ffirs.qxd 2/2/2006 3:49 PM Page iii 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 ffirs.qxd 2/2/2006 3:49 PM Page i CONFORMAL ARRAY ANTENNA THEORY AND DESIGN ffirs.qxd 2/2/2006 3:49 PM Page ii IEEE Press 445 Hoes Lane Piscataway, NJ 08854 IEEE Press Editorial Board Mohamed E. El-Hawary, Editor in Chief M. Akay T. G. Croda M. S. Newman J. B. Anderson R.J. Herrick F. M. B. Pereira R. J. Baker S. V. Kartalopoulos C. Singh J. E. Brewer M. Montrose 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. Series Editor Donald G. Dudley University of Arizona Advisory Board Robert B. Collin Akira Ishimaru D. S. Jones Case Western Reserve University of Washington University of Dundee University Associate Editors ELECTROMAGNETICTHEORY, SCATTERING, INTEGRALEQUATIONMETHODS ANDDIFFRACTION Donald R. Wilton Ehud Heyman University of Houston Tel-Aviv University 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 ffirs.qxd 2/2/2006 3:49 PM Page iii 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 ffirs.qxd 2/2/2006 3:49 PM Page iv 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. 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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 ftoc.qxd 2/2/2006 3:51 PM Page v CONTENTS Preface xi Abbreviations and Acronyms xiii 1 INTRODUCTION 1 1.1 The Definition of a Conformal Antenna 1 1.2 Why Conformal Antennas? 2 1.3 History 4 1.4 Metal Radomes 9 1.5 Sonar Arrays 9 References 11 2 CIRCULAR ARRAY THEORY 15 2.1 Introduction 15 2.2 Fundamentals 16 2.2.1 Linear Arrays 16 2.2.2 Circular Arrays 19 2.3 Phase Mode Theory 23 2.3.1 Introduction 23 2.3.2 Discrete Elements 27 2.3.3 Directional Elements 29 2.4 The Ripple Problem in Omnidirectional Patterns 34 2.4.1 Isotropic Radiators 37 2.4.2 Higher-Order Phase Modes 40 2.4.3 Directional Radiators 40 2.5 Elevation Pattern 41 2.6 Focused Beam Pattern 41 References 46 3 THE SHAPES OF CONFORMAL ANTENNAS 49 3.1 Introduction 49 3.2 360° Coverage 52 v ftoc.qxd 2/2/2006 3:51 PM Page vi vi CONTENTS 3.2.1 360° Coverage Using Planar Surfaces 52 3.2.2 360° Coverage Using a Curved Surface 54 3.3 Hemispherical Coverage 57 3.3.1 Introduction 57 3.3.2 Hemispherical Coverage Using Planar Surfaces 58 3.3.3 Half Sphere 60 3.3.4 Cone 60 3.3.5 Ellipsoid 62 3.3.6 Paraboloid 63 3.3.7 Comparing Shapes 64 3.4 Multifaceted Surfaces 67 3.5 References 70 4 METHODS OF ANALYSIS 73 4.1 Introduction 73 4.2 The Problem 75 4.3 Electrically Small Surfaces 76 4.3.1 Introduction 76 4.3.2 Modal Solutions 76 4.3.2.1 Introduction 76 4.3.2.2 The Circular Cylinder 77 4.3.2.3 A Unit Cell Approach 79 4.3.3 Integral Equations and the Method of Moments 80 4.3.4 Finite Difference Time Domain Methods (FDTD) 81 4.3.4.1 Introduction 81 4.3.4.2 Conformal or Contour-Patch (CP) FDTD 82 4.3.4.3 FDTD in Global Curvilinear Coordinates 83 4.3.4.4 FDTD in Cylindrical Coordinates 84 4.3.5 Finite Element Method (FEM) 87 4.3.5.1 Introduction 87 4.3.5.2 Hybrid FE-BI Method 88 4.4 Electrically Large Surfaces 89 4.4.1 Introduction 89 4.4.2 High-Frequency Methods for PEC Surfaces 90 4.4.3 High-Frequency Methods for Dielectric Coated Surfaces 93 4.5 Two Examples 95 4.5.1 Introduction 95 4.5.2 The Aperture Antenna 95 4.5.3 The Microstrip-Patch Antenna 98 4.6 A Comparison of Analysis Methods 100 Appendix 4A—Interpretation of the ray theory 100 4A.1 Watson Transformation 103 4A.2 Fock Substitution 103 4A.3 SDP Integration 104 4A.4 Surface Waves 105 4A.5 Generalization 107 References 108 ftoc.qxd 2/2/2006 3:51 PM Page vii CONTENTS vii 5 GEODESICS ON CURVED SURFACES 123 5.1 Introduction 123 5.1.1 Definition of a Surface and Related Parameters 125 5.1.2 The Geodesic Equation 127 5.1.3 Solving the Geodesic Equation and the Existence of Geodesics 128 5.2 Singly Curved Surfaces 130 5.3 Doubly Curved Surfaces 135 5.3.1 Introduction 135 5.3.2 The Cone 135 5.3.3 Rotationally Symmetric Doubly Curved Surfaces 137 5.3.4 Properties of Geodesics on Doubly Curved Surfaces 139 5.3.5 Geodesic Splitting 141 5.4 Arbitrarily Shaped Surfaces 149 5.4.1 Hybrid surfaces 150 5.4.2 Analytically Described Surfaces 152 References 152 6 ANTENNAS ON SINGLY CURVED SURFACES 155 6.1 Introduction 155 6.2 Aperture Antennas on Circular Cylinders 157 6.2.1 Introduction 157 6.2.2 Theory 157 6.2.3 Mutual Coupling 158 6.2.3.1 Isolated Mutual Coupling 158 6.2.3.2 Cross Polarization Coupling 168 6.2.3.3 Array mutual coupling 168 6.2.4 Radiation Characteristics 173 6.2.4.1 Isolated-Element Patterns 175 6.2.4.2 Embedded-Element Patterns 176 6.3 Aperture Antennas on General Convex Cylinders 192 6.3.1 Introduction 192 6.3.2 Mutual Coupling 193 6.3.2.1 The Elliptic Cylinder 193 6.3.2.2 The Parabolic Cylinder 194 6.3.2.3 The Hyperbolic Cylinder 194 6.3.3 Radiation Characteristics 194 6.3.3.1 The Elliptic Cylinder 196 6.3.3.2 End Effects 196 6.4 Aperture Antennas on Faceted Cylinders 200 6.4.1 Introduction 200 6.4.2 Mutual Coupling 207 6.4.3 Radiation Characteristics 209 6.5 Aperture Antennas on Dielectric Coated Circular Cylinders 209 6.5.1 Introduction 209 6.5.2 Mutual Coupling 213 6.5.2.1 Isolated Mutual Coupling 213 6.5.2.2 Array Mutual Coupling 215 6.5.3 Radiation Characteristics 221 ftoc.qxd 2/2/2006 3:51 PM Page viii viii CONTENTS 6.5.3.1 Isolated-Element Patterns 221 6.5.3.2 Embedded-Element Patterns 223 6.6 Microstrip-Patch Antennas on Coated Circular Cylinders 230 6.6.1 Introduction 230 6.6.2 Theory 231 6.6.3 Mutual Coupling 232 6.6.3.1 Single-Element Characteristics 232 6.6.3.2 Isolated and Array Mutual Coupling 232 6.6.4 Radiation Characteristics 237 6.6.4.1 Isolated-Element Patterns 237 6.6.4.2 Embedded-Element Patterns 238 6.7 The Cone 245 6.7.1 Introduction 245 6.7.2 Mutual Coupling 246 6.7.2.1 Aperture Antennas 246 6.7.2.2 Microstrip-Patch Antennas 247 6.7.3 Radiation Characteristics 248 6.7.3.1 Aperture Antennas 248 6.7.3.2 Microstrip-Patch Antennas 257 References 258 7 ANTENNAS ON DOUBLY CURVED SURFACES 265 7.1 Introduction 265 7.2 Aperture Antennas 267 7.2.1 Introduction 267 7.2.2 Mutual Coupling 267 7.2.2.1 Isolated Mutual Coupling 269 7.2.2.2 Array Mutual Coupling 282 7.2.3 Radiation Characteristics 283 7.3 Microstrip-Patch Antennas 289 7.3.1 Introduction 289 7.3.2 Mutual Coupling 289 7.3.2.1 Single-Element Characteristics 291 7.3.2.2 Isolated Mutual Coupling 294 7.3.3 Radiation Characteristics 297 References 302 8 CONFORMAL ARRAY CHARACTERISTICS 305 8.1 Introduction 305 8.2 Mechanical Considerations 306 8.2.1 Array Shapes 306 8.2.2 Element Distribution on a Curved Surface 308 8.2.3 Multifacet Solutions 308 8.2.4 Tile Architecture 309 8.2.5 Static and Dynamic Stress 312 8.2.6 Other Electromagnetic Considerations 312 8.3 Radiation Patterns 313 8.3.1 Introduction 313