Arrays of Cylindrical Dipoles

508 Pages·2009·11.1 MB·English

by  R. W. P. King

ARRAYS OF CYLINDRICAL
DIPOLES

ARRAYS OF
CYLINDRICAL
DIPOLES
RONOLD W. P. KING
Gordon McKay Professor of Applied Physics
Harvard University
RICHARD B. MACK
Research Physicist
Air Force Cambridge Research Laboratories
SHELDON S. SANDLER
Associate Professor of Electrical Engineering
Northeastern University
Research Fellow, Harvard University
CAMBRIDGE
AT THE UNIVERSITY PRESS
1968
CAMBRIDGE UNIVERSITY PRESS
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Published in the United States of America by Cambridge University Press, New York
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Information on this title: www.cambridge.org/9780521114851
© Cambridge University Press 1968
This publication is in copyright. Subject to statutory exception
and to the provisions of relevant collective licensing agreements,
no reproduction of any part may take place without the written
permission of Cambridge University Press.
First published 1968
This digitally printed version 2009
A catalogue record for this publication is available from the British Library
Library of Congress Catalogue Card Number: 67-26069
ISBN 978-0-521-05887-2 hardback
ISBN 978-0-521-11485-1 paperback
To
Tai Tsun Wu
Good reasons must, of force, give place to better.
Shakespeare
CONTENTS
page
Preface xi
CHAPTER 1. INTRODUCTION 1
1.1 Fundamentals—field vectors and potential functions 1
1.2 Power and the Poynting vector 9
1.3 The field of the electrically short antenna; directivity 11
1.4 The field of antennas with sinusoidally distributed
currents; radiation resistance 14
1.5 The field of a two-element array 16
1.6 Fields of arrays of N elements; array factor 19
1.7 Impedance of antenna; EMF method 22
1.8 Coupled antennas; self- and mutual impedances 29
1.9 Radiation-pattern synthesis 32
1.10 The circular array 40
1.11 Limitations of conventional array theory 44
CHAPTER 2. AN APPROXIMATE ANALYSIS OF
THE CYLINDRICAL ANTENNA 46
2.1 The sinusoidal current 46
2.2 The equation for the current 47
2.3 Properties of integrals 49
2.4 Rearranged equation for the current 51
2.5 Reduction of integral equation to algebraic equation 52
2.6 Evaluation of coefficients 54
2.7 The approximate current and admittance 55
2.8 Numerical examples; comparison with experiment 56
2.9 The radiation field 58
2.10 An approximate two-term theory 63
2.11 The receiving antenna 65
Vlll CONTENTS
CHAPTER 3. THE TWO-ELEMENT ARRAY 70
3.1 The method of symmetrical components 70
3.2 Properties of the integrals 73
3.3 Reduction of integral equations for phase sequences
to algebraic equations 75
3.4 The phase-sequence currents and admittances 78
3.5 Currents for arbitrarily driven antennas; self- and
mutual admittances and impedances 80
3.6 Currents for one driven, one parasitic antenna 82
3.7 The couplet 83
3.8 Field patterns 84
3.9 The two-term approximation 85
CHAPTER 4. THE CIRCULAR ARRAY 95
4.1 Integral equations for the sequence currents 97
4.2 Sequence functions and array properties 103
4.3 Self- and mutual admittances 105
4.4 Currents and fields; arrays with one driven element 112
4.5 Matrix notation and the method of symmetrical com-
ponents 121
4.6 General formulation and solution 125
CHAPTER 5. THE CIRCUIT AND RADIATING
PROPERTIES OF CURTAIN ARRAYS 130
5.1 General comparison of conventional and new theories 130
5.2 New theory of curtain arrays 133
5.3 Examples 143
5.4 Electronically scanned arrays 150
5.5 Examples of the general theory for large arrays 158
5.6 The special case when fth = n/2 171
o
5.7 Design of curtain arrays 173
5.8 Summary 179
CONTENTS IX
CHAPTER 6. ARRAYS WITH UNEQUAL ELEMENTS;
PARASITIC AND LOG-PERIODIC ANTENNAS 181
6.1 Application of the two-term theory to a simple parasitic
array 181
6.2 The problem of arrays with parasitic elements of un-
equal lengths 188
6.3 Application to the Yagi-Uda array 191
6.4 Evaluation of coefficients for the Yagi-Uda array 195
6.5 Arrays with half-wave elements 198
6.6 The far field of the Yagi-Uda array; gain 201
6.7 Simple applications of the modified theory; compari-
son with experiment 207
6.8 The three-element Yagi-Uda array 215
6.9 The four, eight and ten director Yagi-Uda array 218
6.10 Receiving arrays 232
6.11 Driven arrays of elements that differ greatly in length 237
6.12 The log-periodic dipole array 244
6.13 Analysis of the log-periodic dipole array 247
6.14 Characteristics of a typical log-periodic dipole array 251
6.15 Frequency-independent properties of the log-periodic
dipole array 258
6.16 Experimental verification of the theory for arrays of
unequal dipoles 269
CHAPTER 7. PLANAR AND THREE-DIMENSIONAL
ARRAYS 272
7.1 Vector potential and integral equations for the currents 273
7.2 Vector potential differences and integral equations 277
7.3 Approximate distribution of current 278
7.4 Evaluation of coefficients 280
7.5 The field patterns 283
7.6 The general two-element array 286
7.7 A simple planar array 293