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CONFORMAL ARRAY ANTENNA THEORY AND DESIGN Lars Josefsson Chalmers University of Technology, Sweden Patrik Persson Royal Institute of Technology, Sweden IEEE Antennas and Propagation Society, Sponsor IEEE Press A WILEY-INTERSCIENCE PUBLICATION

CONFORMAL ARRAY ANTENNA THEORY AND DESIGN

IEEE Press 445 Hoes Lane Piscataway, NJ 08854 IEEE Press Editorial Board Mohamed E. El-Hawary, Editor in Chief M. Akay J. B. Anderson R. J. Baker J. E. Brewer T. G. Croda R.J. Herrick S. V. Kartalopoulos M. Montrose M. S. Newman F. M. B. Pereira C. Singh G. Zobrist Kenneth Moore, Director of IEEE Book and Information Services (BIS) Catherine Faduska, Senior Acquisitions Editor IEEE PRESS SERIES ON ELECTROMAGNETIC WAVE THEORY The IEEE Press Series on Electromagnetic Wave Theory consists of new titles as well as reprints ahd revisions of recognized classics in electromagnetic waves and applications which maintain long-term archival significance. Robert B. Collin Case Western Reserve University Series Editor Donald G. Dudley University of Arizona Advisory Board Akira Ishimaru University of Washington Associate Editors ELECTROMAGNETIC THEORY, SCATTERING, AND DIFFRACTION Ehud Heyman Tel-Aviv University D. S. Jones University of Dundee INTEGRAL EQUATION METHODS Donald R. Wilton University of Houston BOOKS IN THE IEEE PRESS SERIES ON ELECTROMAGNETIC WAVE THEORY Christopoulos, C., The Transmission-Line Modeling Methods, TLM Clemmow, P. C., The Plane Wave Spectrum Representation of Electromagnetic Fields Collin, R. B., Field Theory of Guided Waves, Second Edition Dudley, D. G., Mathematical Foundations for Microwave Engineering, Second Edition Elliot, R. S., Antenna Theory and Design, Revised Edition Elliot, R. S., Electromagnetics: History Theory, and Applications Felsen, L. B., and Marcuvitz, N., Radiation and Scattering of Waves Harrington, R. F, Field Computation of Moment Methods Harrington, R. F, Time Harmonic Electromagnetic Fields Hansen et al., Plane-Wave Theory of Time-Domain Fields. Near-Field Scanning Applications Ishimaru, A., Wave Propagation and Scattering in Random Media Jones, D. S., Methods in Electromagnetic Wave Propagation, Second Edition Lindell, I. V., Methods for Electromagnetic Field Analysis Lindell, I. V, Differential Forms in Electromagnetics Peterson et al., Computational Methods for Electromagnetics Tai, C. T., Generalized Vector and Dyadic Analysis. Applied Mathematics in Field Theory Tai, C. T., Dyadic Green Functions in Electromagnetic Theory, Second Edition Van Bladel, J., Singular Electromagnetic Fields and Sources Volakis et al., Finite Element Method. for Electromagnetics: Antennas, Microwave Circuits, and Scattering Applications Wait, J., Electromagnetic Waves in Stratified Media

Copyright © 2006 by the Institute of Electrical and Electronics Engineers, Inc. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. 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, or online at http://www.wiley.com/go/permission. 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 or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States 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 may not be available in electronic format. For information about Wiley products, visit our web site at www.wiley.com. Library of Congress Cataloging-in-Publication Data is available. ISBN-13 978-0-471-46584-3 ISBN-10 0-471-46584-4 Printed in the United States of America. 10 9 8 7 6 5 4 3 2 1

Preface Abbreviations and Acronyms 1 2 The Definition of a Conformal Antenna INTRODUCTION 1.1 1.2 Why Conformal Antennas? 1.3 1.4 Metal Radomes 1.5 References Sonar Arrays History CIRCULAR ARRAY THEORY 2.1 2.2 Introduction Fundamentals 2.2.1 Linear Arrays 2.2.2 Circular Arrays Phase Mode Theory 2.3.1 Introduction 2.3.2 Discrete Elements 2.3.3 Directional Elements The Ripple Problem in Omnidirectional Patterns 2.4.1 Isotropic Radiators 2.4.2 Higher-Order Phase Modes 2.4.3 Directional Radiators Elevation Pattern Focused Beam Pattern 2.3 2.4 2.5 2.6 References 3 THE SHAPES OF CONFORMAL ANTENNAS 3.1 3.2 Introduction 360° Coverage CONTENTS xi xiii 1 1 2 4 9 9 11 15 15 16 16 19 23 23 27 29 34 37 40 40 41 41 46 49 49 52 v

vi CONTENTS 3.3 3.2.1 360° Coverage Using Planar Surfaces 3.2.2 360° Coverage Using a Curved Surface Hemispherical Coverage 3.3.1 Introduction 3.3.2 Hemispherical Coverage Using Planar Surfaces 3.3.3 Half Sphere 3.3.4 Cone 3.3.5 Ellipsoid 3.3.6 Paraboloid 3.3.7 Comparing Shapes 3.4 Multifaceted Surfaces 3.5 References 4 METHODS OF ANALYSIS 4.1 4.2 4.3 Introduction The Problem Electrically Small Surfaces 4.3.1 Introduction 4.3.2 Modal Solutions 4.3.2.1 Introduction 4.3.2.2 The Circular Cylinder 4.3.2.3 A Unit Cell Approach 4.3.3 Integral Equations and the Method of Moments 4.3.4 Finite Difference Time Domain Methods (FDTD) 4.3.4.1 Introduction 4.3.4.2 Conformal or Contour-Patch (CP) FDTD 4.3.4.3 FDTD in Global Curvilinear Coordinates 4.3.4.4 FDTD in Cylindrical Coordinates 4.3.5 Finite Element Method (FEM) 4.3.5.1 Introduction 4.3.5.2 Hybrid FE-BI Method 4.4 4.5 Electrically Large Surfaces 4.4.1 Introduction 4.4.2 High-Frequency Methods for PEC Surfaces 4.4.3 High-Frequency Methods for Dielectric Coated Surfaces Two Examples 4.5.1 Introduction 4.5.2 The Aperture Antenna 4.5.3 The Microstrip-Patch Antenna A Comparison of Analysis Methods 4.6 Appendix 4A—Interpretation of the ray theory 4A.1 Watson Transformation 4A.2 Fock Substitution 4A.3 SDP Integration 4A.4 Surface Waves 4A.5 Generalization References 52 54 57 57 58 60 60 62 63 64 67 70 73 73 75 76 76 76 76 77 79 80 81 81 82 83 84 87 87 88 89 89 90 93 95 95 95 98 100 100 103 103 104 105 107 108

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