Antenna Arrays: A Computational Approach

549 Pages·2010·13.38 MB·English

by  Randy L. Haupt

ANTENNA ARRAYS

ANTENNA ARRAYS
A Computational Approach
Randy L. Haupt
Pennsylvania State University
State College, Pennsylvania
WILEY
JOHN WILEY & SONS, INC., PUBLICATION
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Library of Congress Cataloging-in-Publication Data
Haupt, Randy L.
Antenna arrays : a computational approach / Randy L. Haupt.
p. cm.
Includes bibliographical references and index.
ISBN 978-0-470-40775-2
1. Antenna arrays-Mathematical models. I. Title.
TK7871.67.A77H38 2010
621.382'4-dc22
2009041904
Printed in the United States of America
10 9 8 7 6 5 4 3 21
To my father, Howard Haupt, and the memory of my mother

CONTENTS
Preface
1. Antenna Array Basics
1.1. History of Antenna Arrays 3
1.2. Electromagnetics for Array Analysis 7
1.3. Solving for Electromagnetic Fields 13
1.3.1. The Wave Equation 13
1.3.2. Point Sources 15
1.3.3. Hertzian Dipole 17
1.3.4. Small Loop 19
1.3.5. Plane Waves 21
1.4. Antenna Models 22
1.4.1. An Antenna as a Circuit Element 22
1.4.2. An Antenna as a Spatial Filter 24
1.4.3. An Antenna as a Frequency Filter 27
1.4.4. An Antenna as a Collector 29
1.4.5. An Antenna as a Polarization Filter 30
1.5. Antenna Array Applications 34
1.5.1. Communications System 34
1.5.2. Radar System 35
1.5.3. Radiometer 38
1.5.4. Electromagnetic Heating 40
1.5.5. Direction Finding 42
1.6. Organization and Overview 42
References 43
2. Array Factor Analysis
2.1. The Array Factor 45
2.1.1. Phase Steering 48
2.1.2. End-Fire Array 51
2.1.3. Main Beam Steering with Frequency 52
2.1.4. Focusing 53
2.2. Uniform Arrays 55
2.2.1. Uniform Sum Patterns 55
viii CONTENTS
2.2.2. Uniform Difference Patterns 61
2.3. Fourier Analysis of Linear Arrays 63
2.4. Fourier Analysis of Planar Arrays 67
2.5. Array Bandwidth 75
2.6. Directivity 78
2.7. Amplitude Tapers 82
2.8. z Transform of the Array Factor 84
2.9. Circular Arrays 88
2.10. Direction Finding Arrays 91
2.10.1. Adcock Array 92
2.10.2. Orthogonal Linear Arrays 93
2.11. Subarrays 94
2.12. Errors 99
2.12.1. Random Errors 100
2.12.2. Quantization Errors 105
2.13. Fractal Arrays 108
References 112
3. Linear and Planar Array Factor Synthesis 115
3.1. Synthesis of Amplitude and Phase Tapers 115
3.1.1. Fourier Synthesis 115
3.1.2. Woodward-Lawson Synthesis 118
3.1.3. Least Squares Synthesis 120
3.2. Analytical Synthesis of Amplitude Tapers 121
3.2.1. Binomial Taper 121
3.2.2. Dolph-Chebyshev Taper 123
3.2.3. Taylor Taper 127
3.2.4. Bickmore-Spellmire Taper 140
3.2.5. Bayliss Taper 141
3.2.6. Unit Circle Synthesis of Arbitrary Linear Array
Factors 143
3.2.7. Partially Tapered Arrays 149
3.3. Numerical Synthesis of Low-Sidelobe Tapers 151
3.4. Aperiodic Arrays 156
3.4.1. Thinned Arrays 156
3.4.2. Nonuniformly Spaced Arrays 165
3.5. Low-Sidelobe Phase Taper 177
3.6. Suppressing Grating Lobes Due to Subarray
Weighting 179
3.6.1. Subarray Tapers 179
3.6.2. Thinned Subarrays 183
3.7. Plane Wave Projection 193
CONTENTS ix
3.8. Interleaved Arrays 197
3.9. Null Synthesis 203
References 210
Array Factors and Element Patterns 216
4.1. Pattern Multiplication 216
4.2. Wire Antennas 223
4.2.1. Dipoles 223
4.2.2. Helical Antenna 231
4.3. Aperture Antennas 234
4.3.1. Apertures 234
4.3.2. Open-Ended Waveguide Antennas 239
4.3.3. Slots in Waveguides 244
4.3.4. Horn Antennas 249
4.4. Patch Antennas 257
4.5. Broadband Antennas 264
4.5.1. Spiral Antennas 264
4.5.2. Dipole-Like Antennas 271
4.5.3. Tapered Slot Antennas 272
4.5.4. Dielectric Rod Antennas 278
References 283
Nonplanar Arrays 287
5.1. Arrays with Multiple Planar Faces 287
5.2. Arrays on Singly Curved Surfaces 290
5.2.1. Circular Adcock Array 300
5.3. Arrays Conformal to Doubly Curved Surfaces 309
5.4. Distributed Array Beamforming 319
5.5. Time-Varying Arrays 323
5.5.1. Synthetic Apertures 323
5.5.2. Time-Modulated Arrays 328
5.5.3. Time-Varying Array Element Positions 331
References 337
Mutual Coupling 339
6.1. Mutual Impedance 341
6.2. Coupling Between Two Dipoles 342
6.3. Method of Moments 349
6.4. Mutual Coupling in Finite Arrays 358
6.5. Infinite Arrays 368
6.5.1. Infinite Arrays of Point Sources 369
6.5.2. Infinite Arrays of Dipoles and Slots 371