Theory and Application of Antenna Arrays

THEORY AND APPLICATION OF ANTENNA ARRAYS M.T.Ma Senior Member of the Technical Staff Institute for Telecommunication Sciences Office of Telecommunications U. S. Department of Commerce Boulder, Colorado and Professor-Adjoint of Electrical Engineering University of Colorado A Wiley-Interscience Publication John Wiley & Sons New York London Sydney Toronto Copyright @ 1974, by John Wiley & Sons, Inc. All rights reserved. Published simultaneously in Canada. No part of this book may be reproduced by any means, nor transmitted, nor translated into a machine language without the written permission of the publisher. Library of Congress Cataloging in Publication Data: Ma,M.T. Theory and application of antenna arrays. "A Wiley-Interscience publication." Includes bibliographies. 1. Antenna arrays. I. Title. TK7871.6.M3 621.38'0283 73-15615 ISBN 0-471-55795-1 Printed in the United States of America 10 9 8 7 6 5 4 3 2 I To Simone, Beverly, and John PREFACE Since early 1959when I was first engaged in research on antenna arrays at Syracuse University, my interest in this subject has been divided into two major phases. One of these, which occupied most of my attention from 1959 to 1966, was concerned primarily with basic analysis and synthesis techniques pertinent to antenna arrays, which, for the most part, is an applied mathematics problem. The goals then were to produce a particular class of radiation patterns, to reduce sidelobe levels, to maximize the directivity, and to synthesize an array with a relatively broad frequency band, or to achieve some combinations of these. Isotropic elements were mostly used for the sole purpose of developing general mathematical models, which should not be limited to any particular kind of antennas or frequency bands. Thus, mutual impedances and effects from the ground were usually ignored. The arrays considered were either linear or two dimensional with the number of elements in the array, amplitude and phase excitations, or spacing distributions as controlling parameters. The results so obtained constitute the basis of the first three chapters in this book. They form the mathematical foundation for the theory of antenna arrays and should satisfy the general need to present relevant array topics with modern approaches and ample numerical illustrations in a single volume. Chapter I introduces the reader to the fundamentals of linear arrays of discrete elements. It starts with the analysis for simple uniform arrays and then proceeds to arrays with tapered amplitudes, phases, and spacings. A relatively new approach, using finite Z-transforms for analyzing arrays with nonuniform amplitude excitations, is presented in detail with illustrative examples. Difference patterns produced by a monopulse array are also formulated and studied. Chapter 2 offers many recently developed techniques for synthesizing various linear arrays. It is here that power and field patterns are equally emphasized. Considerable effort is devoted to the understanding of arrays with equal sidelobes. In addition to the synthesis of array patterns, optimization of the array directivity is also thoroughly discussed. As an extension to the material presented in the first two chapters, both analysis and synthesis of two-dimensional arrays are given in Chapter 3. Greater attention is placed on ring and elliptical arrays. vii viii PREFACE My interest since 1966 has gradually shifted to the "real world" with emphasis on applications. In particular, the ionospheric prediction program was then an activity of major importance at the Central Radio Propagation Laboratory, then a part of the National Bureau of Standards. In this program, there was a strong need to develop reasonably accurate theoretical models for those HF antennas frequently involved in various communication systems. Specifically, expressions for input impedances, mutual impedances, radiated fields, and power gains were formulated with some simplified assumption for current distribution on antennas and many other necessary approximations. These imperfections, of course, will show some effects on the final antenna performance, but were considered adequate in view of the other uncertainties associated with the ionosphere. Major results from this activity were compiled and issued as a laboratory technical report in early 1969. Overwhelming response from a large number of users has since been received in the form of requests for reprints and inquiries about possible computer programs suitable for numerical results. In fact, over one hundred copies of this report have been requested. Because of this strong demand, I was prompted to make further impro- vements on formulations and to produce more quantitative data. These are essentially reflected in the last three chapters. A significant difference between the book form and the previous report form is that the three-term current distribution proposed originally by Professors R. W. P. King and T. T. Wu of Harvard University has been used in Chapters 4 and 5 to replace the simple sinusoidal current distribution that had been assumed in the earlier report. In Chapter 4, currents, impedances, fields, and power gains for simple antennas such as dipoles, monopoles, and sleeve antennas above lossy ground are presented in detai1. Equal attention is also given to arrays of these antennas in the form of the Yagi-Uda antenna, the curtain array, or the Wullenweber antenna. The basic principle and analytical formulation for a class of broadband antennas, namely, the log-periodic dipole array above lossy ground, are given in Chapter 5. Placing this array in alternative geometric positions (relative to the ground) to yield maximum radiations at low or high angles from the ground plane is also explored for different possible applications. In Chapter 6, a few commonly used traveling-wave antennas above lossy ground are analyzed. Throughout this book, numerical examples are always presented for each antenna or array subject. These examples are prepared not only to serve the illustrative purpose, but also to give some design insight as to how the various parameters will affect the result. The contents presented in the last three chapters should directly benefit field engineers, design PREFACE ix engineers, and other users in their applications, although the first three chapters also provide them with fundamental principles. This entire volume could be used as textbook for a course sponsored by companies for their staffs engaging in array and antenna designs. On the other hand, parts of Chapters 1, 2, 4, and 5 are also suitable for classroom use for a graduate course on arrays or antennas, or as self-study materials for students interested in research on antenna arrays. In fact, a major portion of the first three chapters was once given in a special course on "Antenna Array Theory" at the University of Colorado. For this latter purpose, selected problems are attached at the end of each of the first three chapters as student exercises and as reviews of the material discussed. For each chapter, references are listed to guide the reader to related topics, although there has been no attempt to make the reference list complete. To the management of my governmental agency I wish to express my thanks for its encouragement and support throughout this undertaking. In particular, D. D. Crombie (Director), W. F. Udaut (Deputy Director), and F. W. Smith (Executive Officer) of the Institute for Telecommunication Sciences (ITS) at Boulder offered many valuable suggestions, administrative assistance, and initial approval for this manuscript to be published by a nongovernmental publisher. J. M. Richardson (Director), R. C. Kirby (Associate Director), R. Gary (Special Assistant to the Director), and D. M. Malone (Attorney-Adviser) of the Office of Telecommunications at Washington, D. C. also rendered their blessing and frequent services in administrative regards. I wish to express my heartfelt appreciation to Mrs. Lillie C. Walters for her masterful skill in developing computer programs to produce such extensive numerical results for antennas presented in Chapters 4, 5, and 6, without which the value of the book would diminish substantially. I am also indebted to my colleagues at Boulder-£. L. Crow, H. T. Doughtery, E. C. Hayden, R. B. Stoner, Lillie C. Walters (all of ITS), and C. O. Stearns (National Oceanic and Atmospheric Administration), who reviewed parts or all of the chapters and made constructive suggestions for improvement. To Miss Ruth B. Hansen I offer my sincere gratitude for her expert and patient typing of the entire manuscript. Last but not least, my special thanks go to my wife and children for their understanding of my temporary lapse of participation in family affairs, school work, and evening football practice while I was busy preparing this volume. M.T.Ma Boulder, Colorado July 1973 CONTENTS Chapter 1 Analysis of Discrete Linear Arrays 1 1.1 Radiation Characteristics To Be Studied 2 1.2 Uniform Arrays 4 1.3 Improved Uniform Endfire Arrays of Isotropic Ele- ments 19 1.4 Finite Z Transforms-A Different Approach for Nonuniform Arrays 24 1.5 Nonuniformly Spaced Arrays 37 1.6 Arrays of Isotropic Elements with Nonuniformly Progressive Phases 42 1.7 Monopulse Arrays 55 1.8 Concluding Remarks and Discussion 65 Problems 66 References 67 Additional References 70 Chapter 2 Synthesis of Discrete Linear Arrays 73 2.1 Power Patterns and Relations to Excitation Coefficients and Others 74 2.2 Arrays with Equal Sidelobes 82 2.3 Optimization with Smaller

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