Spherical near-field antenna measurements

404 Pages·1988·17.35 MB·English

by  Hansen

Electromagnetic Waves Series 26
Spherical Near-Field AS Spherical Near-
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The subject of antenna measurements is one which Jørgen Haid received his MSc and PhD degrees in electrical engineering from ee
has undergone revolutionary changes in recent the Technical University of Denmark (TUD) in 1978 and 1984 respectively, with aa
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This book represents the specific measurement aJensdp neer aEr-.f iHeladn asceonu srteicc ehiovelodg rhaips hMy.Sc and PhD degrees in electrical engineering mld
technique known as the spherical near-field method. from TUD in 1957 and 1965 respectively. Since 1966 he has been an associate e
The theoretical treatment of the method is detailed but professor and head of the antenna group at the Electromagnetics Institute, TUD. n
of sufficient generality to make the book useful as a He has been project manager for a number of research projects carried out ts
basis for further research on near-field measurements for the European Space Agency within the areas of spacecraft antennas and
and antenna coupling problems. Practical aspects spherical near-field antenna measurements.
of antenna test ranges, data processing schemes Frank Jensen received his MSc and PhD degrees in electrical engineering
and measurement procedures are described. Other from TUD in 1968 and 1971 respectively. Since 1982, he has been with TICRA,
Copenhagen, where he works in the field of satellite antennas. He has special
topics covered are measurement error analysis and
experience within near-field measurement techniques, design and construction
generation of plane wave fields. of dual polarised high-precision measurement probes, and interaction between
The authors draw on the experience from the satellite antennas and the structures on which they are mounted.
development, sponsored by the European Space Flemming Holm Larsen received his MSc and PhD degrees in electrical
Agency, of one of the first spherical near-field test engineering from TUD in 1973 and 1982 respectively. At present, he is an
ranges. They have contributed to the establishment assistant professor at the TUD Electromagnetics Institute, where he has been Edited by J.E. Hansen
involved in research on antenna measurements since 1974. In particular, he
of spherical near-field testing as a highly accurate and
has developed a number of computer programs for spherical near-field far-field
versatile method, currently under implementation at
test ranges worldwide. transformation with probe correction. Ed
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The Institution of Engineering and Technology s
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www.theiet.org n
0 86341 110 X
978-0-86341-110-6
IET ElEcTromagnETIc WavEs sErIEs 26
Series Editors: Professor P.J.B. Clarricoats
Professor J.R. Wait
Spherical Near-
Field Antenna
Measurements
Other volumes in this series:
Volume 1 Geometrical theory of diffraction for electromagnetic waves, 3rd edition
G.L. James
Volume 10 Aperture antennas and diffraction theory E.V. Jull
Volume 11 Adaptive array principles J.E. Hudson
Volume 12 Microstrip antenna theory and design J.R. James, P.S. Hall and C. Wood
Volume 15 The handbook of antenna design, volume 1 A.W. Rudge, K. Milne, A.D. Oliver
and P. Knight (Editors)
Volume 16 The handbook of antenna design, volume 2 A.W. Rudge, K. Milne, A.D. Oliver
and P. Knight (Editors)
Volume 18 Corrugated horns for microwave antennas P.J.B. Clarricoats and A.D. Oliver
Volume 19 Microwave antenna theory and design S. Silver (Editor)
Volume 21 Waveguide handbook N. Marcuvitz
Volume 23 Ferrites at microwave frequencies A.J. Baden Fuller
Volume 24 Propagation of short radio waves D.E. Kerr (Editor)
Volume 25 Principles of microwave circuits C.G. Montgomery, R.H. Dicke and E.M. Purcell
(Editors)
Volume 26 Spherical near-field antenna measurements J.E. Hansen (Editor)
Volume 28 Handbook of microstrip antennas, 2 volumes J.R. James and P.S. Hall (Editors)
Volume 31 Ionospheric radio K. Davies
Volume 32 Electromagnetic waveguides: theory and applications S.F. Mahmoud
Volume 33 Radio direction finding and superresolution, 2nd edition P.J.D. Gething
Volume 34 Electrodynamic theory of superconductors S.A. Zhou
Volume 35 VHF and UHF antennas R.A. Burberry
Volume 36 Propagation, scattering and diffraction of electromagnetic waves
A.S. Ilyinski, G. Ya.Slepyan and A. Ya.Slepyan
Volume 37 Geometrical theory of diffraction V.A. Borovikov and B.Ye. Kinber
Volume 38 Analysis of metallic antenna and scatterers B.D. Popovic and B.M. Kolundzija
Volume 39 Microwave horns and feeds A.D. Olver, P.J.B. Clarricoats, A.A. Kishk and L. Shafai
Volume 41 Approximate boundary conditions in electromagnetics T.B.A. Senior and
J.L. Volakis
Volume 42 Spectral theory and excitation of open structures V.P. Shestopalov and
Y. Shestopalov
Volume 43 Open electromagnetic waveguides T. Rozzi and M. Mongiardo
Volume 44 Theory of nonuniform waveguides: the cross-section method
B.Z. Katsenelenbaum, L. Mercader Del Rio, M. Pereyaslavets, M. Sorella Ayza and
M.K.A. Thumm
Volume 45 Parabolic equation methods for electromagnetic wave propagation M. Levy
Volume 46 Advanced electromagnetic analysis of passive and active planar structures
T. Rozzi and M. Farinai
Volume 47 Electromagnetic mixing formulae and applications A. Sihvola
Volume 48 Theory and design of microwave filters I.C. Hunter
Volume 49 Handbook of ridge waveguides and passive components J. Helszajn
Volume 50 Channels, propagation and antennas for mobile communications
R. Vaughan and J. Bach-Anderson
Volume 51 Asymptotic and hybrid methods in electromagnetics F. Molinet, I. Andronov
and D. Bouche
Volume 52 Thermal microwave radiation: applications for remote sensing
C. Matzler (Editor)
Volume 53 Principals of planar near-field antenna measurements S. Gregson,
J. McCormick and C. Parini
Volume 502 Propagation of radiowaves, 2nd edition L.W. Barclay (Editor)
Spherical Near-
Field Antenna
Measurements
Edited by J.E. Hansen
The Institution of Engineering and Technology
Published by The Institution of Engineering and Technology, London, United Kingdom
First edition © 1988 Peter Peregrinus Ltd
Reprint with new cover © 2008 The Institution of Engineering and Technology
First published 1988
Reprinted 2008
This publication is copyright under the Berne Convention and the Universal Copyright
Convention. All rights reserved. Apart from any fair dealing for the purposes of research
or private study, or criticism or review, as permitted under the Copyright, Designs and
Patents Act, 1988, this publication may be reproduced, stored or transmitted, in any
form or by any means, only with the prior permission in writing of the publishers, or in
the case of reprographic reproduction in accordance with the terms of licences issued
by the Copyright Licensing Agency. Inquiries concerning reproduction outside those
terms should be sent to the publishers at the undermentioned address:
The Institution of Engineering and Technology
Michael Faraday House
Six Hills Way, Stevenage
Herts, SG1 2AY, United Kingdom
www.theiet.org
While the authors and the publishers believe that the information and guidance given
in this work are correct, all parties must rely upon their own skill and judgement when
making use of them. Neither the authors nor the publishers assume any liability to
anyone for any loss or damage caused by any error or omission in the work, whether
such error or omission is the result of negligence or any other cause. Any and all such
liability is disclaimed.
The moral rights of the authors to be identified as authors of this work have been
asserted by them in accordance with the Copyright, Designs and Patents Act 1988.
British Library Cataloguing in Publication Data
Spherical near-field antenna measurements theory and practice. –
(Electromagnetic waves series; 26).
1. Antennas (Electronics) – Measurement
I. Hansen, J.E. II. Hald J.
III. Institute of Electrical Engineers
IV. Series
621.38’028’3 TK7871.6
ISBN (10 digit) 0 86341 110 X
ISBN (13 digit) 978-0-86341-110-6
Reprinted in the UK by Lightning Source UK Ltd, Milton Keynes
Contributing authors
J. Hald, Briiel & Kjaer, Naerum, Denmark
J. E. Hansen, Technical University of Denmark
F. Jensen, TICRA, Copenhagen, Denmark
F. Holm Larsen, Technical University of Denmark

Contents
Contributing authors listed v
Preface xiii
1 Introduction 1
1.1 Background 1
1.1.1 Introduction 1
1.1.2 Brief outline of antenna testing 1
1.1.3 Spherical near-field testing 2
1.2 Organization of (this) book 4
References 6
2 Scattering matrix description of an antenna 8
2.1 Introduction 8
2.2 Spherical waves 9
2.2.1 Introduction 9
2.2.2 Power-normalized spherical waves 12
2.2.3 The spherical waveguide 15
2.2.4 Power flow 23
2.3 The antenna scattering matrix 27
2.3.1 Definitions 27
2.3.2 Reciprocity 32
2.3.3 The field from electric and magnetic dipoles 37
2.3.4 Scattering matrices for electric and magnetic dipoles 40
2.3.5 Remarks on the definition of antenna scattering matrices 46
2.4 Antenna parameters expressed by spherical waves 48
2.4.1 Far-field patterns 48
2.4.2 Polarization 50
2.4.3 Directivity and gain 54
2.4.4 Maximum directivity 55
References 59
3 Scattering matrix description of antenna coupling 61
3.1 Introduction 61
3.2 The transmission formula 62
3.2.1 Geometry 62
3.2.2 Test antenna transmitting, probe receiving 63
viii Contents
3.2.3 Test antenna receiving, probe transmitting 67
3.2.4 Reciprocal and non-reciprocal test antennas 69
3.2.5 Iterative scheme for probe calibration 71
3.3 Special cases of the transmission formula 73
3.3.1 Linearly polarized probe with \i = ± 1 73
3.3.2 The Hertzian dipole as a probe 76
3.3.3 Friis' transmission formula 79
3.4 The transmission formula with multiple reflections included 82
References 87
Data reduction in spherical near-field mesaurements 89
4.1 Introduction 89
4.2 Measurement without probe correction 92
4.2.1 Introduction 92
4.2.2 General case 92
4.2.3 Measurement of the radial field components 98
4.2.4 Measurement of two tangential field components 100
4.2.5 Wood's method 102
4.3 Measurement with probe correction 104
4.3.1 Introduction 104
4.3.2 Analytical solution of the transmission formula 104
4.3.3 Discrete solution of the transmission formula 107
4.3.4 Field transformations and radiated fields 117
4.4 Outline of a spherical near-field transformation algorithm 125
4.4.1 Introduction 125
4.4.2 Summary of the theory underlying a transformation algorithm 125
4.4.3 On the number of sample points 128
4.4.4 Block diagram of a transformation algorithm 132
4.4.5 A simple example 132
4.4.6 A test case 138
4.5 Review of spherical near-field transformations 140
References 145
Measurements 147
5.1 Introduction 147
5.2 Probes for near-field scanning 147
5.2.1 Introduction 147
5.2.2 Rotationally symmetric probes 149
5.2.3 Polarization correction 153
5.2.4 Polarization calibration 157
5.2.5 Pattern calibration 163
5.3 Probe-corrected measurements 165
5.3.1 Introduction 165
5.3.2 The spherical near-field test range 165
5.3.3 Basic measurement procedures 181
5.3.4 Measurement examples 197
5.4 Determination of gain 206
5.4.1 Introduction 206
5.4.2 Gain calibration of horns 207
5.4.3 Gain determination by substitution 210
References 214
Contents ix
6 Error analysis of spherical near-field measurements 216
6.1 Introduction 216
6.2 Near-field measurements 216
6.3 Mechanical inaccuracies 218
6.4 Receiver inaccuracies 222
6.5 Probe correction 228
6.6 Truncation 232
6.6.1 Introduction 232
6.6.2 Polar truncation 234
6.6.3 Equatorial truncation 240
6.6.4 Repetition and overlay of truncated fields 245
6.7 Evaluation of measurements 250
6.8 Conclusion 252
References 253
7 Plane-wave synthesis 255
7.1 Introduction 255
7.2 Spherical near-field far-field transformation as a plane-wave synthesis
method 258
7.3 Basic concepts in generation of plane-wave fields 263
7.3.1 Introduction 263
7.3.2 Equivalence principle 264
7.3.3 Relationship to a scattering problem 265
7.3.4 Truncation and sampling of continuous sources of plane waves 267
7.4 The Sheffield method 271
7.4.1 Introduction 271
7.4.2 Measurement without probe correction 271
7.4.3 Measurement with probe correction 277
7.5 Figures of merit for plane-wave deviation 280
7.5.1 Introduction 280
7.5.2 General figures of merit for plane-wave deviation 281
7.5.3 Spherical test zone geometry 28-3
7.5.4 Measurement error upper bounds 285
7.6 Numerical optimization methods for plane-wave synthesis 287
7.6.1 Introduction 287
7.6.2 Arbitrary array and test zone geometry 288
7.6.3 Ring sources and spherical test zones 291
References 310
Appendices
Al Spherical wave functions, notation and properties 312
A 1.1 Notation 312
A 1.1.1 The general spherical wave expansion 312
A 1.1.2 Single index convention 313
Al.1.3 Representation of far fields 314
A1.2 Elementary functions 314
Al.2.1 Radial functions 314
A 1.2.2 Angular functions 318
A1.3 Wave functions 325
A 1.3.1 The spherical wave functions 325
A 1.3.2 The far-field pattern functions 328