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Finite Antenna Arrays and FSS
Finite Antenna Arrays and FSS Ben A. Munk A John Wiley & Sons, Inc., Publication
This book is printed on acid-free paper. Copyright  2003 by John Wiley & Sons, Inc. All rights reserved. Published simultaneously in Canada. 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, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, 978-750-8400, fax 978-750-4470, or on the web at www.copyright.com. Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, e-mail: permreq@wiley.com. Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose. No warranty may be created or extended by sales representatives or written sales materials. The advice and strategies contained herein may not be suitable for your situation. You should consult with a professional where appropriate. Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages. For general information on our other products and services please contact our Customer Care Department within the U.S. at 877-762-2974, outside the U.S. at 317-572-3993 or fax 317-572-4002. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print, however, may not be available in electronic format. Library of Congress Cataloging-in-Publication Data: Munk, Ben (Benedikt A.) Finite antenna arrays and FSS / Ben A. Munk. p. cm “A Wiley-Interscience publication.” Includes bibliographical references and index. ISBN 0-471-27305-8 (cloth) 1. Microwave antennas. 2. Antenna arrays. 3. Frequency selective surfaces. I. Title. TK7871.67.M53M88 2003 621.381 3—dc21 Printed in the United States of America 10 9 8 7 6 5 4 3 2 1 2003041132
To the increasing number of my friends who realize that computer power is a supplement, not a substitute, for brain power. The constant support of the Electroscience Laboratory and my family—in particular, my wife Aase—is deeply appreciated. B. A. M.
Contents Foreword Preface Acknowledgments Symbols and Definitions 1 Introduction 1.1 Why Consider Finite Arrays? / 1 1.2 Surface Waves Unique to Finite Periodic Structures / 4 1.3 Effects of Surface Waves / 5 1.3.1 Surface Wave Radiation from an FSS / 5 1.3.2 Variation of the Scan Impedance from Column to Column / 7 1.4 How do We Control the Surface Waves? / 7 1.4.1 Phased Array Case / 7 1.4.2 The FSS Case / 9 1.5 Common Misconceptions / 10 1.5.1 On Common Misconceptions / 10 1.5.2 On Radiation from Surface Waves / 11 1.5.3 Should the Surface Waves Encountered Here Be Called Edge Waves? / 11 xvii xxi xxiii xxv 1 vii
viii CONTENTS 1.6 Conclusion / 12 Problems / 13 2 On Radar Cross Section of Antennas in General 15 2.1 Introduction / 15 2.2 Fundamentals of Antenna RCS / 17 2.2.1 The Antenna Mode / 17 2.2.2 The Residual Mode / 20 2.3 How to Obtain a Low σtot by Cancellation (Not Recommended) / 22 2.4 How do We Obtain Low σtot Over a Broad Band? / 22 2.5 A Little History / 23 2.6 On the RCS of Arrays / 24 2.6.1 Arrays of Dipoles without a Groundplane / 24 2.6.2 Arrays of Dipoles Backed by a Groundplane / 26 2.7 An Alternative Approach: The Equivalent Circuit / 27 2.8 On the Radiation from Infinite Versus Finite Arrays / 29 2.8.1 Infinite Arrays / 29 2.8.2 Finite Array / 29 2.9 On Transmitting, Receiving, and Scattering Radiation Pattern of Finite Arrays / 31 2.9.1 Example I: Large Dipole Array without Groundplane / 31 2.9.2 Example II: Large Dipole Array with Groundplane / 33 2.9.3 Example III: Large Dipole Array with Oversized Groundplane / 34 2.9.4 Final Remarks Concerning Transmitting, Receiving, and Scattering Radiation Pattern of Finite Arrays / 34 2.10 Minimum Versus Nonminimum Scattering Antennas / 34 2.10.1 The Thevenin Equivalent Circuit / 35 2.10.2 Discussion / 35 2.11 Other Nonminimum Scattering Antennas / 36 2.11.1 Large Array of Full-Wave Dipoles / 36
CONTENTS ix 2.11.2 Effect of a Tapered Aperture / 37 2.11.3 The Parabolic Antenna / 39 2.12 How to Prevent Coupling Between the Elements Through the Feed Network / 40 2.12.1 Using Hybrids / 40 2.12.2 Using Circulators / 42 2.12.3 Using Amplifiers / 42 2.13 How to Eliminate Backscatter due to Tapered Aperture Illumination / 43 2.14 Common Misconceptions / 45 2.14.1 On Structural Scattering / 45 2.14.2 On RCS of Horn Antennas / 46 2.14.3 On the Element Pattern: Is It Important? / 46 2.14.4 Are Low RCS Antennas Obtained by Fooling Around on the Computer? / 48 2.14.5 How Much Can We Conclude from the Half-Wave Dipole Array? / 48 2.14.6 Do “Small” Antennas Have Lower RCS Than Bigger Ones? / 48 2.14.7 And the Worst Misconception of All: Omitting the Loads! / 49 2.15 Summary / 49 Problems / 51 3 Theory 3.1 Introduction / 56 56 3.2 The Vector Potential and the H Field for Column Arrays of Hertzian Elements / 57 3.3 Case I: Longitudinal Elements / 59 3.3.1 Total Field from Infinite Column Array of z-Directed Elements of Arbitrary Length 2l / 60 3.3.2 The Voltage Induced in an Element by an External Field / 61 3.3.3 The Mutual Impedance Zq ,q Between a Column Array q and an External Element q 3.4 Case II: Transverse Elements / 64 3.4.1 The x Component of Eq / 65 / 62
x CONTENTS 3.4.2 The y Component of Eq / 69 3.4.3 The z Component of Eq / 72 3.5 Discussion / 74 3.6 Determination of the Element Currents / 76 3.7 The Double Infinite Arrays with Arbitrary Element Orientation / 77 3.7.1 How to Get Well-Behaved Expressions / 77 3.8 Conclusions / 81 Problems / 82 4 Surface Waves on Passive Surfaces of Finite Extent 84 4.1 Introduction / 84 4.2 Model / 85 4.3 The Infinite Array Case / 85 4.4 The Finite Array Case Excited by Generators / 89 4.5 The Element Currents on a Finite Array Excited by an Incident Wave / 89 4.6 How the Surface Waves are Excited on a Finite Array / 90 4.7 How to Obtain the Actual Current Components / 93 4.8 The Bistatic Scattered Field from a Finite Array / 94 4.9 Parametric Study / 96 4.9.1 Variation of the Angle of Incidence / 96 4.9.2 Variation of the Array Size / 100 4.9.3 Variation of Frequency / 102 4.10 How to Control Surface Waves / 108 4.11 Fine Tuning the Load Resistors at a Single Frequency / 108 4.12 Variation with Angle of Incidence / 111 4.13 The Bistatic Scattered Field / 114 4.14 Previous Work / 115 4.15 On Scattering from Faceted Radomes / 117
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