Aperture antennas and diffraction theory

185 Pages·1981·6.86 MB·English

by  Jull

ELECTROMAGNETIC WAVES SERIES 10
APERTURE
ANTENNAS AND
DIFFRACTION
T HEORY
E.V. JULL
PETER PEREGRINUS LTD
on behalf of the
Institution of Electrical Engineers
IEE ELECTROMAGNETIC WAVES SERIES 10
SERIES EDITORS: PROFESSOR P. J. B. CLARRICOATS,
G.MILUNGTON,
E.D.R. SHEARMAN
AND J.R. WAIT
APERTURE
ANTENNAS AND
DIFFRACTION
THEORY
Previous volumes in this series
Volume 1 Geometrical theory of diffraction for
electromagnetic waves
Graeme L. James
Volume 2 Electromagnetic waves and curved
structures
Leonard Lewin, David C. Chang and
Edward F. Kuester
Volume 3 Microwave homodyne systems
Ray J. King
Volume 4 Radio direction-finding
P. J. D. Gething
Volume 5 ELF communications antennas
Michael L. Burrows
Volume 6 Waveguide tapers, transitions
and couplers
F. Sporleder and H.-G. Unger
Volume 7 Reflector antenna analysis
and design
P. J. Wood
Volume 8 Effects of the troposphere on
radio communication
Martin P. M. Hall
Volume 9 Schumann resonances in the
earth-ionosphere cavity
P. V. Bliokh, A. P. Nicholaenko
and Yu. F. Filippov
APERTURE
ANTENNAS AND
DIFFRACTION
THEORY
E.V.Jull
Department of Electrical Engineering
The University of British Columbia
Vancouver
Canada
PETER PEREGRINUS LTD.
On behalf of the
Institution of Electrical Engineers
Published by: The Institution of Electrical Engineers, London
and New York
Peter Peregrinus Ltd., Stevenage, UK, and New York
© 1981: Peter Peregrinus Ltd.
All rights reserved. No part of this publication may be reproduced,
stored in a retrieval system or transmitted in any form or by any
means—electronic, mechanical, photocopying, recording or otherwise-
without the prior written permission of the publisher.
British Library Cataloguing in Publication Data
Jull, Edward V.
Aperture antennas and diffraction theory. —
(Electromagnetic wave series; 10)
1. Radio waves — Diffraction
2. Antennas (Electronics)
I. Title
621.380'28'3 TK6553
ISBN 0-906048-52-4
Typeset at the Alden Press Oxford London and Northampton
Printed in England by A. Wheaton & Co., Ltd., Exeter
Contents
Preface ix
1 Introduction 1
1.1 Historical background *
1.2 Outline of the book 3
2 Plane waves from apertures 7
2.1 Plane wave solutions of Maxwell's equations 7
2.2 General plane wave solutions 8
2.3 Homogeneous and inhomogeneous plane waves 9
2.4 Plane wave spectrum 10
2.5 Radiation pattern H
2.6 Plane wave spectra in three dimensions 14
2.7 Arbitrarily polarised aperture fields 16
3. Fourier transform representation of aperture patterns 18
3.1 Separable aperture distribution 18
3.2 Simple aperture distributions 20
3.3 Compound aperture distributions 22
3.4 Displaced aperture distributions 24
3.5 Aperture fields with linear phase variations 26
3.6 Gaussian distribution 27
3.7 Circular aperture 28
3.8 Operational calculation of radiation patterns 29
4 Near-field radiation patterns 31
4.1 Near-field criteria 31
4.2 Near-field patterns from aperture distributions 32
4.3 Near-field patterns from far-field patterns 34
4.4 Effect of measuring antenna directivity 35
4.5 Far-field patterns from near-field measurements 38
5 Aperture gain* 42
5.1 Gain of aperture antennas 42
5.2 Effective area 43
5.3 Supergain antennas and aperture Q 44
5.4 Near-field and far-field axial gain 46
5.4.1 Uniform circular aperture 46
vi Contents
5.4.2 Uniform rectangular aperture 47
5.4.3 Uniform and cosinusoidal aperture 48
5.4.4 Axial gain reduction 50
6 Applications of aperture theory to antennas 52
6.1 Approximations and limitations 52
6.2 Open-ended rectangular waveguides 52
6.3 Pyramidal horns 55
6.3.1 Aperture field 55
6.3.2 Radiation patterns 56
6.3.3 Near-field patterns 59
6.3.4 Pyramidal horn gain 60
6.4 Sectoral horns 62
6.4.1 Radiation patterns 62
6.4.2 Sectoral horn gain 63
6.5 Paraboloidal reflectors 66
6.5.1 Geometrical considerations 66
6.5.2 Radiation field and axial gain 67
6.6 Horn reflectors 68
6.6.1 Radiation patterns 69
6.6.2 Horn-reflector gain 71
7 Diffraction by conductors with sharp edges 74
7.1 Boundary conditions on conductors and at edges 74
7.2 Babinet's principle 75
7.3 Two-dimensional electromagnetic fields 76
7.4 Diffraction by a conducting half-plane 77
7.4.1 TE polarisation 7 7
7.4.2 TM polarisation 79
7.5 Oblique incidence on a half-plane 80
7.6 Line source diffraction by a half-plane 82
7.7 Diffraction by a wedge 84
7.7.1 Series solution 84
7.7.2 An asymptotic solution 85
8 Geometrical theory of diffraction by edges 87
8.1 The far-field in half-plane diffraction 87
8.2 Keller's geometrical theory of diffraction for edges 89
8.3 Diffraction by a slit 90
8.3.1 Single diffraction 90
8.3.2 Multiple diffraction 91
8.3.3 TM polarisation 94
8.3.4 Diffraction by a strip 95
8.4 Diffraction by a curved edge 95
8.5 Diffraction by a circular aperture 97
8.6 Diffraction coefficients for oblique incidence and for a wedge 98
8.7 Uniform solutions 9 9
8.7.1 Uniform diffraction theories 99
8.7.2 Uniform asymptotic theory of diffraction 101
9 Applications of geometrical diffraction theory to antennas 104
9.1 Scope and limitations 104
9.2 Reflection from open-ended parallel-plate waveguides 105
Contents vii
9.2.1 TM polarisation 105
9.2.2 TE polarisation 111
9.2.3 Flanged waveguides 111
9.2.4 Coupling between adjacent waveguides 111
9.3 Radiation from open-ended parallel-plate waveguides 112
9.3.1 TM polarisation 112
9.3.2 TE polarisation 115
9.3.3 Axial gain 117
9.4 Electric line sources 120
9.4.1 Strip reflector 120
9.4.2 Corner reflector 122
9.4.3 Parabolic cylinder reflector 125
9.5 Magnetic line sources 127
9.5.1 Slot in a conducting half-plane 127
9.5.2 Radiation from pyramidal and sectoral horns 128
9.5.3 Comparison with the Kirchhoff result 134
9.5.4 Gain of a two-dimensional iT-plane sectoral horn 136
9.5.5 Reflection from an E-plane sectoral horn 140
References 147
Appendixes 153
A. 1 Fourier integrals and transforms 153
A.2 Stationary phase evaluation of integrals 154
A.2.1 Single integrals 154
A.2.2 Double integrals 156
A.3 Integral and asymptotic forms of the Hankel functions 156
A.4 Solution of the dual integral equations of half-plane diffraction 160
A.5 Reduction of the half-plane diffraction solution to Fresnel
integrals 162
A.6 Transmission cross-section of a slit 164
Author index 167
Index 169

Preface
This book originated with an invitation to give a few lectures on aperture an-
tennas to students during a stay at the Technical University of Denmark in 1964.
The plane wave spectrum method of aperture analysis was adopted from the work
of P.C. Clemmow and my former graduate supervisor J. Brown. It was then a new
and refreshing change from the traditional approach. At about the same time,
J.B. Keller visited the laboratory and introduced me to the geometrical theory of
diffraction, from which has evolved an entirely new and in most respects more
effective method of aperture antenna analysis. The ideas in this book owe much
to these individuals.
The basis of the aperture analysis in Chapters 2-6 is, in essence, Kirchhoff s
diffraction theory. In the remaining Chapters 7-9, the newer geometrical theory of
diffraction is used. The analysis is almost entirely two-dimensional or scalar, with
extensions to three dimensions indicated. In this way the essential concepts are
conveyed in a simple form. Many practical antennas yield to a two-dimensional
analysis as shown in the examples of Chapters 2 and 9. Also in at least the initial
stages of antenna design it is usually convenient to assume a two-dimensional
model.
As the book developed in response to teaching needs it contains some elemen-
tary material which may be helpful to those with no background in electromagnetic
theory beyond Maxwell's equations. Much of Chapters 2-6 has benefitted from
exposure to senior undergraduates at the University of British Columbia. Portions
of Chapters 6-8 have been used as well in graduate courses at UBC, Carleton and
Queen's universities.
Although intended primarily as a text, it is hoped the book may also be useful to
practising engineers. Consequently, in the chapters dealing with applications, com-
parisons with experiment are made wherever possible. Examples of this are the
horn pattern comparisons of Chapters 6 and 9. Most of these results were obtained
by students and have not been published previously. The numerical data of Figs.
6.4 and 6.6 were obtained by Miss S.L. Paige and K.A. Grey and that of Fig. 6.5
by P.T.K. Chun. A. Safaai-Jazi obtained the geometrical diffraction theory patterns
of Figs. 9.15 and 9.19 and N. Donatucci the experimental patterns.
Most of my contributions in this book were made in the Division of Electrical