 5'.3 7.4 9.3 11.0 12.6 14.1 15.7 17.1 18.6 20.0 21.4 22.8 24.2 25.5 26.9 28.2 29.5 30.8 32.1 33.4 34.7 36.0 37.3 38.5 39.8 41.0 42.3 43.5 44.8 46.0 47.3 48.5 49.7 50.9 52.1 53.4 54.6 55.8 57.0 58.2 59.4 60.6 61.8 63.0 64.2 65.4 66.6 67.8 68.9 70.1 71.3 72.5 73.7 74.8 76.0 77.2 78.4 79.5 80.7 81.9 83.0


463

(,Continued)

TABLE 2 Confidence Level

90%

95%

99%

Errors (e)

Lower Limit

Upper Limit

Lower Limit

Upper Limit

Lower Limit

Upper Limit

61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91

48.8 49.6 50.5 51.4 52.3 53.2 54.1 55.0 55.9 56.8 57.7 58.6 59.6 60.5 61.4 62.3 63.2 64.1 65.0 65.9 66.8 67.7 68.6 69.5 70.4 71.4 72.3 73.2 74.1 75.0 75.9 76.8 77.7 78.7 79.6 80.5 81.4 82.3 83.2 84.2

75.5 76.6 77.7 78.8 79.9 81.0 82.1 83.2 84.3 85.4 86.5 87.6 88.7 89.8 90.9 92.0 93.0 94.1 95.2 96.3 97.4 98.5 99.6 100.7 101.8 102.9 103.9 105.0 106.1 107.2 108.3 109.4 110.5 111.5 112.6 113.7 114.8 115.9 117.0 118.0

46.6 47.5 48.4 49.3 50.1 51.0 51.9 52.8 53.7 54.5 55.4 56.3 57.2 58.1 59.0 59.9 60.7 61.6 62.5 63.4 64.3 65.2 66.1 67.0 67.9 68.8 69.7 70.6 71.5 72.4 73.2 74.1 75.0 75.9 76.8 77.7 78.6 79.5 80.4 81.3

78.4 79.5 80.6 81.7 82.9 84.0 85.1 86.2 87.3 88.5 89.6 90.7 91.8 92.9 94.0 95.1 96.3 97.4 98.5 99.6 100.7 101.8 102.9 104.0 105.1 106.2 107.3 108.4 109.5 110.6 111.7 112.8 114.0 115.1 116.2 117.3 118.4 119.4 120.5 121.6

42.7 43.6 44.4 45.2 46.1 46.9 47.8 48.6 49.5 50.3 51.1 52.0 52.8 53.7 54.5 55.4 56.2 57.1 58.0 58.8 59.7 60.5 61.4 62.2 63.1 64.0 64.8 65.7 66.5 67.4 68.3 69.1 70.0 70.9 71.7 72.6 73.5 74.3 75.2 76.1

84.2 85.4 86.5 87.7 88.8 90.0 91.2 92.3 93.5 94.6 95.8 96.9 98.1 99.2 100.4 101.5 102.7 103.8 105.0 106.1 107.2 108.4 109.5 110.7 111.8 113.0 114.1 115.2 116.4 117.5 118.6 119.8 120.9 122.0 123.2 124.3 125.4 126.6 127.7 128.8

92

93 94 95 96 97 98 99 100

The results of Table 2 were taken from Poisson distribution tables. For e > 30, the table values may be determined (or extended) by using the following formulas:

euppe r - e

elowe

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1 Z2

e + (~)Z

+

:

-

Z(e

+ 1) ° '

Z ( e ) 0"5

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1

464

George Kizer

For the above, Z is the number of standard deviations for a given confidence level based on a zero mean unity variance two-tailed normal distribution integral. For the listed confidence levels Z = 1.64 for the 90% confidence level Z = 1.96 for the 95% confidence level Z = 2.58 for the 99% confidence level. It has been assumed for the above that a period of time was chosen for the error measurements prior to evaluating BER. This is termed direct binomial sampling (DBS). If an arbitrary number of errors is defined prior to the experiment and testing is stopped when this level is reached, this testing procedure is termed inverse binomial sampling (IBS). The calculation procedure for BER estimation is the same with the following exceptions: e u p p e r (IBS)

=

e upper (DBS)

- 1

e,ower(IBS) = elower(DBS). The last digital quality factor considered is errored seconds or the related parameter, error-free seconds. For a measurement period, errored seconds is the sum total number of seconds containing at least one error. Error-free seconds is the difference between the measurement period (in seconds) and the errored seconds measured. Unlike BER, ES measurements do not remain the same at different multiplexing levels. The ES of the DS-3 input of a (M13) multiplexer is not the same as the ES of the DS-1 multiplexer output. If errors are uniformly distributed in a data stream, the theoretical percentage of a measurement period containing errored seconds, denoted ESt, would be given by the following: ES t (%) = (100 x BER x binary transmission rate)

or

(100),

whichever is less. Unfortunately error correction algorithms and descrambiers cause errors to be bunched rather uniformly distributed. Figures 7 and 8 compare theoretical and actual ES measurements made with test generators and fade RSL digital microwave radios.


465

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3. T r a n s m i s s i o n - P a t h - D e p e n d e n t

Radio P e r f o r m a n c e

The ultimate end-to-end performance of a microwave radio is limited by the nominal and time-dependent characteristics of the transmission path. Some of the characteristics of the path affect both analog and digital systems similarly. In other cases, the effects are different. General characteristics will be overviewed. Specific methods of calculating both analog and digital system performance will then be given.

GeorgeKizer

466 Transmission Path Loss

An isotropic source is a hypothetical radiator which transmits or receives power equally in all directions. In an infinite homogeneous lossless medium, the power density P at a distance, d, from an isotropic source is the total power transmitted Wt, divided by the surface area of a sphere with radius d. The power received Wr by a receiving antenna with effective a r e a A r is the product of A r and P. The free space loss is defined as W r / W t. L (dB) = 10 log( Wr / Wt). The formula is more commonly expressed in decibels in one of the following ways: L (dB) = - 7 4 . 3 + 20log f (GHz) - 20log d (miles) + 10log

A t (ft 2)

+ 10 log Z r ( f t 2) - t t (dB) - Z r (dB) = - 4 9 . 5 + 20 log f ( G H z ) - 20 log d (km) + 10 log A t (m 2) -k- 1 0 1 o g A

r ( m 2) - L t ( r i B ) - L r ( d B ) .

Transmission line losses are significant at microwave frequencies and must be accounted for. L t is the transmission line loss between the transmitter and the transmit antenna and L r is the transmission line loss between the receive antenna and the receiver. A x is the effective area of projection of the antenna aperture in the direction of transmission and 3 is the antenna efficiency. If the transmit antenna has axial gain (relative to an isotropic radiator) G t and effective a r e a A t and the receiving antenna has axial gain G r (relative to an isotropic radiator) and effective a r e a A r , the free-space transmission loss formula becomes L (dB) = - 96.6 - 20 log f ( G H z ) - 20 log d (miles) -- L t ( d B )

+ G t (dB)

+ G r (dB)

- L r (dB)

= - 9 2 . 4 - 20log f (GHz) - 20log d (km) - L t (riB) -k- G t ( d B )

+ G r (dB)

- L r (dB),

where the antenna gain is given by G~ (dB) = + 11.1 + 20 log f (GHz) + 10 log A (ft 2) + 10 log(6) = + 21.5 + 20 log f (GHz) + 10 log A ( m 2) + 10 log(a). The typical value of 6 varies from 0.45 to 0 . 5 5 for commercial parabolic antennas (see Table 3) and 0.90 to 1.0 for passive reflectors. For parabolic

467


TABLE 3 Typical Worst-Case Commercial Parabolic Antenna Gain (Decibels Relative to the Isotropic Radiator) DIAMETER m (ft)

0.6(2)

1.2(4)

1.8(6)

2.4(8)

3.0(10)

3.7(12)

4.6(15)

24.3 25.0 25.8 26.3 27.2 27.9 27.9

27.8 28,5 29.3 29.3 30.9 31.0 31.1 34.5 34.9 34.9 36.4 38.4 38.5 39.4 40.0 40.7 40.8 41.0 43.1 44.0 44.8 45.1 45.1 46.1 47.9 49.7

30.0 31.0 31.9 32.2 33.3 33.5 33.6 36.7 36.8 37.3 38.9 41.2 41.3 42.0 42.5 43.3 43.3 43.5 45.8 46.4 47.3 47.6 47.6 48.6

32.0 32.9 33.8 34.2 35.2 35.2 35.4 38.7 38.8 39.0 40.8 42.9 43.1 43.8 44.5 45.2 45.2 45.4 47.8 47.8 48.5 48.8 48.8 50.5 -

33.7 34.5 35.4 35.7 36.9 37.4 37.4 40.4 40.4 41.0 42.4 44.5 44.8 45.4 46.0 46.7 46.7 47.0 49.2 49.8 50.6 50.9 50.9

35.7 36.4 37.3 37.6 -

Frequency 1.7 1.9 2.1 2.2 2.4 2.5 2.6 3.7 3.9 4.0 4.7 5.9 6.2 6.8 7.4 8.0 8.1 8.4 10.6 11.2 12.5 12.7 13.0 14.9 18.7 22.4

31.4 33.O

34. I 34.5 35.4 35.5 35.6 36.5 38.5 40.5

35.0 36.0 36.5 37.1 37.2 39.6 40.5 40.7 40.8 41.0 42.5 44.7 46.3

-

42.1 42.3 42,7 44.3 46.1 46,4 46,9 47.7 48.6 48.6 48.8 51,3 51.6 51.9

-

antennas, A is merely the frontal area (Tr × d i a m e t e r 2 / 4 ) o f the reflector since the antenna is aligned in the direction of transmission. For passive reflectors, A is the area of the passive reflector projected onto a plane passing through the passive reflector which is orthogonal to the direction of transmission. For a passive reflector, the effective area is the total surface frontal area multiplied by COS ( C / 2 ) , where C is the angle formed by the two transmission paths which converge at the reflector. The above loss formulas are commonly written as L (dB) = - L t (dB) + G t (dB) + c~ (dB) + G,. ( d B ) -

L r (dB)

(dB) = free-space loss = - 96.6 - 20 log f ( G H z ) - 20 log d (miles) = - 92.4 - 20 log f ( G H z ) - 20 log d ( k m ) . L t and L r may be estimated using Tables 4 and 5. It is possible to use one, two, or more passive reflectors between a transmitter and a receiver. In the far field one can treat each path independently. The reflector acts as a

468

George Kizer TABLE 4 Typical Copper Corrugated Elliptical Waveguide Loss FREQUENCY (GHz)

1.9 2.1 2.2 2.4 2.5 2.6 3.7 3.9 4.0 4.7 5.9 6.2 6.8 7.4 8.0 8.1 8.4 10.6 11.2 12.5 12.7 13.0 14.9 18.7

LOSS

WAVEGUIDE TYPE

EW20 EW20 EW20 EW20 EW20 EW20 EW37 EW37 EW37 EW44 EW52 EW52 EW63 EW64 EW77 EW77 EW77 EW90 EW90 EW127 EW127 EW127 EW132 EW 180

dB100 m

dB/100 ft

2.0 1.7 1.6 1.5 1.4 1.4 3.1 2.9 2.8 4.0 4.0 3.9 4.4 4.8 5.8 5.8 5.6 10.5 10.0 11.8 11.7 11.5 15.4 19.4

0.60 0.52 0.49 0.45 0.44 0.43 0.94 0.87 0.85 1.2 1.2 1.2 1.4 1.5 1.8 1.8 1.7 3.3 3.1 3.6 3.6 3.5 4.7 5.9

TABLE 5 Typical Copper Circular Waveguide Loss FREQUENCY (GHz)

4.0 4.7 5.9 6.2 6.8 7.4 8.0 8.1 8.4 10.6 11.2 12.5

LOSS

WAVEGUIDE TYPE

WC-281/-269 WC-281/-269 WC-281/-269 WC-281/-269/-205 WC-281/-269/-166 WC-281/-166 WC-281/-166 WC-281/- 166 WC-281/-166 WC-281/-166/-109 WC-281/-166/-109 WC-281/-109

dB100 m

dB/100 ft

1.2/1.3 1.0/1.1 0.91/0.99 0.91/0.98/1.6 0.89/0.97/2.5 0.89/2,3 0.89/2.1 0.89/2.1 0.89/2.1 0.91/1.9/4.5 0.92/1.9/4.3 0.95/4.2

0.36/0.41 0.32•0.35 0.28/0.30 0.28/0.30/0.50 0.27/0.30/0.76 0.27•0.70 0.27/0.65 0.27•0.64 0.27/0.64 0.28/0.57/1.4 0.28/0.57/1.3 0.29/1.30

receiver in one direction and a transmitter in the other. The gain is, of course, the same in either case. The two-way repeater gain referred to by some authors is the sum of the receive and transmit gain (expressed in decibels) of the repeater.

469


The preceding formulas assume that all antennas are far enough from each other that far-field conditions apply. Lewis, as reported by Friis [18], suggested that far-field conditions exist as long as d > 2a2/A a = free-space wavelength - 1 / [1.0167 f (GHz)] in feet = 1/[3.3356 f (GHz)] in meters, where d is the distance between the antennas, a is the largest linear dimension (in the plane of projection of the wave) of the larger antenna, and a is the wavelength of the radio wave. As the antennas are moved closer together, the gain of the two antennas is reduced compared with the far-field gain. Parabolic antennas were addressed by Bickmore and Hansen [6] for the case in which one antenna is much larger than the other (only the large antenna is in the near field). Pace [42] gives an approximation for parabolic antennas of similar size. Based on these results, Figure 9 was produced. This figure graphs the loss in composite antenna gain relative to far-field gain as a function of D a and D b , the diameters of the two parabolic antennas. For this figure, D a >_ D b and the above parameter definitions apply.

0

-1

-2 dB -3 I

-4

-5

0

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-8

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-6 -5 -4 10 log( d/[2Da 2/2 ])

-3

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Figure 9. Dual-parabolic-antenna near-field correction factor,

-1

0

470

George Kizer

It is common to estimate the total path loss through a passive repeater as two independent paths. Often one end of the path has the reflector, parabolic antenna, or both in the near field, reducing effective free-space gain. Jakes [22] considered the case of a parabolic antenna and elliptical (cirular projection) reflector. Medhurst [37] produced a result for both the elliptical (circular projection) and the rectangular (square projection) reflector cases. Based on Medhurst's results, Figures 10 and 11 were produced. They represent the loss in composite antenna and reflector gain when the two approach each other. D r is the diameter or width of the projection of the reflector gain when the two approach each other. D r is the diameter or width of the projection of the reflector in a plane parallel

+6

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6.0 7.0 8.0 9.0

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-25

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0 10 log (d/[2DR2/;k])

+10

Figure I0. Circular reflector and parabolic antenna combined gain.


471

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-15

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10 log (d/[2DR2/X]) Figure I I. Square reflector and parabolic antenna combined gain.

to the parabolic a n t e n n a . D a is the diameter of the primary parabolic antenna. Sometimes a pair of rectangular passive reflectors are used to go over or around obstructions. Although this case may be analyzed as three independent paths, typically the two passive reflectors are in each other's near field. Yang [51] analyzed the case of two rectangular (square projection) passive reflectors in the transmission path. Figure 12 shows the loss in combined far-field gain (relative to the gain of a single smaller reflector) as the two passive reflectors are moved close together. It is assumed that the projection of each rectangular passive reflector in the plane orthogonal to the direction of transmission is square. A is the width of the square

472

George Kizer

•l O f , , , , , , , , , , , 1

,1,4

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4

5 6

8

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-20 -20

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Figure 12. Dual-square-reflector combined gain (relative to a single smaller square reflector).

projection of the smaller reflector and B is the width of the square projection of the larger reflector. Using Figure 12, work the problem as the loss of two independent paths with the smaller reflector as a single reflector and add the loss from the figure. Note that all rectangular reflectors are assumed to have a square shape when they are projected into the path of transmission. If they are rectangular, the width used in the figures is the larger of the two rectangular dimensions. All elliptical reflectors are assumed to have a circular projection. If they are elliptical, the smaller dimension is used for the diameter. In all cases, however, the actual projection area is to be used to calculate far-field gain. The far-field radiation patterns of circular and rectangular reflectors, based upon Silver's results [45], are displayed in Figure 13.

Received Signal Variation ("Fading") The predicted values of received radio signal strength are usually based on a standard atmosphere (one which has no ducts, no refractive index

473

16. Microwave Radio Communication 0

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Figure 13. Far-field patterns for uniformly illuminated apertures.

discontinuities, and no turbulence). Natural variations from the standard atmosphere that occur at various times and places are produced chiefly by variations in the temperature and water vapor content of the actual atmosphere. They can cause considerable variation (fading) in the actual signal strength received compared with that predicted from a theory which assumes a static standard atmosphere. These variations in the predicted values of signal strength produced by natural phenomena should be considered in the design of a radio communication system. Most fading can be categorized as atmospheric absorption (including rain attenuation), multipath, diffraction (shadow), loss (earth bulge), antenna decoupling, and ducting. Often, fading is a combination of these types. A general introduction is given in the following paragraphs.

Atmospheric (Nonrain) Absorption Path loss caused by atmospheric absorption is primarily due to atmospheric gases and rain. At frequencies below 60 GHz, attenuation due to frozen moisture (e.g., snow or ice crystals) can be neglected. The only significant loss due to precipitation is caused by liquid raindrops. This loss will be overviewed later. Atmospheric gas absorption is due to resonance of various molecules and a broad nonresonant loss due to oxygen and

474

George Kizer

0.8 " .

ABSOLUTE HUMIDITY

//.~

(gm/m3! ..................................//...,...~_ .....~.. . . . . . .

0.6

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20

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FREQUENCY (GHz) Figure 14. Nonrain atmospheric transmission loss.

water vapor. Below 100 GHz, the only significant resonances are due to water vapor (H20) at 22 and 68 GHz, ozone ( 0 3) at 67 and 96 GHz, and a broad band of oxygen (O 2) resonances from 61 to 68 GHz. Due to atmospheric pressure, the absorption resonances are broadened so that significant absorption is observed near the resonance frequencies. Nonrain atmospheric losses for 15°C have been plotted in Figure 14. Rain Loss

At higher radio frequencies, large amounts of rain can have a significant effect on system radio interference (rain scatter), cross-polarization discrimination [39], and path attenuation. The interference and cross-polarization discrimination effects are short lived and generally are not a significant degradation to terrestrial paths. Path attenuation, however, has a significant impact on path design. Tillotson [46] observed the considerable effect rain can have on path design. He observed that for a rain rate of 100 mm (4 i n . ) / h , a normal 4- or 6-GHz path of 30 to 60 km (20 to 30 miles) designed for a 40-dB fade margin would be unaffected by rain. However, to maintain the path within the 40-dB fade range, the path length would have to be reduced to 9.2 km (5.7 miles) at 11 GHz, 3.7 km (2.3 miles) at 18 GHz, or 2.1 km (1.3 miles) at 30 GHz. Actual path lengths will vary from rain climate to rain climate. However, the considerable affect of rain on high frequency radio transmission is clear.


475

The rain attenuation observed on a radio path is a function of the following three variables: c~ = (dB) =/3TL, where/3 (dB/kin) is the attenuation of a signal in rain of constant density and rate (attenuation due the point rain rate), y is the path correction factor (conversion factor from the point rain rate to the path averaged rate), and L (krn) is the path length. The attenuation of a signal due to rain is a function of the size distribution of raindrops as well as a function of rain rate and the terminal velocity of the drops. The size distribution is a function of the type of rain (e.g., thunderstorm and drizzle), and terminal velocity is a function of raindrop shape which is a function of rain type and wind. Olsen et al. [40] suggest that the Laws and Parsons [26] size distribution and the Gunn and Kinzer [19] terminal velocity results are the most reliable data to date. Medhurst validated these theoretical results by actual measurement [38]. Photographs have shown that rain, rather than being spherical, is actually flattened or concave. Because of this flattening, linearly polarized signals experience polarization-dependent attenuation. If the raindrops are assumed to be elliptical, /3 is given by the following [40], /3 ( d B / k m ) = aR b, where R ( m m / h ) is the rain rate and a and b are found in Table 6. Figure 15 plots/3 for various rain rates and transmission polarizations. For reference Bussey [8] observed that a rain rate of 1 m m / h represented

TABLE 6 Rain Attenuation Coefficients FREQUENCY 1 2 3 4 5 6 7 8 9 10 11 12 15 20 25 30 35 40 45 50 60 70 80 90 100

aHORIZONTAL

aVERTICAL

bHORIZONTAL

bVERTICAL

0.0000387 0.000154 0.000389 0.000650 0.000871 0.00175 0.00301 0.00454 0.00679 0.0101 0.0141 0.0188 0.0367 0.0751 0.124 0.187 0.263 0.350 0.442 0.536 0.707 0.851 0.975 1.O6 1.12

0.0000352 0.000138 0.000352 0.000591 0.000784 0.00155 0.00265 0.00395 0.00594 0.00887 0.0125 0.0168 0.0335 0.0691 0.113 0.167 0.233 0.310 0.393 0.479 0.642 0.784 0,906 0.999 1.06

0.912 0,963 1,029 1,121 1.291 1.308 1.332 1.327 1.301 1.276 1.243 1,217 1.154 1.099 1.061 1.021 0.979 0.939 0,903 0.873 0.826 0.793 0.769 0.753 0.743

0.880 0,923 0.987 1.075 1.248 1.265 1.312 1.310 1.287 1.264 1.229 1.200 1.128 1.065 1.030 1.000 0.963 0.929 0,897 0.868 0.824 0.793 0.769 0.754 0.744

476

George Kizer

20

H POL RAIN RATE

(mm/hr)

/

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FREQUENCY (GHz) Figure 15. Rain attenuation.

light rain; 4 m m / h , moderate rain; 16 m m / h , heavy rain; and 100 mm / h, a cloudburst. The attenuation measured at one point of a radio path is not totally representative of the attenuation of the path taken as a whole. The point rain rate attenuation is a complex function of rain gauge integration time and the probability of rain cell size and occurrence. A rain rate at one location may be low but it may be much higher elsewhere on the radio path. High rain rates, however, indicate that the observation point is near the center of maximum rain intensity. Several methods, such as Lin's [30] and CCIR's [11], have attempted to modify point rain attenuation for path length variation. The Crane method, given at the end of this chapter, has received the widest acceptance. Rain rate data are taken by measuring the total rain accumulated in a rain gauge in a period of time (integration period) and dividing this by the integration time. The measured rain rate varies considerably with rain gauge integration time [31]. A very short integration time produces widely varying results due to wind and spatial variations. A long integration time reduces the effect of a short-duration high rain rate. Two path rain attenuation calculation methods are popular. Rain loss calculations assume a point rain rate, R, which will not be exceeded more than a percentage of the time. The actual rain rate at any instant is quite erratic. A long-term rain rate gathered from a single rain gauge requires a very long time (several years) to yield stable statistics. If the time base is not sufficiently long, the short-term results tend to


477

underestimate (or occasionally overestimate) the long-term, large sample average. Data taken over a period of less than 10 years [16] are generally unreliable for moderate rain rates. The incidence of high rain rates at a single point is so low that a much longer time base (a few decades) is required to obtain stable statistics [20]. Rain rate calculations assume rain rate distributions measured over one or two decades [33, 35]. The rain rates obtained from these data represent the rates that would have been measured if the radio path had been operating over the previous long time period. Exactly the same data will probably not be obtained if measurements are made over the next couple of decades. However, these data represent the best estimate of the rain rate which would not be exceeded over any one year. The actual rain rate measured over any one specific year will be different than the average value. Average values should not be confused with worst-case values. Osborne [41] observed that the worst-case one-year rain rates can exceed long-term averages by 2.5 to 10 times. Worst-case month or hour rates can exceed long-term averages by extremely large factors. Engineering paths based on worst-case statistics lead to very uneconomical radio systems. As Osborne [41] observed, at the present time there is no definitive proven solution to this problem. There is no practical method to limit the worst-case outage time for radio paths with loss dominated by rain attenuation. However, route diversity can be used to reduce outage time.

Reflection ("Fresnel Zone") Fading A common form of multipath fading is reflective fading (sometimes called Fresnel zone fading). This fading, like that caused by atmospheric multipath, is due to the reception of several signals from several different paths. The concept is exactly the same as one used in optics. Indirect signals arrive due to reflections from the ground, water, nearby objects, or stable atmospheric layers. Unlike atmospheric multipath, fading due to these reflective signals is relatively slow changing since the secondary paths are relatively stable. If the fading is due to cancellation between the main signal and a single reflected signal, the composite signal will be a minimum when the reflected signal is reflected from an obstacle that is an even Fresnel zone radius from the main path. The composite signal will be a maximum if the radius is odd. Generally, reflective fading is not a problem for paths over heavily wooded terrain or for paths so far above the reflecting surfaces that the transmit and receive antenna patterns discriminate against reflections. Flat paths can have reflections. Paths over water or salt flats almost always have reflections. Reflections can be reduced by blocking the reflection (using screen or high-low path design), tilting the antenna, or using spaced antennas. It is common to use two receive

GeorgeKizer

478

antennas (space diversity) to combat the effect of multipath. Another method is to reduce the antenna height at one end of the path while raising it at the other end to block the reflection or move it to a location less likely to be reflective (high-low path design). This technique makes one site elevated so as to provide the required clearance; the other site is located near ground level. The reflection point can be placed at a selected location by slight changes in the lower antenna height and geographical location. Even if the path is reflective, this technique reduces the difference between the direct and the reflected paths when compared with midpath reflection.

Obstruction ("Diffraction") Fading Radio waves normally travel outward along radial lines from their source, except when deviated by refraction or reflection. Another condition under which radio waves deviate from a straight line is called diffraction. Whenever radio waves encounter an obstructing object, some of the energy of the wave is diffracted at the edges of the object and becomes bent around the edge. This is a direct result of Huygens' principle of secondary radiation. This reduces the shadowing effect of objects which are opaque to radio waves. Diffraction fills part of the shadow area with some energy from the wave. The curved surface of the earth is the edge of one such object. Other objects may be buildings, trees, hills, mountains, or structural parts of a ship or airplane. If the obstructing object is small and subtends only a small angle, as seen from the source of radiation, the region at a considerable distance behind the object may become filled in and suffer little or no shadowing effect. Close behind the object, however, shadowing will be observed. Shadowing due to the earth causes the field strength to decrease rapidly with distance beyond the radio horizon. In general, an exact determination of signal strength for various path clearances is difficult. The obstruction loss generally falls somewhere between the knife-edge diffraction and the fiat-sheet reflection cases shown in Figure 16. The first Fresnel zone radius F 1 at any point on the radio path is given by the following: F 1 = first Fresnel zone radius Fn

= nth Fresnel zone radius = sqr(n) F 1

d I = distance from one end of path to reflection point t d e = distance from the other end of path to the reflection point

479

16. Microwave Radio Communication +6

P~

-10

I(NIFE EDGE ROUND EARTH FLAT PLANE - - - - - - - - - - - J

dB

-20

-30

ILk'(lll

II1

IIII

II

IIIII!1

Ilill

II

|1 I11 III

11111

-5

Iili|ll|ll

I III

I III1|

|1 Ii

I IIi

0 h/F1

I I I

ii

Ii

II

LII

1

+5

Figure 16. Two-path reflection gain,

d o = total length of path = d 1 4- d 2

f = frequency of operation, where n = 1, 2, 3 . . . and sqr is the square root. For F 1 in feet; d 0, d 1, and d 2 in miles; and f in gigahertz, F 1 = 72.1 ( d l d z / f d 0 ) a / 2 . For F 1 in meters; d 0, dl, and d 2 in kilometers; and f in gigahertz, F 1 = 17.3 ( d l d 2 / / f d 0 ) l / 2 . From a classical physics (optics) point of view, the quantity (h/F1)2 defines the Fresnel zone (or fraction of the zone) clearance of an obstacle as measured perpendicular to the line of wave propagation. In practice it is measured in a line perpendicular to the earth. For normal microwave paths, there is no significant difference. Bullington [7] used (h/F 1) to define path clearance. Since that time, common usage has been to define (h/F 1) rather t h a n (h/F1)2 as Fresnel zone clearance.

480

George Kizer

The speed of a radio wave varies inversely with the density of the medium through which it travels. The radio refractive index of air is the ratio of the speed of propagation in a vacuum to the radio wave's speed in the atmosphere. This ratio, n, is approximately 1.0003 under standard conditions near the earth's surface. For convenience, a factor, N, refractivity, given by N = (n - 1) X 10 6, is used in propagation studies. Refraction (bending) of a radio wave occurs when the wave speed on one side of the beam is reduced below that on the other. The bending is in the direction of the reduced speed, and its degree is directly proportional to the amount of speed reduction with distance (i.e., speed gradient) normal to the beam axis. Typically the atmosphere has a gradient of - 6 3 N units per mile or - 3 9 N units per kilometer. This gradient causes the radio wave to bend. The curvature of the nearly horizontal radio beam is slightly different from the curvature of the earth. If the actual earth with radius a were replaced by an equivalent earth with radius K a (see Figure 18), horizontal radio waves would travel parallel to the equivalent earth. For microwave radio frequencies, this equivalent earth factor, K, is given by K = 253/[253 + = 157/[ 157 +

(dN/dh)] for (dN/dh)in N units per mile ( dNIdh)] for ( d N I d h ) in N units per kilometer.

60

50

40 FEET 30

METERS

20

10

0 0

I 5

I 10

I 15

20

FREQUENCY (GHz) Figure 17. Suggested minimum vertical spacing (for main and diversity antennas).

25

481

16. Microwave Radio Communication K= -1

K= oo

K=I

" ~

~

K=0.5

~ ~

K=0.33 ~

f

~

~v

[

I I

Figure 18. Ray bending for various K-factors.

The typical value of K is 5. 4 Figure 19 shows the range of possible refractivity when observed on a worldwide basis. To analyze a microwave path for conformance to the above guidelines, the profile of the earth along the transmission path is plotted. The microwave beam is then shown as a straight line between the two points. This represents the radio or light ray for K of infinity. An h value is then subtracted from the ray height to show beam bending due to various potential K values. The h correction value is given by the following: h = the change in vertical distance from a horizontal reference line p = location at which h is determined d 1 -- distance from p to one end of the path d 2 = distance from p to the other end of the path K = effective earth radius factor. For h in feet and d 1 and d 2 in miles

h - [did2]~[1.50 K].

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George Kizer 300

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PERCENT OF TIME ORDINATE IS EXCEEDED Figure 19. Worldwide refractivity gradient (K-factor) variation.

For h in meters and

d I

and

d 2

in kilometers

h = [dld2]/[12.74 K]. To adjust for ray curvature, subtract the above h value from the height of the ray above a flat earth or add the h value to the height of the earth below a straight ray. A particular form of diffraction loss is called obstruction ("earth bulge") fading. When the K factor becomes less than 1, the radio wave is bent upward. Under extreme cases the receive path can be partially or completely blocked. This type of loss is called earth bulging because the earth appears to bulge up into the radio path. The power fades that occur due to diffraction by the earth's surface are generally supported by a subrefractive (positive) gradient of refractive index. This type of fading can persist for several hours to depths of 20 or 30 dB. The fading is essentially independent of small-scale changes of frequency, but may be reduced or avoided by a proper choice of terminal antenna heights. Figure 20 shows areas of the world where this is common. From experience, various rules of thumb have been developed [50] to reduce obstruction fading to an insignificant effect. The following guide-

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with a high probability of earth bulge (percentage of the worst month that the refractivity gradient > 0 N/kin).

Figure 20. W o r l d areas

lines for radio frequencies greater than 2 GHz are based on CCIR criteria [10]. These criteria were developed by Vigants and other in conjunction with Study Group 5 and represent an improvement to Vigants's original published guidelines [47]. The guidelines for 2-GHz radio frequencies and path length guidelines to minimize obstruction fading were developed based upon unpublished computer simulations and other studies. Guidelines for Radio Frequencies Greater Than 2 GHz For good propagation areas, allow obstruction clearance of 0.6 F 1

for K = 1

or

0.00

F 1 (grazing)

2

for K = 5,

whichever is greater clearance. For average propagation areas, allow obstruction clearance of 4

1.0F 1

forK=5

0.3 F 1

for K = 5,

or

2

484

George Kizer 0.9

Ki

CLEARANCE CRITERIA 0.8

....................................................................................................

....

: ' : ' : ' : . .................... ............

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n0 0.7 I

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0.5

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CLEARANCECRITERIA K -- 112

I 60 80 PATH LENGTH

I 100

I 120

I 140

Figure 21. Modified K-factor for long paths.

whichever is greater clearance. For difficult propagation areas, allow obstruction clearance of 4

1.0 F 1

for K = 5

0.00 F 1 (grazing)

for K = 3,

or 1

whichever is greater clearance. The preceding guidelines apply to the normal or main antennas for short to medium-length paths. For long paths, the clearance criteria may be relaxed, as shown in Figure 21. This accounts for the observation that obstruction fading is typically caused by localized refractivity gradient changes. For long paths, the average refrac4 tivity gradient is closer to the normal K value of 5.

Guidelines for 2-GHz Radio Frequencies Since Fresnel zones are much larger for 2 GHz than for higher frequencies, the above guidelines may be relaxed for low-frequency paths. For good or average propagation areas, allow obstruction clearance of 0.6 F 1 for K = 43 " For difficult propagation areas, allow obstruction clearance of 4

1.0 F 1 for K = g.

485


Guidelines for Space Diversity Antenna Placement If space diversity is used, the criterion for diversity antenna clearance is less stringent. For the diversity antenna path, allow obstruction clearance of 0.60F 1 forK= 4 with at least 10 ft in the first 500 ft from the antenna. This usually permits placement of the diversity antenna at an appropriate level below the main antenna. If the path terrain is nonreflective, multipath fading improvement is achieved by placing the diversity antenna at least 200 wavelengths below (or above) the main antenna. See Figure 17 (page 480) for this distance.

Guidelines for Radio Path Lengths The above guidelines are designed to cover the vast majority of situations. In unusually severe propagation areas (such as the southern United States coastal areas), path lengths must be limited to reduce the occurrence of obstruction fading to a reasonable level. More detailed engineering may be required to design reliable paths in some areas. This engineering generally requires detailed knowledge of refractive index statistics for a given area. Such effort is costly and time consuming and should not be accomplished unless required. Based upon computer simulation, obstruction fading should be investigated if the following path lengths are exceeded. Maximum path length [kilometers (miles)] Frequency (GHz) Climate factors Good (C = 0.5) Average (C = 1.0) Bad (C = 2.0)

2

6

11

18

65 (40) 50 (30) 30 (20)

65 (40) 40 (25) 25 (15)

65 (40) 50 (30) 25 (15)

40 (25) 25 (15) 15 (10)

Refer to the following multipath calculations for further discussion regarding climate factor C. Worst-case conditions were investigated for each climate region. These path length guidelines assume that the preceding criteria for antenna placement were used. It is also assumed that adequate minimum thermal fade margins (35 dB for 2 and 6 GHz, 45 dB for 11 GHz, and 30 dB for 18 GHz)were engineered into the path.

Power Fading Power fading due to antenna decoupling refers to the loss of signal that occurs for transmission and reception of the signal outside of, or at the

486

George Kizer

extremities of, the main lobe of the antenna pattern. Variation of atmospheric refraction can cause changes in the apparent angle-of-arrival of the line-of-sight ray, particularly in the vertical plane, and can therefore effectively cause a reduction in gain in the antennas used at the radio path terminals. Measurements made in the United States over a path of 28 km, at frequencies of 4 and 24 GHz, show that the angle-of-arrival can change rapidly by as much as 0.75 ° above and below the normal line of sight. Another source observed 0.5 ° of angle-of-arrival variation on a 39-km path. Variations in the vertical angle-of-arrival of up to 0.5 ° have been observed on a 40-km path. This effect is proportional to the path length and can introduce several decibels of loss for high-gain antennas and long line-of-sight paths. Because of the vertical variations in angle-of-arrival, antennas having half-power beam widths less than 0.5 ° should generally be avoided for line-of-sight paths. This limitation can be used as one criterion to determine the maximum aperture size for antennas and the maximum vertical dimension for passive repeaters. This loss may be minimized by specifying a sufficiently broad antenna beam so that the expected variations of the angle-of-arrival are matched or exceeded.

Duct Fading Whenever a horizontal layer of air has its normal properties altered so that the refractive index decreases rapidly with an increase in height, strong downward bending of any nearly horizontal rays traversing the layer will occur. The curvature of these rays often exceeds the curvature of the earth's surface. A layer of air having this property is called a duct. Ducts may be divided into two types, ground (surface) and elevated. The underside of a ground-based duct is in contact with the earth's surface, whereas the underside of an elevated duct is above the earth's surface and overlies a layer of normal air. Prolonged fading, or signal enhancement, can result from propagation through ducts, especially when either the transmitter or the receiver is located within the duct. Signals may be trapped within the duct and propagated far beyond the horizon. Ducts may also cause multipath fading. Two conditions are necessary to form a duct. The first is for the refractive index gradient to be equal to or more negative than - 1 5 7 N per kilometer ( - 2 5 3 N per mile). This means that K must be infinite (flat earth) or negative (extreme superrefractivity). The second necessary condition is that the gradient must be maintained over a height of several wavelengths. For ducts 100 to 30 ft thick, trapping will occur for frequencies between 2 and 13 GHz, respectively. Of course, the cutoff relationship is only approximate since ducts have vague boundaries. See Figure 22 for areas in which ducting is highly probable.

487


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I 120

"

I 180

EAST

Figure 22. World areas with a high probability of ducting (percentage of the worst month that the refractivity gradient _~ - 1 5 7 N/km).

Atmospheric Multipath Fading Multipath fading generally takes one of two forms. The first, atmospheric multipath, is caused by the received signal being composed of several signals arriving at the receive site by slightly different paths from the transmitter. The different transmission paths are caused by slight timeand space-dependent variations in the atmospheric refractive index. This phenomenon is the same one that causes stars to twinkle at night. Since the relative time delay of the various received signals will change as the atmosphere varies randomly, the composite received signal will vary widely and rapidly. This fading will be worse if obstruction (earth bulge) or reflective fading has already reduced the level of the dominant receive signal. Figure 23 diagrams the multipath fading mechanisms. Figure 24 shows typical time domain received signal variation during multipath fading. DeLange [17] noticed that for a 22-mile path operating at 4 GHz, path differences were from a fraction of 1 to 7 ft, with 3 ft being the most common. Kaylor [23] made several observations for a typical 31-mile, 4-GHz path with no significant ground reflections. He observed that deep multipath fades (greater than 20 dB relative to normal propagation

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I 50

60

Figure 24. Typical multipath fading,

statistics of the received signal approach the distribution of Rayleigh. After the multipath fading has reached the Rayleigh distribution, further increase in either distance or frequency increases the number of fades to a given depth but decreases the duration so that the product is essentially constant [7]. If a received signal envelope voltage, V, at an instant of time has a Rayleigh distribution (as measured over a long period of time), the probability, p, that it has a value less than or equal to L is given by

p(u 1,

where IFD-thermal is the frequency diversity improvement factor for thermal outages (1 < IFD-thermal ~ 200); IFD-digital is the frequency diversity improvement factor for dispersive outages (1 < IFD-digital -< 200); f is the frequency of operation in gigahertz; D is the path length in miles (0.621 the path length in kilometers); FFM is the fiat fade margin in decibels; DFM is the dispersive fade margin in decibels; G is f3/(fchfeq); feb is the frequency in gigahertz between the two channels for a 1:1 system and the frequency in gigahertz between two adjacent channels for an M:N system; feq is 1 for a 1"1 system, 1/sqr(N) for a I ' N system, 4 . 2 / N °8 for a 2:N system, l l . 2 / N for a 3:N system, and 24.2/N 1"1 for a 4:N system; and sqr(x) is the square root of x. The improvement in a four-receiver system [48] with space diversity and frequency diversity (i.e., quad diversity) is /thermal -" IsD-thermal X IFD-thermal /digital = /SD-digital X /FD-digital"

499


One word of caution. As noted earlier, paths over water have a 1/L, rather than a typical 1 / L 2, fading characteristic. For these paths, space diversity should be considered to have normalized the path to a 1 / L 2 fading characteristic. Therefore, only the frequency diversity improvement factor should be applied to this type of quad diversity path. The improvement in a two-receiver system with space diversity and frequency diversity (i.e., hybrid space diversity using a different frequency on each antenna) is

/thermal-- maximum (/SD_thermal, /FD-thermal) /digital -" maximum (IsD.digital, IFD-digital)" For angle diversity antennas, research results are divided. For some paths, angle diversity outperforms space diversity [6]; for others, angle diversity is little better than no diversity [1]. For some paths, angle diversity will be better than space diversity part of the time and worse other times [21]. When the path thermal noise fade margin is not substantially greater than the dispersive fade margin, vertical space diversity improvement is at least an order of magnitude better than that of angle diversity [32]. Lacking more definitive data, the following provisional improvement factors are suggested:

lAD-thermal --" ( IsD-thermal / 10), lAD-digital--- IsD-digital,

] ~ 1AD_thermaI ~ 20 1 ~ lAD_digital ~ 200.

The thermal improvement /SD-thermal is calculated using a 30-ft equivalent space diversity spacing. Using the Crane path attenuation model [15, 16], rain attenuation is calculated from the following equations, A

R

--

aRb[(e ubD - 1)/ub]

A R = aRb[((e "ha-

for 0 _< D _< d km

1)/ub}-

{(B%Cba)/cb} + ((B%cbD)/cb}] for d < D _< 22.5 km,

where u is ln[BeCd]/d, B is 2.3 R -°17, c is 0 . 0 2 6 - 0.03In(R), d is 3 . 8 - 0.6In(R), A R is the path attenuation due to rain in decibels and equals TFM - WRL, TFM is the thermal fade margin in decibels, WRL is the wet radome loss in decibels, R is the point rain rate in r a m / h , D is the path distance in kilometers (Dmi~¢~ × 1.609), Dmiles is the path distance in miles, and In is the natural (base e) logarithm. For paths longer than 22.5 km, the attenuation A R is calculated for a 22.5-km path and the resulting rain outage time is multiplied by a factor of (D/22.5).

500

George Kizer TABLE 7 Point Rain Rate Distribution Values RAIN CLIMATE REGION

PERCENT OF YEAR RAIN RATE EXCEEDED

1.0 0.5 0.2 0.1 0.05 0.02 0.01 0.005 0.002 0.001 0.0005 0.0002 0.0001

B

1.7 2.5 4.0 5.5 8.0 12 15 19 24 28 32 37 41

1.8 2.7 4.8 6.8 9.5 14 19 26 40 54 68 87 101

C

D1

1.9 2.8 4.8 7.2 11 18 28 41 62 80 98 122 140

2.2 4.0 7.5 11 16 27 37 50 72 90 108 132 150

D(2 )

3.0 5.2 9.5 15 22 35 49 64 86 102 118 139 155

D3

E

F

G

H

4.0 7.0 14 22 31 48 63 81 107 127 147 174 194

4.0 8.5 21 35 52 77 98 117 144 164 184 211 231

0.8 1.2 3.2 5.5 8.0 14 23 34 51 66 81 101 116

3.7 7.0 14 22 33 51 67 85 109 129 149 176 196

6.4 13 31 51 77 115 147 178 220 251 282 323 354

EXPECTED STANDARD DEVIATION OF MEASUREMENTS ABOUT MODEL %

Table value shows rate in mmlhour measured with 1-minute rain gauge integration time.

The coefficients a and b are functions of frequency and polarization [13] and are listed in Table 6. R values are determined from Table 7 based on the rain climate region determined from Figure 31 or 32. To calculate rain outage, an iterative computer program is used to vary the rain rate R until the calculated path attenuation is equal to the rain attenuation margin, A R = T F M - WRL. This rain rate is then applied to a distribution of rain rate vs time for a particular geographic

C

B

Figure 31. Rain rate climate regions within the United States.

501


150

75

120

90

60

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60

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30

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90

120

150

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75

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45

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180

DR ~ 7 ~ ~

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30 ~

120

90

60

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WEST

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~'-A

[[I]]B

[~C

0

ITJJD

-451:~1'-

,=,,

A 30

60

90

120

LONGITUDE [TA

,~

"

[]E

I~F

[]G

O 60 m 150

180

EAST

IH

Figure 32. Worldwide rain rate climate regions.

area to find the rain outage time. Annual rain outage Train in s / y e a r may be converted to worst-month outage Train__mont h in s / m o n t h as follows [14]:

Train__month = 1.22(Train) 0"87.

5. Conclusion Microwave radio system performance is highly dependent on the choice of the appropriate transmission equipment and careful path design. No single chapter can treat the topic exhaustively. This chapter aquaints the reader with the most significant system design topics and overviews the most important calculations necessary to estimate line-of-sight microwave radio performance.

Acknowledgments The author acknowledges and appreciates the assistance of Bill Knight, Chief Transmission Engineer for Alcatel Network Systems, with the guidelines outlined in this chapter.

502

George Kizer

References [1] E. W. Allen, Angle diversity vs. space diversity at 6 GHz: Results of a 3.5 year test, Int. Telecommun. Symp., Taipei, Feb. 1992. [2] G. D. Alley, W. C. Peng, W. A. Robinson, and E. H. Lin, The effect on error performance of angle diversity in a high capacity digital microwave radio system, IEEE/IEICE Global Telecommun. Conf. Rec., pp. 31.5.1-31.5.4, Nov. 1987. [3] W. T. Barnett, Multipath propagation at 4, 6, and 11 GHz, Bell Syst. Tech. J., Vol. 51, pp. 321-361, Feb. 1972. [4] Bellcore Technical Advisory TA-TSY-000009, "Asychronous Digital Multiplexes, Requirements and Objectives," Issue 1, pp. 4-6-4-9, Dec. 1984. [5] Bellcore Technical Reference TR-TSY-000752, "Microwave Digital Radio System Criteria," Issue 1, pp. 6-16, Oct. 1989. [6] R. W. Bickmore and R. C. Hansen, Antenna power densities in the Fresnel region, Proc. IRE, Vol. 47, pp. 2119-2120, Dec. 1959. [7] K. Bullington, Radio propagation fundamentals, Bell Syst. Tech. J., Vol. 36, pp. 593-626, May 1957. [8] H. E. Bussey, Microwave attenuation statistics estimated from rainfall and water vapor statistics, Proc. IRE, Vol. 38, pp. 781-785, July 1950. [9] CCIR Recommendations, Doc. XVIIth Plenary Assem. CCIR, Vol. 9. Geneva: Int. Radio Consultative Comm., 1990. [10] CCIR Rep. 338-6, "Propagation Data and Prediction Methods Required for Terrestrial Line-of-Sight Systems, Annex I, Table II," Doc. XVIIth Plenary Assem. CCIR, Vol. 5, pp. 355-420, 1990. [11] CCIR Rep. 563-4, "Radiometerological Data," Doc. XVIIth Plenary Assem. CCIR, Vol. 5, pp. 105-148, 1990. [12] CCIR Rep. 719-3, "Attenuation by Atmospheric Gases," Doc. XVIIth Plenary Assem. CCIR, Vol. 5, pp. 189-204, 1990. [13] CCIR Rep. 721-3, "Attenuation by Hydrometeors, in Particular Precipitation, and Other Atmospheric Particles," Doc. XVIIth Plenary Assem. CCIR, Vol. 5, pp. 226-245, 1990. [14] CCIR Rep. 723-3, "Worst Month Statistics," Doc. XVIIth Plenary Assem. CCIR, Vol. 5, pp. 262-274, 1990. [15] R. K. Crane, Attenuation due to rainmA mini-review, IEEE Trans. Antennas Propag., Vol. AP-23, pp. 750-752, Sept. 1975. [16] R. K. Crane, Prediction of attenuation by rain, IEEE Trans. Commun., Vol. COM-28, pp. 1717-1733, Sept. 1980. [17] O. E. DeLange, Propagation studies at microwave frequencies by means of very short pulses, Bell Syst. Tech. J., Vol. 31, pp. 91-103, Jan. 1952. [18] H. T. Friis, Microwave repeater research, Bell. Syst. Tech. J., Vol. 27, pp. 183-246, Apr. 1948. [19] R. Gunn and G. D. Kinzer, The terminal velocity of fall for water droplets in stagnant air, J. Meteorol., Vol. 5, pp. 243-248, Aug. 1949. [20] D. C. Hogg, A. J. Giger, A. C. Longton, and E. E. Muller, The influence of rain on design of ll-GHz terrestrial radio relay, Bell. Syst. Tech. J., Vol. 56, pp. 1575-1580, Nov. 1977. [21] R. W. Hubbard, Angle diversity reception for LOS digital microwave radio, IEEE Mil. Commun. Conf. Proc., pp. 19.6.1-19.6.7, Oct. 1985. [22] W. C. Jakes, Jr., A theoretical study of an antennamReflector problem, Proc. IRE, Vol. 41, pp. 272-274, Feb. 1953.


503

[23] R. L. Kaylor, A statistical study of selective fading of super-high frequency radio signals, Bell. Syst. Tech. J., Vol. 32, pp. 1187-1202, Sept. 1953. [24] G. M. Kizer, Microwave Communication, pp. 315-440. Ames: Iowa State Univ. Press, 1990. [25] G. M. Kizer, Multiple hop radio system design to meet end-to-end performance objectives, Bellcore Nat. Radio Wireless Eng. Conf., D5.1-D5.30, May 1991. [26] J. O. Laws and D. A. Parsons, The relation of raindrop-size to intensity, Am. Geophys. Union Trans. 1943, Part II (Apr. 1943), pp. 452-460, Jan. 1944. [27] T. C. Lee and S. H. Lin, A model of space diversity improvement for digital radio, Int. Union Radio Sci. (URSI) Open Symp. Wave Propag.: Remote Sensing Commun., Durham, NH, Symp. Vol. pp. 7.3.1-7.3.4, July/Aug. 1986. [28] T. C. Lee and S. H. Lin, A model of frequency diversity improvement for digital radio, Int. Symp. Antennas Propag., Kyoto, pp. 7.3.1-7.3.4, 1985. [29] T. C. Lee and S. H. Lin, More on frequency diversity for digital radio, IEEE Globecom Conf. Rec., pp. 36.7.1-36.7.4, 1985. [30] S. H. Lin, A method for calculating rain attenuation distributions on microwave paths, Bell Syst. Tech. J., Vol. 54, pp. 1051-1086, July/Aug. 1975. [31] S. H. Lin, Dependence of rain-rate distribution on rain-gauge integration time, Bell Syst. Tech. J., Vol. 55, pp. 135-141, Jan. 1976. [32] S. H. Lin, Measured relative performance of antenna pattern diversity, antenna angle diversity, and vertical space diversity in Mississippi, IEEE Globecom Conf. Proc., pp. 44.1.1-44.1.5, 1988. [33] S. H. Lin, Nationwide long-term rain statistics and empirical calculation of ll-GHz microwave rain attenuation, Bell Syst. Tech. J., Vol. 56, pp. 1581-1604, Nov. 1977. [34] S. H. Lin, Statistical behavior of a fading signal, Bell Syst. Tech. J., Vol. 50, pp. 3211-3269, Dec. 1971. [35] S. H. Lin, H. J. Bergmann, and M. V. Pursley, Rain attenuation distributions on Earth-satellite paths--Summary of 10-year experiments and studies, Bell Syst. Tech. J., Vol. 59, pp. 183-228, Feb. 1980. [36] C. W. Lundgren and W. D. Rummier, Digital radio outage due to selective fadingq Observation vs prediction from laboratory simulation, Bell Syst. Tech. J., Vol. 58, pp. 1073-1100, May/June 1979. [37] R. G. Medhurst, Passive microwave mirrors, Electron. Radio Eng., pp. 443-449, Dec. 1959. [38] R. G. Medhurst, Rainfall attenuation of centimeter waves: Comparison of theory and measurement, IEEE Trans. Antennas Propag., Vol. AP-13, pp. 550-564, July 1965. [39] W. L. Nowland, R. L. Olsen, and I. P. Shkarofsky, Theoretical relationship between rain depolarization and attenuation, Electron. Lett., Vol. 13, pp. 676-678, Oct. 1977. [40] R. L. Olsen, D. V. Rogers and D. B. Hodge, The aR b relation in the calculation of rain attenuation, IEEE Trans. Antennas Propag., Vol. AP-26, pp. 318-329, Mar. 1978. [41] T. L. Osborne, Application of rain attenuation data to ll-GHz radio path engineering, Bell Syst. Tech. J., Vol. 56, pp. 1605-1627, Nov. 1977. [42] J. R. Pace, Asymptotic formulas for coupling between two antennas in the Fresnel region, IEEE Trans. Antennas Propag., Vol. AP-17, pp. 285-291, May 1969. [43] W. D. Rummler, A comparison of calculated and observed performance of digital radio in the presence of interference, IEEE Trans. Commun., Vol. COM-30, pp. 1693-1700, July 1982. [44] W. D. Rummier, More on the multipath fading channel model, IEEE Trans. Commun., Vol. COM-29, pp. 346-352, Mar. 1981.

504

George Kizer

[45] S. Silver, Microwave Antenna Theory and Design, pp. 169-199, 413-542, 574-592. New York: McGraw-Hill, 1949. [46] L. C. TiUotson, Use of frequencies above 10 GHz for common carrier applications, Bell Syst. Tech. J., Vol. 48, pp. 1563-1576, July-August 1969. [47] A. Vigants, Space-diversity engineering, Bell Syst. Tech. J., Vol. 54, pp. 103-142, Jan. 1975. [48] A. Vigants and M. V. Pursley, Transmission unavailability of frequency diversity protected microwave FM radio systems caused by multipath fading, Bell. Syst. Tech. J., Vol. 58, pp. 1779-1796, Oct. 1979. [49] R. F. White, Space diversity on line-of-sight microwave systems, IEEE Trans. Commun. Technol., Vol. 16, pp. 119-133, Feb. 1968. [50] R. F. White, "Engineering Considerations for Microwave Communications Systems," pp. 51-52, GTE Lenkurt, San Carlos, CA, 1975. [51] R. F. H. Yang, Passive repeater using double flat reflectors, IRE Natl. Cony. Rec., pp. 36-41, Mar. 1957.

CHAPTER

17 M icrowave Instrumentation and Measurements Aksel Kiiss

I. Scattering P a r a m e t e r s S-Parameter Measurements S-parameters are complex quantities containing both amplitude and phase information. There are two measurement techniques that are in general use in the industry. One measures both the amplitude and phase of the S-parameters, and the other measures only the amplitude (normally presented in logarithmic form). The first instrument is called a vector network analyzer, and the second, a scalar network analyzer. Vector analyzers are mostly used in design and development work, whereas the scalar analyzers are in wide use as production test equipment. In the United States vector analyzers are manufactured by HP and Wiltron, and scalar analyzers, by HP, Wiltron, and Wavetek among others. Before, we presented vector analysis and its associated uncertainties. Below we will discuss scalar analysis and its associated uncertainties.


505


506

In high-frequency measurements, we know we can characterize a device under test (DUT) by measuring the input and output signals of the device after we have applied the proper stimulus signals. We take this information (the incident waves being a waves and the output waves being b waves) and define a set of equations using the device's S-parameters and the a and b waves. For a two-port device, we define two linear equations.

Aksel Kiiss

SCATTERING

PARAMETER

DEFINITION Incident

S=l

Transmitted

fr so

Reflected

C~

Port 1

Port 2

Transmitted

I I Reflected

II

St2 bl =

S.

b= = S=l

(,

a2

Incident

a 1 +S12

a=

a 1 + $22

a2

To determine the four S-parameters we first terminate port 2 with SCATTERING PARAMETER a Z 0 load, eliminating the a 2 signal. The resulting equations yield MEASUREMENT Sll and S21. S~ is the ratio of S =1 Transmitted b2 Incident biJa I when a 2 is zero, and S2a is 81 ! the ratio of b2/a I. What is the physical meaning of Sll? $1~ is bl ~eflected b~= S. al + ~ 2 a2 a~ equivalent to F since its magnitude b e - S ~ l a t + S , ~ a2 and phase response are identical to those of F (notice that F is also Reflected b1 Sll " I a= = 0 defined a s Vinc/Vrefl or bl/al). Incident a1 That means that the magnitude of Transmitted b2 Sfj is equal to p. In a like manner I a= : o $21 ---- m Incident al , the forward transmission coefficient is equivalent to $2~. The S-parameter numbering convention is, the first number represents the port at which the energy is emerging from the device, and the second number is the port at which energy is entering the device. So S21 means the ratio of the energy emerging at port 2 to the energy incident at port I (gain or loss is indicated by values greater or less than unity).

]j

507

17. Microwave Instrumentation and Measurements

By placing the source at port 2 and terminating the input with a Z 0 load, the a~ term now becomes zero so that S22 and Si2 can be determined. Notice that the S-parameters are referenced to the Z 0 impedance of the network analyzer and in most cases are 50 ,Q. However, a Z 0 impedance of 75 D, is possible with 75 ~ test sets. AN 95-1 and AN 154 give additional details on designing with S-parameters and converting them to other useful quantities.

One of the nice things about S-parameters is that they are intuitive. That is not true for other parameters such as Y-parameters at high frequencies. $2~ is simply the forward gain or loss of the device, expressed in linear form. With this 20-dB attenuator, we see that our familiar measurement loss of the attenuator is transformed to an S-parameter voltage ratio of 0. I. Since these are complex parameters, there is a phase angle associated with each S-parameter. Likewise the more familiar measurement of SWR on the device translates over to an S~ or input voltage reflection coefficient of

REVERSE MEASUREMENT

°'

''

b=

~I

:>

82 b~ Transmitted

St=

Incident

b= Szz =~--= I a , = O

bl St= =~'-= I 8 , = O

ATTENUATOR S - P A R A M E T E R S S~ 20 dB ~ 0.1 ..,,:.~ 1.2 SWR I S~ O.09J~

O.05z~ ~~s22 1.1 SWR

¢
22.5 GHz, 1000 ms Measurement time (typical): Gate time + acquisition time + 100 ms Resolution: 1 Hz-1 MHz, selectable Accuracy: +_1 LSD rms _+ time base uncertainty (Graph 6)

Profile (Input 1) Frequency range (minimum/maximum for the y axis; see FM chirp tolerance for the span): 500 M H z / 2 0 GHz, 500 MHz/26.5 GHz (option 026), and 500 M H z / 4 0 GHz (option 040) FM chirp tolerance (maximum span for the y axis) Manual acquisition, 50 MHz peak to peak (when the entered value equals +_1 MHz of the center frequency); auto acquisition, 10 MHz peak to peak Time range (minimum/maximum span for the x axis): 100 n s / 1 0 ms Time resolution: 1 ns Internal gate width: Minimum, 11 to 23 ns; typical minimum, 14 ns; and maximum, 10 ms External gate width (Minimum): Manual acquisition, 20 ns; auto acquisition, 60 ns Gating/arming: Pulse, internal, external arming, and external gating; CW, external gating Number of data points: Auto profile, up to 75; manual profile, 1 to 99

555


Profile Frequency Measurements Frequency resolution: Selectable, 1 Hz to 1 MHz, and dependent on the internal profile gate width (Graph 4) Printers supported: ThinkJet (HP 2225A), QuietJet Plus (HP 2227B), and PaintJet (HP 3630A, option 002)

Profile phase measurements A computer is required.

See Application Note 377-4 for details.

PULSE PARAMETERS (INPUT I)

Minimum / Maximum LSD Accuracy a (100 average)

Pulse width

PRI

Offtime

60 ns / 10 ms

500 ns / 1 s

400 ns / 1 s

(PW < 1 ms)-I ns; (PW > 1 ms)-100 ns +(20 ns + timebase error × measurement) _+LSD

PRF 1 Hz / 2 MHz To 0.001 Hz +(20 ns) × (PRF) 2 +_LSD _+ timebase uncertainty

Note Measurements are approximately 6 dB below the signal peak. aFor r i s e / f a l l times < 20 ns.

Time Interval Measurements Least Significant Digit Displayed: + -

200 ps ~

'

where N is the number of measurements averaged. Resolution" 150 ps rms _+ start trigger error + stop trigger error

where the start and stop trigger errors are illustrated in Graph 8. Accuracy: _+resolution _+ (time base aging × time interval) + trigger level timing error + 1 ns systematic error,

556

Aksel Kiiss

Input Noise (random)

//

1 ms

100 ns Q

•1,1J I=

10 ns

.s+,y

o O.

._~

1 ns

|

w 100 ps

i 10 ps

1 ps 10 mV

100mV

1 mV

10 mV

100 mV

1V

Input Signal Noise (rms) Graph 8. Noise on the input signal will add uncertainty to time-interval measurements.

where the time interval is illustrated in Graph 9 and the trigger level timing error is illustrated in Graph 10. The systematic error can be reduced to < 10 ps with the HP J06-59992A Time Interval Calibrator.

Time Base Aging (systematic) 100 ns

10 ns

/

•~1

°

;

!/

,000s 1 ps 1m s e c

/

4-, ,,..~ ~/-

lOmsec

lOOmsec

100 msec

10 msec

Measured Time Interval

Graph 9. Time base crystal aging affects time interval measurements.

557


Trigger Level Timing Error(systematic) 1 ms

100 ns

•

-¢= I,M

10 ns

a_

~

1 ns

°-

|

m lOOps

\

10 ps

lps 100 mV/ms

1 V/ms

10 100 mV/ns mV/ns Input Signal Slew Rate

1 V/ns

10 V/ns

Graph I0. Trigger level timing error varies with the input signal slew rate, Uncertainty is associated with both start and stop edges,

Graphs 3, 4, and 5 may serve as an aid to quickly determine the approximate resolution and accuracy of a time interval measurement. EXAMPLE: Measure a single 500-ns interval, from a l-V, 10-ns rise time edge to a 1-V 10-ns edge (time interval, A --* B). The input signal noise (in a 500-MHz bandwidth) is 1 mV rms. It has been one year since time base calibration. The time interval resolution is influenced by trigger noise from the input signal (as well as the signal slew rate) and the internal timing jitter of the HP 5372A (150 ps rms). As shown in the resolution equation, averaging could be used to improve measurement resolution results ( v ~ ) . From Graph 8 it can be determined that the trigger noise contribution for both the start and the stop edges is approximately 10 ps rms. The single-shot time interval resolution is then _+(150 ps rms + 10 ps rms + 10 ps rms) = _+ 170 ps rms. To determine the accuracy of the time interval measurement, you must add time base aging effects, trigger level timing error, and internal systematic uncertainties to the resolution uncertainty. The time base aging uncertainty for this example is much less than 1 ps and can therefore be considered negligible (Graph 9). Graph 10 shows that the trigger level timing error uncertainty is also well below 1 ps. Once again, this effect is negligible with respect to resolution and internal systematic uncertainties.

558

Aksel Kiiss

From the above equation, the total accuracy uncertainty is then approximately + 1.17 ns. Clearly, internal systematic uncertainties are the dominant effect in this measurement. This is due to differential path delays within the HP 5372A, as well as possible differential path lengths in the external measurement setup. The HP J06-59992A Time Interval Calibrator can be used to measure these systematic uncertainties. These uncertainty values can then be subtracted from results, improving measurement accuracy.

9. Measurement of Phase Noise Power Spectral Density An ideal signal source can be regarded as providing an output at a signal frequency or as an infinitely narrow line in the frequency domain. Unfortunately in the practical, real world, other factors enter the picture and degrade the performance of the frequency source. The infinitely narrow function assumption in the frequency domain applies only if the signal existed for an infinite time without any perturbations. Thermal, shot, and flicker noise randomly perturb the phase or frequency of the output signal. Since an oscillation is an inherently nonlinear physical phenomenon, it produces, besides the desired output signal, its harmonics. In a simple oscillator, the magnitude of the noise perturbations depends on the quality of the transistor and other active circuit elements used in the design and on the quality of the tuned circuit used as the frequency determining circuit element (Q of the circuit). As the complexity of the frequency source increases, other factors start to degrade the spectral purity of the signal. In frequency synthesizers, for instance, the output contains, besides the random noise perturbances, discrete outputs. These outputs are the result of frequency conversions and translations between the various signals which are necessary in the design of frequency synthesizers. In this discussion we will establish a simple theoretical basis for general noise perturbations in an oscillator. A signal can be mathematically represented by v(t) = [v 0 +

e(t)]sin[27rfot + A~b(t)],

where e(t) represents random amplitude variations and A~b(t) represents random phase variations. The random amplitude variations are less important in system applications. For instance, in a superheterodyne receiver, the amplitude fluctuations of a local oscillator are suppressed by the double balanced mixer.

559


The phase variations, on the other hand, are directly transferred from the local oscillator to the signal. For these reasons, and also for the much wider use of phase or frequency modulation in information transmission systems, the phase noise perturbations have a more pronounced degrading effect on the overall system performance. Assume that a small baseband noise voltage in a 1-Hz bandwidth at fm, with an amplitude of a l(t), is frequency modulating a carrier at frequency f0; then the instantaneous random frequency can be expressed as w = w 0 q- A w c o s w m t

,

where Aw = a(t)xc, where c is a modulation sensitivity constant of the oscillator. It should be noted that zXw itself is a voltage with random amplitude variation and with statistical peak and RMS values. The time varying signal can be expressed as

(

f ( t ) - A cos w0t +

sin Wm

Wmt

)

Aw =/3 - modulation index. Wm

This function can be expressed in the frequency domain as an infinite series of frequencies, + n , from the carrier f0. Their amplitudes are related to the corresponding Bessel functions. Since in our case/3 ldiverges L = lfails

Un

n~/lUnl = L,

then see above

H ----~oo

Integral test

If

f(z) > 0 for

z > a, then E l ( n ) c o n v e r g e s / d i v e r g e s as

f f f ( x ) dx converges/diverges

Note.

In the ratio and N t h root tests, when L = 1, the behavior of the series cannot be determined.

TABLE 7 Defining Qualities of the Dirac 6 or Impulse Function coo

J

6(x)=O

d(x) dx = 1 for a l l x 4 : 0

TABLE 8 Commonly Used Representations of the Dirac 6 Function

6(x)

=

lim

6~(x)

a ----) O

1

a

6~(x)---a

for [xl < -2-

~(x) = 0 otherwise

_x2)

-1

7 1

~(x)

a

-

7/" t~ 2 +

X 2

f eJxtd,

576

James Richie TABLE 9 Useful Properties of the Dirac t~ Function 1.oo

J_/(x)t~(x)

f~f(x)[cx~(X_

= f(O)

- a) + c2t~(x - b ) ] dx = Cxf(a) + c2f(b) 1 6(ax) = ~--~S(x)

~(-x) = ~(x) N t~(X -- ai) g'(ai)

t~(g[x])=

~1 i=

where g(a i) = 0 for i = 1, 2 . . . . N t~2(X) and e ~(x) are not defined

Unit Step Function: 0(~) T h e definition, r e p r e s e n t a t i o n s , and p r o p e r t i e s are given in Table 10.

3. Vectors and Matrices [5, 13, 45] Definition A = [ajk], w h e r e 1 < j < n rows and 1 < k < m columns. If n = m, A is square. T h e ajk are, in general, complex.

TABLE 10 Definitions and a Representation for the Unit Step Function O(~:)

Definition 1

f?/(x)O(x)

dx = f o f ( X ) dx

Definition 2 dO -

~(x)

dx Representation (e > O) O ( x ) = lim O~(x)

a--~O oo e TM O~ = 2 - ~ f -oo ~t -d Jet 1

577

18. Microwave Mathematics TABLE II

A Partial Listingof Vector Properties Multiplication by a scalar Addition

cA = [cajk] A + B = [ ajk + bjk ]

Multiplication (A is m × n, B is n × I)

C=[ck~,k 2 ] = A B =

n

]~akljbjk 2 i s m × I j=l

[AB]C = A[BC]; [A + B]C = AC + BC;

AB 4= BA in general Transpose

AT = [a~j]

Identity (I is the identity matrix, ajk = 6jk)

IA=M=A

Trace

Tr[A] = Eakk, Tr[AB] = Tr[BA]

Exponentiation (A must be square)

e A= 1 + A +

Unitary matrix

A-1 = AIq implies that A is a unitary matrix

a: 2~

+ -..

Properties S e e T a b l e 11.

Determinant If A is s q u a r e , d e t A = [A[ = [JAil = ~

+_ a l i f l 2 i 2 . . ,

ani,,

(15)

w h e r e { i l , . . . i n} is a p e r m u t a t i o n of { 1 , 2 , . . . , n}, _+ is for e v e n a n d o d d p e r m u t a t i o n s , a n d t h e s u m is over all possible p e r m u t a t i o n s , d e t A B = d e t A d e t B d e t cA = c n d e t A.

Minor T h e m i n o r of ajk is d e f i n e d as an ( n - 1) × ( n - 1) matrix, M j k , by d e l e t i n g t h e j t h row a n d k t h c o l u m n . T h e c o f a c t o r of ajk is given by cjk = ( - 1)(J+k)det Mj~.

(16)

Inverse

A A - 1 = A - 1 A = I. If d e t A = 0, t h e n t h e i n v e r s e d o e s n o t exist ( A is called singular). T h e i n v e r s e of a m a t r i x can be f o u n d u s i n g m i n o r s : [ a j k ] -1 _ -

Ckj

(a7)

578

JamesRichie

Hermitian Adjoint AI-I = [AT]*. If A = An, then A is Hermitian. [AB]/-/= B/-/A/-/.

Commutator and Anticommutator [A, B] = AB - BA is the commutator of A and B. The anticommutator is {A, B} = All + BA. A B = ~ I[A,B] + I{A,B} [All, C] = A[B, C] + [A, C]B.

(18) (19)

Solutions f o r x in A x = Y

Cramer's Rule is

IA/I xs= IAI'

(20)

where A i is defined as the matrix obtained by replacing the i th column of A with the vector Y. Solutions f o r x in A x = 0

There is a trivial solution if x = 0. There is a nontrivial solution if det A = 0.

Eigenvalue Problem If A is an n × n complex matrix and if x is an n × 1 vector, then A is an eigenvalue of A with eigenvector xA if Axx = Axx or [A - Al]xx = 0 (the characteristic equation).

The Cayley-Hamilton Theorem Every matrix satisfies its own characteristic equation.

Derivatives See Table 12.

Tensors and Dyadics [5, 27] A tensor of rank two is an object with nine components defined within a given orthogonal coordinate system. A second rank tensor can be thought

579

18. Microwave Mathematics TABLE 12 Derivitaves with Respect to Vectors

d --(xHx) = 2x dx d --(xUy) = y

dx

d

--(yHx)

=

y

dx d - - ( x H Q x ) = 2Qx

dx

Note. x and y, are vectors, and Q is a matrix.

TABLE 13 Defining Properties of the Elements of a Group

1. Closure 2. Associativity 3. There exists an identity for each element of the group such that I g i = 4. There exists a unique inverse for each element of the group such that

gi

I

gig~

= gi 1 _

g7 l g i

--

I

of as an o u t e r p r o d u c t of two vectors. A vector is a t e n s o r of r a n k o n e and a scalar is a t e n s o r of r a n k zero. A dyad or dyadic is a s e c o n d - r a n k t e n s o r defined as the juxtaposition of two vectors: AB. O n e can o p e r a t e in the usual vector fashion from the left or the right.

Group Theory [24, 27, 39] A g r o u p is a set of e l e m e n t s , {gl, g 2 , . . . }, a n d a binary o p e r a t i o n with the p r o p e r t i e s in Table 13. G r o u p t h e o r y is mostly used to formalize s y m m e t r y conditions.

4. Vector Spaces [5, 12, 20, 33, 45] Definition m A set of e l e m e n t s , V m a field of n u m b e r s , F (complex, in general) m a binary o p e r a t i o n of addition m s c a l a r multiplication defines a vector space (with e l e m e n t s x, y, z) if ~x

+y

=y +x

- - ( x + y) + z = x ( y + z) - - a n identity exists such that x + 0 = x m f o r each x t h e r e exists - x such that x + ( - x )

= 0.

580

JamesRichie TABLE 14 Properties of Scalar Multiplication and Vectors

a(/3x) = (a/3)x a(x + y) = a x + ay lx=x (a +/3)x = a x +/3x Note. a and/3 are elements of F.

See Table 14 for f u r t h e r properties. Vectors ( e l e m e n t s of V) can be written as [x) (bracket notation)

Linear Independence A set (x1, x 2 , . . . ,

Xn)

a l X 1 -k- a

is linearly i n d e p e n d e n t if +

2 x 2 + "'" + a n X n = 0 =~ ogi

=

0Vi

is the only solution.

Inner Product A m a p p i n g from V × V ~ F is written ( y [ x ) = F. T h e dual vector is written (y[ = [/31,/32,''',/3n]- Thus, if Ix) = [a 1 , a 2 , . . . , an] T, t h e n ( y Ix) = F.,ai~ i, w h e r e the sum is from i = 1 to n. See Table 15.

Orthonormality Ix) and [y) are o r t h o g o n a l if ( x l y ) = 0. {X1, X 2 , . . . , set if ( x i [ x j ) = 6is.

X n}

TABLE 15 Properties of the Inner Product between Two Vectors

( x l y ) = (y[x)* (ax +/3ylz) = a(xlz) +/3(ylz)

(x[x) = 0

if and only if I x ) = 0

is an o r t h o g o n a l

581

18. Microwave Mathematics TABLE 16 Vector Inequalities

Ix] 2= (x x) ~ ~ lail 2

Bessel inequality

i=1 If { Ixi )) is complete, then equality holds

I(xly) _< Ix yl

Schwarz inequality

G r a m - Schmitt Process The G r a m - S c h m i t t process is used to find an orthonormal set of vectors, {]yi)}, from a linearly independent set, {Ixi)}. [Yl) ----

IXl) IIx~)l

[x2)- lyl)(yllx 2) ly2> = IIx2>- lya>l

(21)

Inequalities See Table 16.

5. Linear Operator Theory [5, 12, 20, 40, 45] In this section, a physical system is related to a vector space with an assumed basis.

Definition A linear operator, A, on a vector space, V(F), is a mapping from V(F), written as A(x) = z, which satisfies

V(F)

to

A(ax

+/3y) = aA(x) +/3A(y). (22) EXAMPLE: V is a set of polynomials, and operator D is a derivative of a polynomial" Ix(t))"

~ a i ti = x(t)

(23)

i

y(t)

= Dx(t) =

~_~iaiti-1. i

(24)

582

JamesRichie TABLE 17 Properties of Linear Operators

1. AO = OA = 0 2. AI = I A = A 3. A(B + C ) = All + AC 4. A ( B C ) = (AB)C 5. AB :/: BA 6. [A, B] = AB - BA (commutator)

Properties S e e T a b l e 17. T o p r o v e r e l a t i o n s h i p s for l i n e a r o p e r a t o r s , o n e m u s t a p p l y t h e o p e r a t o r to a m e m b e r o f V.

Inverse A n o p e r a t o r is i n v e r t i b l e if 1. for e v e r y l y ) in V t h e r e exists a n Ix ) in V s u c h t h a t Alx) -

ly)

implies

Ix) = A - 1 l y )

2. A Ix 1) = A Ix2) i m p l i e s Ix 1 ) --" IX2 >" EXAMPLE: T h e o p e r a t o r D for d i f f e r e n t i a t i o n is n o t i n v e r t i b l e . A c o u n t e r e x a m p l e is Xl(t) = t + 7; x 2 ( t ) = t + 3 D x I = 1 = D x 2. T h i s viol a t e s t h e s e c o n d r e q u i r e m e n t . F o r t h e o r e m s , s e e T a b l e 18.

Similarity Transformation U s e d to c h a n g e t h e basis of t h e l i n e a r o p e r a t o r . A u n i t a r y m a t r i x , M, is used: At --- M - 1 A M .

(25)

T h i s t r a n s f o r m a t i o n p r e s e r v e s t h e d e t e r m i n a n t a n d t r a c e of A.

TABLE 18 Theorems on the Inverse Operator

If A and B are invertible, then (AB)- 1 = B- 1A- 1 If V(F) is finite dimensional, and Alx) - 0 if and only if Ix) = 0, then A is invertible Suppose that we have an orthonormal basis { I x 1 > . . . . [Xn>},we can specify any linear operator solely in terms of its operation on the basis

583

18. Microwave Mathematics TABLE 19 Properties of Projection Operators

rilx )oeilxi) Pilxj) = 0 if i 4= j, and Pilxj) =

Ixil

when i = j

Pi is idempotent: PiPi = Pi

PiPj = 0 Pi + Pj is a projection onto the subspace s p a n n e d by Ix i), ]xj) ~Pi = I, w h e r e the sum is over i = 1 to n

Projection Operators Pi = Ixi)(xil. See Table 19. EXAMPLE: We shall begin with a basis, Ix1), ]x 2 ), 1

and a second basis,

]Y 1),

0)

1 '

IX2) =

Y2),

(26)

1(2)

1 ( )2 1 V~

lY2) = ~ -

_1

"

(27)

The projection operators P1 and P2 can be found: P1=5

1

[

1

2

2

4

1[ 4 2]

p2 =

5

-2

(28)

1 "

Any Ix ) in the allowed set can be written in the "x" basis: Ix)=

1 "

(29)

Projecting Ix ) onto each of the elements of the "y" basis entails finding

Pl, lx ). For k = 1 and 2 we have P, lx) =

1()6

=

~IYl)

P2lx)=

1(12)

= --~-~lY2)

(30)

g3

or

3

1

Ix) = ~ - lYe) + ~ - l Y 2 ) =

1

~-

3] 1]

for the y basis

(31 )

584

James Richie TABLE 20 Properties of the Adjoint Operator A + exists for all A and is unique (A + B) += A + + B+ A + ( a x + fly)= aA+x + flA+y (All)+= B+A + (aA)+a*A + (A+) += A

TABLE 21 Theorems on Adjoint Operators If {Ix/)} is an orthonormal basis, then Aij = (xilAx j) A = 0 if and only if ( x l A x ) = 0 for all x Suppose that V is a complex inner product space; then A is self-adjoint if and only if ( x l A x ) is real for all Ix) Eigenvalues of self-adjoint operators are real

Adjoint Operators A + is the adjoint of A, where A+: ( x l A + y ) = ( A x l y )

for all x and y.

(32)

A summary of properties is given in Table 20. For theorems, see Table 21.

Unitary Operators A unitary operator, U, is one for which UU += I = U ÷ U. - - U n i t a r y operations preserve inner products: ( U x l U y ) - ( x l y ) . m l f {Ix/)} is an orthonormal basis, so is {IUxi)}.

Eigenvalue Problem Let A be a linear operator in V(F). Then A is an eigenvalue if and only if

Alxi) = Ailxi)

(33)

585

18. Microwave Mathematics TABLE 22 Properties of Eigenvalues

The geometric multiplicity of an eigenvalue is the number of linearly independent eigenvectors associated with the eigenvalue The algebraic multiplicity of an eigenvalue is the number of times that the eigenvalue appears as the solution to the characteristic equation:

IA-AII-0 If A is self-adjoint, then eigenvectors belonging to distinct eigenvalues are orthogonal If A is self-adjoint, then it can be diagonalized by a unitary matrix

for some nontrivial Ix i), where Ix i) is denoted the eigenvector. See Table 22. The solution to the nondegenerate inhomogeneous eigenvalue problem is Ax - Ax = y.

(34)

Suppose A is self-adjoint. The solution is

IX)

=

provided that A is not equal to

.

l~i

--

t~

'

(35)

/~i"

6. Function Spaces [5, 12, 23, 27, 30, 33, 34, 36, 40] Definition. An infinite-dimensional inner product space for which all Cauchy sequences converge is called complete and is denoted a Hilbert space. Definition. A function space is a space whose vectors are functions,

i.e., If): ( x l f )

= f(x).

(36)

Consider an interval (a, b) in variable sc with a denumerable set of functions [real or complex on (a, b)]. The definitions in Table 23 hold. This is useful for expanding arbitrary functions as a series of appropriate basis functions in the minimum mean squared error sense.

586

James Richie

TABLE 23 Definitions of the Properties of Sets of Functions Useful for Minimum Mean Squared Estimation oo

Y'. Un*(~t)Un(~) = t~(~ -- ~')

Complete

n=l

fba Un*(~)Um(~)d~ = 0

Orthogonal

for all m 4: n

fba Un~(~)Um(~) d~ = ¢~mn

Orthonormal

TABLE 24 Brief Summary of the Three Most Commonly Used Coordinate Systems

Coordinate systems Coordinates (Ul, U2, U3) Metric coefficients (hi, h 2, h 3) Unit vectors

Rectangular

Cylindrical

Spherical

X, y, Z 1, 1, 1 ~x, ey, ez

P, 4~, Z 1, p, 1 ep, e~, ez

r, 0, ~b 1, r, r sin 0 er 80, e~b

7. Vector Fields [3, 8, 18, 19, 25] A field is a quantity that depends on position. Scalar fields and vector fields are possible. Metric coefficients are multipliers to make length units consistent in some coordinate systems. See Table 24 and Figures 3 and 4.

P Z

x

Figure 3. Cylindrical coordinate system.

587

18. Microwave Mathematics Z

r

'

P

Y

Figure 4. Spherical coordinate system.

Operations Dot Product

A.B=f;A.B=B.A. (37)

ei " e~ = aij.

Cross Product AXB=C;A×B=

-BXA;A×(B+C)=AXB+A×C. ei x

(38)

ej = Eijkek .

Gradient: Vf is the maximum space rate of change of f, always directed toward increasing f.

1 Of ~el Vf = grad f - hi OUl -- ~

1 Of "+" ~ ~ 0 2

h2 0u2

1 Of "+-

~e3

-~3 0u3

"

(39)

EXAMPLE" Cartesian, Of^

Of

Of

(40)

588

JamesRichie

Divergence The flux per unit volume is V • F; V • (A + B) = V • A + V • B. V.F=

lim Av--~O

96F • dS (41)

AO

where dS encloses and is directed out of Av.

1 [e

( Flh2h3) + -~uz ( F2hlh3) + O--~3(F3h12) . (42)

V • F hlh2h3

EXAMPLE" Cylindrical 103

V "F = ---(pFp) p Op

+

103F~

F~

+ 03--. p o4, Oz

(43)

Curl The tendency of a vector to wrap around a point is V x F; V X (A + B)=V×A+VxB.

(VXF).~= lim

~F" dl u

s--,0

S

(44)

'

where c encircles S in the right-hand sense and t~ is the outwardly pointing normal to the surface.

V×F=

hlel 03

h2e2 03

h3e 3 03

hlh2h3 aUl hlFl

03//2

03//3

hzF2

h3F 3

(45)

EXAMPLE" Spherical, V X F-

1 [O rsinO

+--1[ r

~

l

(F~ sin 0)

aFr

sin 0 0 F ~

OFo ~-

er

l[a a ] Or (rF~) e o + -

aF~ (

Fo)

Laplacian V2f-

V • (Vf) and V2F - V(V • F) - V x V x F.

-

(46)

589

18. Microwave Mathematics

Theorems Divergence Theorem (47)

£V " A dV = ~sA " dS, where the surface S encloses the volume v.

Stokes' Theorem (48)

fs ( v X A)" dS = ~cA" dl, where the surface S is bounded by the closed contour C.

Helmholtz Theorem Any vector field in which the first derivitives exist is completely specified (up to an additive constant) by defining the divergence and curl of the vector field.

Vector identities See Table 25.

8. Differential Equations and Their Solutions

[4,

34, 35]

Series solutions are a straightforward method of solving differential equations. See Table 26.

TABLE 25 Vector Identities

V" (fA) = f ( V - A ) + A" Vf

V(fg) = f vg + g W

(,)

V -r

V x (fA)= Tfx A + I V x A

r2

V.(AX B)= B.(V XA)-A-(V

V x(VxA)=V(V.A)-

x B)

V.(VxA)=0

VxTf=O A.BXC=B.CXA=C'AXB

V2A

Ax(Bx

V(A.B)=(A.V)B+(B'V)A+Ax(Vx

C)=(A.C)B-(A-B)C

B)+Bx(V

XA)

590

James Richie TABLE 26 Functions Used for a Series Solution to Differential Equations

z 0 is a regular point oo

f ( z ) -" E Cm(Z -- Zo)m m=O z o is a regular singular point f ( z ) - ( z - zo)S ~

Cm(Z -- ZO)m

m=O

z o is an irregular singular point f(z) =

E Cm(z - Zo)m m._~-oo

Analytic Techniques [ I, 18, 23, 27, 30, 45] The wave equation

(49)

(V 2 d- k 2 ) ~ = 0

with boundary conditions, where k is the wavenumber, can be solved using separation of variables. Solutions in the standard three-coordinate systems are provided in Tables 27, 28a-28c, 29, and 30. A characteristic equation must also be satisfied. See Figures 5, 6, 7, 8, and 9. Boundary Conditions [30, Chap. 6] Cauchy Boundary Conditions T h e v a l u e a n d n o r m a l g r a d i e n t o f t h e function are specified on the boundary. This provides a unique solution o n l y in i d e a l s p e c i a l cases. TABLE 27 Characteristic Equations and Functional Form of the General Solution to Equation (41), the Helmholtz Equation

Coordinates Cartesian

)--'~kp2 = k 2 P

Cylindrical

Spherical

Solution, ~b, to

Characteristic equation

k2 +

~

(V 2 +

ke)~b = 0

~_,A~lkEF(klx)F(key)F(ke z)

kl k2 k2 = k2

>_ 0 -n n<m 10d A>rrd A>d A > A/(2rr)

White mesh of solid surface

A × A: A < A/IO a = A/(2rr)

Curved wire modeling (R is the radius of curvature)

R>A

Curved surface modeling

R > V/A-7

Note. The wire length is L, wire diameter is d, wire radius is a, wavelength is A, and segment length is A.

References [1] M. Abramowitz, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, Washington, DC: U.S. Gov. Print. Off., 1964. [2] L. V. Ahlfors, Complex Analysis, an Introduction to the Theory of Analytic Functions of One Complex Variable. New York: McGraw-Hill, 1953. [3] C. Balanis, Advanced Engineering Electromagnetics. New York: John Wiley & Sons, 1989. [4] W. E. Boyce and R. C. DiPrima, Elementary Differential Equations and Boundary Value Problems, 3rd Ed. New York: John Wiley & Sons, 1977. [5] F. Byron, Mathematics of Classical and Quantum Physics. Reading, MA: AddisonWesley, 1969. [6] C. Caratheodory, Theory of Functions of a Complex Variable. New York: Chelsea, 1954. [7] H. S. Carslaw, Introduction to the Theory of Fourier's Series and Integrals, 3rd Ed., Rev. and Enl. New York: Dover, 1930. [8] D. K. Cheng, Field and Wave Electromagnetics. Reading, MA: Addison-Wesley, 1983. [9] R. V. Churchil, J. W. Brown, and R. F. Verhey, Complex Variables and Applications, 3rd Ed. New York: McGraw-Hill, 1974. [10] R. E. Collin, Field Theory of Guided Waves, 2nd Ed. New York: IEEE Press, 1991. [11] R. L. Coren, Basic Engineering Electromagnetics: An Applied Approach. Englewood Cliffs, NJ: Prentice-Hall, 1989. [12] R. Courant and D. Hilbert, Methods of Mathematical Physics, 1st Eng. Ed. New York: Interscience, 1962. (Orig. publ. 1953.) [13] F. R. Gantmakher, The Theory of Matrices (K. A. Hirsch, transl.) New York: Chelsea, 1959. [14] J. W. Goodman, Introduction to Fourier Optics. New York: McGraw-Hill, 1968. [15] I. S. Gradshtein and I. M. Ryzhik, Table of Integrals, Series, and Products New York: Academic Press, 1980. (A. Jeffrey, ed.). (Trans. from Russ. by Scripta Technica, Inc.)

18. Microwave Mathematics

603

[16] M. Greenberg, Application of Green's Functions in Science and Engineering. Englewood Cliffs, NJ: Prentice-Hall, 1971. [17] R. F. Harrington, Field Computation by Moment Methods. New York: Macmillan, 1968. [18] R. F. Harrington, Time-Harmonic Electromagnetic Fields. New York: McGraw-Hill, 1961. [19] W. H. Hayt, Engineering Electromagnetics, 4th Ed. New York: McGraw-Hill, 1981. [20] F. B. Hildebrand, Methods of Applied Mathematics, 2nd Ed. Englewood Cliffs, NJ: Prentice-Hall, 1965. [21] S. Hoole and H. Ratnajeevan, Computer-Aided Analysis and Design of Electromagnetic Devices. New York: Elsevier, 1989. [22] A. Ishimaru, Electromagnetic Wave Propagation, Radiation, and Scattering. Englewood Cliffs, NJ: Prentice-Hall, 1991. [23] J. D. Jackson, Classical Electrodynamics, 2nd Ed. New York: John Wiley & Sons, 1975. [24] D. L. Jaggard, H. N. Kritikos, and C. H. Papas, Recent Advances in Electromagnetic Theory. New York: Springer-Verlag, 1990. [25] M. Javid and P. M. Brown, Field Analysis and Electromagnetics. New York: McGraw-Hill, 1963. [26] A. I. Markushevich, Complex Numbers and Conformal Mapping. New York: Gordon & Breach, 1961. [27] J. Matthews and R. L. Walker, Mathematical Methods of Physics. New York: Benjamin, 1965. [28] E. K. Miller, A selective survey of computational electromagnetics, IEEE Trans. Antennas Propag., Vol. AP-36, pp. 1281-1305, 1988. [29] M. A. Morgan, ed., Progress in Electromagnetics Research. New York: Elsevier, 1989. [30] P. M. Morse and H. Feshbach, Methods of Theoretical Physics, Parts I and II. New York: McGraw-Hill, 1953. [31] Z. Nehari, Conformal Mapping. New York: McGraw-Hill, 1952. [32] E. J. Purcell, Calculus with Analytic Geometry, 3rd Ed. Englewood Cliffs, NJ: PrenticeHall, 1978. [33] R. Shankar, Principles of Quantum Mechanics. New York: Plenum, 1980. [34] A. Sommerfeld, Partial Differential Equations in Physics (E. G. Straus, transl.). New York: Academic Press, 1949. [35] M. R. Spiegel, Schaum's Outline of Theory and Problems of Complex Variables, with an Introduction to Conformal Mapping and Applications. New York: McGraw-Hill, 1964. [36] I. Stakgold, Boundary Value Problems of Mathematical Physics. New York: Macmillan, 1967. [37] W. Stutzman, Antenna Theory and Design. New York: John Wiley & Sons, 1981. [38] E. W. Swokowski, Calculus with Analytic Geometry, 2nd Ed. Boston: Prindle, Weber & Schmidt, 1979. [39] M. Tinkham, Group Theory and Quantum Mechanics. New York: McGraw-Hill, 1964. [40] E. C. Titchmarsh, Eigenfunction Expansions Associated with Second-Order Differential Equations. Oxford: Clarendon Press, 1946. [41] E. C. Titchmarsh, Introduction to the Theory of Fourier Integrals, 2nd Ed. Oxford: Clarendon Press, 1948. [42] E. C. Titchmarsh, The Theory of Functions. Oxford: Clarendon Press, 1932. [43] P. L. E. Uslenghi, ed., Electromagnetic Scattering. New York: Academic Press, 1978. [44] H. Wayland, Complex Variables Applied in Science and Engineering. New York: Van Nostrand-Reinhold, 1970. [45] H. W. Wyld, Mathematical Methods for Physics. Reading, MA: Benjamin, Advanced Book Program, 1976.

604

James Richie

[46] R. E. Ziemer, W. H. Tranter, and D. R. Fannin, Signals and Systems: Continuous and Discrete, 2nd Ed. New York: Collier Macmillan, 1989. [47] CRC Handbook of Mathematical Sciences. West Palm Beach, FL: CRC Press, 1978. [48] F. X. Canning, Protecting EFIE-based scattering computations from effects of interior resonances, IEEE Trans. Antennas Propag., Vol. AP-39, pp. 1545-1552, 1991. [49] K. S. Kunz and R. J. Luebbers, The Finite Difference Time Domain Method for Electromagnetics. Ann Arbor, MI: CRC Press, 1993. [50] R. J. Luebbers et al., A finite-difference time-domain near zone to far zone transformation, IEEE Trans. Antennas Propag. Vol. AP-39, pp. 429-433, 1991. [51] G. Mur, Absorbing boundary conditions for finite-difference approximation of the time-domain electromagnetic-field equations, IEEE Trans. Electromagn. Compat., Vol. EMC-23, pp. 1073-1077, 1981. [52] M. N. O. Sadiku, Numerical Techniques in Electromagnetics. Ann Arbor, MI: CRC Press, 1992. [53] A. Taflove and M. E. Brodwin Numerical solution of steady-state electromagnetic scattering problems using the time-dependent Maxwell's equations, IEEE Trans. Microwave Theory Tech., Vol. MTT-23, pp. 623-630, 1975. [54] A. Taflove, K. Umashankar, and T. Jurgens, Validation of FD-TD modeling of the radar cross section of three-dimensional structures spanning up to nine wavelengths, IEEE Trans. Antennas Propag., Vol. AP-33, pp. 662-666, 1985. [55] J. J. H. Wang, Generalized Moment Methods in Electromagnetics. New York: John Wiley & Sons, 1991. [56] K. S. Yee, Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media, IEEE Trans. Antennas Propag., Vol. AP-14, pp. 302-307, 1966.

CHAPTER

19 Microwave Materials Hamid H. S. Javadi

I. I n t r o d u c t i o n

This

chapter will be of some value to the reader who needs to have a better understanding of the fundamental properties of passive microwave materials. It is clear that the present work is a compilation of data available in the literature, and this would not have been possible without the efforts of many individuals in industry and academia. References are cited for many tables and figures. The remaining data are compiled from more scattered sources and citations deemed impractical. Many empty sites in the tables remind us of needed work to be performed (perhaps in locating such data in the literature) in laboratories. This chapter starts with some useful formulas and approximate relations between dielectric parameters [1]. The atmospheric absorption of microwaves and millimeter waves is the subject of Figure 1, whereas Table 1 represents the thermal radiation transmittance of cold window materials [2]. Section 2 is allocated to the dielectric properties of compounds [bulk materials, Corning glasses [3, 4], substrates [5, 6] (plastic, ceramic, semiconductor, and ferrite), epoxies, and radomes [7]]. The anisotropy and power-handling capability of substrates [8, 9], temperature coefficients of some dielectrics [10], and irradiation effects on sapphire [11] are discussed. Section 3 focuses on the properties of manufactured compounds: dielectric resonators, surface acoustic wave materials [12], piezoelectrics [13], and ferrites [14, 15]. Section 4 concentrates on conductive, resistive, and capacitive thin films [16]. Section 5 addresses the physical properties of


605


606

Hamid H. S. Javadi

Wavelength 30 100 1 40

15 i

I

l

( mm

10 8 6 5 i

I

l

l

I

4 3

)

2 1.5

0.8

i

I

IIII

I

I

I

I

l

l

l

l

..I

l

ljs~l

l l

I

/k /'d-

10 4

1 0.4~ 0 .H 4.1

ID

0.1

0.04 ~ 0.01 0.004

02

1:

'i

02

H2

......

O. 001 I

10

H

3000 ft Altitude I

I

20

I

I

I

I

30 40

Frequency

n nw,~ I I Ill

60

A il l i "1i

I i

100

i

200

( GHz

400

)

Figure I. Average atmospheric absorption of millimeter waves (horizontal propagation). Reproduced from a catalog of Hughes millimeter-wave products, Hughes Aircraft Co.

TABLE I Average Room-Temperature-Radiation Transmittance for Materials Cooled to 70 and 15 K Average transmittance at Material PTFE Fluorogold Styrofoam Stycast HIK (E r = 4.) Stycast 0005 (e r = 2.54) Rexolite Fused quartz Crystalline quartz TPX

Thickness (mm) 2.0 0.8 3.0 2.0 2.0 2.0 0.7 1.5 2.0

70 K 0.046 0.114 0.195 0.063 0.220 0.175 0.225 0.022 0.310

+ + + + + + + + +

0.003 0.006 0.010 0.003 0.010 0.010 0.010 0.002 0.015

15 K 0.442 0.005 0.202 0.010 0.185 0.238 0.094 0.910 0.105

+ + + + + + + + +

0.030 0.002 0.010 0.002 0.010 0.012 0.005 0.020 0.005

Note. Calculated from the measured temperature rise of an aluminum plate covered with a thin black drawing paper. Source. Reproduced with permission from Table 2 in [2], copyright © 1984 by Plenum Publishing Corp.

607

19. Microwave Materials

metals; the dependence of surface resistance of metals on their surface roughness is discussed [17], the temperature dependence of the surface resistance of copper is reviewed [18], the reflective losses of some metals are tabulated, and the circuit patterns utilized in radars are presented [19]. Section 6 covers conventional and high-temperature superconductors [20]. The frequency dependence of the surface resistances of YBazCu307_ ~ epitaxial films and single-crystal platelets is compared with that of Cu, Nb, and Nb3Sn at cryogenic temperatures. Finally, important substrates for the growth of epitaxial films of superconducting oxides are also reported in Section 6 together with their physical properties. The field of microwave materials benefits from the efforts of a multidisciplinary pool of researchers, and this chapter is only a very small drop [1-26] from a vast ocean of the current human knowledge. In a medium there may be many contributions to the microwave response which are characterized via (1) Complex conductivity o-* ( f ) = o-' + j'~r" from unbound charge carriers, etc. (2) Complex dielectric constant e * ( f ) = e'r + je r from bound charges, dipoles, polarizable molecules, the background lattice, etc. Due to the presence of free electrons, microwaves will penetrate a skin depth, rl, from the surface of a metal, 10 r / ( m m ) = ~ × [ f (GHz) × o"(~] -1 cm-1)] -1/2, where o-' is the real part of conductivity and r/is the skin depth (mm). The real part of conductivity o-' and the imaginary part of the dielectric constant e" can be interchanged to calculate the microwave loss tangent of a medium with free-charge carriers, tan 6 = e r / e ~ = 1.8 × 1012 X o"(D. -1 c m - l ) / [ f (Hz) × e;],

o"([~ -1 cm -1) = 5.563 × 10 -13 )< E~' x f (Uz), where tan ~ is the loss tangent, e'r is the real part of relative permittivity, and e~ is the imaginary part of relative permittivity. The approximate relation between e'r and tan 6 [1], for a change in the dielectric constant as a function of frequency is A e r / e ' r = 1.5 × tan 6 × log( f 2 / f l ) and for a change in the dielectric constant as a function of temperature is A e ' / e ' = 0.07 × tan ~ × (T 2 - T1).

608

Hamid H. S.Javadi

2. Dielectric Properties of Compounds Throughout this section the dielectric parameters of materials are reviewed. Schematics 1 and 2 are two-dimensional maps of materials in which the horizontal coordinates indicate relative permittivity and the 1.0 0.6 0.3 0.1 O. 08

.

.

.

.

.

.

.

0.06 0.04 Araldlte, CastingB

0.02

3=,

0.01 0.008 0.006 0.004 ~D c

I

0.002

Poraelal 3 GH=

,l~iIazn St.atit.3 GHz

0.001 0.0009 0.0008 0.0007 0.0006 0.0005 0.0004 0.0003 0.0002 0.0001 0.1 MeV) Spallation neutrons a-Particles (0-10 MeV)

Irradiation temperature (°C)

Quantity of dose

e'r ( + 0.02)

tan 6 [10 -4] ( + 1)

9.41a/11.59 b

1.5a/1.5 b

< 215

2.6 x 10 20 n / c m 2

9.49a/11.64 b

10a/ll b

250-400

5 X 1020 n / c m 2

9.43a/11.61 b

2.5a/2.0 b

200-500

0.3 X 1017a/cm 2 0.6 X 1017a/cm 2 1.6 X 1017a/cm 2

9.41a/11.61 b 9.42a/11.62 b

5a/5 b 4a/2 b 4a/3 b

9.43a/11.62 b

Note. Reproduced, with permission, from Table 2 in Heidinger and K6niger [11], copyright

© 1989 by the Society of Photo-Optical Instrumentation Engineers. aordinary ray. bExtraordinary ray.

626

Hamid H. S. Javadi

3. Properties of Manufactured Special-Purpose Compounds Dielectric r e s o n a t o r s are widely used in microwave filters, oscillators, and amplifiers. In such applications the t e m p e r a t u r e coefficients of expansion, of the dielectric constant, and of the r e s o n a n c e frequency are i m p o r t a n t . These, plus composition and o t h e r i m p o r t a n t information, are t a b u l a t e d in Table 15. Table 16 s u m m a r i z e s the i m p o r t a n t physical p r o p e r t i e s of surface acoustic wave materials [12]. T h e insertion loss of c o m m o n S A W materials vs the fractional b a n d w i d t h is the subject of Figure 6 [12]. Piezoelectrics are discussed in Table 17 [13]. T h e dielectric constant, dielectric loss tangent, and m a g n e t i c p r o p e r t i e s of c o m m e r c i a l ferrites are p r e s e n t e d in Table 18 [14]. Figure 7 illustrates the g e n e r a l behavior of s a t u r a t i o n m a g n e t i z a t i o n vs the Curie t e m p e r a t u r e for a l u m i n u m - s u b stituted Y I G [15].

TABLE 15

Dielectric Resonator Materials

Type

C D E F

C D E

•r

z~ (ppm/°C)

Manufacturer, Murata Erie North America, Inc. Brand, Resomics-S Series Composition" Ba(Zr, Zn, Ta)O 3 Minimum Qd, 10,000 (at 10 GHz) Thermal expansion coefficient, 11 ppm/°C Thermal conductivity, 0.0059 cal/cm s °C Water absorption, 0.01% maximuma 28.6 + 0.5 -20.4 + 4 29.2 + 0.5 -24.4 + 4 29.7 + 0.5 -28.4 + 4 30.1 + 0.5 -32.4 + 4 Manufacturer, Murata Erie North America, Inc. Brand, Resomics-E Series Minimum Qd, 20,000 (at 10 GHz) Thermal expansion coefficient, 10.7 ppm/°C Thermal conductivity, 0.0077 cal/cm s °C Water absorption, 0.01% maximuma 24.2 + 0.4 24.4 _+ 0.4 24.7 + 0.4

rf (ppm/°C)

0+ 2+ 4+ 6+

0 2 4

2 2 2 2


627

TABLE 15 (Continued) Type

Unspecified Unspecified

A B C D E F G H

E r

'r E

(ppm/°C)

rf (ppm/°C)

24.9 +_ 0.4 Manufacturer, Murata Erie North America, Inc. Brand, Resomics-K Series Composition: (Ba, Pb)NdzTi5014 Minimum Qd, 1000 (at 3 GHz) Thermal expansion coefficient, 8-9 p p m / ° C Thermal conductivity, 0.0039 c a l / c m s °C Water absorption, 0.01% maximum a 90_+ 2.7 - 2 9 _+ 4 90_+ 2.7 - 1 7 _+4 Manufacturer, Murata Erie North America, Inc. Brand, Resomics-M Series Composition: (Zr, Sn)TiO 4 Minimum Qd, 8000 (at 7 GHz) Thermal expansion coefficient, 6-7 p p m / ° C Thermal conductivity, 0.0046 c a l / c m s °C Water absorption, 0.01% maximum a 37.4 _+ 0.5 - 1 3 _+ 2 37.7 _+ 0.5 - 1 7 _+ 4 38.0 _+ 0.5 - 2 1 _+ 4 38.4 _+ 0.5 - 2 5 _+ 4

0_+2 2+2 4_+2 6_+2

Manufacturer, Murata Erie North America, Inc. Brand, Resomics-R Series Minimum Qd, 12,000 (at 10 GHz) Thermal expansion coefficient, 10.7 p p m / ° C Thermal conductivity, 0.0051 c a l / c m s °C Water absorption, 0.01% maximum a 29.6 _+ 0.5 30.3 _+ 0.5 30.9 _+ 0.5 31.5 _+ 0.5 Manufacturer, Murata Erie North America, Inc. Brand, Resomics-U Series Composition: (Zr, Sn)TiO 4 Minimum Qd, 6000 (at 7 GHz) Thermal expansion coefficient, 6-7 p p m / ° C Thermal conductivity, 0.0046 c a l / c m s °C Water absorption, 0.01% maximum a 36.6 _+ 0.5 b -5 + 4 37.0 _+ 0.5 b -9 + 4 37.4+0.5 b -13 +4 37.7 _+ 0.5 b -17 + 4 38.0 _+ 0.5 b -21 + 4 38.3_+0.5 b -25+4 38.6 _+ 0.5 b -29 + 4 38.9_+0.5 b -33+4

-4 + 2 -2 + 2 0+2 2 + 2 4 + 2 6+2 8 + 2 10_+2

0_+2 6_+2

(Continues)

Hamid H. S. Javadi

628 TABLE 15 (Continued) Type

•r

7"E

(ppm/°C)

D-8810 D-8811 D-8812

Manufacturer, Trans-Tech, Inc. Brand, Trans-Tech 8500 Series Composition: Z r / S n titanate Minimum Qd, 10,000 (at 4.5 GHz) Thermal expansion coefficient, 6.5 p p m / ° C Thermal conductivity, 0.005 c a l / c m s °C Water absorption, 0.01% maximum c 35.7 + 1.5% b 1.6 35.9 + 1.5% b -6.9 36.2 + 1.5% t' - 9.7 36.4 + 1.5% b - 13.1 36.4 + 1.5% b - 19.0 Manufacturer, Trans-Tech, Inc. Brand, Trans-Tech 8800 Series Composition: barium and titanium oxide Minimum Qd, 6000 (at 4.5 GHz) Thermal expansion coefficient, 9.2 p p m / ° C Thermal conductivity, 0.005 c a l / c m s °C Water absorption, 0.01% maximum c 36.6 + 1.5% 38.3 + 1.5% 38.3 + 1.5%

D-8621 D-8622 D-8623 D-8624 D-8625 D-8626

Manufacturer, Trans-Tech, Inc. Brand, Trans-Tech 8600 Series Composition: Ba, lanthanides, and Ti-oxide Minimum Qd, 3000 (at 3.0 GHz) Thermal expansion coefficient, 8.5 p p m / ° C Thermal conductivity, 0.005 c a l / c m s °C Water absorption, 0.01% maximum c 80.0 _+ 1.5% 80.0 _+ 1.5% 80.0 _+ 1.5% 80.0 _+ 1.5% 80.0 _+ 1.5% 80.0 _+ 1.5%

D-8516 D-8515 D-8514 D-8513 D-8517

Tf

(ppm/°C)

-3 0 3 6 9

-6 -3 0 3 6 9


629

TABLE 15 (Continued) Type

D-8731 D-8732 D-8733 D-8734 D-8735

E-1336 E-2036 E-2336 E-2636 E-2936

•r

I"E

(ppm/°C)

r r (ppm/°C)

Manufacturer, Trans-Tech, Inc. Brand, Trans-Tech 8700 Series Composition: Ba, Zn, and Ta-oxide (perovskite) Minimum Qd, 9500 (at 10 GHz) Thermal expansion coefficient, 10 p p m / ° C Thermal conductivity, 0.006 c a l / c m s °C Water absorption, 0.01% maximum c 27.6 _+ 1.5% 28.5 _+ 1.5% 29.4 _+ 1.5% 30.0 _+ 1.5% 30.6 +_ 1.5% Manufacturer, Thomson-CSF Components Corp. Brand, E36 Composition: (Zr, Sn)TiO 4 Minimum Qd, 4000 (at 10 GHz) Thermal expansion coefficient, 5 p p m / ° C 36.9 _+ 0.4 - 4 _+ 1 37.0 +_ 0.4 - 1 0 _+ 1 37.1 _+ 0.4 - 1 6 _+ 1 37.2 _+ 0.4 - 2 2 _+ 1 37.3 _+ 0.4 - 2 8 _+ 1

- 4 - 2 0 2 4

-3 0 3 6 9

_+ 1 +_ 1 + 1 +_ 1 _+ 1

aData reproduced, with permission, from catalog No. 095E-2 (1990) of Murata Erie North America, Inc. tAt 7.5 GHz. CData reproduced, with permission, from catalog No. 50010080, Revision 2 (1990), of Trans-Tech, Inc.

70

60El

"~ 50v I/l O

ST-Quartz..---.-.~~

"

40-

LiTa03BGO

J¢ - 30-

yZ_LiNb0s 0 "~ 20" T28° LiNbO L t#

/ /

__L

I/I

_~ 106 0

I

1

I

I

'

//

Z/ fAX

//,~/

' ,,.I

,

.

.

,

,.,.

10

100

Fractional Bandwidth ( % ) Figure 6. Optimal bandwidth of most commonly used surface acoustic wave materials. Reproduced, with permission, from Figure 6.14 in Penunuri et al. [ 12], copyright © 1989 by John Wiley & Sons, Inc.

ml I~D

"r, ~J

o_u ~J

Q~

E

0

o b E E 3

C

~L

0

c~

o

~

c~O~ .~

Q

o o, cJ

O

0 ~

L~

0

c~

~ i ~ I~

~

I i~

~

N

0

~

~ io

~

m

O

.,~ = 0

@ .~

8

=

.,~

E-

.,-~ .~

.~

=


631

TABLE 17 Piezoelectric Coupling and Frequency- Temperature Coefficients of Thin Plates of Microwave Acoustic Materials

Piezoelectric coupling (%)

Temperature coefficient (10-6/K)

Crystal

Class

Orientation

Mode

GaAs

43M

(110) (111)

Shear extension

6 4

- 34 - 72

Li2B40 7

4MM

49 °

z

Shear extension

26 19

0 + 191

(yxl)

LiTaO 3

3M

(xxl) 50 ° z

Shear extension

5 18

0 - 46

LiNbO 3

3M

x z

Shear extension

70 17

- 60 - 45

AIPO 4

32

(yxl)

31 °

x

Shear extension

12 8

0 - 65

(xyl) 35 ° x

Shear extension

9 10

0 - 20

SiO 2

32

Note.

R e p r o d u c e d , with permission, from Table 2 in Ballato and Lukaszek [13], copyright © 1990 by Horizon House-Microwave, Inc.

2.0 •

A

1.5

AMPEX

x

COUNTIS

o

XTALONIX

[]

TRANS-TECH

{n {n D 1.0 v

0.5

mm

0.0

!

I

i00

150 CURIE

I

200

TEMPERATURE

I

300

250 ( °C

)

Figure 7. Saturation magnetization versus Curie temperature for aluminum-substituted YIG. The data were published by Ampex, Redwood City, CA; Countis San Luis Obispo, CA; Trans-Tech, Adamstown, MD; and Xtalonix, Columbus, OH. Reproduced, with permission, from Figure 5.6 in Hord [15], copyright © 1989 by John Wiley & Sons, Inc.

._1

I11 !._ !._ tll u_

E E 0

t~ Q.

£ u

Q.

~ .~o

~s

g.o

r~ 0

0

o

o

c',l

~~

c¢~

t'xl 1¢3 t'~

c¢~ c¢3 t¢3

VVVV

t'xl ,,~-

~

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t¢3 t¢3

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g

I

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I

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~

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C',l t'-,I t"xl t'-,I t'-,l

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~4A

t'-,1

go~gg

~

~

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~

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~

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¸

d 0 r.~

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0

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6]]

TABLE 19 Properties of Conductor Materials for the Thin-Film Technique

Material Conducting layer material Ag Cu Au A1 Adhesion layer Cr Ta Ti Separation layer Pt Pd

Relative specific resistance, p/Pcu a

0.95 1.0 1.36 1.6

Skin depth, 6 (in micrometers, at 2 GHz)

Thermal expansion coefficient, AITh/(l AT) (in 1 0 - 6 / K )

Adhesion on A I 2 0 3 ceramic

Coating method b

1.4 1.5 1.7 1.9

21 18 15 26

Poor Poor Poor Poor

evap evap, galv evap, galv evap

Good Good Good

evap Sp, evap Sp, evap

7.6 9.1 27.7

4.0 4.5 7.8

8.5 6.6 9.0

6.2 6.2

3.6 3.6

9.0 11.0

Sp, evap Sp, evap

Note. Reproduced, with permission, from Table 1.14 in Hoffmann [16], copyright © 1987 by Artech House, Inc. g Pcu = 1.72 × 1 0 - 6 ~ cm. bevap, evaporation; galv, electrolytic deposition; and Sp, sputtering.

TABLE 20 Properties of Thin-Film Resistors

Material

Specific surface resistance (t

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