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Noise Temperature Theory and Applications for Deep Space Communications Antenna Systems

For a listing of recent titles in the Artech House Antennas and Propagation Series, turn to the back of this book.

Noise Temperature Theory and Applications for Deep Space Communications Antenna Systems

Tom Y. Otoshi

Library of Congress Cataloging-in-Publication Data A catalog record for this book is available from the U.S. Library of Congress. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library. ISBN-13: 978-1-59693-377-4 Cover design by Igor Valdman  2008 ARTECH HOUSE, INC. 685 Canton Street Norwood, MA 02062 All rights reserved. Printed and bound in the United States of America. No part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, or by any information storage and retrieval system, without permission in writing from the publisher. All terms mentioned in this book that are known to be trademarks or service marks have been appropriately capitalized. Artech House cannot attest to the accuracy of this information. Use of a term in this book should not be regarded as affecting the validity of any trademark or service mark. 10 9 8 7 6 5 4 3 2 1

To my wife Haruko Shirley Otoshi, my son John Terence Otoshi, and my daughter Kathryn Ann Otoshi, who all shared in my 40 or more years of aspirations and endeavors at the Jet Propulsion Laboratory, California Institute of Technology in Pasadena, California

Contents

Foreword

xi

Preface

xiii

Acknowledgments

xv

CHAPTER 1 Introductory Topics

1

1.1 Antenna Noise Temperature as Functions of Pointing Angles 1.1.1 Zenith Formula 1.1.2 Sky Brightness Temperature 1.1.3 Ground Brightness Temperature 1.1.4 Formula for Nonzenith Pointing Angles 1.1.5 Tipping Curve Applications 1.2 Cosmic Background Noise Temperature 1.2.1 Introduction 1.2.2 Calibration Equation 1.2.3 Experimental Results 1.2.4 Commentary 1.3 Portable Microwave Test Packages 1.3.1 Introduction 1.3.2 Test-Package Descriptions 1.3.3 Test Configurations and Test Procedure 1.3.4 Noise-Temperature Measurement Method 1.3.5 Noise-Temperature Measurement Results 1.3.6 Concluding Remarks 1.4 Dichroic Plate in a Beam-Waveguide Antenna System 1.4.1 Introduction 1.4.2 Background 1.4.3 Analytical Method 1.4.4 Experimental Work 1.4.5 Conclusions References Selected Bibliography

1 1 6 11 17 22 37 37 37 39 39 40 40 41 42 44 47 50 50 50 51 54 62 66 66 69

vii

viii

Contents

CHAPTER 2 Reflector Surfaces

71

2.1 Perforated Panels 2.1.1 Introduction 2.1.2 Old Calculation Method 2.1.3 New Calculation Method 2.1.4 Perforated-Plate and Perforated-Panel Geometries 2.1.5 Results 2.1.6 Concluding Remarks 2.2 Solid Panels 2.2.1 Basic Noise Temperature Relationships 2.2.2 Dependence on Polarization and Incidence Angle 2.2.3 Electrical Conductivity of Various Metals 2.3 Painted Panels 2.3.1 Background on Paint Study 2.3.2 Background on DSN Antennas 2.3.3 Excess Noise Temperature and Added Gain Loss 2.3.4 Results and Performance Characterizations 2.3.5 Conclusions 2.4 Wet Panels 2.4.1 Theoretical Studies 2.4.2 Experimental Studies References

71 71 73 74 80 82 86 88 88 93 99 108 108 108 110 113 130 131 131 132 134

CHAPTER 3 Noise Temperature Experiments

137

3.1 Horns of Different Gains at f1 3.1.1 Introduction 3.1.2 Analytical Procedure and Results 3.1.3 Experimental Work 3.1.4 Determination of Strut Contribution 3.1.5 Conclusions 3.2 Bird Net Cover for BWG Antennas 3.2.1 Introduction 3.2.2 Description of the Net Cover 3.2.3 Test Results 3.2.4 Concluding Remarks 3.3 G/T Improvement Task 3.3.1 Introduction 3.3.2 Test Configurations and Test Results 3.3.3 Summary and Recommendations 3.4 Measured Sun Noise Temperature at 32 GHz 3.4.1 Introduction 3.4.2 Gain Reduction Methods

137 137 137 144 147 151 152 152 152 153 155 156 156 157 171 172 172 173

Contents

ix

3.4.3 Measurement and Data Reduction Method 3.4.4 Experimental Results 3.4.5 Concluding Remarks References Selected Bibliography CHAPTER 4 Mismatch Error Analyses 4.1 Antenna System Noise Temperature Calibration Mismatch Errors 4.1.1 Introduction 4.1.2 Review 4.1.3 Antenna System Noise Temperature Measurements 4.1.4 Antenna Efficiency Measurements 4.1.5 Applications 4.1.6 Concluding Remarks 4.2 Equivalent Source Noise Temperature at Output of Cascaded Lossy Networks 4.2.1 Matched Case 4.2.2 Mismatched Case 4.3 Effective Input Noise Temperature at Input of Cascaded Lossy Networks 4.3.1 Matched Case 4.3.2 General Mismatched Case References CHAPTER 5 Network Analysis Topics

177 180 185 186 187

189 189 189 190 196 205 210 221 222 222 224 229 229 231 233

235

5.1 Two-Port Network Containing Two Internal Paths 235 5.1.1 Introduction and Background 235 5.1.2 Dissipative Power Ratios of Four-, Three-, and Two-Port Networks 235 5.1.3 Power Flow (PF) Method 239 5.1.4 Voltage Wave (VW) Method 242 5.1.5 Sample Cases 246 5.1.6 Example of the Effects of a Mismatched Component in Path 1 249 5.1.7 Conclusions 252 5.2 Three-Port Network with Two External Noise Sources 252 5.2.1 Introduction 252 5.2.2 Properties of an Ideal Four-Port Coupler 253 5.2.3 Two External Noise Source Outputs Travel Common Paths 254 5.2.4 Two External Noise Source Outputs Travel Individual Paths 262 5.2.5 Conclusions 265 References 266

x

Contents

CHAPTER 6 Useful Formulas for Noise Temperature Applications

269

6.1 Formulas Associated with Solid Metal Reflectors 6.1.1 Conductivity of Metals 6.1.2 Noise Temperature of a Solid Metallic Sheet 6.2 Formulas Associated with Metal Reflectors with Holes 6.2.1 Perforated Plates with Round Holes 6.2.2 Wire Grids 6.3 Other Useful Formulas 6.3.1 Relationship of Insertion Loss to Noise Temperature 6.3.2 Relationship of Return Loss to Reflection Coefficient and VSWR References

269 269 270 271 271 274 276 276

About the Author

281

Index

283

278 279

Foreword Of the many technical considerations that go into realization of the large NASAJPL ground antennas of the Deep Space Network (recently redesignated the InterPlanetary Network), it is the critical microwave receive system performance that often limits deep-space mission data return. Receive system performance is governed by the ratio of gain to noise temperature (G/T), with gain (proportional to the antenna effective collecting area) providing the received signal level; T refers to the underlying noise level or noise temperature, a bandwidth-independent noise power measure. Perhaps obvious, it is vital to maximize G, while minimizing T in such high-performance receive systems. Author Tom Y. Otoshi spent the major part of his more than 40-year career at JPL analyzing, designing, and accurately evaluating many of the detailed elements that comprise minimizing, then stating with known error confidence, the receive system noise temperature. Otoshi remains one of those rare individuals with a commanding presence in both theoretical and practical microwave matters and metrology, as can be seen in his impressive bibliography. In this volume the author first provides the introductory topics necessary and convenient for reader overview. The author then discusses a variety of reflector performance issues, including important detailed information on material conductivities, perforations, protective coatings, terrestrial weather effects, and the influence of the Earth’s Sun. Throughout, the author provides highly useful information for microwave engineers in many allied disciplines, including measurement and accuracy evaluation strategies. In Chapters 4–6 the author continues with error analyses, tutorials and in our considered opinion, a collection of highly useful formulae perhaps never before collected in one compact document. Of especial note in Chapter 5, the author presents for the first time known to us, a practical method for noise temperature prediction of multiports, by use of S-parameters. Practicing microwave engineers in many related fields will likely refer to this carefully considered book, thereby earning it a convenient and permanent place on their bookshelves. Dan A. Bathker (JPL, Ret.) Stephen D. Slobin, JPL May 2008

xi

Preface The importance of minimizing noise temperatures in antenna systems has been stated in the Foreword by Bathker and Slobin and will not be restated here. The author assumes that the reader is somewhat familiar with the fundamentals of noise temperature and knows that a basic antenna receiving system consists of an antenna, the interconnecting network, the front-end low-noise amplifier, and the follow-up receiver. The book starts by discussing the theory of antenna noise temperature for a simple antenna, such as a horn or parabolic antenna, and how to calculate noise contributions from the cosmic background, the galaxy (negligibly small above 8 GHz), the atmosphere, ground, reflector spillover, and reflector surface losses. The noise temperature of a beam waveguide antenna system is described as well as the noise temperature of a dichroic plate installed in the system. Subsequent chapters discuss the noise generated by microwave networks between the receive horn and the front-end low-noise amplifier. This book does not cover the theory of noise generated by the front-end low-noise amplifier or the followup receiver. For this information, the reader can refer to books on these subjects. This book aims to present selected topics related to noise temperature measurements and analyses that the author has performed on deep space antennas and microwave systems in the NASA/JPL Deep Space Network (DSN). Some materials have been extracted from JPL or IEEE Publications while other materials in Section 1.1 and Chapter 5 are new and have not been previously published. Highlights of the chapters in this book are described as follows: Chapter 1 covers introductory topics, including calculating antenna noise temperature as a function of pointing angles from the sky at zenith to the horizon accounting for ground absorption and reflection. Chapter 1 also describes two methods of extracting atmospheric noise temperature at zenith from tipping curve measurements. In addition, Chapter 1 discusses a unique method that was used for evaluating the performance of a new beam waveguide antenna system through the use of portable test packages used to make measurements of system noise temperature and gain at three of the beam waveguide antenna focal points. Chapter 2 provides the theoretical and measured noise temperatures of reflector surfaces including solid-, perforated-, painted- and wet-panels. Chapter 3 covers noise temperature experiments, including: (1) the effects of different gain horns at the Cassegrain focal point on antenna noise temperature, (2) the design of a transparent net placed over the beam waveguide antenna opening to keep birds out, (3) various experiments to lower the system noise temperature, and (4) an absorber sheet method to measure the Sun’s noise temperature (10,000K) without saturating the receiver. Chapter 4 describes some fundamentals of noise temperature and mismatch

xiii

xiv

Preface

theory as applied to basic receive systems. Chapter 4 also presents tables of mismatch error equations in terms of both reflection coefficient magnitudes and VSWRs useful for determining the effects of mismatch on the calibration of system noise temperature and antenna efficiency. In addition, Chapter 4 details equations for determining the equivalent source temperature of cascaded mismatched networks as well as the equivalent input noise temperature of cascaded mismatched networks. Chapter 5 provides a network analysis method for determining the noise temperature of a multiport having two internal paths from source port to the output port and in addition considers the case of two external noise sources connected to a multiport. The author believes that an easy to understand presentation has been offered for a methodology of using S-parameters to analyze noise generated by multiport networks. All the material in Chapter 5 was previously published in an internal JPL report in September 2004, but it was not available to engineers outside of JPL. Finally, Chapter 6 provides useful and simple formulas for calculating the noise temperatures of a solid metallic reflector surface, perforated plates, and wire grids as functions of frequency, incidence angle, and polarization. The author believes that this is the first book on noise temperature intended for the practicing engineer in the field of developing low-noise large microwave antennas for deep-space communication. The author hopes that the material in this book is a good mix of background theory and practical examples that will allow the reader to learn in a short time what the author learned over 43 years at JPL: a comprehensive understanding of the noise generated by the antenna and the environment and microwave networks and receivers following the feed. Mismatch error analyses are a subject generally avoided. This book, however, presents a table of useful mismatch error equations in terms of both reflection coefficient magnitudes and VSWRs. The extensive list of personnel who contributed in various ways to make this book possible are recognized in the Acknowledgments. The author takes sole responsibility for the accuracy of any new material that has not been previously published in JPL Progress Report or IEEE articles.

Acknowledgments

The author would like to specially acknowledge Stephen D. Slobin (JPL) and Dan A. Bathker (JPL-Ret.) whose behind-the-scene efforts and encouragement made it possible for the material presented in this book to become available to the technical world outside of JPL. The author also acknowledges the earlier editorial assistance of Pat Ehlers of the JPL Documentation Section on Progress Report articles from which a large portion of material in this book was used. In addition, the author is deeply indebted to Cindy Copeland, who typed the manuscript, created the graphics for this book, and provided invaluable assistance whenever needed. Numerous persons contributed in various ways to the technical work described in this book. Contributors who were sometimes coauthors on progress report articles are listed as follows: • • • • • • • • • • • •

Section Section Section Section Section Section Section Section Section Section Section Section

1.1 and 1.2: Charles Stelzried; 1.3: Dan Bathker, Scott Stewart, and Manuel Franco; 1.4: Manuel Franco; 2.1: Watt Veruttipong; 2.2: Cavour Yeh; 2.3: Yahya Rahmat-Samii, Rick Cirillo, Jr., and John Sosnowski; 2.4: Manuel Franco; 3.1: Manuel Franco and Paula Brown; 3.2: Watt Veruttipong and John Sosnowski; 3.3: Watt Veruttipong, John Sosnowski, and Rick Cirillo, Jr.; 3.4: Paul Richter, Stephen Keihm, and Stephen Slobin; 4.1: Charles Stelzried.

The author also gratefully acknowledges the DSS 13 crew of G. Bury (supervisor), J. Garnica, B. Reese, and L. Smith for helping him to perform noise measurements on the large beam waveguide antenna in a challenging field environment. The measurements included test package test evaluations, G/T improvement tests, and difficult Sun experiments. D. Wolff of the Planning Research Corporation (PRC) in Pasadena, California, provided the aluminum dots, and N. Bucknam, formerly of PRC, designed the tapered cone transition used in the G/T improvement tests. The author would also like to give special acknowledgment to J. Garnica who prepared many of the experimental setups at DSS 13 station in advance, so

xv

xvi

Acknowledgments

that the author could perform the tests described in this book efficiently and successfully. The research described in this publication was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under a contract with the National Aeronautics and Space Administration.

CHAPTER 1

Introductory Topics

1.1 Antenna Noise Temperature as Functions of Pointing Angles 1.1.1 Zenith Formula

For the spherical coordinate system shown in Figure 1.1, the antenna noise temperature equation that accounts for cross-polarization is given in [1] as 2␲ ␲

冕冕

TA =

[Pc (␪ , ␾ ) Tbc (␪ , ␾ ) + Px (␪ , ␾ ) Tbx (␪ , ␾ )] sin ␪ d␪ d␾

0 0

(1.1)

2␲ ␲

冕冕

[Pc (␪ , ␾ ) + Px (␪ , ␾ )] sin ␪ d␪ d␾

0 0

where Pc (␪ , ␾ ) and Px (␪ , ␾ ), respectively, are the power per unit solid angles for the copolarized and cross-polarized fields. The symbols Tbc and Tbx are the brightness temperatures for the copolarized and cross-polarized directions, respectively. Although Tbc and Tbx are generally the same for the sky region, they are not necessarily the same for the ground region because of ground reflection coefficient dependence on polarization. If the cross-polarized fields are small relative to the copolarized fields, the equation reduces to the familiar equation, ␲ 2␲

冕冕 TA =

P (␪ , ␾ ) Tb (␪ , ␾ ) sin ␪ d␾ d␪

0 0

(1.2)

␲ 2␲

冕冕

P (␪ , ␾ ) sin ␪ d␾ d␪

0 0

where P (␪ , ␾ ) = power per unit solid angle for the copolarized fields in the ␪ , ␾ direction. Tb (␪ , ␾ ) = brightness temperature for the copolarized fields, K.

1

2

Introductory Topics

Figure 1.1

The (R, ␪ , ␾ ) spherical coordinate system.

Since the denominator of (1.2) is the total radiated power P T , and the antenna gain G (␪ , ␾ ) in any direction is [2] G (␪ , ␾ ) = 4␲

P (␪ , ␾ ) PT

(1.3)

substitution into (1.2) gives another familiar expression of ␲ 2␲

1 TA = 4␲

冕冕

G (␪ , ␾ ) Tb (␪ , ␾ ) sin ␪ d␾ d␪

(1.4)

0 0

Ludwig [3] pointed out that the total power pattern of an antenna or horn with complete physical circular symmetry can be described in terms of two selected patterns. For a linearly polarized antenna, the two required patterns are the E- and H-plane patterns. For an RCP antenna, the two required patterns are the receive patterns taken with the illuminator, illuminating first in RCP and then in LCP. For an LCP antenna, the two required patterns are LCP and RCP. The following discussion presents a derivation of the equations for antenna noise temperature of a linearly polarized and circularly symmetric antenna in terms of E- and H-plane patterns. The case for a circularly polarized antenna is not analyzed here, but by expanding the analysis to take into account the 90-degree phase difference between E- and H-plane patterns for the CP case, the derivation to follow can be used for an RCP or LCP antenna.

1.1 Antenna Noise Temperature as Functions of Pointing Angles

3

Following the analysis given by Ludwig in [3], let E 0 (R, ␾ , ␪ ) represent the far-field electric field pattern of any antenna located at the origin of the spherical coordinate system (R, ␾ , ␪ ), as shown in Figure 1.1. R is defined as the distance of E 0 from the origin; ␾ is the azimuthal angle in radians; ␪ is the polar angle in radians; and a R , a ␾ , a ␪ are the associated unit vectors. For this analysis, assume that the antenna has complete physical circular symmetry and is excited by the dominant or any m = 1 cylindrical mode. The modes of a cylindrical waveguide are given in terms of TEmn and TMmn . For a more general expression of the far-field expansion, refer to discussions on spherical wave functions given by Ludwig in [4, 5]. Then E 0 (R, ␾ , ␪ ) =

e −j␬ R [A 1 (␪ ) sin ␾ a ␪ + B 1 (␪ ) cos ␾ a ␾ ] R

(1.5)

where

␬=

2␲ ␭

A 1 (␪ ) = | A 1 (␪ ) | e B 1 (␪ ) = | B 1 (␪ ) | e

j ⌽A 1 (␪ ) j ⌽B 1 (␪ )

The subscript 1 is used to identify the m = 1 cylindrical mode. The terms

| A 1 (␪ ) | , | B 1 (␪ ) | , ⌽A 1 (␪ ), and ⌽B 1 (␪ ) will be defined in the following: Note that if ␾ = 0, (1.5) becomes

E 0 (R, 0, ␪ ) =

| B 1 (␪ ) | R

e

−j [␬ R − ⌽B 1 (␪ )]

a␾

(1.6)

and | E 0 (R, 0, ␪ ) | =

| B 1 (␪ ) |

(1.7)

R

A study of (1.6) and Figure 1.1 will reveal that | B 1 (␪ ) | /R is the H-plane amplitude pattern measured as a function of ␪ at a distance R from the origin. The term ⌽B 1 (␪ ) in (1.6) is the H-plane phase pattern. If ␾ = ␲ /2, (1.5) becomes E 0 (R, ␲ /2, ␪ ) =

| A 1 (␪ ) | R

e

−j [␬ R − ⌽A 1 (␪ )]

a␪

(1.8)

Then | E 0 (R, ␲ /2, ␪ ) | =

| A 1 (␪ ) | R

(1.9)

4

Introductory Topics

The latter equation is the E-plane amplitude pattern as measured at a distance R from the origin. The term ⌽A 1 (␪ ) in (1.8) is the E-plane phase pattern. The complete expression for the far-field electric field amplitude obtained from (1.5) is | E 0 (R, ␾ , ␪ ) | =

1 冋| A 1 (␪ ) | 2 sin2 ␾ + | B 1 (␪ ) | 2 cos2 ␾册1/2 R

(1.10)

The total radiated power is

冉冊

1 ⑀ PT = 2 ␮

␲ 2␲

1/2

R

2

冕冕|

2

E 0 (R, ␾ , ␪ ) | sin ␪ d␾ d␪

(1.11)

0 0

Substitution of (1.10) into (1.11) and integration over ␾ gives ␲

冉冊冕冋|

␲ ⑀ PT = 2 ␮

1/2

2

A 1 (␪ ) | + | B 1 (␪ ) |

2

册 sin ␪ d␪

(1.12)

0

As defined in (1.2), P (␪ , ␾ ) is the power/unit solid angle in any direction (␪ , ␾ ). Then

P (␪ , ␾ ) =

冉冊

1 ⑀ 2 ␮

1/2

R 2 | E 0 (R, ␾ , ␪ ) |

2

(1.13)

Substitution of (1.10) gives

P (␪ , ␾ ) =

冉冊

1 ⑀ 2 ␮

1/2

冋| A 1 (␪ ) | 2 sin2 ␾ + | B 1 (␪ ) | 2 cos2 ␾ 册

(1.14)

Inspection of (1.2) shows that the antenna temperature formula can also be written as

TA =

冤

␲ 2␲

冕冕

Tb (␪ , ␾ ) P (␪ , ␾ ) sin ␪ d␾ d␪

0 0

PT

Substitution of (1.12) and (1.14) into (1.15) gives

冥

(1.15)


TA =

冤

␲ 2␲

冕冕

5

Tb (␪ , ␾ ) 冋| A 1 (␪ ) | sin2 ␾ + | B 1 (␪ ) | cos2 ␾ 册 sin ␪ d␾ d␪ 2

0 0

2

␲

␲

冕冋|

2

A 1 (␪ ) | + | B 1 (␪ ) |

2

册 sin ␪ d␪

0

冥

(1.16)

at the peak of the beam, | A 1 (0) | = | B 1 (0) | . Let the normalized power pattern be calculated from

p 1 (␪ ) =

p 2 (␪ ) =

| A 1 (␪ ) | 2 | A 1 (0) | 2 | B 1 (␪ ) | 2 | A 1 (0) | 2

=

| B 1 (␪ ) | 2 | B 1 (0) | 2

Substitutions into (1.16) give

TA =

冤

␲ 2␲

冕冕

Tb (␪ , ␾ ) [ p 1 (␪ ) sin2 ␾ + p 2 (␪ ) cos2 ␾ ] sin ␪ d␾ d␪

0 0

␲

␲

冕

[ p 1 (␪ ) + p 2 (␪ )] sin ␪ d␪

0

冥

(1.17)

If it is assumed that the peak of the antenna pattern points at zenith sky and the antenna lies above flat ground, it can be assumed that Tb (␪ , ␾ ) = Tb (␪ ) and (1.17) simplifies to

TA =

冤

␲

冕 0

Tb (␪ ) [ p 1 (␪ ) + p 2 (␪ )] sin ␪ d␪ ␲

冕

[ p 1 (␪ ) + p 2 (␪ )] sin ␪ d␪

0

冥

(1.18)

which is a formula not normally found in textbooks or in technical literature. Let (1.18) be expressed as TA = (TA )sky + (TA )ground

(1.19)

6

Introductory Topics

where ␲ /2

(TA )sky

1 = D

冕

Tsky (␪ ) [ p 1 (␪ ) + p 2 (␪ )] sin ␪ d␪

(1.20)

0

␲

(TA )ground

1 = D

冕

TG (␪ ) [ p 1 (␪ ) + p 2 (␪ )] sin ␪ d␪

(1.21)

␲ /2

and ␲

D=

冕

[ p 1 (␪ ) + p 2 (␪ )] sin ␪ d␪

(1.22)

0

where Tsky (␪ ) = sky brightness temperature, K; TG (␪ ) = ground brightness temperature, K. Brightness temperature may be defined as the apparent noise temperature, which is seen by the antenna looking along a direct ray. In the following section, the expressions for Tsky (␪ ) will be derived for a curvedEarth atmosphere, and TG (␪ ) will be derived for a flat ground environment. 1.1.2 Sky Brightness Temperature 1.1.2.1 Path-Length Formula for Curved-Earth Atmosphere

The equation for the noise temperature of a curved-Earth atmosphere may be generally known and given in different forms, but this author has only encountered the expression given by Rafuse in [6]. However, this Rafuse expression is incorrect at the two limits where the zenith angles are 0 degrees and 90 degrees. The correct expression for curved-Earth atmosphere will be derived in the following. Exact Formula

In the geometry of Figure 1.2, R is the radius of the Earth, and H is the height of the atmosphere in the zenith direction. Figure 1.3 is the same as Figure 1.2 except redrawn out of scale to show only the geometry needed for the derivation. Use of the familiar formula for an obtuse triangle such as the one shown in Figure 1.3 results in (R + H )2 = ᐉ 2 + R 2 − 2ᐉR cos (180° − ␪ ) = ᐉ 2 + R 2 + 2ᐉR cos ␪ Then

(1.23)


7

Figure 1.2

Curved-Earth and atmosphere geometry.

Figure 1.3

This is Figure 1.2 purposely redrawn out of scale to show only necessary parameters.

ᐉ 2 + 2ᐉR cos ␪ + R 2 − (R + H )2 = 0

(1.24)

From use of the Quadratic Formula ᐉ=

冉

1 −2R cos ␪ ± 2

√(2R cos ␪ )2 − 4[R 2 − (R + H )2]

冊

(1.25)

Choosing the plus sign for the solution, the desired path length formula is

8

Introductory Topics

ᐉ=

√R 2 cos2 ␪ + 2RH + H 2 − R cos ␪

(1.26)

This expression is equivalent to that given in [6] except that Rafuse omitted the H 2 term. It is important to retain the H 2 term because otherwise the two important limiting case relationships of ᐉ = H for ␪ = 0 degrees and ᐉ=

√2RH + H 2 for ␪ = 90 degrees would not be fulfilled.

Approximate Formula

Let (1.26) be written in the form

冋√

ᐉ = R cos ␪

1+

冉

2RH + H 2 R 2 cos2 ␪

冊

−1

册

(1.27)

For a 4/3 Earth model with a standard reduced atmosphere, H is 5 km, and the Earth radius is 8,500 km. Therefore it is clear that R Ⰷ H and the term

冉

2RH + H 2 2

2

R cos ␪

R cos2 ␪ . 2 Then using the formula that

冊

≈

is valid for H Ⰶ

2H R cos2 ␪

Ⰶ1

x

√1 + x ≈ 1 + 2 for x Ⰶ 1, then (1.27) becomes

冋冉

ᐉapprox ≈ R cos ␪ 1 +

2H 1 2 R cos2 ␪

冊册

−1 =

H cos ␪

(1.28)

R cos2 ␪ . 2 Equation (1.28) is the well-known formula for the path length through a flat slab atmosphere having a height H and could have been derived directly from inspection of Figure 1.4. In (1.28) ᐉapprox becomes increasingly inaccurate at large angles of ␪ and becomes infinity when ␪ = 90 degrees, which is clearly invalid. For the 4/3 Earth model and reduced atmosphere, it was found that the difference between the approximate formula given by (1.28) and the exact formula given by (1.26) is less than 0.1 km until ␪ becomes larger than 76 degrees. For larger angles, the exact formula given by (1.26) should be used. A practical use of this approximate formula is to divide (1.28) by H and derive which is valid for H Ⰶ

p ′(␪ ) = (ᐉapprox /H ) = 1/cos ␪

(1.29)

␪ = cos−1 [1/p ′(␪ )]

(1.30)

which leads to

This expression can be used for finding the angle ␪ that corresponds to a given integer number of atmospheric layers sometimes called air masses for a flat


Figure 1.4

9

Flat Earth–flat atmosphere geometry.

atmosphere. Then for p ′(␪ ) = 2, 3, 4, the corresponding values of ␪ are found to be 60, 70.529, and 75.222 degrees, respectively. These values will be used later in Section 1.1.5.4. 1.1.2.2 Atmosphere Noise Temperature Formula for Curved-Earth Atmosphere

Let

␣ = the atmosphere power absorption per unit length due to water vapor and oxygen. Tatm (␪ ) = noise temperature due to atmospheric absorption at angle ␪ , K. TP, atm = effective physical temperature of the atmosphere, K. Then for the curved atmosphere shown in Figure 1.2 Tatm (␪ ) = TP, atm (1 − e −␣ ᐉ )

(1.31)

Tatm (0) = Tzen = TP, atm (1 − e −␣ H )

(1.32)

At zenith

Manipulation of (1.32) leads to e −␣ H = 1 − and it follows that

Tzen TP, atm

(1.33)

10

Introductory Topics

冉

e −␣ ᐉ = (e −␣ H )ᐉ /H = 1 −

Tzen TP, atm

冊

ᐉ /H

−1

= L atm (␪ )

(1.34)

−1

where the term L atm (␪ ) is an expression often used by microwave engineers to describe dissipative loss. Substitution of (1.34) into (1.31) gives the desired curved atmosphere noise temperature expression of

冋冉

Tatm (␪ ) = TP, atm 1 − 1 −

Tzen TP, atm

冊册 ᐉ /H

= TP, atm 冋1 − L atm (␪ )册 −1

(1.35)

and where from (1.26) ᐉ = H

√冉冊 R H

2

cos2 ␪ + 2

冉冊 R H

+1−

冉冊 R H

cos ␪

(1.36)

Allowing this ratio to be written as p (␪ ) = ᐉ /H and then solving the explicit relationship for ␪ as a function of p (␪ ) from (1.36), one can derive the curvedEarth relationship of

␪ = cos−1

再冋

1 p 2(␪ ) − 1 1− p (␪ ) 2R /H

册冎

(1.37)

that can be used to find the angle that corresponds to a specified value of p (␪ ) for a curved atmosphere. For example, if for the curved Earth, substitutions of R = 8,500 km and H = 5 km and p (␪ ) = 2, 3, 4 into (1.37) the corresponding values of ␪ are found to be 60.029, 70.576, and 75.588 degrees, respectively. These values are slightly larger than the corresponding angles that will be calculated when using the same values of p (␪ ) in (1.30) for the flat atmosphere. The total sky brightness temperature is calculated from −1

Tsky (␪ ) = Tatm (␪ ) + L atm (␪ ) Tcb −1

(1.38)

where L atm (␪ ) = e −␣ ᐉ as calculated from (1.34), and Tcb is the effective cosmic background noise temperature taking into account frequency and stated to be nominally about 2.7K for frequencies in the region of 2.3 GHz. From (1.35) and (1.36), it can be seen that the parameters needed for calculation of atmospheric noise temperature are R, H, TP, atm , and Tzen . For calculations done by this author, the values H = 5 km and R = 8,500 km have been assumed. Even though there is some effect due to the curvature of the ground when ␪ is 90 degrees, calculations show that at the end of the curve, there is less than 1 degree departure from a flat ground environment for the 4/3 Earth model. Therefore, for practical purposes of calculating the reflection coefficient of ground and sky


11

brightness temperatures at the horizon, it will be assumed that the reflection coefficient of ground for curved Earth at the horizon is the same as the reflection coefficient for flat ground at the horizon. In the past, brightness temperature of the sky was obtained by using sky data from Hogg’s curves [7]. Currently, atmospheric noise temperature Tzen and other atmospheric parameters for an average clear atmosphere at the Goldstone, CA, tracking station are obtained from a JPL document [8] and are given for three DSN frequencies in Table 1.1. For parameters other than Tzen and Tcb , the formulas used to derive values in Table 1.1 as stated in [8] are TP, atm = 255 + 25 × CD, K

(1.39)

where CD = cumulative distribution (0.25 for the values in Table 1.1) and

冉

1/L zen = 1 −

冊

Tzen TP, atm

(1.40)

In recent years, accurate atmospheric noise temperature values for local conditions were also obtained by using measured values from a water vapor radiometer [9] at 31.4 GHz. Then the zenith values were extrapolated to other frequencies.

1.1.3 Ground Brightness Temperature

In Section 1.1.1 it was shown that, for an antenna with physical circular symmetry, excited by modes with one azimuthal variation (m = 1 modes), the complete farfield electric field may be expressed as E 0 (R, ␾ , ␪ ) =

| A 1 (␪ ) | R +

(sin ␾ ) e

| B 1 (␪ ) | R

−j [␬ R − ⌽A 1 (␪ )]

(cos ␾ ) e

a␪

−j [␬ R − ⌽B 1 (␪ )]

(1.41) a␾

where | A 1 (␪ ) | /R and | B 1 (␪ ) | /R were defined as the absolute E- and H-plane amplitude patterns, respectively. Definitions of other quantities were given in Section 1.1.1. For purposes of deriving the expression for ground brightness tempera-

Table 1.1 Zenith Atmospheric Parameters at Goldstone, CA , for an Average Clear Sky (0.25 Cumulative Distribution) [8] Frequency, GHz

Tzen , K

Tp, atm , K

1/L zen

L zen , dB

Effective Tcb , K

2.295 8.42 32 20.7a

1.93 2.31 9.15 15.71

261.25 261.25 261.25 282.16

0.99261 0.99118 0.96498 0.94428

0.032 0.038 0.155 0.249

2.7 2.5 2.0 2.23

a

Although not given in [8], the values at 20.7 GHz are based on an analysis performed at JPL [12].

12

Introductory Topics

ture, it is desirable that (1.41) be expressed as components of a wave incident upon the ground. The geometry of a zenith-oriented antenna situated above flat ground infinite in extent may be seen in Figure 1.5. Since E 0 (R, ␾ , ␪ ) is actually the incident wave for this geometry, let E i (R, ␾ , ␪ ) = E 0 (R, ␾ , ␪ )

(1.42)

E i (R, ␾ , ␪ ) = E i␪ a ␪ + E i␾ a ␾

(1.43)

Since

then it follows that E i␪ =

| A 1 (␪ ) | R

(sin ␾ ) e

−j [␬ R − ⌽A 1 (␪ )]

(1.44)

and E i␾ =

Figure 1.5

| B 1 (␪ ) | R

(cos ␾ ) e

Antenna situated over flat ground.

−j [␬ R − ⌽B 1 (␪ )]

(1.45)


13

The term E i␪ represents an incident electric field polarized in the plane of incidence, and the E i␾ term represents an incident electric field polarized perpendicular to the plane of incidence. Similarly, at the incident point (R, ␾ , ␪ ) on the ground, the expression for the total reflected wave may be written as E r (R, ␾ , ␪ ) = E r␪ a ␪ + E r␾ a ␾

(1.46)

At any particular point (R, ␾ , ␪ ) at which E i is incident upon the ground, we may by definition, let ⌫|| (␪ ) = voltage reflection coefficient of the ground for a parallel (in-plane) polarized wave =

E r␪ ␲ for ≤ ␪ ≤ ␲ E i␪ 2

⌫⊥ (␪ ) = voltage reflection coefficient of the perpendicular polarized wave =

(1.47)

(1.48)

E r␾ ␲ for ≤ ␪ ≤ ␲ E i␾ 2

Note that ⌫|| (␪ ) and ⌫⊥ (␪ ) are phasors (complex numbers) so that they possess both magnitude and phase. The expression for the total reflected wave at the coordinate (R, ␾ , ␪ ) intercept point would be E r (R, ␾ , ␪ ) = ⌫|| (␪ ) E i␪ a ␪ + ⌫⊥ (␪ ) E i␾ a ␾

(1.49)

The generalized expression for the total power reflection coefficient at (R, ␾ , ␪ ) will be defined as

冋

册

␲ | E (R, ␾ , ␪ ) | 2 | ⌫T (␾ , ␪ ) | 2 = | Er (R, ␾ , ␪ ) | , for 2 ≤ ␪ ≤ ␲ i

(1.50)

Substitutions of (1.49) and (1.43) into (1.50) give

| ⌫T (␾ , ␪ ) | 2 =

冋

| ⌫|| (␪ ) | 2 | E i␪ | 2 + | ⌫⊥ (␪ ) | 2 | E i␾ | 2 2

| E i␪ | + | E i␾ |

2

册

, for

␲ ≤ ␪ ≤ ␲ (1.51) 2

and in terms of E- and H-plane amplitude patterns, substitutions of (1.44) and (1.45) into (1.50) give

| ⌫T (␾ , ␪ ) | 2 =

冋

| ⌫|| (␪ ) | 2 | A 1 (␪ ) | 2 sin2 ␾ + | ⌫⊥ (␪ ) | 2 | B 1 (␪ ) | 2 cos2 ␾ | A 1 (␪ ) | 2 sin2 ␾ + | B 1 (␪ ) | 2 cos2 ␾

册

, for

␲ ≤␪≤␲ 2 (1.52)

14

Introductory Topics

For zenith antenna temperature calculations, assuming uniform ground properties are independent of ␾ , it would be desirable to use an average brightness temperature based on an average or effective power reflection coefficient that is independent of ␾ , and is therefore a function of ␪ (antenna polar angle) only. Over an annular solid angle segment, the average or effective power reflection coefficient may be defined as follows: 2␲

1 | ⌫E (␪ ) | 2 = 2␲

冕|

2

⌫T (␾ , ␪ ) | d␾

(1.53)

0

Special case. For the special case where the amplitude patterns for the E- and H-planes are identical, for all values of ␪ , that is

| A 1 (␪ ) | = | B 1 (␪ ) | substitution into (1.52) gives

␲

| ⌫T (␾ , ␪ ) | 2 = 冋 | ⌫|| (␪ ) | 2 sin2 ␾ + | ⌫⊥ (␪ ) | 2 cos2 ␾册, for 2 ≤ ␪ ≤ ␲ (1.54) and from (1.53) 2

| ⌫E (␪ ) | =

冋

| ⌫|| (␪ ) | 2 + | ⌫⊥ (␪ ) | 2 2

册

, for

␲ ≤␪≤␲ 2

(1.55)

It can be shown that this effective power reflection coefficient can be used for zenith antenna temperature calculations for the circularly polarized antenna case as well. The parallel and perpendicular voltage reflection coefficients ⌫|| (␪ ) and ⌫⊥ (␪ ) for the general case are functions of frequency, incidence angle, dielectric constant, and electrical conductivity of the second medium. As derived in [10] and general electromagnetic theory textbooks, such as [11], the index of refraction of the ground can be determined from the expression

冉

⑀r 2 − j

n=

␴2 ␻⑀ 0

冊

1/2

(⑀ r 1 )1/2

where

⑀ r 2 = relative dielectric constant of medium 2 (ground in this case). ␴ 2 = electrical conductivity of medium 2 (ground), mhos/m. ⑀ r 1 = relative dielectric constant of medium 1 (air = 1). ␻ = radian frequency in rad/sec. ⑀ 0 = dielectric constant of free space = (1/36␲ ) × 10−9, h/m.

(1.56)


15

For the case of the electric field polarized normal to the plane of incidence, the phasor expression for the voltage reflection coefficient in terms of incidence angle ␤ and n is ⌫⊥ ( ␤ ) =

冋

√n 2 − sin2 ␤

cos ␤ −

√n

cos ␤ +

2

2

− sin ␤

册

,0≤␤≤

␲ 2

(1.57)

From Figure 1.5, it can be seen that ␤ = ␲ − ␪ , and substitution into (1.57) results in

⌫⊥ (␪ ) =

冋

cos (␲ − ␪ ) − cos (␲ − ␪ ) +

√n 2 − sin2 (␲ − ␪ )

√

2

2

n − sin (␲ − ␪ )

册

␲ ≤␪≤␲ 2

,

(1.58)

For the case of the electric field polarized parallel to the plane of incidence, the phasor expression of the voltage reflection coefficient is

⌫|| ( ␤ ) =

冋

√n 2 − sin2 ␤ n 2 cos ␤ + √n 2 − sin2 ␤

n 2 cos ␤ −

册

,0⬉␤⬉

␲ 2

(1.59)

or

⌫|| (␪ ) =

冋

√n 2 − sin2 (␲ − ␪ ) n 2 cos (␲ − ␪ ) + √n 2 − sin2 (␲ − ␪ )

n 2 cos (␲ − ␪ ) −

册

,

␲ ≤␪≤␲ 2

(1.60)

For calculating antenna temperature in (1.21), the ground brightness temperature function is determined from the expression TG (␪ ) = 冋1 − | ⌫E (␪ ) |

2

册 Tpg + | ⌫E (␪ ) | 2 Tsky (␲ − ␪ ), for ␲2 ≤ ␪ ≤ ␲

(1.61)

where

| ⌫E (␪ ) | 2 = effective power reflection coefficient of the ground as previously defined by (1.55). Tpg = physical ground temperature, K. Tsky (␲ − ␪ ) = sky brightness temperature corresponding to incidence angle ␤ , K, (Figure 1.5) where Tsky (␪ ) is given in (1.38). Special case plot. A sample plot of 2,295-MHz brightness temperatures for an antenna situated over flat desert ground is shown in Figure 1.6. For this plot, the brightness temperatures for antenna polar angles ␪ = 0 to 90 degrees are the

16

Introductory Topics

Figure 1.6

Brightness temperature curve for antenna over flat desert ground at 2,295 MHz.

sky brightness temperatures as obtained from Hogg’s curves [7] for the specified frequency. The ground brightness temperature values for antenna polar angles ␪ = 90 to 180 degrees are computed from use of (1.61). The effective power reflection coefficient from (1.55) for an antenna with identical E- and H-plane patterns was used. For evaluation of ⌫⊥ (␪ ) and ⌫|| (␪ ), given by (1.58) and (1.60), respectively, and for computing the index of refraction n in (1.56), the parameters

⑀ r 2 = 3.0 ␴ 2 = (1/9) × 10−1 mhos/m were used. These parameters are appropriate for desert ground based on data taken from curves presented in [10].


17

As may be observed in the brightness temperature curve of Figure 1.6, a decrease in brightness temperature occurs in the region just beyond the horizon point (90 degrees for flat ground). The minimum point appears to be centered at about the antenna polar angle of 93 degrees. From the substitutions of the above ground parameters into (1.61), it was found that this minimum in ground brightness temperature occurs very close to the angle at which brightness temperature is contributed to equally by the sky and ground environments. 1.1.4 Formula for Nonzenith Pointing Angles

When the antenna beam is not pointed in the zenith direction but at some other direction, the antenna temperature is calculated from 2␲ ␲

冕冕

P (␪ , ␾ ) Tb (␪ e , ␾ e ) sin ␪ d␪ d␾

0 0

TA (␪ 1 , ␾ 1 , ␾ 0 ) =

(1.62)

2␲ ␲

冕冕

P (␪ , ␾ ) sin ␪ d␪ d␾

0 0

where

␪ , ␾ = the angles of the antenna patterns in the antenna spherical coordinate system. ␪ e , ␾ e = spherical coordinate angles of the brightness temperature in the Earth’s coordinate system and are functions of the antenna pattern angles ␪ , ␾ . The relationship between the angles will be shown by coordinate transformation equations to be presented. ␪ 1 = antenna pointing angle measured relative to the Z-axis of the Earth’s rectangular coordinate system. ␾ 1 = antenna azimuthal angle measured relative to the X-axis of the Earth’s rectangular coordinate system. ␾ 0 = polarization angle measured in the antenna XY plane relative to the X-axis of the antenna mechanical coordinate system. These definitions will become clearer with the presentation of the coordinate transformation equations to follow. 1.1.4.1 Transformation Equations

x

冤冥冤 y z

=

cos ␾ sin ␪ sin ␾ sin ␪ cos ␪

冥

(1.63)

18

Introductory Topics

x d′ y d′

冤冥冤 =

cos ␾ 0

−sin ␾ 0

0

sin ␾ 0

cos ␾ 0

0

0

0

1

z d′

xd

=

yd zd

0

0

0

cos (−␪ 1 )

−sin (−␪ 1 )

0

sin (−␪ 1 )

cos (−␪ 1 )

xe

冤冥冤 =

ye

cos ␾ 1

−sin ␾ 1

0

sin ␾ 1

cos ␾ 1

0

0

0

1

ze

␪ e = tan−1

冉√

ze

x e2

冥冤冥

1

冤冥冤

+

y e2

冊

valid for

x y

(1.64)

z

x d′ y d′

冥冤冥

(1.65)

z d′

xd

冥冤冥 yd

(1.66)

zd

␲ −␲ ≤ ␪ e ≤ in radians 2 2

(1.67)

and for ␾ e that applies to all four quadrants use mathematical function

␾ e = ATAN2 (x e , y e )

(1.68)

Figure 1.11 shows the relationship of the antenna azimuth angle ␾ 1 and the Earth’s azimuth angle ␣ az . As a reminder, note that the peak of the main beam lies in the Yd Z e plane. The Earth’s azimuth angle ␣ az is measured clockwise from Ye (due North) to Yd . Therefore the relationship between ␾ 1 and ␣ az is

␾ 1 = 360° − ␣ az

(1.69)

which may be substituted into (1.66) if it is preferable to have the antenna structure azimuth angle be expressed in terms of the Earth’s azimuth angle. 1.1.4.2 Derivation of Equations

An attempt will be made to explain the above transformation equations with the aid of Figures 1.7 through 1.11. Starting with the antenna pattern spherical coordinate system shown in Figure 1.7, the angles ␪ , ␾ are as defined for a right-hand system where ␾ is the azimuthal angle that lies in the XY plane and is measured counterclockwise from the X-axis. The angle ␪ lies in the plane of the ␾ cut and is measured clockwise from the Z-axis. The relationships of the (␪ , ␾ ) angles to the (x, y, z) coordinates are shown in (1.63). Now define the polarization angle ␾ 0 as shown in Figure 1.8. It lies in the XY plane of the antenna pattern system but is measured relative to the elevation axis of the antenna mechanical system whose rectangular coordinates are x d′ , y d′ , and z d′ . The angle ␾ 0 might be useful if there is a need to align the antenna pattern polarization to an antenna reference axis, which for this analysis is chosen to be the elevation axis X d′ . The coordinate transformation equation from the (x, y, z) to the 冠x d′ , y d′ , z d′ 冡 system is shown in (1.64).


19

Figure 1.7

The antenna pattern spherical and rectangular coordinate system. The angles (␪ , ␾ ) are any angles in the antenna pattern system. For convenience assume that the peak of the main beam lies on the Z-axis or spherical coordinate ␪ = 0 degrees.

Figure 1.8

The antenna pattern X-axis is rotated an angle ␾ 0 about the antenna structure Z d′ -axis. This angle ␾ 0 is measured relative to the antenna structure X d′ elevation axis and lies on both the XY plane and the X d′ Yd′ plane, which are coplanar.

Figure 1.9 shows X d′ as being the antenna elevation axis. It is assumed that the peak of the main beam points along the Z d′ axis. A clockwise rotation of the Z d′ (and also the Y d′ ) axis is made about the elevation axis to define angle ␪ 1 . In practice this angle is sometimes referred to as the main beam tipping angle. Since Y d′ is rotated clockwise rather than counterclockwise, then −␪ 1 rather than +␪ 1 is used in the usual counterclockwise transformation equation as shown in (1.65). Both the planes Y d′ Z d′ and Yd Z d contain the tipping angle ␪ 1 . The zenith direction

20

Introductory Topics

Figure 1.9

The antenna beam is tipped at angle ␪ 1 from the Z d axis in the Yd Z d plane about the antenna elevation axis. The Yd′ Z d′ and Yd Z d planes are coplanar.

is now denoted by the axis Z d , and the new antenna coordinate system axes are X d , Yd , Z d . In the new system the X d axis becomes the new elevation axis even though it is the same as the X d′ axis. Figure 1.10 shows elevation axis X d rotated counterclockwise about the antenna zenith axis Z d by an amount ␾ 1 in the X e Ye plane, which are the coordinate axes of the flat Earth coordinate system. The angle ␾ 1 is referred to as the antenna azimuth angle. The axis Ye points due north and X e points east. As previously described, the peak of the main beam lies in the Yd Z d plane and points in the direction of the ray path defined by tipping angle ␪ 1 . The antenna Z d axis is identical to the Z e axis in the Earth coordinate system, and the coordinate trans-

Figure 1.10

The antenna elevation axis is rotated an azimuth angle ␾ 1 about the antenna Z d axis which is aligned to the Earth’s Z e -axis. This angle is measured relative to the Earth’s X e axis and lies in both the X d Yd and X e Ye planes, which are coplanar.


21

formation from the (x d , y d , z d ) to the (x e , y e , z e ) system involves the ␾ 1 rotation. The transformation equation is given in (1.66). Transformation from the Earth’s (x e , y e , z e ) rectangular coordinate system to the Earth’s spherical coordinate angles (␪ e , ␾ e ) is done through the use of (1.67) or (1.68). Figure 1.11 shows the relationship of the antenna azimuth angle ␾ 1 and the Earth’s azimuth angle ␣ az . As a reminder, note that the peak of the main beam lies in the Yd Z e plane. The Earth’s azimuth angle ␣ az is measured clockwise from Ye (due north) to Yd . Therefore the relationship between ␾ 1 and ␣ az was previously given in (1.69) as ␾ 1 = 360° − ␣ az , which may be substituted into (1.66) if it is preferable to have the antenna structure azimuth angle be expressed in terms of the Earth’s azimuth angle. In summary, the antenna temperature as given by (1.62) is calculated as follows. From the given ␪ , ␾ of the antenna patterns, and pointing directions given by ␪ 1 , ␾ 1 , and ␾ 0 , calculate ␾ e and ␪ e using (1.63) through (1.68). Then from a lookup table of discrete values of Tb (␪ e , ␾ e ) stored in a computer file, use double linear interpolation to get the precise values of Tb (␪ e , ␾ e ) needed to perform the integration of (1.62) in digital form. Note that Tb (␪ e , ␾ e ) is a function of ␪ , ␾ , ␪ 1 , ␾ 1 , and ␾ 0 . Generally once ␾ 0 is known, it is fixed in (1.64), and one need only vary ␪ 1 to get a plot of TA versus ␪ 1 for a given value of ␾ 1 . This plot is generally known as a tipping curve. Note that if ␾ 1 = 0, tipping as a function of ␪ 1 will occur in the Ye Z e plane. If tipping is desired in the X e Z e plane, then make ␾ 1 = −90°. Similarly, for fixed values of ␾ 0 and ␪ 1 , vary ␾ 1 to get an azimuth scan plot. All of the equations given in this section have been programmed in Fortran. The source code is given in [12]. For generality, values of Tb (␪ e , ␾ e ) stored in the lookup table are those for a flat Earth as described in Section 1.1. If desired, new nonflat Earth values of Tb (␪ e , ␾ e ) can be read into the computer program, overwriting corresponding flat Earth values. This was done for instance to get an antenna temperature map of the antenna when scanning through a rectangular ground mask of 300K located at the horizon [13, 14] at 20.6 GHz.

Figure 1.11

Relationship of antenna azimuth angle ␾ 1 to the Earth’s azimuth angle ␣ az .

22

Introductory Topics

1.1.5 Tipping Curve Applications 1.1.5.1 Parabolic Antenna at 20.6 GHz

Figure 1.12 shows the brightness temperature of the sky curved atmosphere, cosmic background noise temperature, and flat desert ground at 20.6 GHz as calculated from the equations given previously in this chapter. The same dielectric constant and electrical conductivity for desert ground as given previously for 2.295 GHz in Figure 1.6 were used for 20.6 GHz. The zenith atmospheric value at 20.6 GHz was obtained from a computer program furnished by S. Slobin of JPL. His program inputs are ground-level parameters such as station height above sea level, groundlevel barometric pressure, relative humidity, and air temperature. Figure 1.13 shows the calculated E- and H-plane patterns for a symmetrical parabolic antenna at 20.6 GHz [12]. This symmetric high-gain antenna is studied here because the theoretical data was already available from a prior study that was

Figure 1.12

Brightness temperature of sky and flat desert ground region at 20.6 GHz.

0

RELATIVE POWER, dB

-10 -20 -30

H-PLANE

ISOTROPIC LEVEL

-40 -50 -60 -70 E-PLANE

-80 -90 -100 0

5

10

15

20

25

30

35

40

ANGLE OF ROTATION, DEG

Figure 1.13

WVR antenna patterns at 20.6 GHz. Relative power for angles greater than 40 degrees is below 83.8 dB [12]. (Courtesy NASA/JPL-Caltech.)


23

done to assist in the development of an offset reflector antenna for the operational advanced water vapor radiometer (AWVR) system [15]. For the purposes of this study, the symmetrical parabolic antenna shall be referred to as the water vapor radiometer (WVR) antenna, because the beamwidth and patterns were similar to that of the AWVR antenna that was eventually fabricated and used by Keihm, Tanner, and Rosenberger for measurements of tropospheric delays at Goldstone, California [15]. The half 3-dB beamwidth is equal to 0.6 degrees or 1.2 degrees for a full 3-dB beamwidth. Note that the antenna pattern is a Gaussian shape and the isotropic level, which is 43.4 dB down from the peak, is reached at a theta value of 5 degrees for the H-plane pattern and stays below this level for larger values of theta. The E- and H-plane patterns are identical only down to 25 dB from the peak. The calculated antenna temperature versus tipping angle curve is shown in Figure 1.14 for the AWVR antenna using the brightness temperatures of Figure 1.12, the patterns of Figure 1.13, and the coordinate transformation equations given in this section. The tipping angle ␪ 1 is measured from zenith. For tipping angles from 0 to 75 degrees, the differences between the calculated antenna temperature and the brightness temperature are small (typically less than 0.1K) and hence antenna and brightness temperatures are plotted only from 75 to 90 degrees. Although not plotted, the antenna temperature is higher than the brightness temperature by a maximum of 0.03K between 0 and 57 degrees; a maximum of 0.04K higher between 57 and 65 degrees; and a maximum of 0.1K higher between 65 and 75 degrees. Knowledge of these differences will become important for determining errors of a Tipping Curve Method that will be presented later. Figure 1.14

Figure 1.14

Calculated tipping curve for a 20.6-GHz WVR antenna (Figure 1.13) over flat desert ground, and comparison to brightness temperature. In the plot Tb is the sky brightness temperature (from Figure 1.12), and TA is the calculated antenna temperature.

24

Introductory Topics

shows that the antenna temperature and brightness temperature values begin to depart only slightly at a tipping angle of about 88 degrees from zenith or about 2 degrees above flat ground. The maximum difference between the antenna temperature and brightness temperature at 90 degrees is only 11.6K. This small difference at most of the tipping angles is attributed to a full 3-dB beamwidth of only 1.2 degrees for this antenna. The full 10-dB beamwidth is 2.4 degrees. Note that the value of antenna temperature at a tipping angle of 90 degrees is lower than the brightness temperature value. The explanation is that at 90 degrees half of the antenna beam still points toward the sky region and half points at the ground region. Since the sky brightness temperature in the sky region around 90 degrees is still less than the brightness temperature in the ground region, the calculated antenna noise temperature is less than the brightness temperature. Had this study been done with a circular horn of smaller aperture and a wider 3-dB beamwidth, it is expected that there would have been larger differences between the antenna temperature and brightness temperature as the tipping angle approached the horizon. The following example will confirm this expectation. 1.1.5.2 X-Band Corrugated Horn at 8.45 GHz

Figure 1.15 shows the brightness temperature of the sky and flat desert ground at 8.45 GHz. The same dielectric constant and electrical conductivity for desert ground as given previously for 2.295 GHz were used. The E-plane patterns for a 22.4-dBi corrugated horn at 8.45 GHz and for a 22.6-dBi dual-mode horn at 2.297 GHz are shown in Figure 1.16. The corresponding H-plane patterns for both horns are shown in Figure 1.17. The X-band horn aperture diameter is 17.98 cm (7.077 inches). At 8.45 GHz, the half 3-dB beamwidth is 7.39 degrees and the full 3-dB

300

Noise Temperature, K

250

200

150

100

Ground Region: 90 to 180 deg

Sky Region: 0 to 90 deg

50

0 0

50

100

150

Theta, deg

Figure 1.15

Brightness temperature at 8.450 GHz for surface temperature of 20°C, 30% relative humidity, flat desert ground at DSS 13 elevation of 1.055 km above sea level.


25

0

-10 Isotropic Level

-20

-30

Relative power, dB

E-Plane S-band Horn -40

-50

-60

E-Plane X-band Horn

-70

-80

-90

-100 0

20

40

60

80

100

120

140

160

180

Rotation angle, deg

Figure 1.16

E-plane patterns for the 22.6 dBi S-band horn and the 22.4 dBi X-band horn.

beamwidth is equal to 14.8 degrees, as compared to a full 3-dB beamwidth of 1.2 degrees for the WVR antenna at 20.6 GHz. Figure 1.18 shows the calculated tipping curve for the horn at 8.45 GHz over the full sky region of 0 to 90 degrees. The calculated antenna temperature TA and brightness temperature Tb begin to deviate from each other by about 0.4K at a tipping angle of about 60 degrees. Also shown is the ground-only contribution Tag to the antenna temperature as a function of tipping angle. Figure 1.19 shows the noise temperatures only for tipping angles between 50 and 80 degrees. This plot shows changes of TA , Tb , Tatm , and Tag more clearly as the horn is tipped toward the horizon. Note that the Tb and Tatm curves do not seem equally spaced near 80 degrees. The reason is that the brightness temperature Tb is composed of not only Tatm , but also of a cosmic background term Tcb that is attenuated by a longer lossy atmosphere as the antenna points toward the horizon.

1.1.5.3 S-Band Dual-Mode Horn at 2.297 GHz

Figure 1.6 showed the brightness temperature of sky and flat desert ground at 2.295 GHz and is applicable to 2.297 GHz. Figures 1.16 and 1.17 showed the E- and H-plane pattern for a 22.6-dBi dual-mode horn at 2.297 GHz. The horn

26

Introductory Topics 0 -10 Isotropic Level -20 -30

Relative power, dB

-40 H-plane S-band Horn

-50 -60 -70 -80

H-Plane X-band Horn

-90 -100 -110 -120 0

20

40

60

80

100

120

140

160

180

Rotation Angle, deg

Figure 1.17

H-plane patterns for the 22.6-dBi S-band horn and the 22.4-dBi X-band horn.

aperture diameter is 66.17 cm (26.05 inches). At 2.297 GHz, the full 3-dB beamwidth is equal to 14.4 degrees. Note in Figures 1.16 and 1.17 that the patterns and beamwidth of the S-band horn are almost identical to those of the X-band horn described in Section 1.1.5.2. This is because the dimensions of the X-band horn were frequency-scaled from the corresponding dimensions of the S-band horn. However, the patterns of the S-band horn and X-band horn are not the same below the isotropic level because the S-band horn is a dual-mode horn, and the X-band horn is a corrugated horn. The S-band horn patterns were measured by Bathker’s antenna group [16] while the X-band horn patterns were computer-generated. Note that the faroff sidelobes for the S-band horn are not as far below the isotropic level as for the X-band horn. Figure 1.20 shows the calculated tipping curve for the horn at 2.297 GHz. Similar to the X-band tipping curve shown in Figure 1.19, the S-band tipping curve in Figure 1.20 shows that the antenna temperature TA becomes increasingly higher than the brightness temperature Tb because the horn gradually picks up more noise as it is tipped toward the horizon. This S-band horn is of interest because it was the same one used in conjunction with successfully measuring the cosmic background noise temperature Tcb at 2.297 GHz using a method described in Section 1.2.


27

100

90 Tb Tzen = 2.36 K

80


70

60

50

40 TA

30

20

10

Tag

0 0

10

20

30

40

50

60

70

80

90

Tipping Angle, deg

Figure 1.18

Calculated tipping curve for the 22.4-dBi X-band horn over flat desert ground at 8.45 GHz. [Tb is the sky brightness temperature (from Figure 1.15), TA is the calculated antenna temperature, and Tag is the ground contribution to TA .]

1.1.5.4 Extraction of Zenith Atmospheric Noise Temperature from Tipping Curves

A tipping curve method [17, 18] has been used in conjunction with use of a 34-m beam waveguide (BWG) antenna to determine the atmospheric noise temperature at zenith. However, the method described in this chapter will not apply to BWG antennas because only the case of horns and high-gain parabolic antennas with minimal strut scattering will be considered here. For the tipping curve method to be applied to a BWG antenna described in Section 1.3, any antenna motion-induced changes in the loss in the BWG path (from the Cassegrain focal point to the horn focal point located in a pedestal room) would have to be accounted for. Furthermore, noise temperature due to strut scattering would have to be modeled. There are indications from measurements made at the Ka-band on the DSN 34-m BWG antenna that unknown changes of noise temperature with elevation angles might be due to strut scattering. Tipping curve methods that have been used to derive Tatm (0) in the past assumed that the atmosphere is flat. In the following, the errors associated with a tipping curve method are analyzed for flat and curved atmospheres for a parabolic

28

Introductory Topics 25

Tzen = 2.36 K


20

TA

15

Tb

10

Tatm 5

Tag

0 50

55

60

65

70

75

80

Tipping Angle, deg

Figure 1.19

Calculated tipping curve from 50 to 80 degrees for the 22.4-dBi X-band horn at 8.45 GHz. At 60 degrees, TA = 7.58K, Tb = 7.16K, Tatm = 4.7K, and Tag = 0.15K.

antenna and DSN horns whose patterns and tipping curves have been presented in the previous sections. A methodology used by this author and others can be expressed mathematically as follows. It is assumed in this section that tipping curve measurements are being done with a feed horn or a parabolic antenna similar to that of a WVR antenna that is fed by a horn onto an offset reflector assumed to have negligible spillover losses and no strut scattering losses or resistive losses. The measured operating system noise temperature is written as Top (␪ ) = TA (␪ ) + TK

(1.70)

where TK is a constant that includes the antenna or horn, waveguide, and LNA noise temperatures and the symbol TA (␪ ) is the antenna temperature defined at the horn or antenna aperture as a function of tipping angle and is calculated from patterns and the brightness temperature using equations given previously. For most of the sky region, the brightness temperature consists of the atmospheric noise temperature and cosmic noise temperature as attenuated by the atmospheric loss as a function of tipping angle. It follows from (1.70) that


29

25

Tzen =2.13 K

20


TA 15

Tb

10

Tatm 5

Tag

0 50

55

60

65

70

75

80

Tipping Angle, deg

Figure 1.20

Calculated tipping curve from 50 to 80 degrees for the 22.6-dBi S-band horn at 2.297 GHz. At 60 degrees, TA = 7.48K, Tb = 6.84K, Tatm = 4.24K, and Tag = 0.4K.

⌬Top (␪ ) = Top (␪ ) − Top (0) = ⌬TA (␪ )

(1.71)

⌬TA (␪ ) = TA (␪ ) − TA (0)

(1.72)

where

The tipping curve method to be described here for extracting atmosphere noise temperatures at zenith are based on the following four assumptions: (1) the atmosphere is flat, (2) the antenna has a main beam that is very narrow (1 degree or less) and has very low sidelobes, (3) the cosmic background noise temperature contribution does not change with tipping angles, and (4) the antenna does not have spillover and strut scattering losses that change with tipping angles. It is therefore assumed that the change in operating temperature is equal to the change in atmosphere noise temperature. It is known that these assumptions become increasing erroneous as the tipping angles approach the horizon because the finite width antenna main beam and sidelobes begin to pick up ground noise temperatures and at the horizon, the antenna main beam of an ideal antenna sees half sky and half ground.

30

Introductory Topics

Expressing the tipping curve method mathematically, the noise temperature of the atmosphere at zenith is calculated from ′ (␪ ) = T zen

⌬Top (␪ ) ⌬TA (␪ ) = for 1.5 ≤ M ≤ 4 [M − 1] [M − 1]

(1.73)

where M = p (␪ ) = ᐉ(␪ )/H corresponding to the ratio of atmospheric path length at angle ␪ to the atmospheric path length H at zenith. The value of M is restricted to the range of values shown because it is difficult to measure change in Top accurately at angles less than about 40 degrees, and because for angles greater than 75 degrees, noise picked up from the ground become significant. The expressions of p (␪ ) for a flat atmosphere and a curved atmosphere were previously given in (1.29) and (1.36), respectively. For the tipping curve method, (1.73) is normally used when p (␪ ) = M where M is usually an integer value corresponding to the number of zenith thickness atmospheric layers sometimes referred to as air masses. It need not be an integer. For the WVR project [9], one of the angles it obtains data for is at tipping angle of ␪ = 48.2 degrees, which corresponds to M = 1.5. For a flat atmosphere, the values of M = 2, 3, and 4 occur at tipping angles of 60, 70.529, and 75.522 degrees, respectively. The corresponding tipping angles for a curved atmosphere are 60.029, 70.576, and 75.588 degrees. For the following error analyses, there will be negligible difference whether flat or curved atmosphere tipping angles corresponding to M ≤ 4 are used in (1.73). Therefore, for simplicity, the tipping angles for a flat atmosphere will be used for M ≤ 4. The error in determining the atmospheric noise temperature at zenith by this tipping curve method is ′ (␪ ) − Tzen E (␪ ) = T zen

(1.74)

′ (␪ ) is the measured zenith atmosphere where ␪ is the main beam tipping angle, T zen noise temperature determined from (1.73), and Tzen = Tatm (0) is the true atmospheric noise temperature at zenith. For this theoretical study, the true value Tzen was known a priori and was used in the computer program to compute Tb (␪ ) and TA (␪ ). In practice (1.73) should not be used for tipping angles greater than 80 degrees, because the errors will become unacceptably large due to ground noise pickup. Examples of the use of (1.73) are shown in Table 1.2. The first example is the application to a 43.4-dBi parabolic antenna whose full 3-dB beamwidth is 1.2 degrees at 20.7 GHz, and the brightness temperatures and antenna patterns were given in Figures 1.12 and 1.13, respectively. The true atmospheric noise temperature at 20.7 GHz is assumed to 15.71K. Performing the integration of (1.62) will give TA as a function of tipping angle and further uses of (1.71) through (1.74) gives the result summarized in Table 1.2(a). There are three decimal places for noise temperatures because early roundoff to two decimal places sometimes leads to results that appear to be wrong. The last column shows that at 20.7 GHz, the errors for this parabolic antenna at the three tipping angles are −1K, −1.4K, and −1.8K. Note in Table 1.2 that the antenna temperature change ⌬TA (␪ ) for this narrow beam antenna is very close to the curved Earth brightness temperature


31

Table 1.2 Tipping Curve Summary for a Parabolic Antenna and Horns Used in the DSN Flat Earth M Number of Atmospheres

Main Beam Pointing Angle ␪ , Degree

⌬Tb , K

⌬TA , K

⌬TA /(M − 1), K

Tatm (0), K

Error, K

2 3 4

(a) Ka-band 43.4-dBi Parabolic Antenna with Full 3-dB Beamwidth of 1.2 degrees at 20.7 GHz 60.00 14.69 14.718 14.718 15.710 −0.99 70.53 28.52 28.650 14.325 15.710 −1.39 75.52 41.52 41.706 13.902 15.710 −1.81

2 3 4

(b) DSN X-band 22.4-dBi Corrugated Horn with Full 3-dB Beamwidth of 14.8 degrees at 8.450 GHz 60.00 2.32 2.691 2.691 2.364 0.33 70.53 4.61 6.039 3.019 2.364 0.66 75.52 6.86 10.516 3.505 2.364 1.14

2 3 4

(c) DSN S-band 22.6-dBi Dual Mode Horn with Full 3-dB Beamwidth of 14.4 degrees at 2.297 GHz 60.00 2.09 2.641 2.641 2.129 0.51 70.53 4.15 5.776 2.888 2.129 0.76 75.52 6.19 10.088 3.363 2.129 1.23

Note: ⌬Tb = [Tb (␪ ) − Tb (0)] and ⌬TA = [TA (␪ ) − TA (0)]

change ⌬Tb (␪ ). The errors shown in Table 1.2(a) have negative values because the path length of the curved atmosphere is shorter than that of the flat Earth atmosphere. Although not obvious, substitutions of R = 8,500 km and H = 5 km into (1.26) and (1.28) will show that the curved atmosphere is shorter than the flat atmosphere by 8.8m, 35.1m, and 37.4m at tipping angles 60, 70.53, and 75.52 degrees, respectively. Further substitutions of these values into (1.35) will show that a shorter length atmosphere will have atmospheric noise temperatures less than those of the flat atmosphere. It is important to point out that the error expression of (1.74) applies only if the described tipping curve method is used for determining Tzen = Tatm (0). A second example of the tipping curve method is to apply it to the 22.4-dBi X-band corrugated horn with a 3-dB beamwidth of 14.8 degrees instead of 1.2 degrees as was shown in Figure 1.18. This horn begins to pick up significant ground contributions at the tipping angle of 60 degrees as shown by the plot of Tag in Figure 1.18. As shown in Table 1.2(b), the errors at 8.450 GHz (in determining the true zenith atmospheric noise temperature value of 2.364K from use of the tipping curve method) are 0.33K, 0.66K, and 1.14K, respectively, at tipping angles of 60, 70.5, and 75.5 degrees. These positive-valued errors are caused by the noise picked up from the ground. A third example of the tipping curve method is to apply it to the 22.6-dBi S-band dual-mode horn that has a 3-dB beamwidth of 14.4 degrees as described in Section 1.1.5.3. As shown in Figure 1.20, the horn begins to pick up ground noise at a tipping angle of 60 degrees. As shown in Table 1.2(c), the errors at 2.297 GHz are 0.51K, 0.76K, and 1.23K, respectively, at the three tipping angles. Errors for the S-band horn are close to the errors of the X-band horn, but are slightly larger. Even though both horns have nearly the same 3-dB beamwidth, the S-band horn patterns are for a dual-mode horn and the far out side lobes are not as deep below the isotropic level as are the patterns for the X-band horn as shown

32

Introductory Topics

in Figures 1.16 and 1.17. Significant differences in the X- and S-band horn patterns can be seen at tipping angles greater than 40 degrees. Although these errors may seem small for most applications, they are not small for the cosmic background noise temperature determination of about 2.7K to be discussed in the following section. Determining this small noise temperature to about 0.1K accuracy requires that the atmospheric noise temperature at zenith be known to better than 0.1K. Prior to this study, it was not known that use of the tipping curve method for a DSN 22.6-dBi horn would result in errors of 0.5K or greater. Table 1.3 shows predictions of tipping curve errors for a parabolic antenna with an even a higher gain and narrower beamwidth than those for the AWVR antenna. For a high-gain antenna with narrow beamwidth and low sidelobes, it ′ (␪ ) can be calculated from is assumed that ⌬TA (␪ ) = ⌬Tb (␪ ) and T zen [Tb (␪ ) − Tb (0)]/(M − 1) where Tb (␪ ) is the brightness temperature for a curved atmosphere. The values of Tb (␪ ) were calculated from substitution of ᐉ (␪ )/H given by (1.36) for a curved atmosphere into (1.34) and (1.35) and then final substitutions were made into (1.38). The brightness noise temperature (Tb )F for flat atmosphere is similarly calculated by letting ᐉ (␪ )/H = 1/cos ␪ and making substitutions into (1.34), (1.35), and (1.38). Note in Table 1.3 that the values of [(Tb )C − (Tb )F ] are very small up to about a 60-degree tipping angle for 20.7 GHz. In Table 1.3, calculations for the same narrow-beam antenna are made at DSN frequencies 20.7, 32, and 8.45 GHz. The reason that the brightness temperatures are much higher at 20.7 GHz than at 32 GHz is that 20.7 GHz is in the region of high water vapor absorption. Table 1.3 Predicted Tipping Curve Errors for High-Gain Parabolic Antennas Flat Earth M Number of Atmospheres

Main Beam Pointing Angle ␪ , Degree

1.5 2 3 4

48.19 60.00 70.53 75.52

1.5 2 3 4 1.5 2 3 4

[(Tb )C − (Tb )F ] , K ⌬Tb , K

⌬Tb /(M − 1), K

Tatm (0), K

Error, K

(a) Ku-band High-Gain Parabolic Antenna at 20.7 GHz 25.272 −0.059 7.456 14.913 32.509 −0.117 14.693 14.693 46.340 −0.227 28.524 14.262 59.332 −0.331 41.517 13.839

15.71 15.71 15.71 15.71

−0.80 −1.02 −1.45 −1.87

48.19 60.00 70.53 75.52

(b) Ka-band High-Gain Parabolic Antenna at 32 GHz 15.495 −0.005 4.415 8.831 19.827 −0.015 8.747 8.747 28.240 −0.058 17.160 8.580 36.315 −0.140 25.235 8.412

9.15 9.15 9.15 9.15

−0.32 −0.40 −0.57 −0.74

48.19 60.00 70.53 75.52

(c) X-band High-Gain Parabolic Antenna at 8.45 GHz 5.925 −0.001 1.135 2.270 7.054 −0.004 2.264 2.264 9.290 −0.016 4.500 2.250 11.494 −0.039 6.704 2.235

2.31 2.31 2.31 2.31

−0.04 −0.05 −0.06 −0.08

Tb , K

Notes: 1. The symbols (Tb )C and (Tb )F refer to brightness temperatures for the curved and flat atmosphere models, respectively, and their values were calculated from the use of (1.38). The differences between the sky brightness temperatures for curved and flat atmospheres are small for tipping angles up to four atmospheres. These differences are not related to the errors shown in the last column. 2. ⌬Tb = [Tb (␪ ) − Tb (0)] for curved atmosphere.


33

The last column of Table 1.3 shows the errors that will result if the described tipping curve method is used to find Tatm (0) for this narrowbeam antenna. The reason why errors in the last column of Table 1.3 are larger than expected is because it is common practice to assume that Tatm (␪ ) ≈ Tzen /cos ␪ and if values of Tb (␪ ) are calculated based upon this assumption and then used in Table 1.3, the errors will erroneously be negligibly small. As will be shown in Section 1.1.5.5, this assumption is invalid and will lead to misleading and erroneous results. This author and others have attempted to use the described Tipping Curve Method in the past to obtain Tatm (0) at 8.45 GHz and 32 GHz not knowing that at 32 GHz, the errors could be as large as those shown in Tables 1.2 and 1.3. This Tipping Curve Method as described above is not used by Keihm [9] to find Tzen . In the Keihm Method, the AWVR antenna is scanned at tipping angles of 0, 48.2, and 60 deg corresponding to M = 1, 1.5, and 2 air masses. Then an iterative process is performed on measured data from a Dicke Radiometer and a theoretical expression involving a flat atmosphere model, atmospheric opacity, and radiometer gain. It is expected that there will be negligible differences whether the Keihm Method as described in [9] uses the flat- or curved-atmosphere model. Morabito [17] uses a different method than the described Tipping Curve Method to find Tatm (0). He uses an iteration method similar to the Keihm Method, but solves for Tatm (0) from ⌬Top (␪ ) measured data and a theoretical expression modeled for a Beam Waveguide (BWG) antenna system. For a BWG antenna system, it is difficult to accurately account for noise temperature changes occurring on the main reflector (spillover and strut scatter) and unknown noise temperature changes occurring in the BWG path between focal points f1 and f3 (see Figure 1.28) as a function of tipping angles. A new method is proposed by Otoshi for determining zenith atmospheric noise temperature from measurements of Top (␪ ) tipping curve data. This method is intended for use with offset-fed reflector antennas similar to the AWVR antenna or for Cassegrain antennas having narrow beamwidth, low spillover, and low strut scatter. For convenience (1.38) is repeated and renumbered here and for simplification of notation, let Tb, sky (␪ ) = Tb (␪ ) so that −1

Tb (␪ ) = Tatm (␪ ) + L atm (␪ ) Tcb

(1.75)

Tatm (␪ ) = Tp, atm 冋1 − L atm (␪ )册

(1.76)

where from (1.35) −1

and from (1.34) −1

冉

L atm (␪ ) = 1 −

Tzen Tp, atm

冊

p(␪ )

(1.77)

and as a reminder, Tzen = Tatm (0) and all terms in (1.75)–(1.77) have been previously defined in Section 1.1.2.2. The expression of p (␪ ) for a curved atmosphere was given in (1.36).

34

Introductory Topics

Let it be assumed that ⌬Top (␪ ) = ⌬Tb (␪ ) for narrow beam antennas so that the substitution of (1.76) into (1.75) and further substitutions into ⌬Top (␪ ) = ⌬Tb (␪ ) = Tb (␪ ) − Tb (0) give ⌬Top (␪ ) = 再Tp, atm 冋1 − L atm (␪ )册 + Tcb L atm (␪ )冎 − 再Tp, atm 冋1 − L atm (0)册 + Tcb L atm (0)冎 (1.78) −1

−1

−1

−1

Collection of terms results in ⌬Top (␪ ) = (Tp, atm − Tcb ) 冋L atm (0) − L atm (␪ )册 −1

−1

(1.79)

and further substitutions of (1.77) and p (0) = 1 into (1.79) give ⌬Top (␪ ) = (Tp, atm − Tcb ) [(1 − Tzen /Tp, atm ) − (1 − Tzen /Tp, atm ) p(␪ ) ] (1.80) The expression given by (1.80) is the new proposed Tipping Curve Equation for a curved atmosphere. The values of Tp, atm and Tcb are known constants (to be discussed later) so that the only unknown on the right-hand side of (1.80) is Tzen . The only variables are the tipping angle ␪ and the measured values of ⌬Top (␪ ). A nonlinear best-fit computer program can now be used to solve for Tzen in (1.80) by performing a best fit of the measured data on the left hand side of (1.80) to the equation on the right hand side. Otoshi has successfully used a public domain nonlinear least square fit program [19] and experimental data to find magnitudes and locations of multiple discontinuities in a coaxial transmission line. It is suggested that for this proposed method, Top (␪ ) be measured only at air masses p (␪ ) = 1.0, 1.5, 2.0, and 2.36 corresponding to tipping angles 0, 48.21, 60.03, and 65 degrees as calculated from (1.37) for a curved atmosphere. For best accuracy, measurements should not be made for p (␪ ) = 3.0 or a tipping angle of 70.53 degrees because in practice, the noise pickup from ground can become significant. This method is proposed for use only for narrow-beam antennas where TA (␪ ) ≈ Tb, sky (␪ ) up to at least a 65-degree tipping angle. In (1.80), the values of the effective Tcb can be obtained from Table 1.1 for DSN frequencies. The value of Tp, atm can be calculated from use of (1.39) for an average clear atmosphere at Goldstone, California. It was found that the solution for Tzen by the proposed Tipping Curve Method is insensitive to a ±5K tolerance on the value of Tp, atm provided that it is the value that applies to the weather conditions that existed when measurements of Top were made in the field. For the proposed tipping curve method, it is desirable to use more accurate real-time values of Tp, atm , taking into account the prevailing weather conditions. In the past circa 1990, real time values of Tp, atm were calculated from use of a BASIC program named SDSATM7M.BAS whose Method 1 was originally written


35

by S. Slobin of JPL. This program was later modified by T. Otoshi to include a more accurate Method 2 that uses radiative transfer equations. All of the program steps for Method 2 can be found in the Appendix of a JPL Document [13] that can be obtained by writing to the JPL Library. The inputs to this program are frequency, station height above sea level, surface level air temperature, barometric pressure, and relative humidity. With the exception of frequency, these quantities are routinely measured every 10 minutes at the deep space stations and stored onto a computer disc for later retrieval by an experimenter making noise temperature measurements at a particular deep space station. The zenith atmosphere above Earth is modeled as consisting of 300 layers each having 0.1-km thickness to give a total height of 30 km. Each layer has a physical temperature and pressure profile as a function of height above the station location above sea level. From the use of the input data, the program proceeds to compute water vapor and oxygen content in each individual atmospheric layer for the frequency of interest. In Method 2, noise contribution and loss of each layer in decibels is then computed and properly summed according to radiative transfer equations to give the total noise temperature Tzen and the total loss L atm in decibels for the entire atmosphere in the zenith direction. The loss L atm in decibels is converted to a power loss ratio L atm ≥ 1 and used in the expression of Tp, atm = Tzen L atm /(L atm − 1), which was derived from manipulation of (1.76). The outputs of the program are calculated values of Tzen , L atm in decibels, and Tp, atm . The calculated values of Tzen from the program are not accurate above 8.45 GHz, and, therefore, should not be used except to make comparisons with measured values. However, calculated values of Tp, atm are sufficiently accurate for use in (1.80) to enable accurate values of Tzen to be determined for frequencies as high as 32 GHz for clear sky and a variety of surface level weather conditions. 1.1.5.5 Approximate Formula for Brightness Temperature

In the past years, well-known approximate formulas have been used for atmosphereand brightness-temperatures without knowing their origins. It is the purpose here to derive these approximate formulas from the curved atmosphere expressions and show the limits of their accuracies. For convenience, (1.77) will be repeated here as

冉

−1

L atm (␪ ) = 1 −

Tzen Tp, atm

冊

p(␪ )

When Tzen /Tp, atm Ⰶ 1, the binomial expansion can be applied to derive the approximate relationship

冋

册

1 L atm (␪ )

冋

= 1− approx

p (␪ ) Tzen Tp, atm

册

(1.81)

Then substitution of p (␪ ) = 1/cos ␪ for a flat atmosphere into (1.81) results in

冋

册

1 L atm (␪ )

冋

= 1− F, approx

Tzen Tp, atm cos ␪

册

(1.82)

36

Introductory Topics

where subscript F is used to denote the flat atmosphere model. Finally, the substitution of (1.82) into (1.76) gives the commonly used approximate expression of [Tatm (␪ )]F, approx =

Tzen cos ␪

(1.83)

and substitutions of (1.82) and (1.83) into (1.75), and letting [Tb (␪ )]approx = [Tb (␪ )]F, approx for the convenience of simplifying symbols, the approximate sky brightness temperature formula is obtained as [Tb (␪ )]approx =

冉

冊

Tzen Tzen + 1− Tcb cos ␪ Tp, atm cos ␪

(1.84)

Then assuming that the change in the Tcb term in the following expression will be negligibly small and can be omitted [⌬Tb (␪ )]approx = [Tb (␪ )]approx − [Tb (0)]approx ≈ Tzen [1/cos ␪ − 1]

(1.85)

It follows that [⌬Tb (␪ )]approx Tzen [1/cos ␪ − 1] = = Tzen M−1 M−1

for ␪ ≠ 0

(1.86)

if a flat atmosphere model is assumed, and one substitutes M = 1/cos ␪ for the number of atmospheres as a function of tipping angle. However, this result is erroneous and misleading. If one does not perform calculations from both the approximate formula given by (1.84) and the exact curved atmosphere formula given by (1.75)–(1.77) and compare the results, one would not know that the approximate formula becomes inaccurate when (Tzen /Tp, atm )/cos ␪ becomes greater than 0.05. The values of Tb (␪ ) already given in Table 1.3 are correct, and those from the approximate formula would give erroneous results if used. For example, at 20.7 GHz the differences of Tb (␪ ) − [Tb (␪ )]approx are as large as −0.3K, −0.9K, −2.7K, and −5.2K at the 1.5, 2, 3, and 4 atmosphere tipping angles, respectively. The differences at 32 GHz are as large as −0.1K, −0.3K, −1.0K, and −2.0K at the 1.5, 2, 3, and 4 atmosphere tipping angles, respectively. At 8.45 GHz the differences are smaller, but are nonnegligible at the 3 and 4 atmosphere tipping angles. 1.1.5.6 Concluding Remarks

In conclusion, it has been shown that the current Tipping Curve Method described in this section should not be used with high gain antennas at 20.7 GHz or 32 GHz, but that a proposed Otoshi method be used instead to find Tzen from measured Top (␪ ) tipping curve data. The proposed method can be expanded to include antennas having significant strut and spillover noise temperatures by adding a term ⌬Tant (␪ ) to the right hand side of (1.80) and preceding equations. This term can be modeled with a second-order polynomial equation that is a function of tipping angle similar to that given in [17]. A nonlinear least fit squares program can be used to get best-fit values of the polynomial coefficients and Tzen simultaneously. More data points can be added by measuring Top (␪ ) at two or three more tipping

1.2 Cosmic Background Noise Temperature

37

angles between 50 and 65 degrees. This new proposed method should not be used with DSN horns because of significant noise pickup from the ground (see Figures 1.19 and 1.20). An approximate formula given in 1.1.5.5 to calculate atmospheric noise temperatures as functions of tipping angles, should not be used as it can lead to erroneous results.

1.2 Cosmic Background Noise Temperature 1.2.1 Introduction

It is now generally accepted that the cosmic background radiation over the microwave region is the remnant of an intense radiation associated with the initial expansion of the universe. An accurate measurement of the cosmic background radiation (CBR) at 2.297 GHz was made by Otoshi and Stelzried [20] and reported to be 2.66K ± 0.77K (3␴ ). Calibration was done at this space communication frequency because cosmic background noise temperature is an important consideration in the expected signal-to-noise ratios for spacecraft and ground receiving systems. 1.2.2 Calibration Equation

Table 1.4 defines the principal symbols used in this section. For a low-noise horn pointed in the zenith direction, the calibration equation to measure the cosmic background noise temperature is TCB = L ATM [(TA )OBS − (TA )ATM − (TA )FG − ⌬TA ] − (TA )GAL

(1.87)

where for an antenna such as the dual-mode horn having low-level backlobes

冋

L ATM ⯝ 1 −

(TA )ATM (TP )ATM

册

−1

(TA )OBS = L WG (TiA − TWG )

(1.88) (1.89)

= L WG TiA − (L WG − 1) (TP )WG ␲ /2

(TA )ATM

1 = 2

冕

TATM (␪ ) G (␪ ) sin ␪ d␪

(1.90)

0

␲

(TA )FG

1 = 2

冕

[1 − R FG (␲ − ␪ )] (TP )G G (␪ ) sin ␪ d␪

␲ /2 ␲

1 + 2

冕

␲ /2

R FG (␲ − ␪ ) TATM (␲ − ␪ ) G (␪ ) sin ␪ d␪

(1.91)

38

Introductory Topics Table 1.4 Definition of Terms G(␪ )

Antenna gain function

L ATM

Effective atmospheric power loss factor (> 1), ratio

L WG

Dissipative power loss factor (> 1) of the waveguide between the antenna aperture and receiver input, ratio

R FG (␲ − ␪ )

Effective power reflection coefficient of flat ground for (␲ − ␪ )

sx

Calculated standard error of the mean due to dispersion of the data points

␴

Standard deviation due to all known error sources

(TA )ATM

Antenna noise temperature component defined at the antenna aperture and attributed to the Earth’s atmosphere, K

(TA )FG

Antenna noise temperature component defined at the antenna aperture and attributed to a flat ground environment, K

(TA )GAL

Antenna noise temperature component as defined outside the Earth’s atmosphere and attributed to the galaxy, K

(TA )OBS

Observed or calibrated noise temperature of the antenna as defined at the antenna aperture, K

TATM (␪ )

Brightness temperature function of the Earth’s atmosphere, K

TCB

Brightness temperature of the cosmic background (assumed to be independent of ␪ ), K

TGAL (␪ , ␾ )

Brightness temperature of the galaxy as defined outside the Earth’s atmosphere, K

TiA

Calibrated noise temperature of the antenna input termination as defined at the receiver input, K

(TP )ATM

Mean physical temperature of the Earth’s atmosphere, K

(TP )G

Mean physical temperature of the ground environment, K

(TP )WG

Physical temperature of the waveguide between the antenna aperture and receiver input, K

TWG

Noise temperature due to losses of the waveguide between the antenna aperture and receiver input, K

␪ ␾

Zenith angle Azimuth angle 2␲ ␲ /2

(TA )GAL

1 ⯝ 4␲

冕冕 0

TGAL (␪ , ␾ ) G (␪ ) sin ␪ d␪ d␾

(1.92)

0

and ⌬TA is a correction term to account for a nonflat ground environment. It can be seen from (1.87) that the calibration of the cosmic background temperature requires knowledge or accurate evaluation of the individual noise temperature components that contributed to the observed antenna temperature. The critical parameters appearing in (1.89) to (1.91), such as TiA , L WG , (TP )WG , G (␪ ), and TATM (␪ ), are determined from experimentally obtained data. Other parameters, such as (TP )ATM , (TP )G , and R FG (␲ − ␪ ), can also be experimentally determined but are less critical. An error analysis indicates that the less critical parameters can be estimated or theoretically calculated to sufficiently good accuracy. The technique of measurement and evaluation of parameters is described in [20], and, therefore, this section will not repeat what is already described in detail there.

1.2 Cosmic Background Noise Temperature

39

1.2.3 Experimental Results

Experimental results of specific runs showing measured values of contributions of (1.89) through (1.92) are given in a table in [20] and will not be repeated here. The cosmic background radiation at 2.297 GHz was measured to be 2.66K ± 0.77K (3␴ ). The main contributions to this measured value and associated calibration errors are shown in Table 1.5. This table indicates that increased accuracy in the measurement of cosmic radiation could have resulted from: (1) the use of a more accurately calibrated cryogenic termination, (2) better calibrations of the antenna transmission line loss, (3) reduction of the antenna and maser mismatches, and (4) a more accurate determination of the atmospheric noise temperature contribution. 1.2.4 Commentary

A 1995 tabulation of cosmic microwave radiation values measured at different microwave frequencies by various experimenters was made by Partridge [21]. In a private correspondence to this author in September 1996, Partridge stated that the 1975 Otoshi–Stelzried CBR measurement at 2.297 GHz was especially significant because of the difficulty in making accurate measurements of the galactic contributions at the S-band and lower frequencies. In [21] Partridge goes further and suggests that the atmospheric contribution stated by Otoshi and Stelzried was possibly too high by about 0.1K. The atmospheric contribution was not based on an actual measurement, but was based on an atmospheric model described by Potter [22] and measured weather data. This model, which was the best available at the time, used ground surface

Table 1.5 Tabulation of Calibration Errors Calibrated Noise Temperature

Mean Value,a K

(TA )ATM

2.27

Antenna gain function Atmospheric brightness temperature

Negligible +0.20 −0.15

(TA )FG

0.04

Ground brightness temperature

±0.02

⌬TA

0.02

Horizon profile correction inaccuracy

±0.01

(TA )OBS

5.29

Helium load thermal reference temperature Ambient load thermal reference temperature Waveguide physical temperature Line loss calibrations: Cryogenic load line Antenna line Y-factor ratio errors due to inaccuracy of IF attenuator Mismatch errors

±0.50

Sources of Error

Peak Uncertainty on Calibrated Noise Temperature, K

Negligible Negligible ±0.07 ±0.34 ±0.10 +0.00/−0.40

(TA )GAL

0.32

Spectral index uncertainty

±0.13

TCB

2.66

Peak RSS error on TCB

±0.77

a

Mean value is shown for informational purposes only

40

Introductory Topics

weather parameters of ground surface temperature, barometric pressure, and relative humidity. In 1967, when the cosmic background measurement was made, a WVR was not available at JPL. As described in Section 1.1.5.4, a tipping curve method is sometimes used to find the atmospheric noise temperature at zenith. However, the S-band Cassegrain antenna ultra cone, into which the S-band horn was mounted, was too large to tip to perform a tipping curve measurement of the atmosphere on the roof of JPL’s telecommunications building. Partridge’s comment was not a criticism but rather a helpful suggestion. His analysis of the data enabled arriving at an atmospheric noise temperature contribution of 2.17K rather than the 2.27K value used by Otoshi and Stelzried. Partridge also wrote that Otoshi and Stelzried probably underestimated the galactic contribution at low Galactic altitudes by 0.2–0.3K. If the Partridge value of atmosphere is used, and dropping the two runs with (TA )GAL > 0.4K in [20] as he suggests, then the Otoshi–Stelzried measured CBR noise temperature would become a corrected value of 2.76 ± 0.30 (1␴ ) K. This new value remains in excellent agreement with measured values of other experimenters at other microwave frequencies.

1.3 Portable Microwave Test Packages 1.3.1 Introduction

A prototype 34-m diameter beam waveguide (BWG) antenna has been built in 1990 at the NASA/JPL Goldstone, California, tracking facility. A unique experimental technique was used to evaluate this antenna. The methodology involved the use of portable test packages transported to different focal-point locations of the BWG system. Focal points f1, f2, and f3 are depicted in Figure 1.21. Focal point f1 is the Cassegrain focal point near the main reflector vertex. An intermediate focal point f2 lies above the azimuth track; the focal point f3 is the final BWG focal point, located in a subterranean pedestal room. Degradations caused by the BWG system mirrors and shrouds were determined from comparisons made of values measured at the different focal points. The idea of using portable test packages for the purposes of evaluating system performances at f1, f2, and f3 was conceived by Bathker of JPL. The fabrication designs and test package evaluations in the field were done primarily by Katow and Otoshi of JPL, respectively. The complete experimental program used three different microwave test packages and tested the antenna at three frequency bands: X-band (8.45 GHz), Ku-band (12 GHz), and Ka-band (32 GHz). With the exception of holography data obtained at 12 GHz, all microwave performance data on the BWG antenna were based on noise-temperature measurement data obtained through the use of the test packages and a total-power radiometer system. This section will present brief descriptions of the test packages, test procedures, installations, noise-temperature measurement method, and a summary of operating system-noise temperatures measured at various focal points. The material presented here was extracted from an article by Otoshi et al. [23]. More detailed descriptions of the various test packages, tabulated data and plots for operating system-noise temperatures for different observation periods, and radiometer system performance may be found in [24–28]. The results of X- and Ka-band antenna efficiency tests

1.3 Portable Microwave Test Packages

Figure 1.21

41

View of the BWG antenna in the centerline mode, showing focal points [24]. (Courtesy NASA/JPL-Caltech.)

at f1 and f3 are presented in [29]. Ku-band holography tests at f1 were successfully performed, and the results are presented in [30].

1.3.2 Test-Package Descriptions

Figure 1.22 is a photograph of the X-, Ku-, and Ka-band (partially assembled) test packages under test at JPL before shipment to Deep Space Station 13 (DSS 13). In their final configurations, both the X- and Ka-band test packages contain many of the familiar Cassegrain cone components such as a 22-dBi horn, polarizer, roundto-rectangular transition, waveguide switch, waveguide ambient load, directional coupler, cryogenically cooled low-noise amplifier, noise diode assembly, and downconverter (receiver). Figure 1.23 is a block diagram of the X-band test package. The block diagram for the Ka-band test package is nearly identical, with the exceptions that: (1) the Ka-band test package does not have the two circular rotary joints and (2) the Ka-band downconverter local-oscillator frequency is derived from a 32-GHz Gunn oscillator.

42

Introductory Topics

Figure 1.22

X-band test package under test at JPL. The Ku- and Ka-band (partially assembled) test packages are also shown. (Courtesy NASA/JPL-Caltech.)

After amplifications by the high-electron-mobility transistors (HEMTs), the X- and Ka-band microwave signals were downconverted to, respectively, 350-MHz and 60-MHz IF and sent via coaxial cable to a total-power radiometer system located in the pedestal room. Block diagrams of the downconverter and noise-box assemblies for the X- and Ka-band test packages are given, respectively, in [24–26]. 1.3.3 Test Configurations and Test Procedure

Figures 1.24 and 1.25, respectively, show the mounting structure (removable after test) and the X-band test package installed at the Cassegrain focal point f1. Figure 1.26 shows the X-band test package installed on a universal three-axis adjustable mounting table at the f3 pedestal-room location. The mounting structure at f1 and mounting table at f3 allow any of the three test packages to be easily interchanged. At f1, the test packages are in a 29-dBi horn configuration, while at f3, the X- and Ka-band test packages are in 22-dBi and 23-dBi horn configurations, respectively. To test the BWG antenna at f1 and f3, it was required that each test package be convertible between 22-dBi (or 23-dBi) and 29-dBi horn configurations. The conversions were accomplished through the use of horn extensions of the same taper going from the 22- (or 23-) to the 29-dBi horn aperture diameters appropriate for the horn design frequencies. The mounting assemblies (Figures 1.25 and 1.26) were designed such that, upon installation of a particular test package at the desired antenna focal-point location, the phase center of the horn coincided with the focal


Figure 1.23

43

The X-band test package system [24]. (Courtesy NASA/JPL-Caltech.)

point. Where necessary, any deviation of phase center from the focal-point location was compensated through adjustments of the subreflector Z-focus position for f1 measurements and adjustments of the test-package mounting table (in the pedestal room) for f3 measurements. The test procedure required clear sky reference measurements first with the test package located on the ground with the horn pointed at zenith. Noise-temperature and antenna-efficiency measurements were then made as functions of antenna pointing angles with the appropriate portable test package installed at the Cassegrain focal point f1. The test package was then transported to other focal points of the BWG mirror system, and measurements were again made. Degradations caused by the BWG mirror system were determined by taking the differences of

44

Introductory Topics

Figure 1.24

Overall view of the mounting structure and the X-band test package at f1 in the 29-dBi horn configuration [24]. (Courtesy NASA/JPL-Caltech.)

operating noise temperature and antenna gain1 values measured at the various focal points. 1.3.4 Noise-Temperature Measurement Method

Figure 1.27 shows the block diagram of the automated radiometer system used with the test packages for making noise temperature measurements. Measurements of the IF power output from the downconverter are made on an HP 436A power meter. The power-meter readings are sent to an IBM-AT computer that averages 15 readings per second and converts the values into noise temperatures. Best accuracy is achieved if the system operates well below the saturation point in the linear region. Only two points are then needed to establish a power-reading versus noise-temperature linear calibration curve. The first point corresponds to the power1.

Antenna gain is determined from the efficiency, aperture area, and frequency, and is expressed in dB.


45

Figure 1.25

Partial view of the X-band 29-dBi horn test package and mounting structure installed at the Cassegrain focal point f1 [25]. (Courtesy NASA/JPL-Caltech.)

Figure 1.26

X-band 22-dBi horn test package and mounting table installed in the pedestal room focal point f3 [25]. (Courtesy NASA/JPL-Caltech.)

46

Introductory Topics

Figure 1.27

The interface between the X- or Ka-band test package and the total-power radiometer system [24]. (Courtesy NASA/JPL-Caltech.)

meter reading when the power meter is zeroed, and the second required point corresponds to the power-meter reading when the waveguide switch is in the ambient-load position. Operating noise temperatures are computed from equations found in [31]. The method is based on knowing the ambient load physical temperature and the effective noise temperature of the HEMT (from lab or field tests). It is assumed that the HEMT noise temperature does not change with time or testpackage motions. The basis of the real-time corrections for receiver system gain changes is precise knowledge of the current ambient-load physical temperature. The ambient-load physical temperature is measured at ±0.01°C resolution through the aid of a digital readout thermometer embedded in the ambient-load reference termination. Nonlinearity of the system is determined from power-meter readings when the noise diode signal is injected into the HEMT and the switch is first in the ‘‘antenna’’ position and then in the ‘‘ambient-load’’ position. The test packages are designed to have nonlinearity errors of less than 1%. Nonlinearity errors are kept small by use of appropriate padding, filters, and amplifiers and mixers that do not saturate at the expected input levels. All measurements and data processing are performed automatically by the computer. The system is recalibrated periodically or instantaneously as desired by the experimenter. Correction factors for system nonlinearity [32] and gain changes are computed from the last system calibration. An option for displaying corrected noise temperatures in real time is available. Most options are executed by means of a single keystroke command from the user.


47

1.3.5 Noise-Temperature Measurement Results

Noise-temperature symbols are used in an equation and the tables that follow. For the reader’s convenience, the symbols are defined in Table 1.6. Measurements with the test packages on the ground and at various focal points of the BWG antenna covered a span of several months. Tables 1.7 and 1.8 show the final grand averages of zenith operating system-noise temperatures at X-band and Ka-band, respectively. Corrections have been made for weather and waveguide ambient temperatures. All values have been normalized for Goldstone average clear X- and Ka-band atmospheres and a waveguide ambient temperature of 20°C. More details on the methodology for data reduction may be found in [25, 27]. When the test package is on the ground, the general expression for the operating system-noise temperature is ′ /(L atm L wg ) + Tatm /L wg + Twg + Themt + Tfup Top = Tcb

(1.93)

where the symbols are defined in Table 1.6. Under standard conditions at 8.45 GHz, the component values are ′ Tcb = 2.5K, Tatm = 2.17K, Twg = 4.69K, Themt = 13K, and Tfup = 0.4K; L atm = 1.00814 (corresponding to 0.0352 dB) and L wg = 1.0163 (corresponding to 0.07 dB). Substitutions of the values into (1.93) result in a predicted Top of 22.7K, which agrees with the measured ground value of 22.7K shown in Table 1.7. An estimate of the one standard deviation of the tabulated measured value for each configuration shown in Table 1.7 is ±0.3K. Table 1.6 Definitions of Symbols and Abbreviations for Noise Temperature Studies Symbol

Definition

T cb ′

Effective noise temperature contribution to Top from the cosmic background radiation, K. This value is a function of frequency and will differ from the actual cosmic background noise temperature of 2.7K. T c′b = Tcb

冋

册

x , where x = hf /(kTcb ) exp (x) − 1

Tcb

Cosmic background radiation noise temperature, nominally 2.7K

h

Planck’s constant

f

Frequency, Hz

k

Boltzmann constant

Tatm

Atmosphere noise temperature, K

Twg

Noise temperature due to waveguide loss between the horn aperture and the input flange of the HEMT, K

Themt

Effective noise temperature of the HEMT as defined at the input flange of the HEMT, K

Tfup

Effective noise temperature of the follow-up receiver (down-converter + cables + power meter, and so forth) as defined at the input flange of the HEMT, K

Top

Operating system-noise temperature as defined at the input flange of the HEMT, K

Ts

Source noise temperature, K

L wg

Loss factor for waveguide between the horn aperture and the input flange of the HEMT, power ratio > 1

L atm

Loss factor of the atmosphere, power ratio > 1

48

Introductory Topics Table 1.7 Summary of X-Band Zenith Operating System-Noise Temperatures at DSS 13 from June 10, 1990–February 2, 1991 Configuration

Observation Dates

Ground

06/10/90, 01/21/91, 01/26/91

Grand Average a Top , K

Peak Deviation from Grand Average, K

22.7

+0.3 −0.3

f1

10/04/90

25.9

—

f2

01/12/91, 01/12/91 (two different time periods, same day)

30.1

+0.2 −0.3

f3

11/06/90, 11/09/90

34.2

+0.1 −0.2

After Mirrors and Ellipsoid Realigned on December 18, 1990 f3

01/31/91, 02/02/91

34.8

a

+0.1 −0.1

For each observation period, the measured Top was normalized to a Goldstone average clear zenith X-band atmosphere of 2.17K for DSS 13 and an X-band test package waveguide noise temperature Twg = 4.69K as based on a standard waveguide physical temperature of 20°C. (See [24] for methodology.)

Under standard conditions at 32.0 GHz, the component values are ′ = 2.0K, Tatm = 7.02K, Twg = 17.67K, Themt = 56.6K, and Tfup = 1.8K; L atm = Tcb 1.02683 (corresponding to 0.115 dB) and L wg = 1.06414 (corresponding to 0.27 dB). Substitutions of the values into (1.93) result in a predicted Top of 84.5K, which agrees closely with the measured ground value of 84.7K shown in Table 1.8. An estimate of the one standard deviation of the tabulated measured value for each configuration shown in Table 1.8 is ±0.7K. One of the primary goals of the experimental project was to determine degradations caused by the BWG mirror system. The results given in Table 1.9 show that

Table 1.8 Summary of Ka-Band Zenith Operating System-Noise Temperatures at DSS 13 from October 12, 1990–January 31, 1991 Grand Average a Top , K

Peak Deviation from Grand Average, K

Configuration

Observation Dates

Ground

10/12/90, 11/09/90, 01/19/91, 01/31/91

84.7

+1.6 −1.7

f1

10/13/90, 10/14/90, 01/11/91

91.8

+0.4 −0.6

f2

01/16/91, 01/17/91

97.0

+0.4 −0.4

f3

11/10/90, 12/18/90

102.4

+0.1 −0.0

After Mirrors and Ellipsoid Realigned on December 18, 1990 f3 a

01/23/91, 01/25/91, 01/30/91

98.6b

+0.8 −0.7

For each observation period, the measured Top was normalized to a Goldstone average clear zenith Ka-band atmosphere of 7.02K for DSS 13 and a Ka-band test package waveguide noise temperature Twg = 17.67K as based on a standard waveguide physical temperature of 20°C. (See [26] for methodology.) b This number cannot be compared with the above f2 value. It is probable that the new f2 value is also lower after the mirror realignment, but a measurement was not made.


49

Table 1.9 Differential Zenith Operating Noise Temperatures (from Values Given in Tables 1.7 and 1.8) Frequency, GHz

System Configurations

Differential Values Predict, K Measured, K

Measured-Pred, K

8.450 8.450 32.0 32.0

f1-ground f3–f1 f1–ground f3–f1

3.3 9.4 3.7 7.4

−0.1 −0.5 3.4 −0.6

3.2 8.9 7.1 6.8

this goal was achieved. The difference between f1 and ground operating systemnoise temperatures reveals the amount of degradation caused by spillover of the subreflector and main reflector, scattering from the tripod legs, and leakage through gaps between panels and perforations in the main reflector surfaces. The difference between f2 and f1 operating system-noise temperatures provides information on the upper four mirrors (two flat mirrors and two paraboloids), while the difference between f3 and f1 provides data on the upper four mirrors, the ellipsoid, and a flat mirror above the feed horn. The predicted values shown in Table 1.9 were extracted from [33]. The reason for the large difference between measured and predicted ‘‘f1-ground’’ values at Ka-band is discussed in [33]. Table 1.10 lists the microwave performance characteristics of the X- and Ka-band test packages. The characteristics are based on error analyses and several months of field data [24–27]. The test packages performed better than expected with regard to the linearity and short- and long-term gain stability. All test packages

Table 1.10 X- and Ka-Band Test-Package Performance Characteristics Parameter

X-Band

Ka-Band

Receive polarization

RCP, LCP or fixed linear

RCP or LCP (if reconfigured)

Receive frequencies

8.4–8.5 GHz (predetermined by inherited DSN downconverter)

31.865–32.085 GHz from lab tests

Top on ground at DSS-13, zenith clear sky

< 23K

85K actuala

Measured Top resolution for the above Top value, ␶ = 1s 100-MHz BW

< 0.02K

< 0.06K

Gain stability over 0 to 40°C ambient temperature range

< 0.3 dB p-p, < 0.1 dB typical, < 0.05 dB/h (Downconverter in an ovenized box)

< 0.2 dB p-p, < 0.05 dB/h Downconverter has thermoelectric temperature control

Total calibrated nonlinearity error

< 1%

< 2%

Radio source temp (Ts ) measurement accuracy (a delta measurement)

± [0.02 + 0.010 × Ts ]K for 2 < Ts < 10K

± [0.06 + 0.020 × Ts ]K for 2 < Ts < 10K

Overall Top measurement accuracy,b K

< 0.4K p-p for 10 < Top < 150K

< 0.8K p-p for 10 < Top < 150K

a

A major part of the total is due to 56.6K from the HEMT and 17.7K from waveguide losses. Based on error analysis, calibration errors, and estimated mismatch errors.

b

50

Introductory Topics

were designed to be mechanically stable, and, in the field, their stabilities were verified by the fact that the microwave performance characteristics were maintained whenever any of the test packages was mounted at f1 and the antenna was tipped from zenith to the 5-degree elevation angle. The test packages proved to be rugged in hostile environments and continued to work well even after repeated moves between f1, f2, f3, and the ground. The outstanding electrical and mechanical characteristics of the X- and Ka-band test packages (and radiometer system) enabled the packages to be used for BWG system diagnostic purposes as well as for efficiency [29], pointing-error, subreflector defocusing-curve, and tipping-curve measurements. Tipping-curve and subreflector test data for different focal points of the BWG antenna at X- and Ka-band may be found in [25, 27].

1.3.6 Concluding Remarks

The goal of measuring BWG systems’ degradation through the use of portable test packages has been achieved at X- and Ka-band. Tests using a Ku-band (12-GHz) test package for holography purposes were similarly successful [30]. From the tests results presented in this section, it can be stated that the test packages and radiometer system are state-of-the-art antenna performance evaluation instruments. To the author’s knowledge, the test-package method is the first known experimental method for determining the degradations caused by the BWG system of a large antenna.

1.4 Dichroic Plate in a Beam-Waveguide Antenna System 1.4.1 Introduction

A 34-m-diameter antenna, built for NASA/JPL in 1990 at Goldstone, California, utilizes a beam-waveguide (BWG) design as shown in Figure 1.28. This figure differs from the one shown previously in Figure 1.21 in that the bypass mirror on the dish surface was removed. The BWG antenna performances at three different focal points f1, f2, and f3 (circa 1990) were reported in [33] and in Section 1.3. The ellipsoid in the subterranean room has since been made rotatable so that numerous feed systems can be installed in a circular perimeter around the ellipsoid and operated from their own individual f3 positions. One of the feed systems installed at f3 is the S/X system that allows simultaneous reception of S-band (2.295 GHz) and X-band (8.45 GHz). As depicted in Figure 1.29, a dichroic plate is installed to reflect S-band, but pass X-band frequencies. This dichroic reflector will be referred to as the S/X dichroic plate. When the S/X dichroic plate was first installed at one of the new f3 positions, the measured increase in Top was 18K compared to an expected value of about 2K. After considerable diagnostic work, the cause of the high increase in Top was found. It is the purpose of this section to document what was learned and the steps taken to bring the Top close to the expected value. It is important to document this information so that similar problems can be avoided in the future.

1.4 Dichroic Plate in a Beam-Waveguide Antenna System

Figure 1.28

51

BWG antenna in the centerline mode showing focal points f1, f2, and f3. Bypass mode removed. (Courtesy NASA/JPL-Caltech.)

The first part of this section will provide a background on the first dichroic plate developed for the DSN. Theoretical analysis will then be presented to show how dichroic plate noise temperature is calculated from: (1) horn patterns, (2) insertion loss of the plate, and (3) resistive losses of the plate surfaces and waveguide holes. Then it is shown how to calculate the effective noise temperature as a function of bandwidth. It is shown how the noise temperature of the dichroic plate can dramatically increase (for some situations) if used in a system that has a bandwidth much wider than the design bandwidth of the dichroic plate. 1.4.2 Background

The first DSN dichroic plate, developed by Potter [34], was based on the highpass filter characteristics of perforated plates used as antenna reflector surface panels. Perforated plates are described in Chapter 2. Figure 1.30 shows the geometry for a DSN dichroic plate (as well as a perforated plate) illuminated by a plane wave. The holes on adjacent rows are staggered such that they form an equilateral

52

Introductory Topics

Figure 1.29

X-band feed-horn and dichroic plate of the S/X-band system in the pedestal room.

Figure 1.30

Dichroic plate geometry [35]. (Courtesy NASA/JPL-Caltech.)


53

triangle arrangement of holes. In the actual operational configuration, the plate is purposely tilted an angle ␪ 0 = 30 degrees such that the central ray from the feed will be incident on the plate at a 30-degree incidence angle. At this incidence angle, the S/X-band dichroic plate is designed to have minimum insertion losses of about 0.01 dB between 8.4 and 8.5 GHz. As described by Potter [34], the first DSN dichroic plate that was developed had circular holes with diameters of 2.286 cm (0.900 inch). The problem encountered was that the minimum insertion loss passbands for perpendicular and parallel polarizations were not at the same frequencies. The two slightly different passbands gave rise to an ellipticity of 1.8 dB, which was considered unacceptable. Potter redesigned the plate so that the ellipticity was reduced to 0.4 dB at 8.415 GHz by using Pyle waveguides (also referred to as Pyleguides) rather than circular waveguide holes. The Pyleguide is a circular waveguide with flats on opposite sides, as shown in Figure 1.31. Two critical dichroic plate dimensions not shown in Figure 1.31 are: (1) the horizontal hole-to-hole spacing of 2.388 cm (0.940 inch) and (2) a thickness of 3.576 cm (1.408 inches). The thickness of the plate is close to being equal to one-half waveguide wavelength at the center frequency of the passband except for an adjustment of the thickness needed to compensate for the phase shift introduced by the discontinuity of free space and waveguide impedances at the two interfaces of the plate. Another type of dichroic plate was later developed by Otoshi [35, 36] to have passbands for both X-band uplink frequencies (7.145 to 7.235 GHz) and X-band downlink frequencies (8.4 to 8.5 GHz). This plate had round holes that were filled

Figure 1.31

Dimensions of the Pyleguide holes in the Dichroic Plate. (Courtesy NASA/JPL-Caltech.)

54

Introductory Topics

with Teflon so that the holes could be made smaller and be packed closer together. By packing the holes closer together, the frequencies at which grating lobes could be generated were moved higher and out of the X-band downlink frequency range. As expected in this first phase of development, the frequencies at which insertion losses were at a minimum were different for perpendicular and parallel polarizations. Before a plate with Pyleguide filled with Teflon could be developed to make the passbands the same for both perpendicular and parallel polarizations, it was decided by the funding organization that this new phase of the development project be terminated. The decision was based on a 2-K higher noise temperature contributed by the dissipative losses in the Teflon dielectric material used to fill the holes. At the time, there was (and still is) no other known inert and inexpensive dielectric material having a relative dielectric constant ≥ 2 and a lower loss tangent than Teflon. Hence all dichroic plates that were later developed for the DSN did not have any dielectric material filling the holes. A selected bibliography, of dichroic plates work done in later years for the DSN, is provided after the chapter references. 1.4.3 Analytical Method

This section will discuss the method for calculating the S/X dichroic plate noise temperature due to: (1) insertion loss, (2) dissipative loss due to surface resistivity, and (3) dissipative loss due to resistivity of the waveguide holes. 1.4.3.1 Contribution Due to Plate Insertion Losses

Figure 1.32 shows the theoretical insertion loss characteristics for the S/X dichroic plate in the X-band region from 7 GHz to 9 GHz for the plate tilted for a 30-degree incidence angle. The insertion losses are shown for both perpendicular and parallel polarizations. These polarizations are identified by E ⊥ and E || , respectively, in Figure 1.30. Insertion losses were measured with a network analyzer that had an accuracy in the passband of ± 0.02 dB. However, much better accuracy is needed for knowledge of minimum insertion loss values in the passband for noise temperature calculations. Theoretical insertion losses can be resolved to within ± 0.001 dB in the passbands. The agreement between theoretical and measured insertion loss values published previously [35] was considered to be sufficiently close for purposes of this study. Therefore, theoretical data shown in Figure 1.32 was used instead of measured values. Examination of Figure 1.32 shows that the minimum insertion losses are in the region of 8.4–8.5 GHz. Below 8.2 GHz, the plate has insertion loss characteristics similar to those of a waveguide below cutoff. The 3-dB insertion loss points for both polarizations occur at about 8.0 GHz. At 7.0 GHz, the dichroic plate insertion loss is about −22 dB and −19.3 dB for perpendicular and parallel polarizations, respectively. Far below cut-off, at the frequency of 2.295 GHz (S-band), measurements showed that the return loss from the dichroic plate was the same as that from a solid metal aluminum sheet [35]. These properties make the S/X dichroic plate ideal for its intended purpose of being transparent at desired X-band downlink frequencies and completely reflective at S-band frequencies. In the actual operation at DSS 13, the S/X dichroic plate is illuminated with a 25-dBi horn at 8.450 GHz. The E- and H-plane patterns at 8.450 GHz for this horn are


Figure 1.32

55

Theoretical passband for the dichroic plate at 8.45 GHz for ␪ = 30 degrees, ␾ = 90 degrees [35]. (Courtesy NASA/JPL-Caltech.)

shown in Figure 1.33. Also shown in Figure 1.33 is the beam efficiency curve where beam efficiency is defined as the fraction of the total power contained between theta = 0 degree and the theta angle of interest. At the boundary of outer holes shown in Figure 1.31 and for the plate tilted at an angle of 30 degrees, the horn illumination angle is 23.5 degrees. At this boundary, the beam efficiency is 99.7%. Outside this boundary, the plate is made from solid 6061-T6 aluminum and is completely reflective. The 0.3% of total power reflects off the plate and is completely absorbed by the pedestal room ambient temperature environment. In practice, the dichroic plate is not illuminated by a plane wave, but by waves that originate from a feed horn and illuminate the dichroic plate at various theta and phi angles. Noise temperature of the dichroic plate for the installed configuration is calculated from 2␲ ␲

冕冕

Tdp =

p (␪ h , ␾ h ) Tb (␪ h , ␾ h ) sin ␪ h d␪ h d␾ h

0 0

(1.94)

2␲ ␲

冕冕

p (␪ h , ␾ h ) sin ␪ h d␪ h d␾ h

0 0

where ␪ h , ␾ h are spherical coordinate angles of the horn system. The parameter p (␪ h , ␾ h ) is the normalized horn pattern obtained from the principal E- and

56

Introductory Topics

Figure 1.33

E- and H-plane patterns for the 25-dBi X-band horn.

H-plane patterns shown in Figure 1.33 and the equations discussed earlier in this chapter. Accurate knowledge of the horn-plate geometry and use of coordinate transformation equations leads to the derivation of expressions and contour plots (Figure 1.34) that relate horn pattern angles (␪ h , ␾ h ) to dichroic plate angles (␪ , ␾ ). Use of these relationships allows Tb (␪ h , ␾ h ) values to be calculated from brightness temperature formulas to be presented in the following. Then substitutions of horn pattern and brightness temperature data into (1.94) lead to a calculated value of Tdp at a particular frequency. Contribution from Inside the Boundary of Outer Holes

First assume that there is no X-band filter in the system but that all components (feed horn, LNA) other than the dichroic plate operate from 7.0–9.0 GHz. Then the brightness temperature of the system is determined entirely by the dichroic plate reflection characteristics. Inside the boundary of outer holes shown in Figure 1.31, brightness temperature is calculated from 2

Tb (␪ , ␾ ) = | S 11 (␪ , ␾ ) | Tp where

(1.95)


Figure 1.34

57

Contours of ␪ h on dichroic plate surface for ␪ 0 , ␾ 0 = 30, 90 degrees. The horn pattern is symmetric about the horn z-axis so over a particular ␪ h contour, ␾ h goes from 0 to 360 degrees [39]. (Courtesy NASA/JPL-Caltech.)

| S 11 (␪ , ␾ ) | 2 = 1 − | S 21 (␪ , ␾ ) | 2

(1.96)

and (␪ , ␾ ) are spherical coordinate angles of the dichroic plate system (Figure 1.30) and Tp is the physical temperature of the pedestal room absorbing environment assumed to be 290K. As can be seen from (1.95), the brightness temperature of the dichroic plate is determined from the plate power reflection coefficient | S 11 (␪ , ␾ ) | 2, which is related to the power transmission coefficient by the relationship given in (1.96). Temporarily assume that the dissipative losses of the plate due to plate surface resistivity and waveguide losses are zero. Power transmission coefficient is calculated from insertion loss in decibels by the relationship

| S 21 (␪ , ␾ ) | 2 = 10(IL /10)

(1.97)

where IL is the insertion loss of the dichroic plate in negative decibels. If IL = 0 dB, then | S 21 | = 1 and | S 11 | = 0. For circular polarization, the average | S 21 (␪ , ␾ ) | 2 is used and computed from 2 = 冋10(IL ⊥ /10) + 10(IL || /10)册 | S 21 (␪ , ␾ ) | avg 2

1

(1.98)

where IL ⊥ and IL || are the insertion losses (in negative decibels) for perpendicular and parallel polarizations, respectively. The insertion loss characteristics of this

58

Introductory Topics

dichroic plate were shown previously in Figure 1.32. At all frequencies, the insertion loss is entirely due to reflective loss, because the Chen computer program that was used to compute insertion losses of the dichroic plates has no provisions to compute the dissipative loss of the plate surface or dissipative loss due waveguide conductivity wall losses. Noise temperature contributions due to dissipative losses are treated separately. Figure 1.35 shows the brightness temperature for circular polarization calculated from (1.95) to (1.97) for the region inside the outer hole boundary over the frequency range from 7.0 to 9.0 GHz. In the passband of 8.4–8.5 GHz, the insertion losses in decibels are at a minimum and hence brightness temperatures are close to zero Kelvin. At frequencies above 8.5 GHz, insertion losses begin to increase and hence the brightness temperature increases correspondingly. At frequencies below 8.2 GHz, insertion losses become increasingly large because of cutoff characteristics, and brightness temperatures are corresponding higher in these regions. At 7.0 GHz, which lies entirely in the cutoff region, the brightness temperature is about 287K. Note from Figure 1.35 that if there were a filter in the system that restricts the frequency range of operation to 8.2–8.6 GHz, the average brightness temperatures would be much lower than if the entire frequency range of 7.0–9.0 GHz were involved.

Figure 1.35

Brightness temperatures due to dichroic plate reflection characteristics for circular polarization, ␪ = 30 degrees, ␾ = 90 degrees.


59

Contribution from Outside the Boundary of Outer Holes

Outside the boundary of outer holes (shown in Figure 1.31), the plate is made from solid 6061-T6 aluminum metal and, although there is some dissipative loss due to finite conductivity of the metal, it will be assumed that all of the incident power illuminating this outer plate region gets reflected and is completely absorbed by the pedestal room environment so that Tb (␪ , ␾ ) = Tp

(1.99)

where as previously defined, Tp is the physical temperature of the pedestal room environment assumed to be 290K. This formula for the noise temperature outside the hole boundary applies to all frequencies in the dichroic insertion loss band shown in Figure 1.32. If instead the dichroic plate was mounted at the Cassegrain f1 focal point location (Figure 1.28), then at 8.45 GHz, Tb in the zenith direction at f1 would be about 9K due to Tsky and other noise temperature contributions from subreflector and main reflector losses [33]. It was stated previously that, from the beam efficiency curve shown in Figure 1.33, only 0.3% of the total power illuminates this solid portion of the plate and is reflected and absorbed by the pedestal room environment. Therefore, the noise temperature contribution for this region outside the hole boundary is only 0.003 × 290 = 0.87K and is tabulated in Table 1.11.

1.4.3.2 Contribution Due to Insertion Loss with Filter in the System

When there is a filter in the system, whether it is in the X-band waveguide system or in the downconverter IF system, the effective dichroic noise temperature contribution over the passband is calculated from

Table 1.11 Comparison of Calculated and Measured Noise Temperature (NT) Due to Dichroic Plate

(a) Calculated Reflective loss inside outer hole boundaries Reflective loss outside outer hole boundaries Surface conductivity losses* Pyle waveguide conductivity loss* Total

Fractional Power at 8.450 GHz

NT, K Bandpass #1 8.17–8.62 GHz

NT, K Bandpass #2 8.4–8.5 GHz

99.7%

13.6

1.03

0.3%

0.87

0.87

99.7%

0.02 0.84

0.02 0.79

15.33

2.71

(b) Measured

18 ±1

2.6 ±0.3

(c) Difference

2.67

*Dich Plate is made from aluminum with a normalized electrical conductivity = 2.32. Bandpass #1 is due to a nominal 400-MHz bandwidth IF filter after the down-converter. Bandpass #2 is due to a 100-MHz bandwidth X-band waveguide filter after the HEMT.

−0.11

60

Introductory Topics f2

冕 (Tdp )eff =

g ( f ) Tdp ( f ) df

f1

(1.100)

f2

冕

g ( f ) df

f1

where g ( f ) = 10G dB ( f )/10, and G dB ( f ) is the receive system relative gain response in decibels at frequency f , and f 1 and f 2 represent the X-band cutoff frequencies of the system frequency response curve that needs to be determined if not already known. Since no information about the actual bandwidth of the X-band system was available at the time, Franco of JPL measured the system frequency response of the X-band receive system with an X-band frequency synthesizer for the input signal and a power meter at the output of the downconverter. His measurements produced the gain frequency response curve shown in Figure 1.36. The cutoff frequencies were found to be close to 8.17 and 8.62 GHz. Substitutions of the gain data shown in Figure 1.36 into (1.100) along with dichroic plate noise temperatures calculated over the same frequency from use of (1.94) to (1.98) resulted in an effective dichroic plate noise temperature of 13.6K due only to insertion losses of the holes inside the outer hole boundary. Then to this value it was necessary to add: (1) the contribution outside the hole boundary region already calculated in Section 1.4.3.1, (2) the contribution due to plate surface resistivity, and (3) the contribution due to conductivity loss of the Pyle waveguides. The methodology to perform these theoretical calculations will be given in the following sections. As verification of the system bandwidth measurements made by Franco, Paul Dendrenos of DSS-13 later found and furnished technical information on the downconverter in the X-band receive system. The downconverter LO frequency is 8,100 MHz, and the manufacturer’s specification of the IF filter after the mixer gives a passband of 99–502 MHz [private communication with Paul Dendrenos at DSS 13, December 5, 2003]. From this information, corresponding X-band cutoff frequencies were calculated to be 8.199 and 8.602 GHz. Each of the cutoff frequencies agrees with those determined from Franco’s measurements to within 20 MHz.

Figure 1.36

Measured passband of the X-band receive system [39]. (Courtesy NASA/JPL-Caltech.)


61

Therefore, it is concluded that the cutoff frequencies as determined from Franco apply to the actual system, and the value of 13.6K obtained through the use of these cutoff frequencies is tabulated in Table 1.11. 1.4.3.3 Contribution Due to Plate Surface Resistivity

For circular polarization, the noise temperature of a solid plate due to finite conductivity of the metal is calculated from the formula given in [36] as Tsolid =

冉冊冉

4R s 1 ␩o 2

cos ␪ i +

冊

1 Tp cos ␪ i

(1.101)

where R S is the surface resistivity of the metallic surface, ␩ o is the free space impedance equal to 120␲ ohms, and ␪ i is the incidence angle (assumed to be 30 degrees). The surface resistivity in ohms per square can be calculated from normalized electrical conductivity with the formula R S = 0.02␲

√

f GHz 10␴ n

(1.102)

where f GHz is the frequency in gigahertz and ␴ n is the normalized conductivity derived by dividing the actual conductivity in mhos/m by 107. The noise temperature due to resistivity of a perforated plate is calculated from Tperfpl = Tsolid (1 − P )

(1.103)

where P is the plate porosity ratio, which for the S/X dichroic plate is 0.823. This formula was not rigorously derived, but based on the fact that it is valid for P = 0 and P = 1. The material used to fabricate this S/X dichroic plate was made from 6061-T6 aluminum, which after being irridited, has a measured normalized electrical conductivity of 2.32 at 8.450 GHz [37]. The average R S over the frequency range of 8.17 GHz to 8.62 GHz was calculated to be 0.0378 ohm per square, and from (1.101) the average Tsolid for a 30-degree incidence angle is 0.118K, and from (1.103) Tperfpl is only 0.021K. This value is tabulated in Table 1.11. 1.4.3.4 Pyle Waveguide Conductivity Loss

The noise temperature contribution due to Pyle waveguide wall conductivity loss is computed as follows. The waveguide cutoff wavelength is calculated for the E-field perpendicular to the flat wall and for the E-field parallel to the flats using the modified curves given for the Pyle waveguide given by Potter in [34]. Once the cutoff wavelength ␭ c is known, the equivalent circular hole diameter is computed from d = ␭ c /1.706. This procedure led to the Pyle waveguide cutoff wavelength equal to 3.838 cm (1.511 inches) and the equivalent round hole diameter of 2.250 cm (0.886 inch) for perpendicular polarization. For parallel polarization, the Pyle waveguide cutoff wavelength was 3.909 cm (1.539 inches) and the equiva-

62

Introductory Topics

lent round hole diameter was 2.291 cm (0.902 inch) [38]. Then the TE 11 mode power loss due to 6061-T6 aluminum conductivity is computed for the appropriate length of circular waveguide where the appropriate length is the thickness of the dichroic plate. The conductivity power loss is computed for the E-field perpendicular to the flats and then parallel to the flats and averaged. Then noise temperature is calculated from

冉

Twg = ␩ b 1 −

冊

1 Tp L avg

(1.104)

where ␩ b is the beam efficiency of the pattern illuminating the hole region, and L avg is the average power loss factor (≥ 1) due to conductivity of the aluminum material for waveguide walls. The average Twg over the frequency range of 8.17– 8.62 GHz without the beam efficiency factor was 0.864K. Then accounting for the beam efficiency factor previously shown to be 0.997, the noise contribution is 0.838K. This value is tabulated in Table 1.11. 1.4.3.5 Total Calculated Dichroic Plate Noise Temperature

The average dichroic plate noise temperature as calculated for the frequency range of 8.17–8.62 GHz is determined from summing up all the previous calculated values. The calculated dichroic plate noise temperature is shown in Table 1.11 to be 15.3K as compared to the measured value of (18 ± 1)K. 1.4.4 Experimental Work 1.4.4.1 Measurement Method

The technique used to measure the noise temperature of a dichroic plate is to measure the operating system noise temperature Top without and with the plate inserted above the feed horn (see Figure 1.29). It was difficult to install the plate quickly because of its large dimensions of 190.5 cm (75 inches) × 193.04 cm (76 inches) × 3.576 cm (1.408 inches) and the heavy weight of the plate. Even though the plate was made of aluminum and even though most of the area is perforated, it required a forklift inside the pedestal room to lift the plate into the required 30-degree tilt angle position. The time interval between measurements made without and with the plate was several hours. Only one measurement of ⌬Top was made. To show why the measurement of Top with and without the plate yields a measurement of the dichroic plate noise temperature, first refer to Figure 1.37 to study the noise sources that contribute to Top . Noise sources are located at the ceiling, walls, and floor of the pedestal room. It is easiest to think of the horn in the transmit mode and find where the transmitted power is absorbed. By reciprocity, the same equations apply except the absorbing media becomes the noise source that radiates noise into the receiver via the reverse path. At f3, without the dichroic plate Top = TS + Thorn + Twg + TLNA + Tfu

(1.105)


Figure 1.37

63

Noise source from ceiling contributing to S/X dichroic plate noise temperature at 8.45 GHz. Other noise sources not shown come from the walls and floor of the pedestal room.

At f3, with the dichroic plate above the horn ′ = TS L −1 冠1 − | ⌫ | 冡 + 冠1 − | ⌫ | 冡 (1 − L −1 ) TP Top dp dp 2

2

(1.106)

2

+ | ⌫ | dp TPR + Thorn + Twg + TLNA + Tfu where TS = source noise temperature at f3 and consists of sky, main reflector resistive and spillover losses, mirror losses, and BWG wall losses, K. L = dissipative power loss factor (≥ 1) due to dichroic plate surface resistive loss and Pyleguide conductivity losses.

| ⌫dp | 2 = power reflection coefficient of the dichroic plate. It is equal to | S 11 | 2 defined in (1.96). TP = ambient temperature of dichroic plate, K. TPR = ambient temperature of the pedestal room absorbing environment, K.

64

Introductory Topics

and Thorn , Twg , TLNA , and Tfu are, respectively, the noise temperatures of the horn, waveguide components, low noise amplifier (LNA), and the follow-up receiver in Kelvin. The expression given in (1.106) assumes that the dichroic plate is operating within its design band where the return losses of the dichroic plate have more negative values than −20 dB. When the dichroic plate is operating out of its design band, multiple reflections occur between the two Pyleguide interfaces, and dissipative losses could be higher than the loss for the matched case. Taking the difference of the two measured Top values leads to ′ = Tdp + Terror ′ − Top = Tdp Top

(1.107)

where Tdp is the true dichroic plate noise temperature defined here to include contributions due to dissipative loss of the Pyleguide and to reflections from the plate and expressed as Tdp = (1 − L −1 ) Tp + | ⌫ dp | TPR 2

(1.108)

and Terror is the error term calculated as Terror = TS 冋L −1 冠1 − | ⌫ dp |

2

冡 − 1册 − | ⌫ dp | 2 (1 − L −1 ) Tp

(1.109)

Note that if it is assumed that L ≈ 1 then the error term simplifies to Terror ≈ −TS | ⌫ dp |

2

(1.110)

Note that Terror includes the noise source temperature coming down the BWG from the main reflector, subreflector, and the four mirrors. This source temperature appears in the experimental method and not in the analytical method for calculating the dichroic plate noise temperature contribution. Since the error term is a negative number, the true dichroic temperature would be even larger than the measured Top difference. For example, at the center frequency of 8.45 GHz, L dB = 0.013 dB, corresponding to L −1 = 0.99701

| ⌫ dp | 2 = 0.00355, corresponding to a return loss of −24.5 dB TS at f3 = 17.5K [33] Tp = TPR = 290K Substitutions of these values into (1.108) gives a measured Tdp value of 1.9K and an error term of −0.12K at 8.45 GHz. Even though (1.106) is somewhat inaccurate near the cutoff region, a calculation for Tdp will be made at 8.17 GHz. Let


65

L dB = 0.013 dB, corresponding to L −1 = 0.99701 and for convenience is assumed to be independent of frequency

| ⌫ dp | 2 = 0.2057, corresponding to a return loss of −6.87 dB TS at f3 = 17.5K [33], assuming it to be independent of frequency Tp = TPR = 290K Substitutions of these values into (1.108) gives a measured Tdp value of 60.5K with an error term of −3.82K at 8.17 GHz. Again, it should be stated that when the dichroic plate is not operating in its design bandwidth, and when the | ⌫ dp | 2 > 0.1, the expression for Top at f3 with the dichroic plate as given by (1.106) is only approximately correct. The purpose of presenting these equations here is to show that the contribution to dichroic plate noise temperature depends on whether the measurements are made on the ground, on the antenna reflector surface near f1, or at f3 in the pedestal room. The error in measurement of Tdp is proportional to TS (see 1.110). The worst case occurs when the dichroic plate reflections are absorbed completely by an ambient temperature environment and the source temperature TS is about 8K at f1, but instead it has increased to as high as 17.5K at X-band [33] by the time the source temperature arrives at f3. 1.4.4.2 Experimental Results

At the time the S/X dichroic plate was installed at DSS 13, the X-band receive system was designed with no filter installed other than an IF filter in the downconverter. The contribution of the dichroic plate was measured by measuring the X-band Top before and after the S/X dichroic plate was installed. There were several hours separating the times of the ‘‘before’’ and ‘‘after’’ measurements, and, therefore, there is about 1K uncertainty in the measured value due to drift. The dichroic plate contribution was measured to be 18K. This value was far greater than the 2K value that was expected. A subsequent diagnostic analysis was made, and it was determined that a very high noise temperature was being contributed by the dichroic plate operating outside its design bandwidth of 8.4–8.5 GHz. As confirmation, an X-band waveguide filter with a passband of 8.4–8.5 GHz was inserted after the HEMT, and when this was done, the Top dropped close to expected values. Table 1.11 shows the comparison of the measured and calculated dichroic plate noise temperatures. Calculations yielded a value of 15.3K as compared to a measured value of 18 ± 1K for the receive system passband of 8.17–8.62 GHz. A cause of the unexplained residual difference of about 3K might be that the dichroic plate is located in the near field of the feed horn and the calculated patterns are for the horn located in the far field. Another cause of the unexplained difference might be that the same horn patterns computed for the center frequency of 8.45 GHz were assumed to be the same over the entire frequency range of 8.17–8.62 GHz. Although refinements of the analytical methodology could be made, it can be concluded that the methodology employed thus far sufficiently explains the main causes of the unexpected 18K discrepancy between measured and expected values.

66

Introductory Topics

When an X-band waveguide filter with a passband of 8.4–8.5 GHz was inserted after the HEMT, the measured dichroic plate contribution was determined to be 2.6 ± 0.3K. When compared to the calculated value of 2.7K, it can be seen that there was excellent agreement between measured and calculated values. As may be seen in Table 1.11, the calculated value was based on adding up the contributions over the narrower passband.

1.4.5 Conclusions

A methodology has been presented for calculating the noise temperature contribution of the dichroic plate when used in a system whose operating bandwidth is larger than the bandwidth for which the dichroic plate was designed. In the past, such analytical procedures did not have to be employed because the receive system operated narrowband. Good agreement was usually obtained between measured and expected values for the noise contributions of the dichroic plate. In recent years, there have been requirements for users of the BWG antenna to use the system operating at wider bandwidths, such as for VLBI or radio science experiments. Instead of bandwidths of 100 MHz, it was requested that the system operate with bandwidths of 500 MHz or greater. Due to new requirements for the system to operate over a wider bandwidth, the X-band downconverters were designed with an IF filter that had a bandwidth of about 400 MHz instead of 100 MHz. At the time it was not widely known that, when operating with wide bandwidths, the operational bandwidth could overlap into the frequencies below 8.2 GHz where the S/X dichroic plate begins to function like a waveguide below cutoff. Therefore, instead of looking transparent, the dichroic plate reflects much of the X-band signal into a 290K environment. The result could be a measured Top that is unacceptably high. In the case that was described, the solution was to insert an X-band waveguide filter after the X-band HEMT. The filter had the same center frequency and bandwidth (that the dichroic plate was designed to operate in), where the dichroic plate looks transparent. If wider bandwidth is required, a solution might be to redesign the dichroic plate to have larger diameter holes so as to move the lower cutoff frequency from 8.2 GHz to 8.0 GHz. It should be designed so that the minimum insertion losses still occur between 8.4–8.5 GHz. Many design improvements have been made since this work done by this author was reported. Nearly all of the follow-up work done at JPL is described in the articles listed in the selected bibliography after the references.

References [1]

[2]

Lambert, K. M., and R. C. Rudduk, ‘‘Calculation and Verification of Antenna Temperature for Earth-Based Reflector Antennas,’’ Radio Science, Vol. 27, No. 1, January–February 1992, pp. 23–30. Silver, S., Microwave Antenna Theory and Design, Radiation Laboratory Series, Vol. 12, New York: McGraw-Hill, 1949.

1.4 Dichroic Plate in a Beam-Waveguide Antenna System [3] [4] [5] [6]

[7] [8]

[9]

[10] [11] [12]

[13]

[14]

[15]

[16]

[17]

[18]

[19]

[20]

[21]

67

Ludwig, A. C., ‘‘Antenna Feed Efficiency,’’ SPS 32-26, Vol. IV, Jet Propulsion Laboratory, Pasadena, CA, April 30, 1964, pp. 200–208. Ludwig, A. C., ‘‘Antenna Feed Efficiency,’’ SPS 32–24, Vol. IV, Jet Propulsion Laboratory, Pasadena, CA, December 31, 1963, pp. 150–154. Ludwig, A. C., ‘‘Antenna Feed Efficiency,’’ SPS 32–26, Vol. IV, Jet Propulsion Laboratory, Pasadena, CA, April 30, 1964, pp. 197–200. Rafuse, R. P., ‘‘Characterization of Noise in Receiving Systems,’’ Chapter 15 in Lectures on Communication System Theory, E. J. Baghdady, (ed.), New York: McGraw-Hall, 1961, p. 380. Hogg, D. C., ‘‘Effective Antenna Temperature Due to Oxygen and Water Vapor in the Atmosphere,’’ Journal of Applied Physics, Vol. 30, No. 9, September 1959, pp. 1417–1419. Deep Space Network Flight Project Interface Design Handbook 810-5, Rev. E, Atmospheric and Environmental Effects 105, Rev. A (internal document), Jet Propulsion Laboratory, Pasadena, CA, December 15, 2002. Keihm, S. J., ‘‘Water Vapor Measurements of the Tropospheric Delay Fluctuations at Goldstone over a Full Year,’’ TDA PR 42-122, Jet Propulsion Laboratory, Pasadena, CA, August 15, 1995, pp. 2–11. Reed, H. R., and C. M. Russell, Ultra-High-Frequency Propagation, New York: John Wiley and Sons, 1953, pp. 82–97. Ramo, S., and J. R. Whinnery, Field and Waves in Modern Radio, New York: John Wiley and Sons, 1953. Otoshi, T. Y., ‘‘Antenna Noise Temperature Analysis,’’ Status Report, Rev. 8/19/96, JPL Document D-15554 (internal document), Jet Propulsion Laboratory, Pasadena, CA, August 8, 1996. Otoshi, T. Y., ‘‘Part 1. Horizon Mask Studies with Antenna Noise Temperature Program TSTSPILL.FOR,’’ JPL D-15555, Rev. 1, (internal document), Jet Propulsion Laboratory, Pasadena, CA, April 16, 1997. Otoshi, T. Y., ‘‘Part 2. Horizon Spillover Studies with Antenna Noise Temperature Program HRNSPL3.FOR,’’ JPL D-15556 (internal document), Jet Propulsion Laboratory, Pasadena, CA, May 7, 1997. Keihm, S. J., A. Tanner, and H. Rosenberger, ‘‘Measurements and Calibration of Tropospheric Delay at Goldstone from the Cassini Media Calibration System,’’ IPN PR 42-158, Jet Propulsion Laboratory, Pasadena, CA, August 15, 2004, pp. 1–17. Stelzried, C. T., and T. Y. Otoshi, ‘‘Radiometric Evaluation of Antenna-Feed Component Losses,’’ IEEE Trans. on Instrumentation and Measurement, Vol. IM-18, No. 3, September 1969, pp. 172–183. Morabito, D., and L. Skjerve, ‘‘Analysis of Tipping-Curve Measurements Performed at the DSS-13 Beam-Waveguide Antenna at 32 and 8.45 Gigahertz,’’ TDA Progress Report 42-122, Jet Propulsion Laboratory, Pasadena, CA, August 15, 1995, pp. 151–174. Morabito, D., R. Clauss, and M. Speranza, ‘‘Ka-Band Atmospheric-Noise Temperatur Measurements at Goldstone, California, Using a 34-Meter Beam-Waveguide Antenna,’’ TDA Progress Report 42-132, Jet Propulsion Laboratory, Pasadena, CA, February 15, 1996, pp. 1–20. Otoshi, T. Y., ‘‘Simulation Diagnostics of Multiple Discontinuities in a Microwave Coaxial Transmission Line,’’ IEEE Trans. on Microwave Theory Tech., Vol. MTT-43, June 1995, pp. 1310–1314. Otoshi, T. Y., and C. T. Stelzried, ‘‘Cosmic Background Noise Temperature Measurements at 13-cm Wavelength,’’ IEEE Trans. on Instrumentation and Measurement, Vol. IM-24, No. 2, June 1975, pp. 174–179. Partridge, R. B., 3 K: The Cosmic Microwave Background Radiation, New York: Cambridge University Press, 1995. (See Table 4.2 and discussion of the Otoshi-Stelzried result on p. 133.)

68

Introductory Topics [22]

[23]

[24]

[25]

[26]

[27]

[28]

[29]

[30] [31] [32]

[33]

[34]

[35]

[36] [37]

[38]

Potter, P. D., ‘‘System Noise Temperature as a Function of Meteorological Conditions,’’ Space Programs Summary 37-43, Vol. III, Jet Propulsion Laboratory, Pasadena, CA, January 31, 1967, pp. 63–71. Otoshi, T. Y., S. R. Stewart, and M. M. Franco, ‘‘Portable Microwave Test Packages for Beam-Waveguide Antenna Performance Evaluation,’’ IEEE Trans. on Microwave Theory Tech., Vol. 40, No. 6, June 1992, pp. 1286–1293. Otoshi, T. Y., S. R. Stewart, and M. M. Franco, ‘‘A Portable X-Band Front-End Test Package for Beam-Waveguide Antenna Performance Evaluation, Part 1: Design and Ground Tests,’’ TDA Progress Report 42-103, Jet Propulsion Laboratory, Pasadena, CA, November 15, 1990, pp. 135–150. Otoshi, T. Y., S. R. Stewart, and M. M. Franco, ‘‘A Portable X-Band Front-end Test Package for Beam-Waveguide Antenna Performance Evaluation, Part II: Tests on the Antenna,’’ TDA Progress Report 42-105, Jet Propulsion Laboratory, Pasadena, CA, May 15, 1991, pp. 54–68. Otoshi, T. Y., S. R. Stewart, and M. M. Franco, ‘‘A Portable Ka-Band Front-end Test Package for Beam-Waveguide Antenna Performance Evaluation, Part I: Design and Ground Tests,’’ TDA Progress Report 42-106, Jet Propulsion Laboratory, Pasadena, CA, August 15, 1991, pp. 249–265. Otoshi, T. Y., S. R. Stewart, and M. M. Franco, ‘‘A Portable Ka-Band Front-end Test Package for Beam-Waveguide Antenna Performance Evaluation, Part II: Tests on the Antenna,’’ TDA Progress Report 42-106, Jet Propulsion Laboratory, Pasadena, CA, August 15, 1991, pp. 266–282. Otoshi, T. Y., S. R. Stewart, and M. M. Franco, ‘‘A Portable Ku-Band Front-End Test Package for Beam-Waveguide Antenna Performance Evaluation,’’ TDA Progress Report 42-107, Jet Propulsion Laboratory, Pasadena, CA, November 15, 1991, pp. 73–80. Slobin, S. D., et al., ‘‘Efficiency Measurement Techniques for Calibration of a Prototype 34m-Diameter Beam-Waveguide Antenna at 8.45 and 32 GHz,’’ IEEE Trans. on Microwave Theory Tech., Vol. 40, No. 6, June 1992, pp. 1301–1309. Rochblatt, D. J., and B. L. Seidel, ‘‘Microwave Antenna Holography,’’ IEEE Trans. on Microwave Theory Tech., Vol. 40, No. 6, June 1992, pp. 1294–1300. Stelzried, C. T., ‘‘Operating Noise Temperature Calibrations of Low-Noise Receiving System,’’ Microwave J., Vol. 14, No. 6, June 1971, pp. 41–46, 48. Stelzried, C. T., ‘‘Nonlinearity in Measurement Systems: Evaluation Method and Application to Microwave Radiometers,’’ TDA Progress Report 42-91, Jet Propulsion Laboratory, Pasadena, CA, November 15, 1987, pp. 57–61. Bathker, D. A., et al., ‘‘Beam-Waveguide Antenna Performance Predictions with Comparisons to Experimental Results,’’ IEEE Trans. on Microwave Theory Tech., Vol. 40, No. 6, June 1992, pp. 1274–1285. Potter, P. D., ‘‘Improved Dichroic Reflector Design for the 64-m Antenna S- and X-Band Feed Systems,’’ JPL Technical Report 32-1526, Vol. XIX, Jet Propulsion Laboratory, Pasadena, CA, February 15, 1974, pp. 55–62. Otoshi, T. Y., and M. M. Franco, ‘‘Dual Passband Dichroic Plate for X-Band,’’ Telecommunications and Data Acquisition Progress Report 42-94, Jet Propulsion Laboratory, Pasadena, CA, August 15, 1988, pp. 110–134. Otoshi, T. Y., ‘‘Noise Temperature Due to Reflector Surface Resistivity,’’ IPN Progress Report 42-154, Jet Propulsion Laboratory, Pasadena, CA, August 15, 2003. Otoshi, T. Y., and M. M. Franco, ‘‘The Electrical Conductivities of Steel and Other Candidate Material for Shrouds in a Beam-Waveguide Antenna System,’’ IEEE Trans. on Instrumentation and Measurement, Vol. IM-45, No. 1, February 1996, pp. 77–83. (Correction in IEEE Trans. on Instrumentation and Measurement, Vol. IM-45, No. 4, August 1996, p. 839.) Otoshi, T. Y., and M. M. Franco, ‘‘Dual Passband Dichroic Plate for X-Band,’’ IEEE Trans. on Antennas and Propagation, Vol. 40, No. 10, October 1992, pp. 1238–1245.

1.4 Dichroic Plate in a Beam-Waveguide Antenna System [39]

69

Otoshi, T. Y., and M. M. Franco, ‘‘Noise Temperature Contribution of a Dichroic Plate in a Beam-Waveguide Antenna System,’’ Conference Digest of 1994 IEEE AP-S Symposium, Vol. 1, Seattle, WA, June 19–24, 1994, pp. 262–265.

Selected Bibliography Britcliffe, M. J., and J. E. Fernandez, ‘‘Noise-Temperature Measurements of Deep Space Network Dichroic Plates at 8.4 Gigahertz,’’ TMO Progress Report 42-145, Jet Propulsion Laboratory, Pasadena, CA, May 15, 2001, pp. 1–5. Chen, J. C., ‘‘Analysis of a Thick Dichroic Plate with Rectangular Holes at Arbitrary Angles of Incidence,’’ TDA Progress Report 42-104, Jet Propulsion Laboratory, Pasadena, CA, February 15, 1991, pp. 9–16. Chen, J. C., ‘‘X/Ka-Band Dichroic Plate Design and Grating Lobe Study,’’ TDA Progress Report 42-105, Jet Propulsion Laboratory, Pasadena, CA, May 15, 1991, pp. 21–30. Chen, J. C., P. H. Stanton, and H. F. Reilly, ‘‘Performance of the X-/Ka-/KABLE-Band Dichroic Plate in the DSS-13 Beam Waveguide Antenna,’’ TDA Progress Report 42-115, Jet Propulsion Laboratory, Pasadena, CA, November 15, 1993, pp. 54–64. Chen, J. C., ‘‘Computation of Reflected and Transmitted Horn Radiation Patterns for a Dichroic Plate,’’ TDA Progress Report 42-119, Jet Propulsion Laboratory, Pasadena, CA, November 15, 1994, pp. 236–254. Chen, J. C., P. H. Stanton, and H. F. Reilly, Jr., ‘‘A Prototype Ka-/Ka-Band Dichroic Plate with Stepped Rectangular Apertures,’’ TDA Progress Report 42-124, Jet Propulsion Laboratory, Pasadena, CA, February 15, 1996, pp. 143–152. Epp, L. W., and P. H. Stanton, ‘‘Experimental and Modal Verification of an Integral Equation Solution for a Thin-Walled Dichroic Plate with Cross-Shaped Holes,’’ TDA Progress Report 42-113, Jet Propulsion Laboratory, Pasadena, CA, May 15, 1993, pp. 46–62. ‘‘Errata,’’ TDA PR 42-114, Jet Propulsion Laboratory, Pasadena, CA, August 15, 1993, p. 346. Imbriale, W. A., ‘‘A New All-Metal Low-Pass Dichroic Plate,’’ TDA Progress Report 42-129, Jet Propulsion Laboratory, Pasadena, CA, May 15, 1997, pp. 1–11. Imbriale, W. A, ‘‘Analysis of a Thick Dichroic Plate with Arbitrarily Shaped Holes,’’ IPN Progress Report 42-146, Jet Propulsion Laboratory, Pasadena, CA, August 15, 2001, pp. 1–21. Otoshi, T. Y., and M. M. Franco, ‘‘Dual Passband Dichroic Plate for X-Band,’’ TDA Progress Report 42-94, Jet Propulsion Laboratory, Pasadena, CA, August 15, 1988, pp. 110–134. Potter, P. D., ‘‘Improved Dichroic Reflector Design for the 64-m Antenna S- and X-Band Feed Systems,’’ Technical Report 32-1526, Vol. XIX, Jet Propulsion Laboratory, Pasadena, CA, February 15, 1974, pp. 55–62. Veruttipong, W., and P. Lee, ‘‘X-/Ka-Band Dichroic Plate Noise Temperature Reduction,’’ TDA Progress Report 42-119, Jet Propulsion Laboratory, Pasadena, CA, November 15, 1994, pp. 255–261.

CHAPTER 2

Reflector Surfaces

2.1 Perforated Panels 2.1.1 Introduction

To reduce wind loading, the outer panels of DSN antennas are perforated. Leakage waves, which pass through holes in the perforated panels, are absorbed by the ground and contribute to the antenna noise temperature and gain loss. When the DSN antennas were designed in the early years (circa 1960), it was desired that the antennas operate satisfactorily at 2.295 GHz (S-band). Later it was desired that the antennas operate also at 8.450 GHz (X-band). To operate at X-band, it was necessary to reduce the size of the holes in the perforated panels. Wind tunnel tests by Katow [S. Katow, personal communication, Jet Propulsion Laboratory, Pasadena, California, January 1963] showed that a 3.175-mm (1/8-inch) hole diameter was as small as could be made for wind-loading relief purposes. Due to turbulence, panels with smaller diameters had the same wind loading as solid panels. Approximate formulas given below were used in the past for calculating leakage through perforated panels with circular holes. For a circular hole array having the geometry of Figure 2.1 and an incident plane wave with the E-field polarized normal to the plane of incidence, the approximate expression for transmission loss in positive decibels is [1]

冋冉

(TdB )⊥ = 10 log10 1 +

3ab␭ 0

2␲ d 3 cos ␪ i

冊册 2

+

32t d

√ 冉 1−

1.706d ␭0

冊

2

(2.1)

where a, b, d Ⰶ ␭ 0 . The parameters a and b are the spacing between holes as shown in Figure 2.1; d is the hole diameter; ␭ 0 is the free-space wavelength; t is the plate thickness; and ␪ i is the incidence angle. For the equilateral triangle hole pattern, shown in Figure 2.1, b = a sin 60°. When the incident wave is a plane wave with the E-field polarized parallel to the plane of incidence, the approximate expression for the transmission loss in positive decibels is [1]

冋冉

(TdB )|| = 10 log10 1 +

3ab␭ 0 cos ␪ i 2␲ d 3

冊册 2

+

32t d

√ 冉 1−

1.706d ␭0

冊

2

(2.2)

71

72

Reflector Surfaces

Figure 2.1

Perforated plate geometry with an obliquely incident plane wave polarized with the E-field perpendicular and parallel to the plane of incidence [6]. (Courtesy of NASA/JPLCaltech.)

where a, b, d Ⰶ ␭ 0 . The square-root factor in (2.1) and (2.2) has a significant effect when ␭ 0 becomes comparable to d, but this square-root factor can be set equal to unity when ␭ 0 Ⰷ d. These formulas were found to be accurate to 1 dB for perforated panels on the 64-m antenna [1] and for perforated plate samples of various hole diameters, hole-to-hole spacing, and thicknesses [2], and were even used to calculate leakage through microwave oven doors. When it was found that these formulas were not sufficiently accurate for predicting transmission losses for dichroic plate designs or perforated plates above 32 GHz, more accurate results were obtained through the use of a C.C. Chen Fortran program [3]. In recent years, requirements arose for DSN antennas to be operable with low noise at 32 GHz (Ka-band). The noise-temperature contribution due to leakage of perforated panels on the 34-m BWG antennas was reported to be 0.67K [4] at 32 GHz, as based on calculations through the use of the above approximate formulas and an approximate method (to be described), which was the best available in the 1990 era. No similar calculations were made for the 70-m antenna. The properties of this perforated panel are described in Section 2.1.4. In recent years, many requests have been made to this author to provide calculations of noise-temperature contributions of particular DSN antennas at special radio science experiment frequencies above 32 GHz, such as 37 GHz,

2.1 Perforated Panels

73

41 GHz, and 50 GHz. This section aims to formally document the results for all frequencies at and above 32 GHz to as high a frequency as these perforated panels can be used before grating lobes cause excessive degradation of performance. Sections 2.1.2 and 2.1.3, respectively, discuss old and new numerical integration techniques employed to make calculations of noise-temperature contributions due to leakage through these perforated panels. Section 2.1.4 discusses the geometries of the perforated panels on both 34-m BWG and 70-m antennas, and Section 2.1.5 presents the calculated results and plots of the data.

2.1.2 Old Calculation Method

Figure 2.2 depicts the antenna with solid- and perforated-panel regions for an antenna pointed in the zenith direction. In previous informal reports, it was assumed that the noise-temperature contribution due to leakage through perforated panels could be calculated by choosing a mid-subreflector pattern angle (the average of ␺ 1 and ␺ E shown in Figure 2.2) and then calculating the leakage or transmission loss at the corresponding incidence angle of a wave impinging upon the perforated panel. The leakage power ratio was then multiplied by an effective ground noise temperature. This result applies to a case for which all radiated power illuminates only the perforated panels. The contribution of only the perforated-panel leakage for the real case was calculated by multiplying the previous result by the ratio of the projected area of the perforated panels to the projected total reflector surface area. The projected area is that area that results when projected onto the aperture

Figure 2.2

Two-dimensional geometry of zenith-oriented parabolic antenna with feed (or apparent feed) located at the focal point [6]. (Courtesy of NASA/JPL-Caltech.)

74

Reflector Surfaces

plane. This method was believed to give sufficiently accurate results when used for frequencies below 32 GHz. However, since the perforated plates no longer appear isotropic at higher frequencies and because the leakage through the plates becomes increasing larger, a more accurate method was needed for calculating noise temperature at frequencies above 32 GHz. Theoretical formulas and the new methodology used for computing antenna noise-temperature contributions and gain losses at the higher frequencies are presented in the following. 2.1.3 New Calculation Method 2.1.3.1 Noise Temperature Contribution

Reflector surface losses that increase antenna noise temperature are: (1) ohmic losses of the metal and paint used as the reflective surface material, and (2) leakage loss of RF energy passing through the perforated surface. Most of the energy that leaks through the surface is absorbed by the ground environment. To obtain estimates of the noise contributions from these two types of absorptive losses, approximate formulas have been derived. These are presented in the following section. Most of this material was extracted from earlier articles by Otoshi [5, 6]. For a zenith-oriented parabolic antenna with circular symmetry, such as that shown in Figure 2.2, the antenna noise temperature is calculated from 2␲ ␲

冕冕

TA =

Tb (␺ , ␾ ) P (␺ , ␾ ) sin ␺ d␺ d␾

0 0

(2.3)

2␲ ␲

冕冕

P (␺ , ␾ ) sin ␺ d␺ d␾

0 0

where Tb (␺ , ␾ ) = effective brightness temperature function as defined at the focal point F (Figure 2.2), K. P (␺ , ␾ ) = power per unit solid angle radiated by the feed or apparent feed at focal point F.

␺ = polar angle. ␾ = azimuthal angle. For the purposes of this study, it is convenient to let (2.3) be expressed in terms of contributions from specific sources as TA = TA′ + (⌬TA )OL + (⌬TA )LL where

TA′ = total antenna temperature when the reflector surface has no ohmic and leakage losses, K.

(2.4)


75

(⌬TA )OL = antenna noise-temperature contribution due to reflector surface ohmic losses, K. (⌬TA )LL = antenna noise-temperature contribution due to reflector surface leakage losses, K. It shall be assumed that the power per unit solid angle as radiated from the focal point is of the form given in (1.14) as 1 冋| A 1 (␺ ) | 2 sin2 ␾ + | B 1 (␺ ) | 2 cos2 ␾ 册 2␩ 0

P (␺ , ␾ ) =

(2.5)

where

| A 1 (␺ ) | = E-plane amplitude pattern. | B 1 (␺ ) | = H-plane amplitude pattern. ␩ 0 = 120␲ = free-space wave characteristic impedance, ohms. After substitutions of (2.5) and the appropriate brightness-temperature functions into (2.3) and integrations with respect to ␾ , it can be shown that ␺E

冉冊冕 4R s TP ␩0

冋

[1 − ␣ (␺ )] p 1 (␺ ) sec

␺0

(⌬TA )OL =

␺ ␺ + p 2 (␺ ) cos 2 2

册

sin ␺ d␺

␲

冕

[ p 1 (␺ ) + p 2 (␺ )] sin ␺ d␺

0

(2.6)

and the equation for noise temperature due to leakage through perforated panels is ␺E

冕

(⌬TA )LL =

TG (␺ ) [t || (␺ ) p 1 (␺ ) + t ⊥ (␺ ) p 2 (␺ )] sin ␺ d␺

␺1

(2.7)

␲

冕

[ p 1 (␺ ) + p 2 (␺ )] sin ␺ d␺

0

where (⌬TA )OL and (⌬TA )LL were defined in (2.4) and

76

Reflector Surfaces

p 1 (␺ ) = p 2 (␺ ) =

| |

A 1 (␺ ) A 1 (0) B 1 (␺ ) A 1 (0)

| |

2

2

TP = physical temperature of the reflector surface, K. R S = surface resistivity of the reflector surface material, ohms/square (a function of frequency and electrical conductivity [7]).

␣ (␺ ) = porosity of the unit cell of the reflector surface and is equal to zero for ␺ 0 < ␺ ≤ ␺ 1 over the solid panel region, and equal to ␲ d 2/(4a 2 sin 60°) for ␺ 1 < ␺ ≤ ␺ E over the perforated panel region where d and a are, respectively, the diameter and spacing of the holes in the perforated plate (see Figure 2.1). TG (␺ ) = effective ground noise temperature function ([8, Equation 21, p. 210]). t || (␺ ) = leakage power-loss ratio for an incident wave polarized with the E-field in the plane of incidence; this loss in positive decibels will be referred to as the transmission loss for parallel polarization. t ⊥ (␺ ) = leakage power-loss ratio for an incident wave polarized with the E-field polarized perpendicular to the plane of incidence; this loss in positive decibels will be referred to as the transmission loss for perpendicular polarization.

␺ 0 , ␺ 1 , ␺ E = polar angles defining boundaries of the solid and perforated reflector surface regions, respectively (Figure 2.2).

Referring to the geometry of Figure 2.2, for a parabolic antenna whose surface is perforated periodically with circular holes, t || (␺ ) and t ⊥ (␺ ) can be calculated through the use of a computer program provided by C. C. Chen employing the equations given in [3]. If only approximate values are needed below 32 GHz, then the approximate Otoshi formulas given in (2.1) and (2.2) can be used. For this section, it will be assumed that there are no losses due to finite metal conductivity and paint. Therefore, in (2.6), it will be assumed that R S = 0 and (⌬TA )OL = 0. If one wishes to compute ohmic losses of a DSN antenna, one can use the value of R S for a painted aluminum surface given in [7] and use that value in (2.6). For circular polarization, let p 1 (␺ ) = p 2 (␺ ) = p (␺ ) in (2.7). Then noise temperature due to leakage through perforated panels becomes


77 ␺E

冕

(⌬TA )LL =

TG (␺ ) p (␺ ) t E (␺ ) sin ␺ d␺

␺1

(2.8)

␲

冕

p (␺ ) sin ␺ d␺

0

where t E (␺ ) is the effective power transmission coefficient expressed as t E (␺ ) =

t || (␺ ) + t ⊥ (␺ ) 2

(2.9)

For best accuracy, p (␺ ) should be determined from subreflector patterns at every frequency of interest. However, subreflector patterns are not usually readily available, and it takes special software to calculate them from horn patterns. If subreflector patterns p 1 (␺ ) and p 2 (␺ ) are known, they should be used in (2.7). For simplicity it will be assumed that p (␺ ) does not change with frequency and the following conditions exist: p (␺ ) = 0 for 0 ≤ ␺ < ␺ 0 p (␺ ) = 1

for ␺ 0 ≤ ␺ ≤ ␺ E

p (␺ ) = 0 for ␺ E < ␺ ≤ ␲ where ␺ 0 is the subreflector angle at which the solid panel section begins. Normally for a focal-point-fed parabola, ␺ 0 would be zero, but for DSN Cassegrain antennas, ␺ 0 is an angle that is typically between 2 and 6 degrees. For example, for the 34-m BWG antenna, the solid panel section actually begins at the outer edge of the BWG hole opening on the main reflector surface. For the 70-m antenna, the solid panel section begins at the base of the cylindrically shaped Mod III section. These assumptions made on subreflector patterns should not cause significant errors in the final noise temperatures because most Cassegrain antennas are designed to have uniform illumination of the main reflector. Application of the above assumptions on p (␺ ) to (2.7) leads to the denominator of (2.7) becoming ␺E

␲

D=

冕

p (␺ ) sin ␺ d␺ =

冕

sin ␺ d␺

(2.10)

␺0

0

= cos ␺ 0 − cos ␺ E The numerator of (2.7) becomes ␺E

N=

冕

␺1

TG (␺ ) t E (␺ ) sin ␺ d␺

(2.11)

78

Reflector Surfaces

It was assumed that t E (␺ ) is independent of ␾ . While this assumption could be made for DSN antenna perforated panels at frequencies below 32 GHz, the assumption becomes increasingly invalid as frequencies go above 40 GHz. The method used to partially overcome the problem was to compute t E (␺ , ␾ ) over a range of 0 ≤ ␾ < 2␲ and then compute an average t E (␺ , ␾ ) and assume that the average value could be used for t E (␺ ) in (2.9). The brightness-temperature function t G (␺ ) was assumed to be independent of ␾ because the antenna is assumed to be located above a flat desert ground environment [8]. Furthermore, it is the practice to assume that t G (␺ ) can be replaced by an effective ground brightness temperature TGE that is a constant. For DSN antennas and a flat desert ground, a value of 268K is assigned for zenith-pointing antennas [4]. Equation (2.11) then becomes ␺E

N = TGE

冕

t E (␺ ) sin ␺ d␺

(2.12)

␺1

The parameter t E (␺ ) varies slowly over the reflector surface so that numerical integration methods can be employed over rather wide intervals. For this section, the integration was performed over four regions of integrations of equal widths computed from ⌬␺ =

冉

冊

␺E − ␺1 5

␺ i + 1 − ␺ i = ⌬␺ for i = 1, 4

(2.13) (2.14)

Now (2.8) can be written as 4

(⌬TA )LL =

∑

i=1

Ti

(2.15)

where ␺i + 1

T t Ti = GE Ei D

冕

sin ␺ i d␺

(2.16)

␺i

=

TGE t Ei (cos ␺ i − cos ␺ i + 1 ) for i = 1, 4 D

Note that when i = 4, then ␺ 5 = ␺ E . Further note that t Ei is the average t E (␺ ) over the interval ␺ i to ␺ i + 1 computed from t Ei =

t E (␺ i ) + t E (␺ i + 1 ) 2

and the expression for t E (␺ ) was given in (2.9).

(2.17)


79

2.1.3.2 Gain Loss

Consider the reflections off the paraboloidal surface as shown in Figure 2.2. Using the same assumptions used to derive the noise temperature equation, the total effective-power reflection coefficient becomes ␺E

1 | ⌫E | 2 = D

冕|

2

⌫ (␺ ) | p (␺ ) sin ␺ d␺

(2.18)

␺0

where the expression for D was given in (2.10). It is assumed that the power 2 reflection coefficient | ⌫ (␺ ) | is a function of ␺ only and not also of ␾ . In the absence of ohmic losses

| ⌫ (␺ ) | 2 = 1 − t E (␺ )

(2.19)

where t E (␺ ) was defined in (2.9). If the integration is performed over the solidand perforated-panel sections numerically, (2.18) can be written as 2

| ⌫E | = I 0 +

4

∑

i=1

Ii

(2.20)

where I 0 is the integrated value for the solid panel section, expressed as ␺1

1 I0 = D

冕|

2

⌫ (␺ ) | p (␺ ) sin ␺ d␺

(2.21)

␺0

2

and assuming that p (␺ ) = 1 and | ⌫ (␺ ) | = 1 over the interval ␺ = ␺ 0 to ␺ 1 , the expression given in (2.21) reduces to I0 =

cos ␺ 0 − cos ␺ 1 D

(2.22)

for the perforated panel regions. Again subdividing it into the same four regions as was done for noise temperature, then for i = 1 to 4, ␺i + 1

1 Ii = D

冕|

2

⌫ (␺ ) | p (␺ ) sin ␺

␺i

=

1 | ⌫ (␺ i ) | 2 (cos ␺ i − cos ␺ i + 1 ) D

(2.23)

80

Reflector Surfaces

where

| ⌫ (␺ i ) | 2 = 1 − t Ei

(2.24)

where t Ei was given in (2.17). Then substitutions into (2.18) give 2

| ⌫E | =

1 1 (cos ␺ 0 − cos ␺ 1 ) + D D

4

∑ 冠1 − t Ei 冡 (cos ␺ i − cos ␺ i + 1 )

(2.25)

i=1

and gain loss in decibels is (G L )dB = 10 log | ⌫E |

2

(2.26)

2.1.4 Perforated-Plate and Perforated-Panel Geometries

It will be assumed that the antenna has panels of the perforated-plate geometry shown in Figure 2.1, where the incident wave E-field is polarized perpendicular and parallel to the incidence plane. The angle of incidence upon the plate is the angle ␪ and is equal to half the subreflector angle ␺ shown in Figure 2.2. The angle ␾ is the spherical coordinate system azimuthal angle that defines the orientation of the plane of incidence about the Z-axis. The rows of holes are staggered to form an equilateral triangle pattern arrangement. For circular polarization, the angle ␾ varies from 0 to 360 degrees, but the properties for this equilateral-triangle hole pattern arrangement repeat every 60 degrees. For this study, calculations were made with the ␾ angle varying from 0 to 90 degrees in 10-degree increments and then the results were averaged. The needed parameters for calculating leakage are the plate parameters d, a, and t, shown in Figure 2.1, which, respectively, are hole diameter, hole-to-hole spacing, and plate thickness. For both the 34-m and 70-m antennas, d, a, and t are 3.2 mm (1/8 inch), 4.8 mm (3/16 inch), and 1.8 mm (0.070 inch), respectively. The main reflectors on 34-m BWG antennas are paneled with curved solid sheet panels starting from the BWG opening radius of 1.2m and going to 13m out from the main reflector Z-axis (Figure 2.2). Then the perforated panels go out from the 13-m radius to an outer reflector edge radius of 17m. This results in the perforated area being 41.74 percent of the total reflector surface area as projected on the aperture plane. The subreflector angles ␺ at the beginning of the perforated section and at the outer edge of the panel sections were calculated to be 61.2 and 75.6 degrees, respectively (see Figure 2.2). For 70-m antennas, the solid-sheet panels go from a Mod III section outer radius of 3.2m out to 18.788m. Then perforated panels begin at the 18.788-m (739.688-inch) radius and go out to the outer reflector edge of 35.0107m (1,378.375 inches). The ratio of the perforated panel area to the total actual reflector area is calculated to be 71.8 percent. The subreflector angles at the beginning of the perforated section and at the outer edge of the panel sections were calculated


81

to be 38.2 and 65.8 degrees, respectively, where the subreflector angle, ␺ , can be seen depicted in Figure 2.2. The subreflector angle from the focal point to a point on an assumed parabolic surface can be calculated from

␺ = 2 tan−1

冉冊 r 2F

(2.27)

and the incidence angle at the reflection point is

␪ = ␺ /2

(2.28)

where r = radius from the paraboloid central z-axis to a point on the parabolic surface. F = paraboloid focal length. If r is not known but ␺ is known, then r can be calculated from r = 2F tan

冉冊 ␺ 2

(2.29)

The parabola focal length F is equal to 11.68m (460 in.) for the 34-m BWG antenna and 28.89m (1,137.3 inches) for the 70-m antenna. Tables 2.1 and 2.2 list other pertinent data needed to perform the integrations of the formulas given in Section 2.1.3.

Table 2.1 Region Boundaries for a 34-m BWG Antenna Region

␺ min , degrees

␺ max , degrees

⌬␺ , degrees

␪ min , degrees

␪ max , degrees

r min , m

r max , m

Solid panel Region 1 Region 2 Region 3 Region 4

5.97 58.18 61.65 65.13 68.60

58.18 61.65 65.13 68.60 72.10

52.21 3.47 3.48 3.47 3.50

2.99 29.09 30.83 32.57 34.30

29.09 30.83 32.57 34.30 36.05

1.22 13.00 13.94 14.92 15.94

13.00 13.94 14.92 15.94 17.00

Table 2.2 Region Boundaries for 70-m BWG Antenna Region

␺ min , degrees

␺ max , degrees

⌬␺ , degrees

␪ min , degrees

␪ max , degrees

r min , m

r max , m

Solid Panel Region 1 Region 2 Region 3 Region 4

2.42 36.04 42.64 49.24 55.84

36.04 42.64 49.24 55.84 62.44

33.62 6.60 6.60 6.60 6.60

1.21 18.02 21.32 24.62 27.92

18.02 21.32 24.62 27.92 31.22

1.22 18.79 22.54 26.47 30.61

18.79 22.54 26.47 30.61 35.01

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Reflector Surfaces

2.1.5 Results

The transmission losses in decibels for this main reflector geometry as a function of frequency at and above 32 GHz are shown in Figures 2.3 and 2.4, respectively,

Figure 2.3

The 34-m BWG antenna perforated-panel transmission loss at and above 32 GHz for ␺ = 65.13 degrees. (‘‘Perp’’ and ‘‘Par’’ are perpendicular and parallel polarizations, respectively.) Invalid beyond 45 GHz due to grating lobes [6]. (Courtesy of NASA/JPLCaltech.)

Figure 2.4

The 70-m antenna perforated-panel transmission loss at and above 32 GHz for ␺ = 49.2 degrees. (‘‘Perp’’ and ‘‘Par’’ are perpendicular and parallel polarizations, respectively.) Grating lobes occur at 48 and 49 GHz [6]. (Courtesy of NASA/JPL-Caltech.)


83

for the 34-m BWG and 70-m antennas. They were calculated for subreflector angles between ␺ 1 and ␺ E , and the corresponding incidence angle thetas were ␺ /2. These losses were calculated through the use of a Fortran computer program furnished to JPL by C. C. Chen [3]. In a previous report [1] the same program was used to compute the transmission losses from 1 GHz to 45 GHz for perforated panels on the 64-m DSN antenna. At the time the article [1] was written, the 64-m antenna had panels of a larger hole diameter of 4.763 mm (0.1875 inch), a larger hole-tohole spacing of 6.350 mm (0.250 inch), and a larger thickness of 2.286 mm (0.090 inch). The larger hole diameter and spacing for the 64-m antenna caused the transmission loss to become 0 dB at about 43 GHz for a 0-degree incidence angle. The first grating lobe appeared at 37 GHz for a 30-degree incidence angle. The perforated panels on the current 34-m BWG and 70-m antennas enable operation at a higher frequency with acceptable noise contribution and gain losses. The plots shown in Figures 2.3 and 2.4 for the current DSN antennas are for transmission losses for the E-field perpendicular and parallel to the plane of incidence for azimuth angles ␾ = 0 and 90 degrees and apply to frequencies of 32 GHz and above. For circular polarization, the transmission losses in decibels are converted to power ratios, and the average is taken of the power ratios of perpendicular and parallel polarizations. Figures 2.3 and 2.4 show that, for the 34-m BWG and 70-m antennas, the transmission losses are about −10 dB at their highest permissible frequencies of operation. Grating lobes appear at frequencies above 45 GHz for the 34-m BWG antenna and above 47 GHz for the 70-m antenna and do not obey Snell’s Laws of Reflection and Transmission. Therefore, no calculations of noise temperatures are attempted when grating lobes appear. The results of calculations of noise-temperature contributions for the 34-m antenna are shown in Table 2.3 and plotted in Figure 2.5 for frequencies at and above 32 GHz. Figure 2.5 shows the contribution from each region and also the total from all four regions of integration. Calculations could not be made above 45 GHz because grating lobes occur in the outer perforated-panel regions. Table 2.4 and Figure 2.6 show similar data for the 70-m antenna. The noise temperature is a function of ␾ as well as ␪ . To partially overcome this problem, noise temperature was computed at ␾ = 0 degrees and then again for a new ␾ increased by 10 degrees until ␾ = 90 degrees was reached. Then the average noise temperature contribution and the standard deviation (SD) from the average were computed and plotted. For the 34-m BWG antenna, the perforated panel noise temperature contribution is about 0.4K at 32 GHz and increases to 6.0K at 45 GHz. For the 70-m antenna, the perforated-panel noise temperature contribution is 0.82K at 32 GHz and increases to 16.4K at 47 GHz. The antenna can be used at and above the grating-lobe-occurrence frequencies if the feed can be designed to illuminate inner perforated panel regions only, as shown in Table 2.5. If this can be done, then calculations show that the perforatedpanel noise temperature contributions are about 7.0K at 46 GHz for the 34-m BWG antenna and 26.5K at 49 GHz for the 70-m antenna, as shown in Table 2.5. However, by under-illuminating the main-reflector surface, the total antenna gain will become significantly lowered just due to the fact that the antenna aperture area is significantly decreased.

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Reflector Surfaces

Table 2.3 The 34-m BWG Antenna Perforated-Panel, Circular-Polarization Noise-Temperature Contributions Averaged over phi 0 to 90 Degrees (Effective Ground Brightness Temperature = 268K) Frequency, GHz

Region 1 Avg NT, K

Region 2 Avg NT, K

Region 3 Avg NT, K

Region 4 Avg NT, K

Total (Regions 1–4) Avg NT, K Std Dev, K

32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

0.095 0.110 0.128 0.150 0.176 0.208 0.247 0.295 0.357 0.436 0.540 0.680 0.878 1.169 1.639 2.554 5.255 Invalid

0.098 0.114 0.133 0.155 0.182 0.216 0.257 0.309 0.375 0.460 0.575 0.733 0.962 1.321 1.985 4.049 Invalid Invalid

0.101 0.117 0.137 0.160 0.188 0.224 0.267 0.322 0.393 0.486 0.612 0.792 1.066 1.545 2.816 Invalid Invalid Invalid

0.104 0.120 0.141 0.165 0.194 0.232 0.277 0.335 0.411 0.513 0.655 0.865 1.212 1.987 Invalid Invalid Invalid Invalid



Notes: ‘‘NT’’ is the noise temperature; ‘‘Avg’’ and ‘‘Std dev’’ are the average and the standard deviation of the average based on values at 10 phi angles going from 0 to 90 degrees in 10-degree increments. Invalid regions are due to the existence of grating lobes.

Figure 2.5

The 34-m BWG antenna perforated-panel noise temperature contributions at and above 32 GHz. The total beyond 45 GHz is invalid due to grating lobes [6]. (Courtesy of NASA/JPL-Caltech.)


85

Table 2.4 The 70-m Antenna Perforated-Panel, Circular-Polarization Noise-Temperature Contributions Averaged over phi 0 to 90 Degrees (Effective Ground Brightness Temperature = 268K) Frequency, GHz

Region 1 Avg NT, K

Region 2 Avg NT, K

Region 3 Avg NT, K

Region 4 Avg NT, K

Total (Regions 1–4) Avg NT, K Std Dev, K

32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49

0.174 0.201 0.233 0.270 0.315 0.369 0.434 0.513 0.610 0.731 0.881 1.073 1.318 1.639 2.065 2.643 3.450 4.611

0.196 0.226 0.262 0.305 0.357 0.418 0.493 0.585 0.698 0.840 1.020 1.251 1.554 1.957 2.511 3.292 4.448 6.268

0.215 0.249 0.289 0.336 0.394 0.463 0.549 0.653 0.784 0.950 1.162 1.440 1.813 2.328 3.075 4.219 6.191 10.695

0.231 0.268 0.312 0.365 0.428 0.505 0.600 0.718 0.867 1.059 1.311 1.649 2.123 2.820 3.955 6.257 Invalid Invalid

0.816 0.944 1.096 1.277 1.494 1.756 2.076 2.469 2.959 3.579 4.374 5.414 6.808 8.744 11.606 16.412 Invalid Invalid

0.002 0.003 0.003 0.004 0.005 0.006 0.008 0.010 0.013 0.019 0.029 0.047 0.083 0.167 0.388 1.339 Invalid Invalid

Notes: 1. ‘‘NT’’ is the noise temperature; ‘‘Avg’’ and ‘‘Std dev’’ are the average and the standard deviation of the average based on values at 10 phi angles going from 0 to 90 degrees in 10-degree increments. 2. Invalid regions are due to the existence of grating lobes. 3. If it is necessary to use the total perforated-panel areas for maximum gain, do not use the 70-m antenna above 47 GHz. At 47 GHz, the worst-case NT contribution will be 16.4 ± 1.34 K.

Figure 2.6

The 70-m antenna perforated-panel noise temperature contributions. Invalid above 47 GHz due to grating lobes in region 4 [6]. (Courtesy of NASA/JPL-Caltech.)

86

Reflector Surfaces Table 2.5 Summary of Results for 34-m BWG Antenna and 70-m Antenna Illuminating the Solid Panels and Only Perforated-Panel Regions Having No Grating Lobes

Frequency, GHz

34-m BWG Antenna Illuminate Only Regions Total NT, K

Std Dev, K

46 47 48

1, 2, and 3 1 and 2 1

7.02 7.90 6.95

1.51 2.57 2.66

16.40 26.51

0.96 3.34

70-m antenna 48 49

1, 2, and 3 1, 2, and 3

If it is necessary to use the total perforated-panel areas for maximum gain, do not use the 34-m antenna above 45 GHz, as shown in Table 2.3. At 45 GHz, the worst-case NT contribution will be 6.02 ± 0.84K. It is of interest to compare the results of the new method against the old method of calculating noise-temperature contribution for a parabolic antenna (see Section 2.1.2). When using the same average power transmission coefficient and effective ground brightness temperature for both methods, for the 34-m BWG antenna the new method gave 0.40 ± 0.002K versus 0.52 ± 0.003K for the old method at 32 GHz. The tolerances are the standard deviation due to ␾ variations. At 45 GHz, the new method gave 6.02 ± 0.84K versus 7.34 ± 0.63K using the old method. For the 70-m antenna, the new method gave 0.82 ± 0.002K versus 0.90 ± 0.002K using the old method at 32 GHz, and at 45 GHz the new method gave 8.74 ± 0.17K versus 9.30 ± 0.09K using the old method. Better agreement was obtained between values from the new and the old methods for the 70-m antenna. The closeness of the results of the new versus the old method seems to be related to the porosities of the two antennas, which is 41.7 percent for the 34-m BWG antenna and 71.8 percent for the 70-m antenna. Porosity here is defined as the ratio of the total perforated panel area to the total reflector surface area of the antenna where the areas are the areas as measured when projected on the aperture plane. At X-band or lower frequencies, it is reasonable to expect that less difference would be observed in values when calculating noise temperatures using the new versus the old method. Gain losses due to leakage through the perforated panels were calculated through use of formulas given in Section 2.1.3 and plotted in Figures 2.7 and 2.8. Figure 2.7 shows the gain loss for the 34-m BWG antenna to be small (about –0.005 dB) at 32 GHz but increasing to about −0.1 dB at 45 GHz. Figure 2.8 shows that, for the 70-m antenna, the gain loss is also small (about −0.01 dB) at 32 GHz, but it increases to about −0.28 dB at 47 GHz. 2.1.6 Concluding Remarks

The noise temperature contributions and gain losses due to leakage through perforated panels on both the 34-m BWG antenna and 70-m antenna have been calculated and presented. For the 34-m antenna, calculations above 45 GHz could not be


87

Figure 2.7

The 34-m BWG antenna gain loss due to leakage through perforated panels at and above 32 GHz. Grating lobes exist beyond 45 GHz [6]. (Courtesy of NASA/JPL-Caltech.)

Figure 2.8

The 70-m antenna gain loss due to leakage through perforated panels at and above 32 GHz. Grating lobes exist beyond 47 GHz [6]. (Courtesy of NASA/JPL-Caltech.)

made due to grating lobes that occur. For the 70-m antenna, grating lobes occur above 47 GHz. The results are worst case because it was assumed that p (␺ ) = 1 such that the subreflector pattern uniformly illuminates the main reflector for all angles of ␺ . If the actual subreflector pattern is known, improved accuracy can be obtained if an average p (␺ ) is calculated for each of the regions 1 through 4 shown in Table 2.3 or Table 2.4. Then multiply this average p (␺ ) by the calculated noisetemperature values of the applicable region and frequency and compute the total contribution as shown in Table 2.3 or Table 2.4. Subreflector patterns can be quite different depending upon the frequency, feed, and subreflector design. A subreflector pattern at 2.1 GHz for a 64-m antenna was shown by Bathker (see

88

Reflector Surfaces

Figure 2 of [9]) to have a spike at ␺ = 0, followed by noticeable ripples. As ␺ approached the edge of the main reflector, the pattern level began to drop rapidly. Subreflector patterns at 8.45 GHz for a shaped 64-m antenna were shown by Potter (see Figures 4–6, [10]) to be closer to the ideal case. Patterns at 8.45 GHz for a 26-m antenna with a vertex plate were shown by Williams and Reilly (see Figure 5a, [11]) to have a deep null in the region of ␺ = 0 degrees. It should be stated that these calculations of noise temperature contributions were made for the antennas pointing at zenith. An analysis by Otoshi [4] showed that simplification could be made by assuming that the effective ground brightness temperatures were 268, 214, and 166K for the antenna pointed at 90-, 30-, and 10-degree elevation angles. These were based on assuming the leakage through the reflector with perforations was mostly absorbed by desert ground and the portions not absorbed were reflected and absorbed by the sky. To compute noise temperatures at a 30-degree elevation angle, it is necessary only to multiply all of the results presented in this section by the ratio 214/268. Similarly, the noise temperatures at 10-degree elevation angles can be obtained by multiplying the results by the ratio 166/268. It is assumed that the strut supports do not scatter or contribute to noise temperature. The reason why the noise-temperature contributions become lower with elevation angle is that less of the leakage sees the ground when the antenna is pointed at low elevation angles. In the ideal case, for an antenna pointed at the horizon, half of the leakage goes up to the sky region. These results should be quite useful for radio scientists who desire use of the DSN antennas at frequencies higher than 32 GHz for radio science experiments.

2.2 Solid Panels 2.2.1 Basic Noise Temperature Relationships

This section presents the derivation of equations necessary to calculate noise temperature of a lossy flat-plate reflector. Reflector losses can be due to metallic surface resistivity and multilayer dielectric sheets, including thin layers of plating, paint, and primer on the reflector surface. The incident wave is elliptically polarized, which is general enough to include linear and circular polarizations as well. The derivations will show that the noise temperature for the circularly polarized incident wave case is simply the average of those for perpendicular and parallel polarizations. 2.2.1.1 Power Relationships

Although equations for power in an incident and reflected elliptically polarized wave can be derived in a straightforward manner, the equations for the associated noise temperatures are not well-known nor, to the author’s knowledge, can they be found in published literature. It is especially of interest to know what the relations are when expressed in terms of perpendicular and parallel polarizations and the corresponding reflection coefficients. The following presents the derivations of noise-temperature equations for three cases of interest. For the coordinate system geometry shown in Figure 2.9, the fields for an incident elliptically polarized plane wave at the reflection point are [12, 13]

2.2 Solid Panels

Figure 2.9

89

Coordinate system for incident and reflected plane waves. The symbols with boldface aˆ are unit vectors and ␪ i and ␪ r are angles of incidence and reflection, respectively. The plane of incidence is the plane of this page. Reproduced from [18].

E i = E xi aˆ xi + E yi aˆ yi

(2.30)

H i = H xi aˆ xi + H yi aˆ yi

(2.31)

E xi = E 1 e j (␻ t − kz i )

(2.32)

E yi = E 2 e j (␻ t − kz i + ␦ )

(2.33)

where

H xi = −

H yi =

E yi ␩

E xi ␩

(2.34)

(2.35)

where ␻ is the angular frequency, t is time, ␩ is the characteristic impedance of free space, k is the free-space wave number, and z i is the distance from an arbitrarily chosen source point on the incident wave ray path to the reflection point on the reflector surface (Figure 2.9). In (2.32) and (2.33), it is important to note that E 1 and E 2 are scalar magnitudes and ␦ is the phase difference between E xi and E yi . The Poynting vector [12] for the incident wave is expressed as Pi =

1 Re 冠E i × H i *冡 2

(2.36)

where ×, *, and Re denote cross product, complex conjugate, and real part, respectively. Then assuming all of the incident power travels through an area A in the direction of the Poynting vector, the total incident wave power is

90

Reflector Surfaces

P Ti =

冕冠

P i ⭈ aˆ zi 冡 dA

(2.37)

where ⭈ denotes the dot product. Substitution of (2.30) through (2.36) into (2.37) results in P Ti =

1 冠E 2 + E 22 冡 A 2␩ 1

(2.38)

The equations for the reflected wave are obtained by replacing the subscript i with r in all of the equations for the incident wave except for (2.32) and (2.33). From Figure 2.9, it can be seen that the expressions for E xr and E yr are E xr = ⌫|| E xi e −jkz r

(2.39)

E yr = ⌫⊥ E yi e −jkz r

(2.40)

where ⌫|| = the voltage reflection coefficient for parallel polarization at the reflection point and is a function of incidence angle ␪ i (see Figure 2.9). ⌫⊥ = the voltage reflection coefficient for perpendicular polarization at the reflection point and is a function of incidence angle ␪ i . z r = the distance from the reflection point on the reflector surface to an arbitrary observation point along the reflected ray path. Then following steps similar to those used to obtain (2.38), the total power for the reflected wave can be derived as P Tr =

1 冋 | ⌫|| | 2 E 12 + | ⌫⊥ | 2 E 22 册 A 2␩

(2.41)

It is assumed that the lossy conductor in Figure 2.9 has sufficient thickness so that no power is transmitted out the bottom side. Then the dissipated power is Pd = P Ti − P Tr

(2.42)

2.2.1.2 Noise Temperature Relationships

For the geometry of Figure 2.9, the equation for the noise temperature due to the lossy flat-plate reflector can be derived from Tn =

冉冊

Pd Tp P Ti

(2.43)

2.2 Solid Panels

91

where Tp is the physical temperature of the reflector in units of Kelvin. For example, if the lossy conductor is at a physical temperature of 20°C, then Tp = 293.16K. Use of (2.38), (2.41), and (2.42) in (2.43) gives Tn = 冠1 − | ⌫ep |

2

冡 Tp

(2.44)

where

| ⌫ep | 2 =

| ⌫|| | 2 E 12 + | ⌫⊥ | 2 E 22 2

(2.45)

2

E1 + E2

Equation (2.44) is the elliptically polarized wave noise-temperature equation that is general enough to apply to linear and circular polarizations as well. In the following, the noise-temperature expressions for three different polarization cases are derived. Case 1. If the incident wave is linearly polarized with the E-field perpendicular to the plane of incidence, then E 1 = 0 and (2.44) becomes Tn = (Tn )⊥ = 冠1 − | ⌫⊥ |

2

冡 Tp

(2.46)

Case 2. If the incident wave is linearly polarized with the E-field parallel to the plane of incidence, then E 2 = 0 and (2.44) becomes Tn = (Tn )|| = 冠1 − | ⌫|| | Case 3. becomes

2

冡 Tp

(2.47)

If the incident wave is circularly polarized, then E 1 = E 2 and (2.44)

Tn = (Tn )cp =

冋

1−

冠 | ⌫|| | 2 + | ⌫⊥ | 2 冡 2

册

Tp

(2.48)

Note then that (Tn )cp is also just the average of (Tn )⊥ and (Tn )|| or (Tn )cp =

1 [(Tn )⊥ + (Tn )|| ] 2

(2.49)

The reader is reminded that, since the reflection coefficients are functions of incidence angle ␪ i , the noise temperatures are also functions of ␪ i as well as of polarization. 2.2.1.3 Excess Noise Temperature Relationships

It is of interest to see what the relationship is for excess noise temperature as well. For painted reflector noise temperature analyses [14], it is convenient to use the term

92

Reflector Surfaces

excess noise temperature (ENT). It is defined in [14] as the total noise temperature of a painted reflector minus the noise temperature of reflector (bare metal) without paint. Mathematically, it is expressed as ⌬Tn = Tn2 − Tn1 = 冠1 − | ⌫2 |

2

冡 Tp − 冠1 − | ⌫1 | 2 冡 Tp

(2.50)

where ⌫1 and ⌫2 are the input voltage reflection coefficients as seen looking at the unpainted (bare conductor) and painted reflector surfaces, respectively, and are functions of incidence angle and polarization. These reflection coefficients can be obtained through the use of multilayer equations such as those given in [15]. Then from (2.46) through (2.50) it follows that, for the perpendicular-, parallel-, and circular-polarization cases, (⌬Tn )⊥ = (Tn2 )⊥ − (Tn1 )⊥

(2.51)

= 冠1 − | ⌫2 | ⊥ 冡 Tp − 冠1 − | ⌫1 | ⊥ 冡 Tp 2

2

(⌬Tn )|| = (Tn2 )|| − (Tn1 )||

(2.52)

= 冠1 − | ⌫2 | || 冡 Tp − 冠1 − | ⌫1 | || 冡 Tp 2

2

(⌬Tn )cp = (Tn2 )cp − (Tn1 )cp

(2.53)

Substitution of (2.49) into (2.53) gives (⌬Tn )cp =

1 1 [(Tn2 )⊥ + (Tn2 )|| ] − [(Tn1 )⊥ + (Tn1 )|| ] 2 2

=

1 {[(Tn2 )⊥ − (Tn1 )⊥ ] + [(Tn2 )|| − (Tn1 )|| ]} 2

(2.54)

Substitutions of (2.51) and (2.52) into (2.54) yield (⌬Tn )cp =

1 [(⌬Tn )⊥ + (⌬Tn )|| ] 2

(2.55)

Equation (2.55) shows that the ENT for the circular-polarization case is simply the average of the ENTs of perpendicular and parallel polarizations. Although not shown mathematically, the ENTs are functions of incidence angle ␪ i . 2.2.1.4 Applications

The NASA Deep Space Network (DSN) operates a network of large reflector antennas for deep-space communications. Minimizing the noise temperatures of these antennas and their associated receiving subsystems translates into maximizing the ground-received signal-to-noise ratios. A noise contributor that has not received

2.2 Solid Panels

93

much attention in the past is the noise-temperature contribution from the paints and primers on the antenna reflector surface. An example of the use of (2.46) and (2.47) is shown in Figure 2.10. Noise temperatures at 32 GHz, due to 6061-T6 aluminum only [14], are shown as functions of incidence angle. An example of the use of (2.55) is a plot of excess noise temperature as a function of the paint thickness of Triangle no. 6 paint [14] and zinc chromate primer. Plots of excess noise temperature for different thickness layers of paint and primer will be shown in Section 2.3. An example of the application of (2.49) was to study the noise temperature of a water film on a solid metallic sheet as a function of water film thickness. This application will be presented later in Section 2.4. 2.2.2 Dependence on Polarization and Incidence Angle 2.2.2.1 Approximate Formulas

In previous years, approximate formulas have been used for estimating the noise temperatures of mirrors caused by resistivity losses of the mirror surfaces as a function of incidence angle, polarization, frequency, and electrical conductivity of the metallic surface. The formulas were especially useful because their simplicity allowed calculations to be made through the use of a hand calculator rather than an extensive Fortran program. These approximate formulas were originally derived by Otoshi but not officially published. Even though the derivations of the formulas are straightforward, the associated equations showing the accuracies of these formulas are involved, and hence are not shown here, but can be found in the appendix of [16]. The approximate formulas were later used in an article by Veruttipong [17] for BWG mirror noise-temperature calculations where the incidence angles could be as high as 60 degrees. Since the formulas were to continue to be used for a

Figure 2.10

The noise temperature of a flat 6061-T6 aluminum mirror at 32 GHz and 293.2 K (20°C) physical temperature. Although not shown, the noise temperature curve for circular polarization is the average of those for parallel and perpendicular polarizations [14]. (Courtesy of NASA/JPL-Caltech.)

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Reflector Surfaces

variety of antenna applications, it was decided that the derivations be documented and the accuracies of the formulas be studied in depth. This section presents the results of the in-depth study. A significant portion of the material presented here was extracted from [16]. For the case of a linearly polarized wave with the E-field polarized perpendicular to the incidence plane, the approximate noise temperatures due to resistivity losses of the mirror surface can be calculated from (Tn′ )⊥ =

冉

冊

4R S cos ␪ i Tp ␩o

(2.56)

For a linearly polarized wave with the E-field polarized parallel to the incidence plane, (Tn′ )|| =

冉

冊

4R S Tp ␩ o cos ␪ i

(2.57)

and for a circularly polarized wave [18], (Tn′ )cp =

1 [(T ′ ) + (Tn′ )|| ] 2 n ⊥

(2.58)

where primes denote approximate formulas in contrast to exact formulas. The symbols ␪ i , R S , ␩ o , and Tp are, respectively, the angle of incidence, surface resistivity in ohms per square, the characteristic impedance of free space, and the physical temperature of the mirror surface in Kelvin. The surface resistivity for nonmagnetic metal is calculated from R s = 0.02␲

√

f GHz 10␴ n

(2.59)

where f GHz is the frequency in gigahertz and ␴ n is the normalized electrical conductivity of the metal calculated by dividing the actual electrical conductivity by 107. For example, for 6061-T6 aluminum, the actual electrical conductivity is 2.3 × 107 mhos/m, so that ␴ n is equal to 2.3 and is assumed to be constant with frequency over the microwave frequency region of 1.0–40 GHz.

2.2.2.2 Exact Formula

The exact values can be obtained from equations of reflection and transmission coefficients for parallel and perpendicular polarizations for a wave incident upon a dielectric sheet [19]. The parameters, which must be input to the exact equations, are frequency, incidence angle, the complex relative dielectric constant of the dielectric, and sheet thickness. For a solid metallic reflector, the real and imaginary parts of the complex dielectric constants are

2.2 Solid Panels

95

∈′ = 1.0 ∈″ =

(2.60)

18␴ f GHz

where ␴ = actual electrical conductivity of the metal or 107 times ␴ n , defined previously in (2.59). For example, for aluminum at 8.45 GHz

␴ = 2.3 × 107 mhos/m so from (2.60) ∈″ = 18 × 2.3 × 107/8.45 = 4.9 × 107 Then let the thickness of the metallic surface be sufficiently large (at least 10 skin depths) so that the transmission coefficient is zero. For example, for 6061-T6 aluminum at 8.42 GHz, with ␴ n = 2.3, 10 skin depths would correspond to 0.0114 mm (0.00045 inch) [7]. Then the dissipative power loss ratio (DPR) for a single mirror is simply [20] DPR = 1 − | ⌫ |

2

(2.61)

where ⌫ is the input voltage reflection coefficient and the vertical bars denote magnitude. The derivation for the expression of DPR for cascaded mirrors is given in [21]. Noise temperature is then calculated from Tn = DPR × Tp

(2.62)

where Tp was previously defined. The exact calculations become too cumbersome to perform with a hand calculator because of the complex parameters, and, therefore, should be done through the use of a Fortran program such as the one called SLAB.FOR written for this purpose. It was discovered later that nearly identical exact values could be obtained with the simpler formulas given in this section for metal sheets.

2.2.2.3 Applications Sample Case 1

For this analysis, let Tp = 290K, ␩ o = 120␲ ohms, and f GHz = 8.45, with the metal reflector made from 6061-T6 aluminum, which has a normalized electrical conductivity of 2.3 at 8.45 GHz based on actual measurements [7]. Approximate noise temperatures as calculated from (2.56) through (2.58) are easy to calculate based on these input parameters. Although noise temperatures can be plotted, it is thought that displaying the errors associated with the formulas would be more informative.

96

Reflector Surfaces

The conventional practice is to define error as Error = (Approximate Value) − (Exact Value)

(2.63)

Figure 2.11 shows that, for perpendicular polarization, the approximate formula is valid up to ␪ i = 89.9 degrees, and the errors fall between the bounds of ± 0.0003K and seem to be due mainly to numerical computation errors. Figure 2.12 shows that, for parallel polarization, the error becomes greater than 0.1K at ␪ i = 89.1 degrees, and for circular polarization, the error becomes 0.1K at ␪ i = 89.4 degrees. In Figure 2.12, values below theta of 85 degrees were purposely not plotted because the errors were less than 0.003K and could not be seen on the linear scale of Figure 2.12. Sample Case 2

To see how accurate the approximate formulas are for the same aluminum sheet at a higher frequency such as 32 GHz, a second case was studied. It is generally 0.0004

0.0003

Noise Temperature Error, K

0.0002

0.0001

0.0000

-0.0001

-0.0002

-0.0003

-0.0004 0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90

Theta, deg

Figure 2.11

Approximate Formula Error Plot for Aluminum Sheet at 8.45 GHz, Perpendicular Polarization [16]. (Courtesy of NASA/JPL-Caltech.)

2.2 Solid Panels

97

3.5

3.0


2.5

2.0

1.5

1.0

0.5

Parallel Pol Circ Pol

0.0 85

86

87

88

89

90

Theta, deg Figure 2.12

Approximate Formula Error Plot for Aluminum Sheet at 8.45 GHz, Parallel and Circular Polarizations [16]. (Courtesy of NASA/JPL-Caltech.)

true that while surface resistivity, R S , is a function of frequency [see (2.59)], the value of electrical conductivity of metals generally stays constant with frequency. The surface roughness, however, causes the effective resistivity to be higher than predicted when taking the square root of the ratios of frequencies and, hence, in practice makes the effective electrical conductivity seem lower than the predicted value at higher frequencies. However, for this study, it will be assumed that the normalized electrical conductivity of aluminum remained the same at 32 GHz as it was for 8.45 GHz. Therefore, for this second case, let Tp = 290K, ␩ o = 120␲ ohms, f GHz = 32, and ␴ n = 2.3 for 6061-T6 aluminum. Figure 2.13 shows that at 32 GHz, for perpendicular polarization, the error is less than ±0.0003K up to ␪ i = 89.5 degrees. Figure 2.14 shows that at 32 GHz, for parallel polarization, the error becomes 0.1K at ␪ i = 88.2 degrees, and for circular polarization the error is 0.1K at ␪ i = 88.8 degrees. In Figure 2.14, values below ␪ i = 85 degrees were purposely not plotted because the errors were less than 0.01K for ␪ i < 85 degrees and could not be seen on the linear scale of Figure 2.14.

98

Reflector Surfaces 0.0004

0.0003


0.0002

0.0001

0.0000

-0.0001

-0.0002

-0.0003

-0.0004 0

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

90

Theta, deg

Figure 2.13

Approximate formula error plot for aluminum sheet at 32 GHz, perpendicular polarization [16]. (Courtesy of NASA/JPL-Caltech.)

Although not shown plotted, the errors are higher if the electrical conductivity of the metal is lower. For example, a case where ␴ n = 1.0 rather than 2.3 for the metal showed that the error for parallel polarization is 0.2K at 89.1 degrees at 8.45 GHz as compared to an error of 0.1K when ␴ n = 2.3. These results show that the errors as functions of incidence angles go up when frequency is higher and if conductivity is lower. It is desirable to be able to predict the accuracies of the approximate formulas given by (2.56) through (2.58) for any given set of parameters such as incidence angle, frequency, and electrical conductivity of the metal without having to resort to use of a Fortran program that is not generally available to workers in the field. It would be desirable also to be able to calculate these errors easily and accurately through the use of simple formulas and a hand calculator. Simple formulas for this purpose have been derived and are given in the appendix of [16]. 2.2.2.4 Conclusions

Approximate formulas have been presented and shown to be very accurate for incidence angles as high as 89.2 degrees even at frequencies as high as 32 GHz.

2.2 Solid Panels

Figure 2.14

99

Approximate formula error plot for aluminum sheet at 32 GHz, parallel and circular polarizations [16]. (Courtesy of NASA/JPL-Caltech.)

The maximum value at which the formulas can be used, therefore, is much higher than the 40-degree upper limit previously assumed. Most of the noise temperatures and associated errors can be calculated through the use of a hand calculator. A Fortran program will need to be used only if it is desired that accurate noise temperatures be calculated for incidence angles above the 89.5-degree region (or incidence angles close to grazing angles).

2.2.3 Electrical Conductivity of Various Metals

This section presents the results of electrical conductivity measurements made at 8.420 GHz on samples of the structural steel material used to fabricate shrouds on a DSN 34-m-diameter BWG antenna. Test results show that the structural steel samples at this microwave frequency had effective conductivities that were about 50 times worse than published dc values and 230 times worse than the measured conductivities of aluminum test samples. Conductivity data is also presented for other candidate materials that could be used to fabricate BWG shrouds. Of interest

100

Reflector Surfaces

are the improvements or degradations that were observed after some of the metal test samples were surface treated, plated, or painted.

2.2.3.1 Introduction

The shroud material used in the DSS-13 BWG antenna was made from structural steel rather than aluminum for the following reason. For a properly designed BWG system, only a small fraction of the total beam power illuminates the BWG shroud walls, and it was reasoned that currents on the BWG walls had to be small. Then it followed that shroud-generated noise temperature (due to resistive losses in the shroud walls) would be small whether steel or aluminum was used. In the absence of objections based on electrical requirements, structural steel was chosen for the shroud material on the basis of superior structural strength. What was not considered was the increased illumination of shroud walls and potentially significant increase of noise temperature that would occur when mirrors were imperfectly aligned. For this practical situation, good electrical conductivities of the shroud walls become very important. It was previously assumed that the conductivity of steel was close to being the same as the dc value of 0.5 × 107 mhos/m [22], and preliminary calculations showed that the noise contributions (due to BWG wall losses) were negligibly small. Later, it was noted by this author that the electrical conductivity of steel might be significantly worse at microwave frequencies than at dc. Due to the scarcity of conductivity data of steel at the initial phase of this study, an experimental program was initiated to obtain samples of the BWG shroud material and other candidate shroud materials. The primary goal was to measure their electrical conductivities at an X-band frequency close to the BWG antenna frequency of operation. A secondary goal was to determine the amounts of improvement or degradation that resulted after the test samples were surface treated, plated, or painted. The purpose of this section is to make available the findings of this experimental program. The following subsections present the formulas needed to calculate conductivity and skin depth at microwave frequencies, the measurement method used, and the test results.

2.2.3.2 Theory

The expression for the surface resistivity of a magnetic or nonmagnetic conductor in ohms/square is [12] R S = 20␲

√

f GHz ␮ r ␴

(2.64)

where f GHz is the frequency in gigahertz, ␮ r is the relative permeability, and ␴ is the electrical conductivity in mhos/m. It is important to note that ␴ is the absolute electrical conductivity and not the normalized value, which is smaller by a factor of 107. By defining effective conductivity as

2.2 Solid Panels

101

␴ eff =

␴ ␮r

(2.65)

Equation (2.64) then becomes R S = 20␲

√ √

f GHz ␴ eff

= 0.02␲

(2.66)

f GHz 10(␴ eff )n

where (␴ eff )n is the normalized effective conductivity derived by dividing the actual effective conductivity in mhos/m by 107. The expression for the effective conductivity, as derived from (2.66), is

␴ eff =

冉冊 20␲ RS

2

f GHz

(2.67)

where ␴ eff is in units of mhos/m and (␴ eff )n = ␴ eff × 10−7. The value of R s is usually known from previous measurements made at test frequency f GHz . Skin depth [7] in micrometers is calculated from

␦␮m =

100 2␲␮ r √10f GHz (␴ eff )n

(2.68)

For example, a nonmagnetic material such as aluminum has a ␮ r = 1.0 and a typical conductivity of 2.3 × 107 mhos/m or a normalized effective conductivity of 2.3 at 8.42 GHz. Then from (2.68), the skin depth is 1.14 ␮ m (45 ␮ in.). In contrast, a highly magnetic material, such as ASTM1 A36 steel, as will be shown later, has a ␮ r = 9985 and (␴ eff )n = 0.01. Substitutions into (2.68) reveal that the skin depth is only 0.0017 ␮ m (0.07 ␮ in.). Approximate formulas for computing noise temperature from R S were given previously in (2.56) and (2.57). The relationships of R S to reflection coefficient for a metallic surface are

| ⌫⊥ | ≈

√

1−

4R S cos ␪ i ␩0

(2.69)

and

| ⌫|| | ≈

√

1−

4R S ␩0

冉冊 1 cos ␪ i

and for circular polarization [18], 1.

ASTM is the abbreviation for American Society for Testing and Materials.

(2.70)

102

Reflector Surfaces

| ⌫cp | =

√

| ⌫⊥ | 2 + | ⌫|| | 2 2

(2.71)

where ␩ 0 = 120␲ and ␪ i is the incidence angle. The above relationships are known to be valid for ␪ i up to 40 degrees, but could be valid for higher incidence angles depending on the value of R S /␩ 0 . An empirical formula, supported by substantial experimental data, has been derived showing the relationship of reflection coefficient to noise temperature due to a shroud in a BWG system. The formula is Tn = ␣ 冠1 − | ⌫e |

2N

冡 Tp

(2.72)

where

␣ = fraction of the total radiated horn power that strays from the primary BWG path and illuminates the shroud material, power ratio. ⌫e = effective voltage reflection coefficient of the stray signal at the shroud wall, taking into account the polarization and incidence angle [see (2.45)]. N = number of times that the stray incident waves reflect off the shroud walls before arriving at cold sky. Tp = physical temperature of the shroud walls, K. 2.2.3.3 Measurement Technique

The TE011 mode resonant-cavity technique used to obtain the test results for this section is described in [23] and in an earlier paper by Bussey [24]. Figure 2.15

Figure 2.15

The TE 011 mode X-band cavity used for resistivity measurements at 8.420 GHz. (Courtesy of NASA/JPL-Caltech.)

2.2 Solid Panels

103

shows the X-band cavity that was used for these measurements. A flat plate sample of a metallic material to be tested is placed on top of the open cylindrical cavity. For accurate measurements of Q, an HP 8510C automatic network analyzer (ANA) was employed. Insertion losses at frequencies of interest are measured with the ANA. Upon command, the computer finds the required frequency of minimum insertion loss and the frequencies of the 3-dB points to 0.1-kHz resolution, as compared to 1-kHz resolution obtained previously with other setups. Insertion loss can be measured to 0.02-dB resolution. Visual displays of insertion loss versus frequency are available on screen. An option is available for real-time hard copies of the frequency-response plots. Resistivity is determined from measured loaded- and unloaded-Q at a nominal frequency of 8.420 GHz. Effective conductivity is calculated from the measured resistivity using (2.67). Henceforth, for convenience the term effective electrical conductivity will be shortened to conductivity. 2.2.3.4 Description of Shroud Test Samples

Test samples were made from ASTM A36 steel, AISI grade 1108 steel, galvanized steel, copper, brass, and 6061-T6 aluminum. All test samples were 10.16 cm × 10.16 cm square. The thicknesses were arbitrary. Nonflatness of the test samples will cause the resonant frequency to shift from the nominal cavity resonant frequency of 8.42 GHz. One of the test samples (see Figure 2.16) was made from a bare type of ASTM A36 structural steel, the same material used to fabricate the shrouds for the DSS 13 BWG antenna. The chemical composition of this material [other than iron (Fe)] is 0.26 percent maximum carbon, 0.04 percent maximum phosphorus, and 0.05 percent maximum sulfur [25]. Samples of this material were tested before and after being painted with 0.015-mm (0.6-mil) thickness zinc-chromate primer and with 0.025-mm (1-mil) thickness thermal-diffusive white paint.2 In the attempt to find ways to improve the electrical conductivity of ASTM A36 steel for BWG shroud applications, a new test sample was made by treating the bare-metal surface with a zinc-plating process. For the zinc-plating process, a black-colored dye arbitrarily was used, but clear zinc plating could have been specified instead. Other samples were made by spray painting bare metal surfaces with cold galvanized paint. One of the other candidate materials tested was AISI grade 1018 steel [26] and shall henceforth be referred to as 1018 steel. This material has dc conductivity and magnetic properties similar to those of ASTM A36 steel and is readily available in flat sheet stocks. This material was also tested with and without thermal-diffusive white paint. Aluminum is one of the most commonly used materials for antenna reflector applications and is a prime candidate for use as shroud material for BWG systems. To prevent oxidation in hostile environments, aluminum is sometimes surfacetreated. Two types of aluminum samples with surface treatments were fabricated and tested. These aluminum samples were treated either with: (1) an irriditing process, or (2) an anodizing process. The term ‘‘irridite’’ is used to describe the 2.

This special paint is called Triangle no. 6, synthesized and patented by the Triangle Paint Company.

104

Reflector Surfaces

(b)

(a)

(d)

(c)

Figure 2.16

Samples of the tested ASTM A36 shroud material (10.16 cm × 10.16 cm): (a) painted with primer and Triangle #6 thermal diffusive white paint; (b) bare metal; (c) zincplating (with black dye) surface treatment; and (d) galvanized spray-painted surface. (Courtesy of NASA/JPL-Caltech.)

surface treatment of aluminum samples or parts by a chemical dipping process. Not generally well known is the fact that irridite, yellow chemical film, and alodine are identical surface-treatment processes. Confusion sometimes occurs between the terms alodine and anodize, which are not equivalent processes. Alodine involves a chemical dipping process, whereas anodize refers to an electrochemical-oxidizing surface-treatment process. 2.2.3.5 Test Results

Table 2.6 summarizes the test results of the treated and untreated samples. It may be seen that unpainted and painted samples of type ASTM A36 steel had conductivities of 0.01 × 107 and 0.004 × 107 mhos/m, respectively, at 8.420 GHz. Slightly better conductivities of 0.023 × 107 and 0.008 × 107 mhos/m were measured for 1108 steel unpainted and painted samples, respectively.

2.2 Solid Panels

105

Table 2.6 Summary of Conductivity Measurements at 8.420 GHz

Relative Permeability a

Number of Samples Tested

Average Surface Roughness, ␮ m ( ␮ in.)

Normalized Skin Depth, Effective ␮ m ( ␮ in.) Conductivity b Comments

9,985

2

>6.35 (>250)

0.0017 (0.068)

0.010

BWG antenna 9,985 shroud ASTM A36 steel, primer only

1

1.78–2.62 (70–103)

0.0019 (0.077)

0.008

BWG antenna 9,985 shroud ASTM A36 steel, primer and thermaldiffusive white paint

1

2.36 (93)

0.0027 (0.108)

0.004

BWG antenna shroud ASTM A36 steel, zinc plating (with black dye)

9,985

3

6.35 (250)

0.0003 (0.010)

0.444

Significant improvement over bare metal

BWG antenna shroud ASTM A36 steel, cold galvanized spray paint

9,985

2

2.79–4.27 (110–168)

0.010 (0.395)

0.0003

Very bad conductivity might be due to surface roughness and paint

BWG antenna shroud ASTM A36 steel, cold galvanized spray paint

9,985

3

3.18 (125)

0.0025 (0.097)

0.005

About the same as with thermaldiffusive white paint

BWG antenna shroud ASTM A36 steel, silver painted

9,985

1

not measured 0.0012 (0.046)

0.022

Only a factor of 2 improvement

1018 steel

> 9,000

2

1.47 (58)

0.0013 (0.05)

0.023

1018 steel, same as above except painted with primer and thermaldiffusive white paint

> 9,000

1

0.64 (25)

0.0022 (0.085)

0.008

Paint had a big effect

Galvanized steel

not measured

2

0.58 (23)

not known

1.33

Good conductivity attributed to zinc content

Copper

1.0

3

0.71 (28)

0.80 (31.6)

4.68

Brass

1.0

1

0.53 (21)

1.51 (59.4)

Description BWG antenna shroud ASTM A36 bare steel

1.32

106

Reflector Surfaces

Table 2.6 Summary of Conductivity Measurements at 8.420 GHz (continued)

Relative Permeability a

Number of Samples Tested

Average Surface Roughness, ␮ m ( ␮ in.)

Normalized Skin Depth, Effective ␮ m ( ␮ in.) Conductivity b Comments

Aluminum 6061-T6

1.0

2

0.33 (13)

1.14 (44.9)

2.31

Aluminum 6061-T6, irridite

1.0

1

0.41 (16)

1.14 (44.8)

2.32

Aluminum 6061-T6, black anodized type IIc

1.0

1

0.46 (18)

1.24 (48.8)

1.96

Aluminum 6061-T6, black anodized type IIId

1.0

1

0.46 (18)

1.24 (48.8)

1.96

Aluminum 6061-T6 new samples

1.0

5

0.58 (25)

1.13 (44.5)

2.36

Aluminum 6061-T6 sample painted with zinc-chromate primer (Thickness of primer ~0.015 mm (0.6 mil))

1.0

2

1.63 (64)

1.18 (46.5)

2.16

Aluminum 1.0 6061-T6 with primer plus thermaldiffusive white paint (Thickness of primer plus paint ~0.025 mm (1 mil))

2

1.47 (58)

1.26 (49.5)

1.90

Description

a

The relative permeability values are relative to air.

b To get absolute conductivity in mhos/m, multiply values in this column c Type II refers to an anodizing process that treats the surface only. d

by 107.

Type III refers to an anodizing process that typically goes about 0.013 mm (0.5 mil) into the metal.

The zinc-plating process on ASTM A36 steel improved the conductivity from 0.01 × 107 to about 0.44 × 107 mhos/m. In contrast, the galvanized-paint process made the conductivity much worse than that for bare ASTM A36 steel and even worse than ASTM A36 steel painted with thermal-diffusive white paint. It is suspected that galvanized spray paint is not purely metallic and has lossy epoxy compounds. It might seem that if the paints were more highly conductive, then better results would be obtained. However, as shown in Table 2.6, the application of a very high grade of silver paint only improved the conductivity slightly from 0.01 × 107 mhos/m for bare metal ASTM A36 steel to 0.022 × 107 mhos/m for the silver-painted sample.

2.2 Solid Panels

107

Table 2.6 also shows the results of aluminum samples with surfaces treated with: (1) irriditing and (2) anodizing processes. Irriditing caused no noticeable change in the conductivity properties of bare aluminum, whereas anodizing degraded the conductivity only from 2.31 × 107 to 1.96 × 107 mhos/m, which is still acceptable. In addition, Table 2.6 shows that primer and thermal-diffusive white paint also did not significantly degrade the conductivity of aluminum even though the same paint significantly degraded the conductivity of ASTM A36 steel. It was discovered that the tested steel materials were highly magnetic with measured relative permeabilities in the 9,000–10,000 range (see Table 2.6). These values were about a factor of 3 higher than expected. In comparison, aluminum and copper have relative permeabilities of unity, and most types of stainless steel have relative permeabilities of less than 1.10. Although not reported here, the measured electrical conductivities of some types of stainless steel materials can be found in [27]. In addition, measurements of the conductivities of other metals can be found in [28–30]. The skin depth values shown in Table 2.6 were calculated from (2.68) using the measured permeability and effective conductivity values. It might not be strictly valid to use (2.68) for calculating skin depths of plated or painted materials that are highly magnetic. However, even in extreme limits where the calculated values might be in error by factors of 10 or 100, it can be stated conclusively that the skin depths (for highly magnetic materials) will generally be very small compared to the surface roughness. Vane [31] pointed out that conductive metals having high permeability tend to have poor effective conductivities because high permeabilities cause the skin depth to become very small. The effects of surface roughness and surface layers are accentuated because when skin depth is small, most of the RF currents tend to flow along the irregular surfaces. It is not surprising then that highly magnetic materials, such as ASTM A36 and 1108 steel with painted layers and poor surface finishes, tend to have very poor conductivities. For materials with relative permeabilities close to unity, the skin depth is larger, so RF currents tend to flow through more of the conductor volume rather than just at the surface. 2.2.3.6 Conclusions

Test results showed that zinc plating of the surface of ASTM A36 steel improved the effective conductivity of bare metal from 0.01 × 107 to 0.44 × 107 mhos/m. In contrast to the improved results from zinc plating, the conductivity was degraded to 0.004 × 107 mhos/m when a sample of this base metal was primed and painted with thermal-diffusive white paint. Galvanized spray paint on ASTM A36 steel samples also resulted in poor conductivities. It can be concluded that for highly magnetic steels with rough surfaces, the plating process will help to improve the conductivity significantly, but painting the surfaces with cold conductive paints will not. For comparison, the measured conductivity of aluminum was about 2.3 × 107 mhos/m or about five times better than steel with zinc plating. Irriditing or anodizing processes did not significantly degrade the conductivity. If anodized aluminum

108

Reflector Surfaces

material is chosen as the material for fabricating future BWG shrouds, it is recommended that, for better optical lighting purposes, a clear-dye anodizing process be specified.

2.3 Painted Panels 2.3.1 Background on Paint Study

Large reflector antennas are one of the key components of any communication and tracking systems. The main parameters dictating their electrical performance are the overall antenna system gain and noise temperature. These parameters are affected by many factors, such as aperture size, aperture-tapered illumination, surface tolerance, feed spillover, strut blockage and diffraction, surface conductivity resulting from protective paint, and so forth. A considerable amount of work has been directed toward optimizing every aspect of these factors except the microwave properties of the paint. This is, in particular, an important issue when one deals with extremely sensitive and highperformance antenna systems for deep-space applications. A thorough literature search revealed that very little information has been published on the microwave properties of paints and primers used on antenna reflector surfaces. A paint study was initiated at JPL ([14, 20, 32, 33]) to determine how much degradation of antenna noise temperature and gain occur as a function of paint thickness on antenna reflector surfaces. In this section, a summary of noise temperature and gain loss data will be presented for various combinations of paints and primers as functions of paint thickness, incidence angle, and polarization. 2.3.2 Background on DSN Antennas

All DSN antennas (70-m and 34-m diameter) have main- and subreflector-reflector surfaces that are painted with layers of white thermal diffusive paint to reduce solar heating and keep the reflector surfaces close to the outdoor ambient temperature. Figure 2.17 shows a view of a 34-m BWG antenna depicting the solid and perforated panel sections of the main reflector. Both the solid and perforated panels are made from 6061-T6 aluminum sheets that are painted with a layer of zinc chromate primer layer and a layer of Triangle no. 6 thermal diffusive white paint [20]. Figure 2.18 shows the subreflector, which is also painted with zinc chromate primer and Triangle no. 6 paint. The subreflector support legs, also shown in Figure 2.18, are made from structural steel and painted with organic zinc primer and Triangle no. 710 thermal reflective white paint [20]. As shown in Figure 1.28, the first focal point of this BWG system is the normal Cassegrain focus located close to the vertex of the main reflector, while the final focal point is about 35m and six additional mirrors distant in a subterranean room. Figure 2.19 shows one of the six BWG mirrors whose surfaces were painted with zinc chromate primer to keep the aluminum surfaces from oxidizing. The only BWG mirrors that have zinc chromate primer protective coatings are those for the first NASA/JPL BWG antenna that was built in 1990 at Deep Space Station 13 (DSS 13) for research and development purposes. BWG antennas that were built later for DSN operational

2.3 Painted Panels

109

Figure 2.17

The 34-m-diameter BWG antenna at DSS 13, showing painted solid and perforated reflector surfaces. (Courtesy of NASA/JPL-Caltech.)

Figure 2.18

The 34-m-diameter BWG antenna at DSS13, showing the painted subreflector and subreflector support legs. Author Tom Y. Otoshi is shown standing on the platform above the subreflector. (Courtesy of NASA/JPL-Caltech.)

purposes have aluminum mirror surfaces that were given an irridite surface treatment only. For predicted performance comparison purposes [4], it was of interest to know how much of the total system noise temperature for the DSS 13 BWG antenna was contributed by the paint on the main reflector and subreflector surfaces and zinc chromate primer on the six BWG mirrors. It was also of interest to

110

Reflector Surfaces

Figure 2.19

The 34-m-diameter BWG antenna at DSS13, showing one of the BWG mirrors (in the subterranean room) coated with zinc chromate primer. (Courtesy of NASA/JPLCaltech.)

accurately determine the noise temperature contributions from paints and primers on all DSN antennas. 2.3.3 Excess Noise Temperature and Added Gain Loss

In order to estimate the ‘‘excess noise temperature and added gain loss’’ (to be defined) for a painted reflector antenna, a computational method was applied based on electromagnetic wave reflection from a multilayer structure. A computer program for calculating reflection and transmission coefficients of a multilayer dielectric stack [15] was provided by the University of California, Los Angeles (UCLA) electrical engineering department. The inputs to the UCLA computer program are perpendicular or parallel polarization, frequency, incidence angle, ∈′r , (see Table 2.7), the electrical conductivity, and thickness for each layer in the multilayer stack. For the results at 32 GHz in this section, the measured dielectric constant and electrical conductivity values shown in Table 2.7 were used. The ANA measurement technique, used to obtain the values in this table, is fully described in [32, 33] and will not be discussed here. Figure 2.20 depicts the schematic of the geometrical configuration of the multilayer structure. To employ the UCLA program for the painted reflector case, the final dielectric layer of the stack was chosen to be a thick 6061-T6 aluminum

2.3 Painted Panels

111

Figure 2.20

Schematic configuration of various cases studied by changing the incidence angle, paint and primer thicknesses, and material properties per Tables 2.7 and 2.8. Reproduced from [20].

sheet, which is the material used for the reflector surfaces of DSN antennas. When a thick metallic plate is used as the last layer, the useful outputs of the UCLA program are the overall multilayer input voltage reflection coefficient (magnitude and phase) and return loss in decibels. A second program was written to input the reflection coefficient values and compute noise temperatures and gain losses for perpendicular and parallel polarizations from the equations that will be given next. In practice, what is measured is the total noise temperature of a reflector surface coated with paint and primer layers. Often the changes of noise temperature due to these paint and primer layers are so small that it is difficult to show these changes on a total noise-temperature plot. Therefore, in this section, the contribution of the paint and primer layers only will be shown. This contribution is defined as excess noise temperature, whose equation will be derived and shown below. Once the input reflection coefficient is known for a particular paint/primer thickness, incidence angle, and polarization, the overall noise temperature of a painted reflector can be calculated from the approximate formula Tn = 冠1 − | ⌫in |

2N

冡 Tp

(2.73)

where ⌫in is the input voltage reflection coefficient as seen looking at the painted reflector. It applies to a particular polarization and incidence angle. N is the number of times that the incident wave reflects off reflectors with identical surfaces in cascade before arriving at the receive horn. Tp is the physical temperature of the reflector surface, K. This approximate formula is a simplification of the exact formula derived in [34]. If one is interested in the ENT contribution due to paint or primer or both, the following equation applies for the N number of reflectors case: ⌬Tn = Tn2 − Tn1 = 冠1 − | ⌫2 | = 冠 | ⌫1 |

2N

2N

冡 Tp − 冠1 − | ⌫1 | 2N 冡 Tp

− | ⌫2 |

2N

冡 Tp

(2.74)

112

Reflector Surfaces

where ⌫1 and ⌫2 are the input voltage reflection coefficients as seen looking at the unpainted (bare metal) and painted reflector surfaces, respectively. There are no restrictions in (2.74) regarding the value of N. It is required only that the values of | ⌫1 | and | ⌫2 | be less than or equal to unity and greater than or equal to zero. It also is required that | ⌫1 | ≥ | ⌫2 | . As N increases from one to a very large number, the ENT given by (2.74) increases to a maximum and then goes to zero as N continues to become very large. This is not obvious from a cursory examination of (2.74). To illustrate this behavior, take the case of | ⌫1 | = 0.999, | ⌫2 | = 0.9985, and Tp = 290K. For N = 1, 10, 100, 405, 1,000, 1,500, 2,000, 5,000, and 10,000, the ENTs, as calculated from (2.74) are, respectively, 0.29, 2.8, 22.6, 43.0,24.8, 11.2, 4.6, 0.01, and 0.0K. The reason ENT approaches zero for very large N is that in the limit the noise temperature Tn1 and Tn2 each become equal to the physical temperature Tp and, for thermodynamic reasons, neither can exceed Tp . The N corresponding to maximum ENT can be calculated from the expression below, which was derived from differentiation of (2.74) with respect to N and by using the usual calculus method to find the maximum:

N=

1 2

冤

冉冊冉 || || 冊

log10 log10

A B

⌫1 ⌫2

冥

(2.75)

where A = loge | ⌫2 | and B = loge | ⌫1 | . In the above example, it required 405 reflections for the ENT to reach the maximum. In practice, N is seldom greater than 10 in a BWG system. For low-loss cases and the N ≤ 10 case, an approximate expression for ENT can be derived as follows. Let

| ⌫1 | 2 = (1 − x 1 )

(2.76)

| ⌫2 | 2 = (1 − x 2 )

(2.77)

Then using a series expansion and dropping off higher-order terms,

| ⌫1 | 2N = (1 − x 1 )N ≈ 1 − Nx 1 for | ⌫2 | 2N = (1 − x 2 )N ≈ 1 − Nx 2 for

再再

x 1 ≤ 0.01

N ≤ 10 x 2 ≤ 0.01

N ≤ 10

(2.78)

(2.79)

Substitution of (2.78) and (2.79) into (2.74) gives an approximate equation for the ENT of ⌬Tn ≈ N (x 2 − x 1 ) Tp

(2.80)

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113

The purpose of deriving this approximate expression is to show that for low loss or the x 1 , x 2 Ⰶ 1 and N ≤ 10 cases, the ENT for the N mirror case is approximately equal to N times the ENT for the N = 1 mirror case. Also of interest is the added gain loss due to the paint and primer on a reflector surface. Added gain loss is defined as the total gain loss of the lossy reflector with the paint and primer layers minus the gain loss of the reflector only. For the N number of similarly painted mirror case, the added gain loss expressed in positive decibels is ⌬G dB = 10 log10 | ⌫1 |

2N

− 10 log10 | ⌫2 |

2N

= N 冠10 log10 | ⌫1 | − 10 log10 | ⌫2 | 2

2

(2.81)

冡

Note that the added gain loss for the N mirror case is exactly equal to N times the added gain loss for the single mirror case. This equation can be used for any value of N, but it is required that the values of | ⌫1 | and | ⌫2 | be less than or equal to unity and greater than zero, and it is required that | ⌫1 | ≥ | ⌫2 | . The appropriate reflection coefficient for perpendicular or parallel polarization is used in the above equations to obtain ENTs for perpendicular and parallel polarizations. The ENT for circular polarization is obtained by taking the average of the ENTs of perpendicular and parallel polarizations [18]. 2.3.4 Results and Performance Characterizations 2.3.4.1 General Comments

In order to provide an easy reference for design parameters used in this section, Figure 2.20 shows the schematic configuration of the various cases. The range of parameters used is indicated in Tables 2.7 and 2.8. Even though Table 2.7 shows

Table 2.7 Average Measured Paint/Primer Complex Relative Dielectric Constant Values in the 32-GHz Frequency Regiona

Paint or Primer

Frequency, GHz

⑀ ′r

⑀ ″r

Loss Tangent

Electrical Conductivity, mhos/m

Triangle no. 6 paint

31–33

5.908 0.019 SD

0.148 0.014 SD

0.025 0.002 SD

0.2631

Zinc chromate primer

32–34

4.361 0.001 SD

0.0949 0. 0001 SD

0.0218 0.00003 SD

0.1687

18FHR6 Paint

31–33

5.275 0.012 SD

0.153 0.008 SD

0.0291 0.0014 SD

0.2720

283 Primer

31–33

3.300 0.001 SD

0.121 0.001 SD

0.0367 0.0003 SD

0.2151

500FHR6 Paint

31–33

4.691 0.001 SD

0.111 0.001 SD

0.0236 0.0002 SD

0.1973

a SD = the standard deviation of the average based on the number of frequency points. Complex relative dielectric constant = 冠⑀ ′r − j⑀ ″r 冡. Loss tangent = ⑀ ″r /⑀ ′r . Electrical conductivity = ⑀ ″r × Frequency (GHz)/18. For this table, frequency (GHz) = 32.0 was used.

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Reflector Surfaces

Table 2.8 Comparison of Excess ENTs for Circular Polarization at 32 GHz for Four Different Configurations of Paint and Primer Layers at Selected Thicknesses and Incidence Angles Thickness t, mm

Thickness t, mil

Triangle No. 6 Configuration a ENT, K

0.0508 0.1270 0.1778 0.2540 0.3810

2 5 7 10 15

0.008 0.063 0.154 0.426 1.523

0.0508 0.1270 0.1778 0.2540 0.3810

2 5 7 10 15

0.0508 0.1270 0.1778 0.2540 0.3810

500FHR6 Configuation b ENT, K

18FHR6 Configuation c ENT, K

Zinc Chromate Configuation d ENT, K

0.003 0.034 0.089 0.259 0.932 15-Degree Incidence Angle

0.007 0.063 0.154 0.426 1.498

0.002 0.029 0.077 0.221 0.786

0.015 0.079 0.176 0.455 1.557


0.019 0.086 0.185 0.466 1.548

0.009 0.046 0.100 0.254 0.830

2 5 7 10 15

0.040 0.131 0.245 0.548 1.670


0.058 0.160 0.281 0.594 1.708

0.031 0.100 0.175 0.358 0.972

0.0508 0.1270 0.1778 0.2540 0.3810

2 5 7 10 15

0.088 0.231 0.380 0.731 1.899


0.131 0.301 0.467 0.842 2.023

0.073 0.203 0.318 0.557 1.244

0.0508 0.1270 0.1778 0.2540 0.3810

2 5 7 10 15

0.178 0.420 0.633 1.072 2.308

0.270 0.566 0.814 1.299 2.579

0.151 0.396 0.584 0.923 1.723

0-Degree Incidence Angle

a

0.153 0.405 0.603 0.971 1.876

Triangle no. 6 paint and a 0.0152-mm (0.6-mil)-thick layer of zinc chromate primer.

b 500FHR6 paint only. c 18FHR6 paint and 0.0152-mm d

(0.6-mil)-thick layer of 283 primer.

Zinc chromate primer only.

only values measured in the 31–33-GHz region, complex dielectric constant values were also measured over a frequency range of 23–35 GHz for most of the paint samples [32, 33]. The results presented in this section apply to the plane-wave case, but planewave solutions can be applied to small localized areas of curved mirrors. It was shown in [15] that, when localized individual plane wave contributions were added up, good results for the entire curved surface antenna were obtained. For all noise temperatures and ENTs presented in this section, the operating frequency is 32 GHz, and paints, primers, and reflectors are at a physical temperature of 293.2K (20°C).

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115

2.3.4.2 Plots as Functions of Incidence Angles

Figure 2.21(a, b) shows the total noise temperature and gain loss, respectively, of a 6061-T6 flat mirror for perpendicular and parallel polarizations. The noisetemperature and gain-loss values for 6061-T6 aluminum are based on an electrical conductivity of 2.3 × 107 mhos/m [7]. From Figure 2.21(a, b), it can be seen that, at a 0-degree incidence angle, the noise temperature of 6061-T6 aluminum is 0.23K, and the gain loss is 0.0034 dB. At a 60-degree incidence angle, the noise temperature for parallel polarization increases rapidly and is nearly 0.5K, and gain loss is close to 0.007 dB. Even though the noise temperature of the 6061-T6 aluminum mirror at 32 GHz seems high at a 0-degree incidence angle as obtained through the use of the UCLA computer program (see Section 2.3.3), the same high value was also obtained through the use of the approximate formulas given in (2.56) or (2.57) for ␪ i = 0 degrees. As may be seen from substitution of (2.78) into (2.73), if six mirrors are involved, these noise temperatures for bare-metal mirrors alone are increased by about a factor of six, or to 1.4K, which is surprisingly high.

Figure 2.21

(a) The total noise temperature and (b) the gain loss of a flat 6061-T6 aluminum mirror at 32 GHz [14]. (Courtesy of NASA/JPL-Caltech.)

116

Reflector Surfaces

ENTs and added gain losses as functions of incidence angles at 32 GHz are shown in Figures 2.22–2.25 for four specific thickness layers of paints and primers, as follows: 1. Figure 2.22(a, b) applies to the configuration of 0.127-mm (5-mil)-thick Triangle no. 6 paint and 0.0152-mm (0.6-mil)-thick zinc chromate primer on a 6061-T6 aluminum flat mirror. 2. Figure 2.23(a, b) applies to the configuration of 0.0508-mm (2-mil)-thick 500FHR6 acrylic urethane-based paint with no primer on a flat 6061-T6 aluminum mirror. 3. Figure 2.24(a, b) applies to the configuration of 0.127-mm (5-mil)-thick 18FHR6 paint and 0.0152-mm (0.6-mil)-thick 283 water-based primer on a flat 6061-T6 aluminum mirror. 4. Figure 2.25(a, b) applies to the configuration of 0.0152-mm (0.6-mil)-thick zinc chromate primer on a flat 6061-T6 aluminum mirror.

Figure 2.22

(a) The total ENT contribution and (b) the added-gain loss at 32 GHz due to 0.127-mm (5-mil)-thick Triangle no. 6 paint and 0.0152-mm (0.6-mil)-thick zinc chromate primer on a flat 6061-T6 aluminum mirror [14]. (Courtesy of NASA/JPL-Caltech.)

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117

Figure 2.23

(a) The total ENT and (b) the added gain loss at 32 GHz due to 0.0508-mm (2.0-mil)-thick 500FHR6 paint and no primer on a flat 6061-T6 aluminum mirror [14]. (Courtesy of NASA/JPL-Caltech.)

Although not shown in Figures 2.21–2.25, the noise temperatures and ENT curves for circular polarization are the average of those for parallel and perpendicular polarizations [18]. Note that in Figures 2.22–2.25 for parallel polarization, ENTs and added gain losses increase rapidly with increasing incidence angles after 30 degrees, while, for perpendicular polarization, the values decrease with increasing incidence angles. Triangle no. 6 paint, 500FHR6 paint, 18FHR6 paint, and 283 primer are manufactured by Triangle Coatings, Inc., located in San Leandro, California. All of these named paints are thermal-diffusive white paints specially invented for the purpose of diffusing the heat generated when sunlight radiates on the metallic reflector surfaces. It is known that Triangle no. 6 paint’s main ingredient is titanium dioxide, but the main ingredients of the other paints and primers manufactured by Triangle Coatings are not known to this author. It is only known that 500FHR6 paint has an acrylic urethane base, while the 18FHR6 paint and 283 primer are water based.

118

Reflector Surfaces

Figure 2.24

(a) The total excess noise-temperature contribution and (b) the added-gain loss at 32 GHz due to 0.127-mm (5.0-mil)-thick 18FHR6 paint and 0.0152-mm (0.6-mil)-thick 283 primer on a flat 6061-T6 aluminum mirror [14]. (Courtesy of NASA/JPL-Caltech.)

The paint and primer thicknesses given above are based on thickness values in units of mils in the DSN paint specifications document.3, 4 It is easy to confuse metric units of mm (0.001 m) for English units of mils (0.001 inch). The formula for conversion from thickness t in mils to thickness t in millimeters is t mm = 0.0254 × t mil . The plots and tables will show both metric and English units for paint-layer thicknesses in order to avoid confusion. 2.3.4.3 Plots as Functions of Paint and Primer Thickness

An alternate and perhaps better way of showing ENTs is to show ENTs as functions of paint- and primer-layer thicknesses at selected incidence angles. The selected 3.

4.

T. C. Sink, Painting or Thermal-Coating DSN Antenna and Structures Standard Procedure, DSN-STD-1006, Rev. G (internal document), Jet Propulsion Laboratory, Pasadena, California, February 15, 1996. Appendix C specifies zinc chromate primer and Triangle no. 6 paint thicknesses and procedures for thermal coating aluminum for RF reflective surfaces. T. C. Sink, Painting or Thermal-Coating DSN Antenna and Structures Standard Procedure, DSN-STD-1006, Rev. H (internal document), Jet Propulsion Laboratory, Pasadena, California, September

2.3 Painted Panels

119

Figure 2.25

(a) The excess noise-temperature contribution and (b) the added-gain loss at 32 GHz due to 0.0152-mm (0.6-mil)-thick zinc chromate primer on a flat 6061-T6 aluminum mirror [14]. (Courtesy of NASA/JPL-Caltech.)

incidence angles for this section are 0, 15, 30, 45, and 60 degrees. For these plots, the ENTs will be shown for perpendicular, circular, and parallel polarizations. Figures 2.26–2.30 are ENT plots presented as functions of thickness t at these selected incidence angles for Triangle no. 6 with a fixed zinc chromate primerlayer thickness of 0.0152 mm (0.6 mil). Note that when thickness t goes to zero, the noise temperature does not go to zero. The reason is that the residual noise temperature is due to the primer layer, which is not a function of thickness t. Figures 2.31–2.35 are plots as functions of thickness for 500FHR6 paint with no primer; Figures 2.36–2.40 are plots for a 18FHR6 paint layer and a fixed 283 primer-layer thickness of 0.0152 mm (0.6 mil); and Figures 2.41–2.45 are plots for zinc chromate primer only. For the parallel polarization case, high noise temper17, 1999. Appendix C specifies 500FHR6 and no primer for thermal coating of aluminum RF reflective surfaces. Although a thickness of 0.0305 mm (1.2 mils) was specified, it was requested by Cognizant Engineer T. Sink that a thickness of 0.0508 mm (2 mils) be investigated and used instead.

120

Reflector Surfaces

Figure 2.26

The total ENT due to a Triangle no. 6 paint layer of thickness t and a fixed zinc chromate primer-layer thickness of 0.0152 mm (0.6 mil) at a 0-degree incidence angle and 32 GHz. The single curve applies to parallel, circular, and perpendicular polarizations [14]. (Courtesy of NASA/JPL-Caltech.)

Figure 2.27

The total ENT due to a Triangle no. 6 paint layer of thickness t and a fixed zinc chromate primer-layer thickness of 0.0152 mm (0.6 mil) at a 15-degree incidence angle and 32 GHz. The middle curve is the average of parallel and perpendicular polarization ENTs and applies to circular polarization [14]. (Courtesy of NASA/JPLCaltech.)

2.3 Painted Panels

121

Figure 2.28

The total ENT due to a Triangle no. 6 paint layer of thickness t and a fixed zinc chromate primer-layer thickness of 0.0152 mm (0.6 mil) at a 30-degree incidence angle and 32 GHz [14]. (Courtesy of NASA/JPL-Caltech.)

Figure 2.29


122

Reflector Surfaces

Figure 2.30


Figure 2.31

The ENT due to a 500FHR6 paint layer of thickness t and no primer layer at a 0-degree incidence angle and 32 GHz. The single curve applies to parallel, circular, and perpendicular polarizations [14]. (Courtesy of NASA/JPL-Caltech.)

2.3 Painted Panels

123

Figure 2.32

The ENT due to a 500FHR6 paint layer of thickness t and no primer layer at a 15-degree incidence angle and 32 GHz. The middle curve is the average of parallel and perpendicular polarization ENTs and applies to circular polarization [14]. (Courtesy of NASA/ JPL-Caltech.)

Figure 2.33

The ENT due to a 500FHR6 paint layer of thickness t and no primer layer at a 30-degree incidence angle and 32 GHz [14]. (Courtesy of NASA/JPL-Caltech.)

124

Reflector Surfaces

Figure 2.34


Figure 2.35


2.3 Painted Panels

125

Figure 2.36

The total ENT due to a 18FHR6 paint layer of thickness t and a fixed 283 primer-layer thickness of 0.0152 mm (0.6 mil) at a 0-degree incidence angle and 32 GHz. The single curve applies to parallel, circular, and perpendicular polarizations [14]. (Courtesy of NASA/JPL-Caltech.)

Figure 2.37

The total ENT due to a 18FHR6 paint layer of thickness t and a fixed 283 primer-layer thickness of 0.0152 mm (0.6 mil) at a 15-degree incidence angle and 32 GHz. The middle curve is the average of parallel and perpendicular polarization ENTs and applies to circular polarization [14]. (Courtesy of NASA/JPL-Caltech.)

126

Reflector Surfaces

Figure 2.38

The total ENT due to a 18FHR6 paint layer of thickness t and a fixed 283 primer-layer thickness of 0.0152 mm (0.6 mil) at a 30-degree incidence angle and 32 GHz [14]. (Courtesy of NASA/JPL-Caltech.)

Figure 2.39


2.3 Painted Panels

127

Figure 2.40


Figure 2.41

The ENT due to zinc chromate primer layer of thickness t at a 0-degree incidence angle and 32 GHz. The single curve applies to parallel, circular, and perpendicular polarizations [14]. (Courtesy of NASA/JPL-Caltech.)

128

Reflector Surfaces

Figure 2.42

The ENT due to zinc chromate primer layer of thickness t at a 15-degree incidence angle and 32 GHz. The middle curve is the average of parallel and perpendicular polarization ENTs and applies to circular polarization [14]. (Courtesy of NASA/JPLCaltech.)

Figure 2.43

The ENT due to a zinc chromate primer layer of thickness t at a 30-degree incidence angle and 32 GHz [14]. (Courtesy of NASA/JPL-Caltech.)

2.3 Painted Panels

129

Figure 2.44

The ENT due to a zinc chromate paint layer of thickness t at a 45-degree incidence angle and 32 GHz [14]. (Courtesy of NASA/JPL-Caltech.)

Figure 2.45

The ENT due to a zinc chromate primer layer of thickness t at a 60-degree incidence angle and 32 GHz [14]. (Courtesy of NASA/JPL-Caltech.)

130

Reflector Surfaces

atures (about 2K) occur for all cases of 0.254-mm (10-mil) thickness at a 60-degree incidence angle. For circular polarization, the ENTs are summarized in Table 2.8 for these paints (with fixed primer layers) for selected thicknesses of 0.0508 mm (2 mil), 0.127 mm (5 mil), 0.1778 mm (7 mil), and 0.254 mm (10 mil). Although not shown in the plots, Table 2.8 also gives the results for a very thick 0.381-mm (15-mil) layer for all paints and zinc chromate primer. Note that at this 0.381-mm thickness the ENTs for the Triangle no. 6 paint cases are 1.5K or greater at all incidence angles. This is important to show because, on some of the 70-m antenna reflector surfaces, repainting several times over 35 years may have built up paint layers to be much thicker than the DSN paint-thickness specifications without knowledge of the detrimental effects that excessive paint thickness have on noise temperature. In Table 2.8, it can be seen that the 0.127-mm (5-mil) thickness for Triangle no. 6 paint and its primer layer thickness produce an ENT of 0.13K at a 30-degree incidence angle as compared with 0.03K for 0.0508-mm (2-mil) 500FHR6 paint. These are of interest because they are the paint and primer thicknesses specified in current DSN antenna paint specification documents. Most of the higher noise temperature for the Triangle no. 6 paint configuration is due to the difference of a larger paint thickness and the existence of a primer layer. Note that the 18FHR6paint with 283-primer-layer results are very similar to those for Triangle no. 6 paint with a zinc chromate primer layer. The ENTs of 500FHR6 paint with no primer are similar to the results produced by zinc chromate primer alone. It was shown in (2.80) that ENT is additive for low-loss reflectors. Therefore, if there are six reflectors involved, such as the six BWG mirrors at DSS 13, each with only a zinc chromate primer layer, the total ENT will be about six times higher than the value for the single zinc chromate primer-painted mirror shown in Table 2.8. This kind of result was not known prior to this paint study. The results of a study of the effects of change in reflection coefficient phase due to paint is not presented here, but can be found in [14, 20]. 2.3.4.4 Depolarization

Depolarization due to paint on a reflector is a topic that has often been overlooked. A literature search revealed two articles [35, 36] that discuss this topic. A complete study of depolarization is beyond the scope of this paint study, but some plots given in [20] show that future studies of depolarization effects need to be done. It was later discovered that the effects of depolarization on dual-offset reflectors caused by a layer of paint had been studied by Hombach and Ku¨hn [37]. This paper stated that the copolar pattern remains almost unaltered for typical thermalpaint data (relative dielectric constants of 3, . . . 4, and for paint-layer thickness/ wavelength of 0.005, . . . 0.01) whereas the cross-polarization pattern undergoes substantial changes. These results give good insight into the effects of paint on depolarization. 2.3.5 Conclusions

A suggested criterion for maximum allowable ENT due to paint and primer is 0.2K at 32 GHz and a 30-degree incidence angle for circular polarization. This

2.4 Wet Panels

131

criterion is selected on the basis that this ENT is a practical achievable value that does not cause significant degradation of DSN antenna performance at 32 GHz. Based on the results presented in this section, a recommendation was made to use a 0.0509-mm (2-mil) or thinner layer of 500FHR6 paint with no primer on reflector surfaces for all new 34-m BWG antennas being built and for all existing 34-m and 70-m DSN antenna reflector surfaces that need repainting. This recommendation was incorporated into the updated DSN antenna paint specification document [T. C. Sink, private communication, Jet Propulsion Laboratory, Pasadena, California, September 1999].

2.4 Wet Panels 2.4.1 Theoretical Studies

Water-film noise-temperature studies also can be made using the equations given in Section 2.2.1. For example, a configuration that was studied in [19] was a plane wave normally incident on a layer of water film terminated by an equivalent load assembly that consisted of a fiberglass dielectric layer bonded to the top surface of a lossless flat-plate reflector. Figure 2.46 shows the overall input reflection coefficient (expressed as return loss) as a function of the equivalent load reflection coefficient phase angle. In practice, this phase angle is made variable by changing the dielectric layer thickness [19]. If the dielectric layer thickness is zero, the phase angle is 180 degrees. If the return losses in Figure 2.46 are converted to voltage

Figure 2.46

Return loss versus load phase angle for various thicknesses of water films terminated in an equivalent load assembly having a voltage reflection coefficient magnitude of 0.9994 at 12 GHz. The incidence angle for the case under study is 0 degrees [40]. (Courtesy of NASA/JPL-Caltech.)

132

Reflector Surfaces

reflection coefficient magnitudes, then for this normal incidence case either (2.46) or (2.47) was used to calculate the noise temperature (of the particular wet reflector configuration under study) as a function of the equivalent load reflection coefficient phase angle. If the water layer is next to the reflector surface, or the load phase angle is 180 degrees, it can be seen in Figure 2.46 that the return loss is zero decibels or the same as the return loss of a lossless metallic sheet. This result indicates that there is negligible absorption due to the water layer when lying directly on the reflector surface. This result was experimentally confirmed by the experiments to be described in Section 2.4.2. 2.4.2 Experimental Studies 2.4.2.1 Test Setup

X-band noise temperature tests made on two types of antenna surface panels are presented. The first type tested was a solid antenna panel, while the second type was a perforated panel with 0.476 cm (3/16-inch)-diameter holes. Measurements were made at 8.45 GHz using an X-band radiometric system [38]. Measured noise temperature contributions were from: (1) thermal diffusive white paint on solid panels and white paint on perforated panels, and (2) water sprayed on both painted and unpainted perforated panels. For the experiments on perforated panels, tests were restricted to the 0.476-cm-diameter hole panels formerly used on DSN 64-m antennas. All tests were done using the test setup shown in Figure 2.47. The results apply for an incidence angle of 45 degrees at 8.45 GHz. A misalignment of the polarizer was later discovered. Instead of the polarizer being set at 45 degrees, it was set at 22.5 degrees [38]. This misalignment resulted in the polarization being elliptical rather than circular. An analysis indicates that the measured noise temperature at the 45 degrees incidence angle with the incorrect polarization follows the following formula:

Figure 2.47

Radiometric test setup [38]. (Courtesy of NASA/JPL-Caltech.)

2.4 Wet Panels

133

(NT )meas = cos2 (22.5°) (NT )|| + sin2 (22.5°) (NT )⊥

(2.82)

(NT )|| ≈ NT (0)/cos (45°)

(2.83)

(NT )⊥ ≈ NT (0) cos (45°)

(2.84)

where the || and ⊥ subscripts apply to parallel and perpendicular polarizations, respectively, and NT (0) applies to the noise temperature at a 0-degree incidence angle. Substitution of (2.83) and (2.84) into (2.82) gives (NT )meas = 1.31NT (0)

(2.85)

(NT )meas = 1.06NT (0)

(2.86)

as compared to

had the polarizer been properly set for circular polarization. The measured noise temperatures given below are about 25 percent too high. 2.4.2.2 Test Results

The following experimental results apply to wet and dry solid sheets. The total thickness of the primer and Triangle Co. no. 6 white thermal diffusive paint on the painted sheets was measured to be 0.051 mm (0.002 inch) thick. Results are also given for wet as well as dry painted and unpainted perforated plates having 0.476 cm (3/16 inch) diameter holes, 0.635 cm (1/4 inch) hole-to-hole spacing, equilateral triangle pattern, and a plate thickness of 0.183 cm (0.072 inch). 1. The increase of noise temperature due to paint on a solid aluminum reflector was measured to be 0.1K at 8.45 GHz for a 45-degree incidence angle. The repeatability of this measurement was ± 0.1K. 2. The increase of noise temperature due to resistive losses of the unpainted perforated plate was 0.6K. 3. The noise temperature component associated with perforated plate leakage was determined to be 0.8K. This measured value compares favorably with a theoretical value of 0.64K calculated from C. C. Chen’s program [3] for the described perforated panel when the incidence angle is 45 degrees and for an elliptically polarized incident wave with 85.4 percent of the total power in the parallel polarization component and 14.6 percent in the perpendicular polarization component. 4. The increase of noise temperature due to paint on the perforated panels with 0.476 cm (3/16 inch) diameter holes was measured to be 0.2K. It is of interest to compare this value to the increase of 0.1K measured for paint contribution on a solid-aluminum plate. 5. The increase of noise temperature due to water spray on an unpainted perforated panel with 0.476-cm-diameter holes was measured to be 11.6K.

134

Reflector Surfaces

The measured value is about three times smaller than a theoretical value calculated for this panel when the holes are completely filled with water. During the measurement, it could be seen that the water layer only covered some of the holes near the panel surface and did not penetrate deeply into the holes. Most of the water began to drain due to gravity, but water in some holes was retained because of surface tension. 6. The increase of noise temperature due to water spray on a painted perforated panel with 0.476 cm diameter holes was measured to be 7.3K. From comparisons with the 11.6K value obtained for the unpainted perforated panel, it can be concluded that less water is retained by the painted panel than by the unpainted panel. 7. The increase of noise temperature due to water on a painted solid plate was measured to be 1.2K. Due to an oversight, no measurements were similarly made of the noise temperature increase due to water sprayed on an unpainted solid-aluminum plate. An accurate, stable radiometric measurement system of the type used for the results of this section made it possible to obtain information that would be much more difficult to obtain using other measurement techniques. A thorough discussion of the errors associated with these measurements can be found in [38]. Independent radiometric testing on wet antenna panels by Britcliffe and Clauss in [39] confirmed the results presented in item (7) above.

References [1]

[2]

[3]

[4]

[5]

[6]

[7]

Otoshi, T. Y., ‘‘RF Properties of the 64-m Diameter Antenna Mesh Material as a Function of Frequency,’’ The Deep Space Network Progress Report for September and October 1972, Technical Report 32-1526, Vol. XII, Jet Propulsion Laboratory, Pasadena, CA, December 15, 1972, pp. 26–31, http://tmo.jpl.nasa.gov/tmo/progress_report2/XII/ XIIG.PDF. Otoshi, T. Y., ‘‘A Study of Microwave Leakage Through Perforated Flat Plates,’’ IEEE Trans. on Microwave Theory and Techniques, Vol. MTT-20, No. 3, March 1972, pp. 235–236. Chen, C. C., ‘‘Transmission of Electromagnetic Waves by Conducting Screen Perforated Periodically with Circular Holes,’’ IEEE Trans. on Microwave Theory Tech., Vol. MTT–19, No. 5, May 1971, pp. 475–481. Bathker, D. A., et al., ‘‘Beam-Waveguide Antenna Performance Predictions with Comparisons to Experimental Results,’’ IEEE Trans. on Microwave Theory Tech., Vol. 40, No. 6, June 1992, pp. 1274–1285. Otoshi, T. Y., ‘‘Antenna Noise Temperature Contributions Due to Ohmic and Leakage Losses of the DSS 14 64-m Antenna Reflector Surface,’’ The Deep Space Network Progress Report for July and August 1971, Technical Report 32-1526, Vol. V, Jet Propulsion Laboratory, Pasadena, CA, October 15, 1971, pp. 115–119, http://tmo.jpl.nasa.gov/tmo/ progress_report2/V/VR.PDF. Otoshi, T. Y., ‘‘Noise Temperature and Gain Losses Due to Leakage Through Deep Space Network Perforated Panels at and Above 32 GHz,’’ IPN Progress Report 42-151, Jet Propulsion Laboratory, Pasadena, CA, November 15, 2002, pp. 1–17. Otoshi, T. Y., and M. M. Franco, ‘‘The Electrical Conductivities of Steel and Other Candidate Material for Shrouds in a Beam-Waveguide Antenna System,’’ IEEE Trans.

2.4 Wet Panels

[8] [9]

[10]

[11]

[12] [13] [14]

[15]

[16] [17]

[18]

[19]

[20]

[21]

[22] [23]

[24]

135

on Instrumentation and Measurement, Vol. IM-45, No. 1, February 1996, pp. 77–83. (Correction in IEEE Trans. on Instrumentation and Measurement, Vol. IM-45, No. 4, August 1996, p. 839.) Otoshi, T., ‘‘Antenna Temperature Analysis,’’ Space Programs Summary No. 37-36, Vol. IV, Jet Propulsion Laboratory, Pasadena, CA, December 31, 1965, pp. 262–267. Bathker, D. A., Predicted and Measured Power Density Description of a Large Ground Microwave System, JPL Technical Memorandum 33-433, Jet Propulsion Laboratory, Pasadena, CA, April 15, 1971. Potter, P. D., ‘‘Shaped Antenna Designs and Performance for 64-m Class DSN Antennas,’’ The Deep Space Network Progress Report 42-20, January and February 1974, Jet Propulsion Laboratory, Pasadena, CA, April 15, 1974, pp. 92–111, http://tmo.jpl.nasa.gov/tmo/ progress_report2/42-20/20P.PDF. Williams, W., and H. Reilly, ‘‘A Prototype DSN X/S-Band Feed: DSS 13 Application Status (Fourth Report),’’ The Telecommunications and Data Acquisition Progress Report 42-60, Jet Propulsion Laboratory, Pasadena, CA, December 15, 1980, pp. 71–88, http:// tmo.jpl.nasa.gov/tmo/progress_report/42-60/601.PDF. Ramo, S., and J. R. Whinnery, Field and Waves in Modern Radio, New York: John Wiley and Sons, 1953. Stratton, J. A., Electromagnetic Theory, New York: McGraw-Hill, 1941. Otoshi, T. Y., et al., ‘‘Noise-Temperature and Gain Loss Due to Paints and Primers on DSN Antenna Reflector Surfaces,’’ The Telecommunications and Mission Operations Progress Report 42-140, February 15, 2000, pp. 1–26, http://tmo.jpl.nasa.gov/tmo/ progress_report/42-140/140F.pdf. Ip, H.-P., and Y. Rahmat-Samii, ‘‘Analysis and Characterization of Multilayered Reflector Antennas: Rain/Snow Accumulation and Deployable Membrane,’’ IEEE Trans. on Antennas and Propagation, Vol. 46, No. 11, November 1998, pp. 1953–1605. Otoshi, T. Y., ‘‘Noise Temperature Due to Reflector Surface Resistivity,’’ IPN Progress Report 42-154, Jet Propulsion Laboratory, Pasadena, CA, August 15, 2003. Veruttipong, W., and M. Franco, ‘‘A Technique for Computation of Noise Temperature Due to a Beam Waveguide Shroud,’’ TDA Progress Report 42-112, Jet Propulsion Laboratory, Pasadena, CA, February 15, 1993, pp. 8–16. Otoshi, T. Y., and C. Yeh, ‘‘Noise Temperature of a Lossy Flat Plate Reflector for the Elliptically Polarized Wave Case,’’ IEEE Trans. on Microwave Theory and Techniques, Vol. MTT-48, No. 9, September 2000, pp. 1588–1591. Otoshi, T. Y., ‘‘Maximum and Minimum Return Losses from a Passive Two-Port Network Terminated with a Mismatched Load,’’ IEEE Trans. on Microwave Theory and Techniques, Vol. MTT-42, No. 5, May 1994, pp. 787–792. Otoshi, T. Y., et al., ‘‘Noise Temperature and Gain Loss Due to Paints and Primers: A Case Study of DSN Antennas,’’ IEEE Antennas and Propagation Magazine, Vol. 43, No. 3, June 2001, pp. 11–28. Otoshi, T. Y., ‘‘Noise Temperature of Cascaded Mirrors Having Resistive and Spillover Losses,’’ IPN Progress Report 42-155, Jet Propulsion Laboratory, Pasadena, CA, November 15, 2003, pp. 1–9. Westman, H. P., ITT Reference Data for Radio Engineers, 5th ed., New York: Howard W. Sams, Inc., 1969. Clauss, R. C., and P. D. Potter, ‘‘Improved RF Calibration Techniques—A Practical Technique for Accurate Determination of Microwave Surface Resistivity,’’ Technical Report 32-1526, Vol. XII, Jet Propulsion Laboratory, Pasadena, CA, December 15, 1972, pp. 54–67. Bussey, H. E., ‘‘Standards and Measurements of Microwave Surface Impedance, Skin Depth, Conductivity and Q,’’ IRE Trans. on Instrumentation, Vol. I-9, No. 2, September 1960, pp. 171–175.

136

Reflector Surfaces [25]

[26] [27]

[28] [29]

[30]

[31]

[32]

[33]

[34]

[35] [36] [37]

[38]

[39]

[40]

American Society for Testing and Materials, Annual Book of ASTM Standards, ‘‘Standard Specification for Structural Steel,’’ Designation A36/A 36M-90, Vol. 01.05, Philadelphia, PA, November 1990. Avallone, E. A.,and T. Baumeister, Mark’s Standard Handbook for Mechanical Engineers 9th ed., Table 6.2.12a, New York: McGraw-Hill, 1987, pp. 6–30. Otoshi, T. Y., M. M. Franco, and H. F. Reilly, Jr., ‘‘The Electrical Conductivities of the DSS 13 Beam Waveguide Antenna Shroud Material and Other Antenna Reflector Surface Materials,’’ TDA Progress Report 42-108, Jet Propulsion Laboratory, Pasadena, CA, February 15, 1992, pp. 154–164. Beck, A. C., and R. W. Dawson, ‘‘Conductivity Measurements at Microwave Frequencies,’’ Proceedings of the IRE, October 1950, pp. 1181–1189. Reilly, H. F., J. J. Bautista, and D. A. Bathker, ‘‘Microwave Surface Resistivity of Several Materials at Ambient Temperature,’’ TDA Progress Report 42-80, Jet Propulsion Laboratory, Pasadena, CA, February 15, 1984, pp. 8–11. Thom, E. and T. Otoshi, ‘‘Surface Resistivity Measurements of Candidate Subreflector Surfaces,’’ TDA Progress Report 42-65, Jet Propulsion Laboratory, Pasadena, CA, October 15, 1981, pp. 142–150. Vane, A. B., ‘‘Measurement of Effective Conductivity of Metallic Surfaces at 3000 Megacycles and Correlation with Surface Conditions and dc Conductivity,’’ Stanford Microwave Laboratory, Report No. 4: III-9, 1949. Otoshi, T. Y., R. Cirillo, Jr., and J. Sosnowski, ‘‘Measurements of Complex Dielectric Constants of Paints and Primers for DSN Antennas: Part I,’’ The Telecommunications and Mission Operations Progress Report 42-138, April–June 1999, Jet Propulsion Laboratory, Pasadena, CA, August 15, 1999, pp. 1–13, http://tmo.jpl.nasa.gov/tmo/progress\_report/ 42-138/138F.pdf. Otoshi, T. Y., R. Cirillo, Jr., and J. Sosnowski, ‘‘Measurements of Complex Dielectric Constants of Paints and Primers for DSN Antennas: Part II,’’ The Telecommunications and Mission Operations Progress Report 42-139, July–September 1999, Jet Propulsion Laboratory, Pasadena, CA, November 15, 1999, pp. 1–7, http://tmo.jpl.nasa.gov/tmo/ progress\_report/42-139/139G.pdf. Otoshi, T. Y., ‘‘Noise Temperature of Cascaded Mirrors Having Resistive and Spillover Losses,’’ IPN Progress Report 42-155, Jet Propulsion Laboratory, Pasadena, CA, November 15, 2003, pp. 1–9. Chu, T. S., and R. A. Semplak, ‘‘A Note on Painted Reflector Surfaces,’’ IEEE Trans. on Antennas and Propagation, AP-24, No. 1, January 1976, pp. 99–101. Chen, K. K. and A. R. Raab, ‘‘Some Aspects of Beam Waveguide Design,’’ IEE Proceedings, 129, pt. H. 4, August 1982, pp. 202–221. Hombach, V., and E. Ku¨hn, ‘‘Complete Dual-Offset Reflector Antenna Analysis Including Near-Field, Paint-Layer and CFRP-Structure Effects,’’ IEEE Trans. on Antennas and Propagation, Vol. AP-37, No. 9, September 1989, pp. 1093–1101. Otoshi, T. Y., and M. M. Franco, ‘‘Radiometric Tests on Wet and Dry Antenna Reflector Surface Panels,’’ The Telecommunications and Data Acquisition Progress Report 42-100, Jet Propulsion Laboratory, Pasadena, CA, February 15, 1990, pp. 111–130. Britcliffe, M. J., and R. C. Clauss, ‘‘The Effects of Water on the Noise-Temperature Contribution of Deep Space Network Microwave Feed Components,’’ TMO PR 42-145, January–March 2001, May 15, 2001 (Article G), pp. 1–5. Otoshi, T. Y., ‘‘Maximum and Minimum Return Losses from a Passive Two-Port Network Terminated With a Mismatched Load,’’ TDA Progress Report 42-113, Jet Propulsion Laboratory, Pasadena, CA, May 15, 1993, p. 80–86.

CHAPTER 3

Noise Temperature Experiments 3.1 Horns of Different Gains at f1 3.1.1 Introduction

The system noise temperature of the BWG system at f3 was found to be significantly higher than predicted [1]. An experimental program was, therefore, initiated to isolate unknown causes of BWG system degradations. This section presents theoretical and measured zenith antenna noise temperature values at 8.45 GHz for the DSS 13 34-m BWG antenna with different gain horns installed at f1, where f1 was previously described as being the Cassegrain focal point near the main reflector vertex; it may be seen in Figure 1.28. The main purpose of these tests at f1 was to isolate and determine the unknown noise temperature contributions from scattering of the subreflector supports. The X-band test package used for the experimental portion of these tests was described in [1] and in Section 1.3. 3.1.2 Analytical Procedure and Results

Figure 3.1 shows the regions contributing to antenna noise temperatures for horns mounted at f1. The calculation methodology differs from others used previously in that: (1) the noise temperature generated by the horn spillover (into the sky regions) between the edges of the subreflector and main reflector is taken into account, (2) subreflector and main reflector efficiencies are applied as necessary in the calculations of noise temperature contributions, and (3) brightness temperatures are computed for each theta for horn, subreflector, and main reflector radiation patterns for the weather conditions that prevailed at the time of the experiments. 3.1.2.1 Radiation Patterns and Spillover Power Ratios

Table 3.1 gives definitions of symbols used in this section. Table 3.2 is a summary of the power ratios of the subreflector forward spillover, the main reflector spillover toward the ground, and the spillover into the BWG opening on the main reflector. Table 3.3 gives fractions of total radiated horn power and efficiencies. These power ratios were obtained by first calculating horn patterns at the frequency of 8.45 GHz for corrugated horns using the circular waveguide mode matching program CWG.F [2]. The radiation pattern from the subreflector was then calculated for eight phi plane cuts with the physical optics program POSUB.F. Next, the spherical wave azimuthal expansion program AZEXP.F was used to integrate the total power in the radiation pattern. This program differs from that

137

138

Noise Temperature Experiments

Figure 3.1

Brightness temperature regions contributing to antenna noise temperatures for horn at f1 [5]. (Courtesy of NASA/JPL-Caltech.)

described earlier in Section 1.1, where only the E- and H-plane patterns were used to obtain the total power. This program uses more phi cuts. The total power was then normalized and subtracted from the horn input power to obtain the subreflector spillover power ratio. Main reflector spillover toward the ground was obtained by using a radiation pattern from the subreflector calculated at a near-field radius of 1780.5 cm, the distance to the outer edge of the main reflector (see Figure 3.2). This pattern was used as input into the programs AZEXP.F and EFFIC.F to calculate the fraction of the power in the radiation pattern incident between the edge of the main reflector surface and the horizon. Spillover into the BWG opening of 243.8-cm diameter was calculated similarly, using a radiation pattern from the subreflector calculated at a near-field radius of 1,191.3 cm, the distance to the edge of the BWG opening. In addition, Table 3.2 shows the spillover into the total BWG opening of the 304.8-cm diameter, which includes the Cassegrain cone mounting ring. However, since this mounting surface reflects power to sky, only the spillover into the actual opening (determined by the 243.8-cm diameter of BWG shroud walls) will be considered for noise temperature analyses. For purposes of determining noise temperature contributions due to radiation of reflected power from the main reflector into the far field, antenna patterns and beam efficiencies were obtained for the 34-m-diameter main reflector when illuminated by the subreflector patterns for the various horn cases. Figure 3.3

3.1 Horns of Different Gains at f1

139

Table 3.1 Definition of Symbols for Different Horns at f1 Tests

␣ H1

Fraction of the total horn radiated power that is captured by the subreflector. This term is equal to the subreflector efficiency. (See Figure 3.1.)

␣ H2

Fraction of the total horn-radiated power that is absorbed by the sky region between the edges of the subreflector and main reflector. (See Figure 3.1.)

␣ H3

Fraction of the total horn-radiated power that goes into cross-pol and becomes absorbed primarily by the sky region, between the subreflector edge and a 50-degree elevation angle. (Figure 3.1)

␣ A1

Fraction of the total horn radiated power that becomes absorbed by zenith sky after reflections from the subreflector and main reflector. (See Figure 3.1.)

␣ A2

Fraction of the total horn radiated power that becomes absorbed by ground and low horizon sky region outside the main reflector edge after reflection from the subreflector. (See Figure 3.1.)

␣ A3

Fraction of the total horn radiated power that becomes absorbed by the environment inside the BWG opening on the main reflector. (See Figure 3.1.)

p S1

Fraction of the total horn radiated power not captured by the subreflector.

p S2

Fraction of the subreflector reflected power that radiates and becomes absorbed by the region outside the main reflector. Normalization is done with respect to the subreflector power pattern and not with respect to the horn radiated power.

p S3

Fraction of the subreflector reflected power that radiates to the BWG opening on the main reflector. Normalization is done with respect to the subreflector power pattern and not with respect to the horn-radiated power.

T fu

Effective noise temperature of the follow-up receiver, K.

T hemt

Effective noise temperature of the HEMT as defined at the input flange of the HEMT, K.

Top

Operating noise temperature, K.

Tstrut

Strut noise temperature, K.

Twg

Noise temperature due to waveguide loss between the horn aperture and the input flange of the HEMT, K.

Tp

Physical temperature of absorbing media inside the BWG hole (approximately 300K).

Table 3.2 Predicted f1 Spillover Amounts, 8.45 GHz, Physical Optics Analysis Horn Diameter, cm (in.)

Horn Gain, dBi

p S1 (Subreflector Spillover)

p S2 (Main Reflector Spill to Ground)

p S3 (Spill into 304.8-cm BWG Opening)

p S3 (Spill into 243.84-cm BWG Opening)

48.346 (19.034) 40.754 (16.045) 31.458 (12.385) 24.948 (9.822) 17.976 (7.077)

29.71

0.0294

0.0022

0.0039

0.0023

28.70

0.0503

0.0030

0.0031

0.0018

26.90

0.0827

0.0036

0.0020

0.0012

25.12

0.1465

0.0082

0.0014

0.00086

22.52

0.3437

0.0149

0.0010

0.00057

shows the far-field radiation patterns for the 34-m BWG antenna for the 29.7-, 26.9-, and 22.5-dBi horn-gain cases. The horns are of the corrugated horn type, each having the same 6.25-degree semi-flare angle but of different lengths and aperture diameters. The patterns for the other intermediate horn-gain cases shown

140

Noise Temperature Experiments Table 3.3 Fractions of Total Radiated Horn Power and Efficiencies at 8.45 GHz (See Figure 3.1 and Table 3.1 for Definitions of Symbols) Horn Gain, dBi

␣ H1 = ␩ SR

␣ H2

␣ H3

␩ MR

␣ A1

␣ A2

␣ A3

29.7 28.7 26.9 25.1 22.5

0.9706 0.9497 0.9173 0.8535 0.6563

0.0264 0.0427 0.0671 0.1231 0.3051

0.0030 0.0076 0.0156 0.0234 0.0386

0.9955 0.9952 0.9952 0.9909 0.9845

0.9662 0.9451 0.9129 0.8457 0.6461

0.0021 0.0028 0.0033 0.0070 0.0098

0.0022 0.0017 0.0011 0.0007 0.0004

Notes: ␩ SR : subreflector efficiency; ␩ MR : main reflector efficiency; ␣ : Fractional power ratio to be multiplied by brightness temperature to give noise temperature contribution. See Table 3.1 for definitions with subscripts. Note that ␣ H1 + ␣ H2 + ␣ H3 = 1, fulfilling the conservation of energy principle.

Figure 3.2

Geometry for calculating the main reflector and BWG opening contribution using the POSUB.F program [5]. (Courtesy of NASA/JPL-Caltech.)

in Table 3.2 fall somewhere between the patterns for the largest, intermediate, and smallest aperture diameter horn cases shown in Figure 3.3. These patterns were obtained by Paula Brown of JPL using the calculated horn patterns as input to the program POJB.F, which is a physical optics program developed by the Ground Antennas and Facilities Engineering Section of JPL. The shapes of the patterns are


Figure 3.3

141

The 34-m BWG antenna far-field patterns and gain at 8.45 GHz for the largest and smallest and intermediate aperture horn at f1 [5]. (Courtesy of NASA/JPL-Caltech.)

approximately J 1 (u)/u, where u is equal to (␲ D /␭ ) sin ␪ where ␪ is the pattern angle, and D is the main reflector diameter and ␭ is the free-space wavelength [3]. Table 3.4 shows the far-field gains of the BWG antenna at 8.45 GHz for the various horn-gain cases. The gain includes only the losses from the main reflector spillover and the subreflector spillover, and the illumination loss at the main reflector aperture. In this section, the term ‘‘gain’’ is the directivity of the horn or antenna based on theoretical patterns. The actual gain would be lower due to any resistive losses in the horn, subreflector, and main reflector surfaces. Beam efficiency will be defined here as the fraction of the total received power contained in the solid angle between the beam peak and the theta angle of interest. Beam efficiencies are

Table 3.4 Far-Field Data for 34-m-Diameter Antenna at 8.450 GHz for Various Horns at f1 34-m-Diameter Antenna Horn Gain, dBi

Gain, dBi

First Null, Degrees

Beam Efficiency At 0.5 Degree At 1.0 Degree

29.71 28.70 26.90 25.12 22.52

69.21 69.10 68.83 68.28 66.80

0.075 0.073 0.069 0.066 0.063

0.9909 0.9921a 0.9838 0.9704 0.9567

a

0.9982 0.9988a 0.9973 0.9939 0.9907

The efficiencies at 0.5 degree and 1.0 degree are slightly larger for the 28.7-dBi gain horn than those for the 29.7-dBi gain horn. This is attributed to slight differences in the main-lobe beamwidths and the close-in sidelobe patterns. These differences affect the power contained inside the patterns up to the arbitrary 0.5-degree and 1-degree angles selected.

142


tabulated in Table 3.4 for theta at 0.5 and 1.0 degree for the various horn-gain cases. 3.1.2.2 Antenna Noise Temperature Contributions

For calculations of antenna noise temperature contributions, it is important that power ratios be correctly multiplied by the applicable subreflector and main reflector efficiencies. Use of the correct power ratios is a necessary step that must be taken to preserve the conservation of power principle in noise temperature calculations [4]. It was shown in Appendix A of [5] that this requirement was met because the sum of all fractional powers involved in the overall noise temperature calculations is equal to unity. Table 3.5 shows a summary of the calculated zenith antenna noise temperature contributions for the 34-m BWG antenna for the various horn-gain cases. For the sake of brevity, supporting data as well as the calculation methodologies used to obtain these final values are omitted here, but they may be found in Appendix A of [5]. To compute horn contributions, the brightness temperatures and horn beam efficiencies were first computed from equations given in Section 1.1 and [6], respectively. A sample output of a Fortran program showing these calculations is given in Appendix B of [5]. Noise temperature contributions from the horn patterns in the sky region (between the subreflector and main reflector edges) were then determined from the program output. Next, as discussed in Section 3.1.2.1, from the spillover power ratios computed for the region outside the outer edge of the main reflector, the noise temperature contribution was determined by first determining an effective brightness temperature of the ground low-horizon sky region. Due to the significant variability of the brightness temperature of this region with changes in weather and ambient temperature as well as zenith angle, the brightness temperatures were calculated for the applicable conditions that existed during the corresponding measurement periods. Generation of brightness temperatures of the sky-ground region as a function of zenith angle theta is discussed in Section 3.1.2.1. Since the Cassegrain mounting ring surface will reflect power into the cold sky region close to zenith, only the 243.8-cm-diameter portion of the BWG shroud opening should contribute significantly to the antenna noise temperature at f1. The brightness temperature as seen looking into the shroud opening was assumed to be equal to the ambient temperature of the antenna at the times that system noise temperature measurements were being performed for corresponding horn configurations. Details of the steps involved in the calculations and the equations used may be found in the appendixes of [5]. To determine the contribution due to sky absorption of the power radiated by the main reflector, it was necessary to compute beam efficiencies [6] as a function of zenith angle for the various horn-gain cases. These values as tabulated in Table 3.4 show that, for all horn-gain cases, 99 percent of the power radiated by the main reflector will be contained inside the main beam between 0 and 1 degree of zenith ␪ angles. Since sky brightness temperature is nearly constant (within 1.5 percent) from a 0- to 10-degree zenith angle, it can be assumed that for these

4.370 4.263 4.125 3.826 2.919

29.7 28.7 26.9 25.1 22.5

0.455 0.595 0.706 1.471 2.059

0.657 0.510 0.329 0.210 0.120

⌬TA3 (Subr → BWG Hole), K

⌬TA1 (Main Refl. → Zenith), K

Horn Gain, dBi

⌬TA2 (Subr → Gnd), K

Summary of Antenna Noise Temperature Contributions at f1

Table 3.5

0.121 0.194 0.307 0.564 1.396

⌬TA4 (Horn → Sky 8.7 → 68.2°), K 0.018 0.046 0.094 0.140 0.232

⌬TA5 (Horn → Other Spills), K

⌬TAi , K 5.621 5.608 5.561 6.211 6.726

i=1

5

∑

— −0.01 −0.06 0.59 1.11

Noise Temperature Difference, K

3.1 Horns of Different Gains at f1 143

144


theoretical cases, 100 percent of the power radiated from the 34-m BWG main reflector surface will be absorbed by sky that has an effective brightness temperature equal to that at the zenith angle of 0 degree. It should be pointed out that the brightness temperature of sky includes the cosmic background as well as atmospheric loss contributions. For the different horns, five calculated contributions to antenna noise temperatures are shown as ⌬TAi for i = 1, 5 in Table 3.5. If the total absolute antenna noise temperature needs to be computed, then knowledge is also required of such additional terms as noise due to tripod scattering of the far-field plane wave illuminating the entire antenna, main reflector panel leakage, main reflector and subreflector resistive losses, and other terms presented in [7]. These contributions will be shown later in this section. 3.1.3 Experimental Work

Operating noise temperature measurements were sequentially made at 8.450 GHz with the phase centers of the 29.7-, 28.7-, 26.9-, 25.1-, and 22.5-dBi gain horns aligned with the geometric focal point f1. Figure 3.4 shows the experimental test setup of the 29.7-dBi horn at f1. The experimental data is presented in Tables 3.6 and 3.7. In Table 3.6, ⌬Top1 = L wg [Top − (Top )ref ]

Figure 3.4

(3.1)

Partial view of the X-band 29-dBi horn test package and mounting structure installed at the Cassegrain focal point f1 [5]. (Courtesy of NASA/JPL-Caltech.)

116.8 82.6 44.5 25.4 7.8

29.7 28.7 26.9 25.1 22.5

5.00 4.42 5.01 5.17 4.92

28.56 28.43 28.80 29.60 29.97

25.47 26.90 25.62 26.67 26.79

Temperature, Relative Degrees C Humidity, Percent Load Outdoor 896.88 895.80 895.59 895.30 894.99

2.5 2.5 2.5 2.5 2.5

Barometric Pressure, mb Tcb , K 0.0334 0.0332 0.0333 0.0334 0.0333

2.481 2.481 2.481 2.481 2.481

2.040 2.028 2.036 2.041 2.035

Tcb /L atm g, K Tatm f, K

= 1.0163 (0.07 dB).

L atm , dB

a Frequency = 8.45 GHz. b Phase center location is measured down from horn aperture. c Data was taken with the research and development X-band test package described in [1]. L wg d Normalized Top corrected for standard atmosphere and waveguide ambient temperature [1]. e See (3.1). f Tatm is low because of low relative humidity. g Latm is a power ratio converted from Latm given in dB in the previous column.

Horn Phase Center,b cm 4.521 4.509 4.517 4.522 4.516

27.08 27.13 27.12 28.07 29.03

27.07 27.14 27.12 28.04 29.00

0.00 0.05 0.04 1.01 1.98

Top , K Measured (T b )zen , K Measured c Normalized d ⌬Top1 , K e

DSS 13 Measured and Normalized Noise Temperature (Top ) Without a Thermax Conducting Plane Below Feedhorn, at f1a

Horn Gain, dBi

Table 3.6

3.1 Horns of Different Gains at f1 145

116.8 82.6 44.5 25.4 7.8

29.7 28.7 26.9 25.1 22.5

5.35 4.33 5.17 5.04 4.93

27.95 28.28 28.73 29.76 29.92

24.87 26.39 25.81 26.59 27.07

Temperature, Relative Degrees C Humidity, Percent Load Outdoor 896.99 895.59 895.59 895.29 894.99

2.5 2.5 2.5 2.5 2.5

Barometric Pressure, mb Tcb , K 0.0335 0.0332 0.0334 0.0334 0.0333

2.481 2.481 2.481 2.481 2.481

2.046 2.024 2.039 2.038 2.036

Tcb /L atm g, K Tatm f, K

= 1.0163 (0.07 dB).

L atm , dB

a Frequency = 8.45 GHz. b Phase center location is measured down from horn aperture. c Data were taken with the research and development X-band test package described in [1]. L wg d Normalized Top corrected for standard atmosphere and waveguide ambient temperature [1]. e See (3.2). f Tatm is low because of low relative humidity. g Latm is a power ratio converted from Latm given in dB in the previous column.

Horn Phase Center,b cm 4.527 4.505 4.520 4.519 4.517

26.67 26.74 26.83 27.80 28.74

26.67 26.76 26.82 27.78 28.71

0.41 0.39 0.31 0.26 0.30

Top , K Measured (T b )zen , K Measured c Normalized d ⌬Top2 , K e

DSS-13 Measured and Normalized Noise Temperature (Top ) with a Thermax Conducting Plane Below Feedhorna

Horn Gain, dBi

Table 3.7

146 Noise Temperature Experiments


147

where (Top )ref is the normalized operating noise temperature of the 29.7-dBi horn, and L wg is the waveguide loss from the horn apertures to the high-electron-mobilitytransistor (HEMT) input. It was assumed that L wg measured for the 22.5-dBi horn [1] applied to all horn-gain cases. To experimentally determine only the noise temperature contribution from spillover into the 243.8-cm diameter BWG opening at f1 below the feedhorn, a ground plane was installed below the feedhorns. Figure 3.5 shows the installation of a Thermax1 ground plane below the 29.7-dBi horn. The last column of Table 3.7 shows the change in Top values measured with and without the Thermax ground plane. The values were computed from ⌬Top2 = L wg [(Top )w/o − (Top )with ]

(3.2)

This difference provides a measured value of the noise contribution due to spillover into the 243.8-cm-diameter BWG opening at f1, and the difference is compared to the calculated ⌬TA3 values shown in Table 3.5. 3.1.4 Determination of Strut Contribution 3.1.4.1 Method 1

The zenith Top values of the 34-m BWG antenna with the X-band test package and a particular feedhorn installed at f1 can be expressed as

Figure 3.5

1.

The installation shown in Figure 3.4 with the addition of a Thermax ground plane that covers the 243.84-cm-diameter BWG opening below the feedhorn [5]. (Courtesy of NASA/JPL-Caltech.)

A trademark of the Celotex Corporation, Tampa, Florida.

148


(Top )f 1 = L −1 wg TA, f 1 + Twg + Themt + Tfu

(3.3)

where TA, f 1 is the 34-m BWG antenna noise temperature at f1; other symbols were defined in Table 3.1. Algebraic manipulation of (3.3) gives TA, f 1 = L wg [(Top )f 1 − (Twg + Themt + Tfu )]

(3.4)

In 1992, it was reported in [1] that, for the test package at f1 at 8.45 GHz, L wg = 1.0163, Twg = 4.69K, Themt = 13.0K, and Tfu = 0.4K, and the normalized (Top )f 1 was reported to be 25.9K. The normalized (Top )f 1 for the 29.7-dBi gain horn shown in Table 3.6 is shown to be 27.07K. This data was taken in September 1993. Note that the normalized Top at f1 increased by about 1.2K from 1990 to 1993. Examination of unpublished experimental data showed that from 1990 to September 1993 Themt was gradually warming. At the time the data for Table 3.6 was taken, Themt was 14K instead of 13K. Substitution of the values (Top )f 1 = 27.1K, L wg = 1.0163, Twg = 4.7K, Themt = 14K, and Tfu = 0.4K into (3.4) gives TA, f 1 = 8.1K, which includes the cosmic background and atmospheric loss contributions. It is also valid to state that 5

TA, f 1 =

∑

i=1

⌬TAi + Tres + Tstrut

(3.5)

which gives 5

Tstrut = TA, f 1 −

∑

i=1

⌬TAi − Tres

(3.6)

where Tstrut is the noise temperature contribution due to strut scattering and Tres is the residual contribution due to subreflector and main reflector surface imperfections, which will be described in the following. The measured value of TA, f 1 and 5 the calculated value of ⌺ i = 1 ⌬TAi apply to the same atmospheric conditions and the same 29.7-dBi horn-gain case at 8.45 GHz. Otherwise the equation for determining Tstrut from (3.6) would be invalid. It should be pointed out that the contribution of the BWG hole on the main reflector surface has been accounted for in 5 ⌺ i = 1 ⌬TAi as the term ⌬TA3 (see Table 3.5). It is now the objective to calculate the residual term Tres . The calculated residual contributions at 8.45 GHz are 0.02K for leakage through holes in the perforated panels [7], 0.13K for resistive loss of the subreflector surface, and 0.14K for the resistive loss of the main reflector surface. The measured residual contributions (tabulated in Tables 3.6 and 3.17) are 0.35K due to 1,714 holography holes, 0.31K due to gaps between panels, 0.08K for openings at the bases of struts, and 0.09K at the top of the struts. The total sum of these calculated and measured contributions is a value of 1.12K for 5 Tres . Substitution of TA, f 1 = 8.1K (previously given above) and ⌺ i = 1 ⌬TAi = 5.62K (from Table 3.5) and Tres = 1.12K into (3.6) gives Tstrut = 1.4K. It is important to 5 note that ⌺ i = 1 ⌬TAi includes the contributions of the sky temperature for the BWG antenna and the contribution of the BWG hole. The uncertainties for all of the


149

measured contributions are estimated to be ±0.3K, and the uncertainties for the calculated values are estimated to be about ±0.1K. Therefore, the value of Tstrut as computed by this combined theoretical and experimental method shall be reported to be 1.4 ± 0.4K. The disadvantage of deriving the value of the strut contribution from (3.6) is that it is strongly dependent upon the values of Twg , Themt , and Tfu being known and having remained unchanged since the time they were first calibrated. As shown in the above, the HEMT could have deteriorated and warmed and therefore, caused the 1990 Themt value to have changed when these tests were performed three years later in September 1993. A new value determined for Themt was used in (3.4). 3.1.4.2 Method 2

The following derivation gives an alternate formula for determining the strut contribution that does not depend upon the absolute value of Twg , Themt , and Tfu having to be known. It does, however, depend upon a differential measurement being made in a reasonable time interval with corrections made for the weather changes. The derivation is as follows for the test package on the ground, (Top )ground = L −1 wg (Ta )ground + Twg + Themt + Tfu

(3.7)

and from (3.3), for the test package at f1, (Top )f 1 = (TA, f 1 ) L −1 wg + Twg + Themt + Tfu

(3.8)

It was given in (3.5) that 5

TA, f 1 =

∑

i=1

⌬TAi + Tres + Tstrut

so that its substitution into (3.8) gives (Top )f 1 =

冢

5

∑

i=1

冣

⌬TAi + Tres + Tstrut L −1 wg + Twg + Themt + Tfu

(3.9)

Subtraction of the two operating system noise temperatures gives ⌬Top = (Top )f 1 − (Top )ground

(3.10)

Substitution of (3.7) and (3.9) gives ⌬Top = L −1 wg

冤冢 ∑ 5

i=1

From Appendix A of [5],

冣

⌬TAi + Tres + Tstrut − (Ta )ground

冥

(3.11)

150


⌬TA1 = ␩ SR ␩ MR Tsky, zen

(3.12)

where it was given previously that −1

Tsky, zen = Tcb L atm + Tatm, zen and the values of ␩ SR and ␩ MR are given in Table 3.3; other terms have been previously defined. The expression for antenna noise temperature of the test package on the ground is dependent on the radiation of the horn pattern and can be expressed as (Ta )ground = ␩ SR Tsky, zen + ⌬TA4 + ⌬TA5

(3.13)

Substitution of (3.12) gives (Ta )ground = ⌬TA1 /␩ MR + ⌬TA4 + ⌬TA5

(3.14)

The value of ␩ MR is given in Table 3.3 as 0.9955 so that to a good approximation (Ta )ground ≈ ⌬TA1 + ⌬TA4 + ⌬TA5

(3.15)

Substitution of (3.15) into (3.11) gives ⌬Top = L −1 wg [⌬TA2 + ⌬TA3 + Tres + (Tstrut )2 ]

(3.16)

where (Tstrut )2 is used to denote the strut contribution derived from the alternate expression. Then (Tstrut )2 = ⌬Top L wg − ⌬TA2 − ⌬TA3 − Tres

(3.17)

Unpublished experimental data from tests performed from May 1 through May 4, 1993, show that ⌬Top was measured to be 3.5K for the 29.7-dBi horn configuration at 8.45 GHz. Substitutions of L wg = 1.0163, ⌬Top = 3.5K, Tres = 1.12K, and values ⌬TA2 = 0.455K and ⌬TA3 = 0.66K from Table 3.5 into (3.17) give a value of (Tstrut )2 = 1.3K. This alternate strut value is in good agreement with the 1.4 ± 0.4K value obtained from (3.6). However, the May 1993 experimental notes show that weather corrections were not made for Top when the X-band test package was on the ground because the weather machine at DSS 13 was broken during this period. The uncertainty of whether weather and normalization corrections were made leads to questions about the accuracy of the 1.3K value. If it is assumed that the 1990 ⌬Top = 3.2K [1] value did not change over a three-year period, and is used in (3.17), then (Tstrut )2 is 1.0K. The question arises as to whether data obtained in 1990 is still applicable to the main reflector configuration in September 1993, for which this analysis is being made. After studying both methods and their uncertainties, it was decided that the value of 1.4K determined by the first method is most likely to be the correct value


151

for the strut noise temperature contribution. It can be concluded that it is very difficult to determine strut contributions using either of the two experimental methods described above. Bathker et al. [7] gave a predicted value of 2.0K for the tripod strut configuration when the DSS 13-BWG antenna is pointed at zenith. Attempts to determine strut contributions by other methods and other JPL authors are described in this chapter’s selected bibliography. It is of interest to compare the 1.4 ± 0.4K value determined by Otoshi to the 0.6K value measured by Prata et al., who used a unique experimental method that involved covering the struts with aluminum plates (see selected bibliography). Differential antenna temperatures (relative to the 29.7-dBi horn) are presented in Table 3.8. Values for this table were derived from values given in Tables 3.5 and 3.6. The differential values shown in the last column of Table 3.8 are attributed primarily to residual tripod (strut) contributions not taken into account thus far by the theoretical method presented in this section. For the DSS 13 BWG antenna, the struts are tripods. Strut (tripod) contributions are difficult to calculate, but an estimate of the changes can be obtained by first accounting for all known or bestestimate contributions (excluding strut contributions) and then subtracting the calculated total from the measured value. Note that more noise contribution from the tripod occurs for the horns of smaller gain. As shown in Table 3.9, horns of smaller gain illuminate more of the tripod legs away from the tripod–subreflector connection points and thus have higher tripod-scatter contributions. 3.1.5 Conclusions

A methodology has been presented for calculating antenna noise temperature contributions of a BWG antenna for horns of different gains installed at f1. A reference antenna noise temperature is based on the 29.7-dBi gain horn because this is the equivalent gain horn for which the BWG antenna was designed. As the horn gains become smaller toward 22.5 dBi, a larger discrepancy of about 0.87K occurs. This discrepancy is attributed to larger unknown noise contributions from tripod scattering as horn gain becomes smaller. Later analytical and experimental work done for horns at the f1, f2, and f3 focal points was reported by Veruttipong [8] and Imbriale [9, 10].

Table 3.8 Relative Differences Between Antenna Temperatures of the 29.7-dBi Horn and Other Horns Installed at f1a ⌬TAb, K Horn Gain, dBi

Measured, K c

Calculated d

Difference

29.7 28.7 26.9 25.1 22.5

— 0.05 0.04 1.01 1.98

— −0.01 −0.06 0.59 1.11

— 0.06 0.10 0.42 0.87

a

Frequency = 8.45 GHz. = [(TA )horn − (TA )29.7 dBi horn ] ≈ ⌬Top1 . From Table 3.6. d From Table 3.5. b ⌬TA c

152

Noise Temperature Experiments Table 3.9 Comparison of Fractional Powers in Scatter Regions Near the Subreflector Edge or Near the Top of the Struts Horn Gain, dBi 29.7 28.7 26.9 25.1 22.5

␪ i , Degrees a

Fraction of Total Power Contained in ␪ i Region

8.7 → 11 11 → 17 8.7 → 11 11 → 17 8.7 → 11 11 → 17 8.7 → 11 11 → 17 8.7 → 11 11 → 17

0.0173 0.0084 0.0291 0.0121 0.0357 0.0282 0.0747 0.0429 0.1533 0.1293

a ␪ i as defined for this table is the zenith angle as seen from f1.

3.2 Bird Net Cover for BWG Antennas 3.2.1 Introduction

A serious problem at Overseas BWG antennas is birds getting inside the BWG opening. Since birds are blackbody noise-temperature radiators, they cause noisetemperature increases and fluctuations whenever they fly through any portion of beam of the downlink signal in the BWG system. Also, the bird droppings on BWG mirrors create a bigger problem. A way to keep birds out of the BWG system is to cover the BWG opening with a low-loss net. It is required that the net be able to withstand high power radiation when the uplink signal transmits through it and that the net contributes negligible (less than 0.2-K) increases in the system-noise temperatures at any of the operating frequency bands. In the following, the design of the net that was developed and tested at DSS 13 is described. Henceforth in this section, the term system temperature will be used. It is synonymous with the terms system-noise temperature and operating-system temperature. 3.2.2 Description of the Net Cover

Figure 3.6 shows the prototype net being installed at the BWG opening on the dish surface at DSS 13. The wooden outer ring that holds the net taut is about 2.438m (8 ft) in diameter, or about the same diameter as the base of a Cassegrain cone. Figure 3.7 shows a birds-eye view of the installed net, and Figure 3.8 shows a close-up view of the design features of the net. The grid size is 3.81 by 3.81 cm (1.5 × 1.5 inches). The net was woven with a 0.46-mm (0.018-inch)-diameter nylon filament thread. Different depth slots in the outer wooden ring force orthogonal weaves to be noncontacting (see Figure 3.8). These orthogonal threads were purposely made to be noncontacting so that water from rain would drip off more quickly than it would for conventional nets whose orthogonal rows have contact points at the four corners of the grid. The prototype net shown in the figures has

3.2 Bird Net Cover for BWG Antennas

Figure 3.6

153

Prototype bird net being installed on the BWG opening on the dish surface [23]. (Courtesy of NASA/JPL-Caltech.)

a wooden retaining ring, but for noise temperature reduction reasons, the final implemented net will have the outer ring fabricated from aluminum. The JPL design is such that if deterioration of the net threads does occur within 6 months or sooner, the deteriorated net and retaining ring can be easily removed and a spare complete net assembly can be installed quickly in its place. 3.2.3 Test Results

After 20 kW of continuous wave (CW) power at 7.165 GHz was radiated out the BWG antenna for 10 minutes on July 29, 1999, the net was inspected for damage. No deterioration of the net was observed. On two test days of the following week (August 5 and 7, 1999) with clear sky conditions, system noise temperature measurements were made with and without the net. Radiometer system gain changes were corrected by performing ‘‘mini-cals,’’ where the term mini-cal is a radiometer calibration sequence [11, 12]. The computer is programmed to allow a mini-cal to be performed whenever a predetermined function key (on the keyboard) is pressed. Typically, three mini-cals are performed in sequence, and then system temperatures are averaged manually after the tests. The variations of system noise temperatures due to weather changes were corrected through the use of atmospheric noise temperatures measured by the AWVR at DSS 13. After making these corrections, the worst-case measured degradations were 0.04K at 8.425 GHz and 0.18K at 32 GHz (see Table 3.10). The AWVR data proved invaluable for correcting

154


Figure 3.7

A bird’s-eye view of the installed bird net [23]. (Courtesy of NASA/JPL-Caltech.)

Figure 3.8

A closeup view showing the bird net design features [23]. (Courtesy of NASA/JPLCaltech.)

3.2 Bird Net Cover for BWG Antennas

155

Table 3.10 Results of Bird Net Tests Frequency, GHz 8.425 32 a

Average Degradation a, K 0.01 + 0.03/−0.0 0.10 ± 0.08

The tolerances are worst-case deviations from the average.

system noise temperature for these types of tests, in which configuration changes took about 30–45 minutes. Without these corrections for atmospheric noise-temperature changes and corrections for radiometer gain changes (through the use of mini-cals), before and after test configuration changes, the results would have shown that installation of the net caused a lowering rather than an increasing of actual system temperatures. To simulate rain, water was sprayed on all parts of the net using a spray bottle. As shown in Figures 3.9 and 3.10, the worst increase of system noise temperature due to this simulated rain water was 0.4K at 8.425 GHz (X-band) and 3K at 32 GHz (Ka-band). It took about 15 minutes for the X- and Ka-band system temperatures to return to their completely dry-state values. As shown in Figure 3.10, the Ka-band system-noise temperature degradation was only 1.5K after 3 minutes of drying. 3.2.4 Concluding Remarks

Test results on a prototype net showed that the net did not deteriorate when 20 kW at 7.165 GHz was transmitted through it. When dry, the net contributed only about 0.04K and 0.08K to the system noise temperature at 8.425 GHz and 32 GHz, respectively. The worst-case degradation when the net was wet was 0.4K at 8.425 GHz and 3K at 32 GHz, and it took about 15 minutes of drying time for the 32-GHz system noise temperature to return to its dry state value. It is concluded from the test results that the JPL-developed bird net contributions to the system noise temperatures at both 8.425 and 32 GHz are sufficiently small

Figure 3.9

Wet net system noise temperature at 8.425 GHz as a function of drying time [23]. (Courtesy of NASA/JPL-Caltech.)

156


Figure 3.10

Wet net system noise temperature at 32 GHz as a function of drying time [23]. (Courtesy of NASA/JPL-Caltech.)

for operational use. The advantages of having a net that keep birds out of the BWG system outweighs the disadvantage of a wet net taking 15 minutes to return to the original Ka-band dry system temperature values. A decision was made to copy this net design with an aluminum outer ring for the DSN BWG antennas in Spain and Australia. After this development, this net design was implemented at all Overseas and two Goldstone Operational stations having a BWG antenna. At R&D DSS 13, birds flying into the BWG system have not been a problem. The absence of this problem might be due to an audio system installed to periodically inject very loud cannon-like explosive sounds into the BWG system. These explosive sounds startle the birds enough that they do not build nests behind the mirrors.

3.3 G/T Improvement Task 3.3.1 Introduction

Improving the G/T of the BWG antennas and their associated receive subsystems translates into increasing the ground received signal-to-noise ratios. The symbol G refers to the receive system gain, and T refers to the receive system noise temperature. The primary objectives of the G/T improvement task are to: (1) identify sources where G/T improvements can be made, and (2) verify the predicted values through analysis or experimental work. W. Veruttipong of JPL was the principal investigator and conducted most of these G/T Improvement improvement tests. Most of the material presented here was extracted from [13]. For convenience, the terms system temperature and operating system temperature (Top ) will be used interchangeably to mean system-noise temperature, and the terms S-, X- and Ka-band will be used to refer to center frequencies of 2.295, 8.420, and 32 GHz, respectively. Although the goal is to simultaneously improve both G and T, the experimental work was restricted to making and testing only

3.3 G/T Improvement Task

157

improvements of system temperature. Any receive-system gain changes caused by a change in test configuration are assumed to be negligibly small or can be predicted through theoretical calculations. The sources of improvement and predicted improvement values at X- and Ka-band are shown in Table 3.11. Some of the values were derived from theoretical predictions while others were based on previous experimental work on the DSS-13 BWG antenna [7]. Even though most of the individual improvement values are small (less than 0.4K), the sum of all improvement values adds up to 3K at Ka-band. Due to staffing and budget constraints, only those experimental tasks that could be done in a reasonable length of time at a low cost were selected to be performed. 3.3.2 Test Configurations and Test Results

Verification tests were performed on seven different G/T improvement configurations. Descriptions of the test configurations and results of the tests that were performed are presented below in chronological order. 3.3.2.1 Covered Openings on Hatch Door and Tripod Leg Bases

The first of the series of G/T improvement tests involved covering an opening 30.5 cm × 30.5 cm (12 inch × 12 inch) on the hatch door with aluminum tape. Table 3.11 Suggested G/T Improvements for 34-m BWG Antennas with Predicted Improvements and Estimated Costa

Item

Suggestions for G/T Improvements

Predicted X/Ka-Band Improvement at 90 Degrees Elevation Angle

Estimated Cost, $K

0.1–0.3K

12

b

1 .

Assemble skirts behind the subreflector

2b.

Cover hatch door opening

0.03K

Negligible

3b.

Cover openings at base of struts

0.1–0.2K

15

4b.

Cover holography holes

0.2–0.4K

10

5b.

Close panel gaps

0.2–0.3K

10

6.

Readjust panel using holography

0.18 dB at Ka-band

25

7.

Eliminate perforations using a solid panel

0.2K at X-band 0.4–0.7K at Ka-band

Very high

8b.

Reduce the size of BWG hole opening near f1

0.1–0.2K

10

9.

Close the gaps between mirrors and shroud

0.1–0.3K

10

10.

Add skirt around the horn aperture

0.1–0.2K

10

11.

Fabricate a new plug at the center of M5

0.2–0.3K

10

12b.

Install a flat cryo load behind a dichroic plate

0.5–1.0K

30

a

This table was taken from Veruttipong and Otoshi, TMO Technology Program Mid-Year Review, 1 (internal document), Jet Propulsion Laboratory, Pasadena, CA, April 1, 1998. Items 2 through 5 above are subdivisions of former items 2 and 3. b Experimental verification tests were performed, and the results are reported in this article.

158


The opening served as a porthole through which a person could view the dish surface from below the surface without having to open the hatch door. Aluminum tape was used to cover this hatch door opening (Figure 3.11) as well as to cover the openings at bases of the tripod legs (Figure 3.12). The function of the aluminum tape on the dish surface was to reflect incoming signals back to the sky rather than to allow them to pass through the openings and be absorbed by the ground environment. The test results in Table 3.12 show that taping the openings caused the system temperature to be lowered by 0.08K at X-band and 0.24K at Ka-band. The measured improvements and predicted values (see Table 3.11, item 3) are in good agreement. However, it should be pointed out that prior to the test, the base of

Figure 3.11

Aluminum tape covering the opening of the hatch door [13]. (Courtesy of NASA/JPLCaltech.)

Figure 3.12

Aluminum tape covering the base of a tripod leg [13]. (Courtesy of NASA/JPL-Caltech.)


159

Table 3.12 System Temperatures Before and After Taping Openings on Hatch Door and Tripod Basesa Test Configuration

8.420-GHz Top , K

32-GHz Top , K

Before taping

43.74 ± 0.05 N = 105

73.48 ± 0.04 N = 105

After taping

43.66 ± 0.02 N = 370

73.24 ± 0.08 N = 370

Change

−0.08 ± 0.05

−0.24 ± 0.09

a

Comments

Minus-sign change means improvement

Top values are the result of averaging measured Top values over the test period and include corrections for weather. Tolerances include standard deviations due to measurement scatter. N is the number of points used in the averaging and unless otherwise specified, the integration time for each point was 6 seconds. Total test period is equal to N × 6 seconds.

one of the tripod legs was already covered with aluminum tape and the aluminum tape on the base of another leg was partially peeling off. This implies that improvements would have been larger had aluminum tape not already covered the openings at the bases of two of the tripod legs. 3.3.2.2 Covered Holography Holes

On all DSN antennas, small holes on the dish surface are purposely left uncovered to allow easy access to bolts that lay below the dish surface and are used for panel height adjustments based on holography measurement results. These holes will be referred to as holography holes. There are 1,714 holography holes on the BWG antenna dish surface. Each hole has a diameter of 3.18 cm (1.25 inch). Predicted values in Table 3.11, item 4, show that about 0.2- to 0.4-K lowering of systemnoise temperature could be achieved if the holography holes were covered with aluminum tape. To verify these predictions, circular aluminum-tape disks, each having a 4.32-cm (1.7-inch) diameter, were made and individually placed on 5.08-cm (2-inch)-wide rolls of wax paper (see Figure 3.13). Each of these disks can be easily peeled off the wax-paper roll whenever needed. The name ‘‘dot’’ will be used to describe one of these aluminum disks. On November 19, 1998, dots were used to cover all 1,714 holography holes on the DSS-13 BWG dish surface. Figure 3.14 shows dots that were taped over two holography holes on adjacent panels. Systemtemperature measurements, made before and after the dots were taped over all holography holes, showed that the final system temperature was lowered by 0.35 ± 0.05K for 8.45 GHz, which is within the range of 0.2- to 0.4-K predicted values (see item 4 in Table 3.17). The same experiment was performed by M. Franco of JPL on the DSS-26 BWG antenna using a different radiometer for his measurements. His measured result for 8.420 GHz was 0.3 ± 0.05K, which agrees well with the result obtained at DSS 13. 3.3.2.3 Reduced BWG Opening Aperture Plate Mounted on Cassegrain Cone Flange

Another G/T improvement test involved reduction of the nominal BWG hole diameter of 2.438m (96 inches) at the dish surface with an aperture plate (see Figure

160


Figure 3.13

Aluminum dots on a strip of waxed paper [13]. (Courtesy of NASA/JPL-Caltech.)

Figure 3.14

Aluminum dots covering two of the holography holes on adjacent main-reflector panels [13]. (Courtesy of NASA/JPL-Caltech.)


161

3.15). For a properly designed BWG system, most of the power from the far field will reflect off the subreflector and enter the BWG hole within the 99 percent beam contour. However, about 1 percent of the power will stray outside this contour, and some of this stray power that enters the BWG hole will be absorbed by the shroud walls or be absorbed inside the BWG system at ambient temperature. This absorption at ambient temperature causes system temperature to rise. Therefore, it seems reasonable that, if the BWG opening is made smaller to allow only the power within the 99 percent beam contour to enter the BWG system and to reflect the remainder back to sky, then system noise temperature would decrease. However, an opening too small will cause more of the radiated receiver noise temperature [14] to be blocked by the plate so that, instead of allowing it to radiate out the opening to cold sky, it causes more of the radiated receiver power to reflect back towards the receiver. This reflected radiated receiver temperature will pick up additional wall-loss contributions and finally combine with the effective receiver noise temperature to cause the system temperature to increase. In the limit, if the hole diameter were made zero so that all of the radiated receiver temperature was reflected, the system temperature would increase to about 300K. This phenomenon was observed in earlier experiments performed in 1991.

Figure 3.15

Radiated receiver noise being reflected by the aperture plate [13]. (Courtesy of NASA/ JPL-Caltech.)

162


The experiments performed to test the BWG hole-reduction hypothesis involved the fabrication of an aperture plate (a plate with a hole in the center). The outer diameter of the aperture plate was designed to be the same as the outer diameter of the Cassegrain cone mounting flange that is located slightly below the surface of the dish. The aperture plate could then be placed on top of the Cassegrain conemounting flange for support purposes. Commercially available foam sheets about 3.56-cm (1.4-inch) thick, with aluminum foil glued to both surfaces, were used to make the aperture plate. A 3.048-m (10-ft) outer-diameter disk was first cut with a razor blade, and then annular removable rings of various inner diameters were cut into this sheet but not removed (see Figure 3.16). After installation on the Cassegrain mounting flange, by removing the inner rings in a systematic sequence, the aperture plate opening could be easily changed from diameters of 0.61m (2 ft) to 1.83m (6 ft) in 0.305m (1 ft) steps. Figure 3.17 shows one of these annular rings removed from the fabricated aperture plate. In May 1998, the aperture plate tests were conducted. The test plan was to determine the optimum BWG opening diameter that will maximize improvement of system temperatures at both X- and Ka-band with acceptable degradation at the S-band. The first step was to make system-temperature measurements with no aperture plate. System temperatures subsequently measured for various holeopening diameters were compared with the system temperature measurements made with the aperture plate removed. Results of these tests are shown in Table 3.13. A maximum lowering of system temperature of about 0.65K was observed at 8.420 GHz when the hole diameter was 0.91m (3 ft). A maximum lowering of system temperature of 0.3K was observed at 32 GHz when the hole diameter was 1.52m (5 ft). At 2.295 GHz, degradations were observed for all of the reduced diameters, and the degradation was as much as 84.4K when the hole diameter was 0.61m (2 ft).

Figure 3.16

Aperture plate with a 0.61-m (2-ft) diameter hole opening installed on the dish surface of the DSS-13 BWG antenna [13]. (Courtesy of NASA/JPL-Caltech.)


Figure 3.17

163

Aperture plate shown with one of the annular rings removed [13]. (Courtesy of NASA/ JPL-Caltech.)

Table 3.13 Noise-Temperature Change Versus Aperture-Plate Hole Diametera, b Hole Diameter, m (ft)

2.295 GHz

Noise-Temperature Change, K 8.420 GHz 32 GHz

Comments

0.61 (2)

84.35 ± 0.15 N = 53

0.15 ± 0.02 N = 53

0.13 ± 0.06 N = 53

Degradations at all frequencies

0.91 (3)

34.40 ± 0.16 N = 53

−0.65 ± 0.01 N = 62

−0.08 ± 0.09 N = 62

Improvements at 8.420 and 32 GHz

1.22 (4)

11.99 ± 0.19 N = 53

−0.57 ± 0.02 N = 53

−0.21 ± 0.09 N = 53


1.52 (5)

3.25 ± 0.43 N = 52

−0.39 ± 0.03 N = 55

−0.29 ± 0.10 N = 55


1.83 (6)

2.11 ± 0.34 N = 51

−0.26 ± 0.27 N = 51

Didn’t measure

Cloudy weather during 32 GHz test; no data taken

a

The noise temperature changes are derived from subtracting the system temperature of the normal 2.438-m (8-ft) hole diameter configuration from the measured system temperatures of the aperture-plate configurations. Plus-sign noise temperature means degradations. Minus sign means improvement. b Noise temperature values are the result of averaging measured Top values over the test period and include corrections for weather and baseline drift due to gain changes. Tolerances include standard deviations due to measurement scatter and uncertainties in baseline corrections for drift. N is the number of points used in the averaging and, unless otherwise specified, the integration time for each point was 6 seconds. Total test period is equal to N × 6 seconds.

Aperture Plate Mounted Above the Dish Surface

A more thorough analysis indicated that the narrowest-beam waist would lie in a region above the Cassegrain cone-mounting flange. Therefore, it was of interest to perform the same tests with the aperture plate raised above the dish surface. This was accomplished by installing four vertical steel rods installed on the Cassegrain cone-mounting flange (see Figure 3.18). The steel rods had threaded portions

164


Figure 3.18

Aperture plate mounted 1.22m (48 inches) above the Cassegrain cone-mounting flange [13]. (Courtesy of NASA/JPL-Caltech.)

that allowed the aperture plate assembly to be raised between 30.48 cm (1 ft) to 152.4 cm (5 ft) above the Cassegrain cone-mounting flange. After installation of the raised aperture plate assembly to a height of 1.22m (4 ft), system-temperature measurements were made for various aperture plate hole openings. Table 3.14 shows that when the aperture plate was raised 1.22m (4 ft),

Table 3.14 Noise-Temperature Change Versus Hole Diameter When the Aperture Plate Was Mounted 1.22m (48 inches) Above the Cassegrain Cone Flange Planea, b Hole Diameter, m (ft)

2.295 GHz

0.91 (3)

Did not test

−0.21 ± 0.02 N = 54

−0.05 ± 0.05 N = 54

Some improvement at 8.420 GHz, but small improvement at 32 GHz

1.22 (4)

Did not test

−0.33 ± 0.03 N = 52

−0.53 ± 0.05 N = 52

Large improvement at 32 GHz

1.52 (5)

Did not test

−0.33 ± 0.02 N = 56

−0.44 ± 0.06 N = 56

Improvements at both 8.420 and 32 GHz

1.83 (6)

Did not test

−0.31 ± 0.03 N = 51

−0.08 ± 0.05 N = 51

Results at 32 GHz are thought to be erroneous

a


Comments

The noise temperature changes are derived from subtracting the system temperature of the normal 2.438-m (8-ft) hole diameter configuration from the measured system temperatures of the aperture plate configurations. Plus-sign noise temperature means degradation. Minus sign means improvement. b Noise temperature values are the result of averaging measured Top values over the test period and include corrections for weather and baseline drift due to gain changes. Tolerances include standard deviations due to measurement scatter and uncertainties in baseline corrections for drift. N is the number of points used in the averaging and, unless otherwise specified, the integration time for each point was 11 seconds. Total test period is equal to N × 11 seconds.


165

only small differences (< 0.2K) of system temperatures were observed from those shown in Table 3.13 for the same hole diameters. However, Table 3.15 shows that, when the aperture plate was raised only 38.1 cm (15 inches), the measured improvement was 0.43K at 32 GHz when the hole diameter was 1.83m (6 ft). This measured improvement is significantly greater than the 0.08-K improvement value that was measured when the aperture plate (with the same 1.83-m hole diameter) was mounted 1.22m (4 ft) above the Cassegrain cone-mounting flange (see Table 3.14). The 0.08-K value in Table 3.14 is thought to be an experimental error due to inability to correct for changing weather conditions. 3.3.2.4 Tapered BWG Hole Opening

Based on the aperture-plate test results, it was concluded that, if the BWG opening at the Cassegrain cone mounting flange could be reduced to a smaller diameter by means of a smooth tapered transition (see Figure 3.19), the radiated receiver noise temperature would be guided smoothly out the BWG opening and go to cold sky. Then system temperature should be reduced both by the reduced hole opening and the smooth transition. To implement this supposition into practice, a cone transition was fabricated from 3.56-cm (1.4-inch) thick Styrofoam sheets covered with aluminum foil on both surfaces. Figures 3.20 and 3.21 show this fabricated cone assembly being prepared for insertion into the BWG opening at the dish surface. The inside diameter at the bottom of the cone is about 2.44m (8 ft) so that, when inserted into the BWG opening, the circumferential outside surfaces at the bottom of the cone will touch the BWG shroud wall. The cone is linearly tapered toward the top end to an inside diameter of 1.52m (5 ft) and has an overall length of about 3.35m (11 ft). Upon insertion of the cone assembly into the BWG opening, the large mounting flange, shown in Figures 3.20 and 3.21, rests on top of the Cassegrain cone mounting flange. On January 28, 1999, system-temperature measurements were made at the S-, X- and Ka-band both before and after installation of the cone transition. For the data processing, the first step was to make corrections for the effects of weather

Table 3.15 Noise-Temperature Change Versus Hole Diameter When the Aperture Plate Was Mounted 38.1 cm (15 inches) Above the Cassegrain Cone Flange Planea, b Hole Diameter, m (ft)

2.295 GHz

1.52 (5)

Did not test

−0.28 ± 0.03 N = 47

−0.35 ± 0.13 N = 47

Improvements at both 8.420 GHz and 32 GHz

1.83 (6)

Did not test

−0.28 ± 0.03 N = 50

−0.43 ± 0.05 N = 50

Improvements at both 8.420 GHz and 32 GHz

a


Comments

The noise temperature changes are derived from subtracting the system temperature of the normal 2.438-m (8-ft) hole diameter configuration from the measured system temperatures of the aperture-plate configurations. Plus-sign noise temperature means degradation. Minus sign means improvement. b Noise temperature values are the result of averaging measured Top values over the test period and include corrections for weather and baseline drift due to gain changes. Tolerances include standard deviations due to measurement scatter and uncertainties in baseline corrections for drift. N is the number of points used in the averaging and, unless otherwise specified, the integration time for each point was 6 seconds. Total test period is equal to N × 6 seconds.

166


Figure 3.19

A cone transition for guiding the radiated receiver noise out of the hole opening to the sky [13]. (Courtesy of NASA/JPL-Caltech.)

on atmospheric-noise temperature (Tatm ) using ground-level weather data and an atmospheric layer model. The program used to make these weather corrections was written by S. Slobin of JPL and modified by Otoshi [15]. After correcting for atmospheric noise temperature changes, the second step in the data reduction process was to make corrections for baseline drifts. The corrected results are shown in Table 3.16. Comparison with the 1.52-m (5-ft) hole-diameter results of Table 3.13 shows that, at 32 GHz, the cone-transition results were poorer than the aperture plate results with the same 1.52-m hole-diameter opening. A reason why measured improvements were poorer might be inadequate corrections made for changing cloudy conditions and large baseline drifts for the cone-transition tests. The atmospheric noise temperature corrections, using ground surface weather data, are only valid for clear-sky and not for cloudysky conditions. The total length of time going from baseline (normal) configuration to the inserted cone-transition test configuration and back to the baseline configuration was about 4–6 hours. The baseline drifts were 0.21K, 0.20K, and 0.74K at 2.295 GHz, 8.425 GHz, and 32 GHz, respectively. The baseline drift at 32 GHz was notably large. It is recommended that these cone transition tests be redone in clear weather in the future, using improved test procedures that were developed later and will be described in Section 3.3.2.7.


167

Figure 3.20

Exterior view of the fabricated cone-transition assembly being tilted for installation into the normal 2.44-m (8-ft) BWG opening on the dish surface [13]. (Courtesy of NASA/JPL-Caltech.)

Figure 3.21

Interior view of the cone transition assembly. The cone has a 1.52-m- (5-ft)-diameter opening on the near end and a 2.44-m (8-ft)-diameter opening on the opposite end [13]. (Courtesy of NASA/JPL-Caltech.)

168

Noise Temperature Experiments Table 3.16 Cone-Transition Test Results (Top of Cone Has a 1.52-m (5-ft) Opening) Frequency, GHz

Change in System Temperature,a K

2.295 8.420 32.0

1.34 ± 0.02 −0.08 ± 0.04 0.01 ± 0.07

a

Comments Degradation Improvement Degradation or improvement if negative tolerance is applied

The change is relative to the no-plate test results. Tolerances shown are uncertainties due to measurement standard deviations and uncertainties in the corrections for atmospheric noise temperature changes and baseline drifts.

3.3.2.5 Subreflector Skirts

On February 11, 1999, noise temperature tests were performed covering portions of the subreflector edge regions with five reflector plates. A plate was installed near the top of each tripod leg. This test configuration will be referred to as the three-plate subreflector skirt configuration. Two additional plates were installed later to cover the subreflector control structure. Normally, without these installed reflector plates, small amounts of subreflector spillover power are scattered toward the ground, thus raising system temperature. The installed plates are designed to reflect that portion of subreflector spillover power toward the main reflector, which re-reflects it to the sky. The lowering of noise temperature due to the installed plates was expected to be between 0.1–0.3K at both X- and Ka-band (see Item 1 of Table 3.11). Experimental verification tests showed that the three-plate subreflector skirt configuration caused a lowering of the system temperatures of 0.09 ± 0.05K at 8.420 GHz and 0.13 ± 0.06K at 32 GHz. Adding two additional plates to cover the subreflector control structure did not improve the three-plate results at either 8.420 GHz or 32 GHz. The measured improvements are within the 0.1- to 0.3-K range of values that was predicted.

3.3.2.6 Liquid Nitrogen Load

A liquid-nitrogen (LN) load in a styrofoam bucket was designed to be placed behind and above the X-/Ka-band dichroic plate in the DSS-13 BWG system. Without the LN load, stray Ka-band signals that do not pass through the X-/Ka-band dichroic plate will reflect up to the ceiling, which is at a physical temperature of 300K. With the LN load installed, these reflected signals will instead be absorbed by the LN load, which is at a physical temperature of about 80K. Depending on the percentage of power that is reflected toward the LN load, a significant lowering of system temperature can result at Ka-band. The LN load that was developed by Veruttipong and Otoshi for this purpose is shown in Figure 3.22. The pyramidal absorbers are installed face down inside a rectangular foam container that has inside-area dimensions of 38.1 cm (15 inches) × 43.18 cm (17 inches). When ready for use, liquid nitrogen is poured into this container. An exterior view of this load assembly installed at DSS 13 is shown in Figure 3.23. Tests were made on August 17, 1999, with this LN load installed, and test results showed that the system temperature was lowered 1.20 ± 0.10K at Ka-band.


169

Figure 3.22

JPL-developed Ka-band liquid-nitrogen load. An absorber piece was removed and shown in an upright position for purposes of this picture. The interior was lined with a Kapton sheet to keep liquid nitrogen from leaking out of the foam container [13]. (Courtesy of NASA/JPL-Caltech.)

Figure 3.23

Exterior view of the JPL-developed Ka-band liquid-nitrogen load installed above the X-band dichroic plate at DSS 13 [13]. (Courtesy of NASA/JPL-Caltech.)

170


Tests were not performed at X-band because, in order to capture stray X-band signals, a fabricated X-band LN load would have to be very large. There was not enough room to accommodate installation of a large X-band LN load.

3.3.2.7 Covered Panel Gaps

Another G/T improvement verification test that was performed involved putting 3.18-cm (1.25 inch) wide aluminum tape over all the gaps between antenna panels. Figure 3.24 shows an example of aluminum tape put over one of the antenna panel gaps. Figure 3.25 shows a partial view of the BWG antenna with all panel gaps covered with aluminum tape. On the first day of the test (August 17, 1999) aluminum tape was used to cover only those antenna surface panel gaps that went in circumferential directions around the dish surface. The changes in Top at both 8.420 GHz and 32 GHz were measured before and after the aluminum tape covered the circumferentially oriented panel gaps. On the second day of the test (August 19, 1999), aluminum tape was used to cover half the number of the radial gaps that ran from the BWG center to the edge of the dish surface. The changes in Top at both 8.420 GHz and 32 GHz were again measured before and after the tape was put on. The final test (performed on August 24, 1999) involved taping the remaining half of the radial panel gaps on the DSS-13 BWG main reflector surface.

Figure 3.24

Aluminum tape placed over a gap between antenna panels [13]. (Courtesy of NASA/ JPL-Caltech.)


Figure 3.25

171

Partial view of the DSS-13 BWG antenna main reflector after all panel gaps were covered with aluminum tape [13]. (Courtesy of NASA/JPL-Caltech.)

For these tests, the test procedure for minimizing baseline drifts was as follows. Just prior to making a configuration change, three successive mini-cals were performed. A mini-cal is a radiometer calibration sequence [11, 12] that can be performed by striking the appropriate key on the computer keyboard. Then immediately after the configuration change, three successive mini-cals were again performed. These mini-cals give Top values that are corrected for radiometer gain changes. Then atmospheric noise temperatures Tatm that were measured by the AWVR during the same test period were subtracted from the Top values (corrected for gain changes) to give Top minus Tatm values. Then these values were averaged for the appropriate test configurations. Remarkable repeatability and consistency of data were obtained using these measurement and data reduction procedures. The final data reductions, after making corrections for changes in gain and Tatm , showed that the system temperature due to taping all panel gaps was lowered by 0.31 ± 0.05 K at 8.425 GHz 0.54 ± 0.31 K at 32 GHz where the tolerances are overall uncertainties that take into account uncertainties in the measurement results obtained on three different test configurations on three different dates. For comparison, the predicted improvement was 0.2 to 0.3K for both X- and Ka-bands (see Table 3.11, Item 5). 3.3.3 Summary and Recommendations

Tests were performed only on those suggested improvement configurations shown in Table 3.11 that could be tested quickly and inexpensively. Table 3.17 gives

172

Noise Temperature Experiments Table 3.17 Comparison of Predicted and Measured G/T Improvements for the DSS-13 34-m BWG Antenna

Item

Suggestions for G/T Improvement

Predicted X-/Ka-Band Improvement at 90-Degree Elevation Angle

Measured Improvement X-band, K Ka-band, K

1a.

Assemble skirts behind the subreflector (only three skirts at top of struts)

0.1–0.3K

0.09 ± 0.05

0.13 ± 0.06

2a.

Cover hatch door opening

0.03K

Included in item 3

Included in item 3

3a.

Cover openings at base of struts with plates

0.1–0.2K

0.08 ± 0.05

0.24 ± 0.09

4a.

Cover holography holes

0.2–0.4K

0.35 ± 0.05

0.5 ± 0.2

5a.

Close panel gaps

0.2–0.3K

0.31 ± 0.05

0.54 ± 0.31

6.

Readjust panel using holography

0.18 dB at Ka-band

7.

Eliminate perforations using a solid panel

0.2K at X-band 0.4–0.7K at Ka-band

8a.

Reduce the size of BWG hole opening near f1 [see Table 3.13, 1.52-m (5-ft) hole]

0.1–0.2K

0.39 ± 0.03

0.29 ± 0.10

9.

Close the gaps between mirrors and shroud

0.1–0.3K

10.

Add skirt around the horn aperture

0.1–0.2K

11.

Fabricate a new plug at the center of M5

0.2–0.3K

12a.

Install a flat cryo load behind a dichroic plate

0.5–1.0K

Not tested

1.20 ± 0.10

—

1.2 ± 0.1

2.9 ± 0.4

Sum of measured improvements and rss of uncertainties a

Experimental verification tests were performed, and the results are reported in this section.

comparisons of predicted and measured improvements. The total improvement was 1.2K ± 0.1K at 8.420 GHz and 2.9 ± 0.4K at 32 GHz. As shown in Table 3.13, an S-band degradation of 3.3K was observed when the aperture plate had a 1.52-m (5 ft)-diameter hole. If this degradation at S-band is acceptable, it is recommended that all the tested improvement configurations described in Table 3.17 be implemented. Otherwise, the aperture-plate configuration (Item 8) should not be implemented.

3.4 Measured Sun Noise Temperature at 32 GHz 3.4.1 Introduction

The purpose of the Sun experiment task was to develop a simple and inexpensive method for measuring the Sun’s noise temperature at 32 GHz with the use of the

3.4 Measured Sun Noise Temperature at 32 GHz

173

DSN 34-m antennas. It was required that new methods be developed to prevent receiver saturation caused by the strong incoming Sun’s noise power. This task is important for increasing the accuracy of measuring system noise temperatures when tracking a spacecraft in the vicinity of the Sun at Ka-band. In addition, if a method is developed that overcomes the receiver saturation problem, it might be possible to employ raster scan techniques to quantify scattering from the antenna’s tripod struts as functions of the Sun’s position. The material presented in this section was extracted from an article written by this author [16]. Only the methodology and some of the results from the article will be presented. Previous work was done by JPL experimenters on noise temperature measurements looking directly at the Sun or in the vicinity of the Sun [17–19]. The 34-m BWG antenna noise temperatures are currently calibrated through the use of an ambient load thermal noise standard and the zero point of a power meter located in the DSS-13 control room. Injected noise diode pulses of about 20K are used to determine receiving system linearity. System noise temperature calibrations are valid only up to the system temperature (or Top ) value measured when the ambient load is connected to the input of the low-noise amplifier (LNA). For the Ka-band monopulse receiving system at DSS 13, the upper limit of valid system-noise temperature calibration is about 350K. Linearity of the receiving system is also not calibrated above this upper limit point. Without running special tests, the saturation point above 350K is not known. The Sun’s noise temperature during the quiet Sun cycle is about 9,960K at 31.4 GHz [17, 20]. When the 34-m BWG antenna points at a quiet Sun and the antenna system has 50 percent efficiency, the measured Sun noise temperature will be about 5,000K at 32 GHz. This high value is far above the calibrated region of the DSS-13 BWG receiving system. Therefore, a need existed to find a way to measure the Sun’s noise temperature accurately at these high levels of 5,000K or more. Although several gain reduction methods were considered for reducing the Sun’s noise temperature so that it would be within the calibrated region of the receiver, only two methods, named the absorber and waveguide attenuator methods, were extensively investigated. In Section 3.4.2, the absorber and waveguide attenuator methods are described. Section 3.4.3 discusses the measurement and data reduction methodology; Section 3.4.4 presents measured Sun noise temperatures; and Section 3.4.5 recommends follow-up work and ways to improve future Sun noise temperature measurements.

3.4.2 Gain Reduction Methods

The absorber and waveguide attenuator methods are two methods that were used for the Sun experiment. For the absorber method, an absorber sheet is used to attenuate the incoming Sun’s noise power in front of the LNA so as not to saturate the LNA. For the waveguide attenuator method, a waveguide variable attenuator is used to attenuate the Sun’s noise power going into the follow-up receiver. For this method, it is assumed that the Sun’s noise power does not saturate the LNA but instead saturates the follow-up receiver. The absorber and waveguide attenuator methods were extensively investigated because: (1) they were easy and inexpensive

174


to implement and (2) they had the potential of giving the most accurate results. Both methods are discussed in detail in the following. 3.4.2.1 Absorber Method

The absorber method involves laying a flat, thin absorber sheet on top of the Kapton cover on the feed-horn aperture. The main advantage of this method is that the technique can be easily used for any 34-m or 70-m antenna receiving system. The receiving system calibrations, which were done without the absorber sheet, do not have to be redone for the system configuration with the absorber sheet. Flat absorber sheets were special ordered from Advanced Electro Magnetics, located in Santec, California. The procurement specifications were that: (1) the overall flat sheet be made of laminated carbon impregnated flat layers, (2) the total thickness should not be greater than 0.953 cm (0.375 inch), (3) the overall oneway transmission loss be about 13 dB when measured in free space for a normal incidence angle at 32 GHz, (4) the VSWR be less than 1.10 at its designated input side at 32 GHz, and (5) the top surface have a blue-colored coating for identification purposes. These flat absorbers are manufactured by gluing together different layers of polyurethane foam material. Each layer is impregnated with different density carbon material. The input-side layer has the least amount of impregnated carbon while the output side has the most. The particular absorber sheet purchased from this manufacturer was made in three laminated layers. In an attempt to meet the VSWR requirements, the author modified the test piece as follows. First the procured absorber sheet was cut apart at the two-layer line with a razor blade. Then, from this two-layer piece, two identical round circles (slightly larger than the horn aperture) were cut. The final step was to glue the pieces back to back such that the designated input side (blue in color) was on both the front and back of the new test piece (see Figure 3.26). By modifying the absorber in this manner, the modified absorber sheet was now symmetrical looking into either input and output sides. The input and output VSWRs were expected to be better than those of the original unsymmetrical sheet. Figure 3.26 shows a view of an edge and the laminations of the absorber sheet. Figure 3.27 shows the absorber sheet and its aluminum ring holder. The holder was used only to ensure that the absorber test piece would lie on top of the horn aperture the same way each time it was used. Also, since the absorber sheet tended to warp, the holder also ensured that the sheet would lie flat on the horn aperture. Determination of the absorber sheet loss was the most difficult aspect of the entire absorber method development. Several loss determination methods based on noise temperature measurements were investigated [16]. The method that gave the correct absorber loss value was to measure the noise temperature of a radio source with and without the absorber sheet placed on the horn aperture of the receive system to be used for the Sun experiments. The Moon was found to be the best source to use for absorber sheet loss calibrations because of its high source temperature and high elevation angles at 32 GHz. The diameter of the Moon, 0.5 degree, was about the same as the diameter of the Sun.


Figure 3.26

175

Closeup view of the outer edge of the absorber sheet cut to cover the horn aperture. Note the four laminated layers [16]. (Courtesy of NASA/JPL-Caltech.)

At the time of calibration on year 2000, day of year (DOY) 325, the Moon was at quarter Moon. The quarter Moon was sufficiently illuminated to enable making accurate source temperature measurements with and without the absorber sheet. Figure 3.28 shows the system noise temperatures measured when scanning the quarter Moon without and with the absorber sheet. The peak Moon temperatures without and with the absorber sheet were 188.10K and 23.95K, respectively. The ratio of the two peak temperatures gave the loss ratio of the absorber to be 7.85, corresponding to a loss of 8.95 dB. This loss-ratio value for the absorber sheet was used for all of the absorber method Sun measurements reported in this section. A similar measurement, made on year 2000, DOY 347 (see Figure 3.29), when the Moon was at full Moon, resulted in the absorber sheet having a loss ratio of 8.08, corresponding to a loss of 9.07 dB. The quarter Moon and full Moon results agreed to within 2.9 percent. These results are significantly different from the 8.18-dB loss measured when the near-field antenna pattern range was used [16]. Once the absorber sheet is determined for the Ka-band horn configuration, the absorber sheet calibration does not have to be repeated if new Sun measurements are done with the same receiving system on another day.

3.4.2.2 Waveguide Attenuator Method

The waveguide attenuator method involves the use of a WR 28 variable attenuator that is installed between the output of the LNA and the input of the downconverter mixer of the Ka-band monopulse feed receiving system. This method assumes that, in the normal configuration, the high Sun noise temperatures will not saturate the LNA but will saturate the downconverter. The variable attenuator is used to attenuate the Sun’s noise power such as to bring it into the linear region of the downconverter. Figure 3.30 shows a variable attenuator that is the same model as the one already installed. For the waveguide attenuator method, the setup procedure

176


Figure 3.27

Absorber sheet and holder: (a) absorber outside of the holder and (b) absorber sheet installed in the holder (as viewed from above the horn) [16]. (Courtesy of NASA/JPLCaltech.)

was to first point the antenna at the Sun. When this was done, the computer monitor for the noise-temperature calibration system displayed a system temperature value of infinity. The next step was then to gradually turn the attenuator screw adjustment on top of the attenuator (see Figure 3.30) so as to increase the attenuation until the monitor showed system temperature values of about 6,500 ± 100K. Since the attenuator did not have a calibration dial mounted on it, it was not possible to know how much attenuation was added in. However, based on power meter readings, it is known that at least 5 dB of attenuation was added. This screw adjustment position was kept fixed for the rest of the measurements on the Sun. The final step was to measure the follow-up receiver temperature by the Y factor on–off method described in [21]. For the Sun experiment results reported in this section, the follow-up noise temperature contribution increased from 2.84K to a surprisingly high value of 21.9K. The final step was to input this new measured follow-up noise temperature of 21.9K into the system temperature calibration program, Topcal, developed by


Figure 3.28

177

Scans for the quarter moon (a) without and (b) on an expanded Top scale with the absorber sheet, 32 GHz, 2000 DOY 325 (November 19). The leading edge of the scan was the lit side of the Moon. The scan for (b) was started 1 minute after the end of the scan for (a). The delta system temperature is about 188K in (a) and 24K in (b) [16]. (Courtesy of NASA/JPL-Caltech.)

Stelzried [12] for DSS 13. Once the Sun noise temperature measurements were completed, it was necessary to adjust the attenuator so that the attenuation was back to its original value so that the station was put back to its normal operating configuration. To verify that the attenuator was set back correctly, a new measurement of the follow-up temperature was required and checked against the original value. This entire setup procedure has to be repeated if new Sun tests are done again with the same receiving system on another day. 3.4.3 Measurement and Data Reduction Method

The initial goal of the Sun experiment task was to find a way to measure the Sun noise temperature only at the Sun’s center. The procedure was to start from different offsets from the Sun center and then move directly to the Sun’s center for an onsource temperature measurement. The starting point offsets were ±5 degrees in

178


Figure 3.29

Scans of the full moon (a) without and (b) on an expanded Top scale with the absorber sheets, 32 GHz, 2000 DOY 347 (December 11). Note that the scan for (b) was started 60 seconds after the end of the scan for (a) [16]. (Courtesy of NASA/JPL-Caltech.)

Figure 3.30

Type of WR28 variable attenuator used for the waveguide attenuator method [16]. (Courtesy of NASA/JPL-Caltech.)


179

cross-elevation (XEL) and ±5 degrees in elevation (EL). The measured Sun noise temperatures differed as much as ±20K starting from the four different offsets. It was concluded that reliable Sun noise temperature data could not be obtained with this procedure. A decision was made that the objective of the Sun experiment task be expanded to measuring the Sun noise temperatures over the entire solar disk and not just at the center. It is convenient to think of the Sun as a circle (disk) that has a radius of 0.25 degrees, and the center of the Sun as the origin of an x-y coordinate system. The x- and y-axes are called the XEL and EL offset axes, respectively, and the offsets are measured from the Sun center in units of degrees. The procedure developed for mapping the entire solar disk was to select a particular fixed EL offset and measure system temperatures while scanning the Sun in XEL from −1.2 degrees to +1.2 degrees. After this scan another XEL scan was made for a new EL offset. This scanning procedure was continued until the entire solar disk plus close-in regions were mapped for −0.35-degree to 0.35-degree EL offsets in increments of 0.05 degree. The XEL scan rate was 2.666 mdeg/s and data were taken every 2 seconds. Measured system temperature values are permanently recorded in a computer data file. In the postprocessing, the noise temperatures recorded in time are converted to noise temperature-versus-XEL offset and plotted. Any portions of the measured noise temperature curves can be expanded to see detail to a resolution of 5.332 mdeg in XEL. These expanded plots might be useful to telecommunications engineers who are interested in knowing what the system temperature increases are in the close-in regions of the Sun [19]. After measuring the system temperature by the described experimental procedure, the data-reduction procedure involved subtracting out the minimum system temperature measured when the antenna was in the ‘‘off-the-Sun’’ region of −1.2 degrees to −0.6 degree XEL from the system temperatures measured at the other XEL angles. The next step was to correct the above differenced data for the absorber sheet loss. The final steps were to correct for the atmosphere loss and the antenna system efficiency. These data reduction steps are expressed mathematically as Tsun =

[(Top )on − (Top )off ] × L abs × L atm × Cr ␩

(3.18)

where (Top )on , (Top )off are the system temperatures measured when the antenna points at the Sun and off the Sun, respectively; L abs is the power loss ratio of the absorber sheet; and L atm and ␩ are, respectively, the atmosphere loss factor and the antenna efficiency at the elevation angle at which the Sun measurements were made. For the waveguide attenuator method, L abs = 1, and for the absorber method, L abs = 7.85 (see discussion in Section 3.4.2.1). The symbol C r is the source size correction factor. If the nonlinearity factor of the receiving system is known accurately, (3.18) is multiplied by the nonlinearity factor. Equation (3.18) was derived from mathematical manipulation of the antenna efficiency formula given in [22] as

␩=

⌬T × L atm T 100 Cr

冋册

(3.19)

180


where ⌬T = (Top )on source − (Top )off source

(3.20)

The delta term in (3.20) is sometimes referred to as the ‘‘system temperature increase’’ due to the radio source. The symbol T 100 is the system temperature increase that would be measured for ⌬T if the antenna system were perfect (i.e., 100 percent aperture efficiency and no losses in the antenna system between the aperture and the Top measurement reference point). For the results presented in this section, T 100 in (3.19) is Tsun in (3.18). A value of C r = 1 was assumed for the results of this section because it is not presently known what the C r value is for measurements on a source as large as 0.5 degree in diameter with an antenna beam of 17 mdeg. Performing a theoretical study to determine the correct C r value is beyond the scope of this section. When a value of C r becomes known, the Sun temperatures presented in this section can be multiplied by the known value of C r [see (3.18)]. However, from the theoretical study done by this author, reported in the appendix of [16], preliminary results indicate that C r is very close to being 0.998 for the Sun. Therefore, there might not be a need to correct the measured Sun noise temperatures for C r . For a BWG antenna system, the term antenna efficiency (or efficiency) is used to mean antenna efficiency that includes all losses of the Cassegrain antenna plus the losses between f1 and the receiver calibration reference point. For DSN systems, the calibration reference point is usually the input of the low-noise amplifier (LNA). For the DSS 13 BWG antenna with the Ka-band monopulse feed, the efficiencies were calculated from the following equations [D. Morabito, JPL, private communication, August 31, 2000]. For source rising,

␩ = 0.1807 + 0.0136019 × EL − 0.000150694 × EL 2

(3.21)

For source setting,

␩ = 0.2415 + 0.015646 × EL − 0.00019589 × EL 2

(3.22)

where EL is the elevation angle in degrees. The atmospheric loss factor L atm values, at 32 GHz as functions of elevation angles for test dates DOY244 and DOY 258, were determined from ground weather data using an Excel program furnished by S. Slobin of the Communications Systems and Research Section at JPL. For test date DOY 293, zenith atmosphere noise temperatures, measured at 31.4 GHz by the AWVR were furnished by A. Tanner and S. Keihm of the Microwave and Lidar Technology Section at JPL. These measured zenith temperatures were converted to L atm (EL ) at 32 GHz using formulas furnished by S. Keihm. 3.4.4 Experimental Results

The receiving system linearity is determined by measuring the amplitudes of the injected noise-diode temperatures when the LNA is connected first to the antenna


181

and then to the ambient load thermal noise standard. The degrees to which the injected noise-diode pulse magnitudes are the same in these two configurations are a measure of the receiver nonlinearity. Measuring the linearity or nonlinearity is part of the calibration sequence called mini-cal [12]. When the absorber sheet and holder were used on the DSS 13 Ka-band monopulse system, the system temperatures on and off the Sun were, respectively, about 1,400K and 308K. Even though 1,400K is outside the calibrated linearity range of about 350K, mini-cals performed with the antenna pointed at the Sun showed that the worst-case linearity factor was about 1.03 to 1.05. This nonlinearity corresponds to about a 3 to 5 percent error in measuring the Sun noise temperature. The causes of variation in measured linearity for the absorber method can be explained as follows. When the antenna was pointed at the Sun and the system temperature was about 1,400K, the standard deviations on the measured Sun noise temperature values every two seconds were about 2K maximum. Standard deviations of this magnitude were significant, but were not large enough to mask out the injected noise-diode temperatures of about 16K. For this method, one needs to do several (or more) mini-cals so that the linearity factors, measured while looking at the Sun, can be averaged. The averaging tends to smooth out the fluctuation effects. Mini-cals that were performed while on the Sun for the waveguide attenuator method gave linearity factors that ranged from 1.01 to 2.0. The high linearity values are partly due to the fact that the noise diode pulse magnitude is only 16K and the standard deviations of the measured Sun noise temperatures, while looking at the active Sun of about 6,500K, were varying from 3 to 21K. The high standard deviations tend to mask out the injected noise diode temperature pulses of about 16K and cause errors in determining linearity. Therefore, it was not certain whether the measurements for the waveguide attenuator method were made in the linear region, and saturation could have occurred. Only some of the results will be shown. All measurements were made in 2000 after July 31 or times of solar max. Figures 3.31 and 3.32 are measured Sun noise temperature plots for EL offsets of 0 degrees with the absorber and WG attenuator method results superimposed. The absorber measurements were done on DOY 244 while the attenuator measurements were done on DOY 258 and DOY 293. These two figures were selected for discussion purposes because they show the results of measurements repeated at the same EL offset angle, but made at different elevation angles and, therefore, different efficiency corrections had to be applied. To facilitate this discussion, elevation angle and efficiency information were incorporated into these two figures. These figures are divided into parts (a) and (b). The curves in part (a) are measured Sun noise temperatures with atmosphere losses removed and not yet corrected for efficiency. The curves in part (b) are the curves in part (a) corrected for efficiency. Note that in Figure 3.31(a) the curve for DOY 258 and the curve for DOY 293 are very close together, but in Figure 3.32(b), after being corrected for efficiencies, they are separated by a significant amount. In Figure 3.32(a), which is a repeat measurement, the curve on DOY 258 for the waveguide attenuator method and the curve on DOY 293 are again close together, but in Figure 3.32(b), after being corrected for efficiency, they are still close together. A possible explanation for the large difference in results obtained by the absorber

182


Figure 3.31

DSS-13 BWG antenna, XEL Sun temperature profile for EL offset = 0.0 degrees, 32 GHz: (a) no corrections made for efficiency and (b) correction made for efficiency. Efficiency values are functions of elevation angle and Sun rising (SR) or Sun setting (SS) [16]. (Courtesy of NASA/JPL-Caltech.)

and waveguide attenuator methods is that the waveguide attenuator method results might be too low due to receiver saturation. Linearity tests for the waveguide attenuator method were inconclusive because noise diode pulses were masked out by high measurement standard deviations. Figure 3.31 shows that the noise temperatures over the Sun surface varied considerably. For example, the Sun noise temperature in Figure 3.31(a) has: (1) a mean value of about 9,425K across the Sun surface, (2) a peak value as high as 10,404K, and (3) a minimum value as low as 8,420K. These peaks and valleys represent deviations from the mean of +979K and −1,005K.


Figure 3.32

183

DSS-13 BWG antenna, XEL Sun temperature profile for EL offset = 0.0 degrees (repeat), 32 GHz, atmosphere removed: (a) no corrections made for efficiency and (b) correction made for efficiency. Efficiency values are functions of elevation angle and SR or SS [16]. (Courtesy of NASA/JPL-Caltech.)

Figure 3.33 shows waveguide attenuator method results of two scans for 0 degrees EL offset but taken one hour apart on the same day. It can be seen from the plot that the measurements on the Sun at the same EL offset were nonrepeatable. Note that, for the scan taken one hour later, a solar flare occurred that was not there on the earlier scan. Other plots covering the entire solar disk for 0.35- to −0.35-degree EL offsets in increments of 0.05 degree can be found in [16]. During the process of performing the Sun experiment measurements, it was puzzling to find that Sun noise temperature measurement results obtained with the absorber method did not repeat. It was later discovered that Sun experiments were

184


SYSTEM TEMPERATURE X Latin, K

12000

EL OFFSET = 0 deg

10000

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