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Electromagnetic Fields in Cavities: Deterministic and Statistical Theories (IEEE Press Series on Electromagnetic Wave Theory) PDF

286 Pages·2009·5.61 MB·English
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Preview Electromagnetic Fields in Cavities: Deterministic and Statistical Theories (IEEE Press Series on Electromagnetic Wave Theory)

ELECTROMAGNETIC FIELDS IN CAVITIES IEEE PRESS SERIES ON ELECTROMAGNETIC WAVE THEORY The IEEE Press Series on Electromagnetic Wave Theory consists of new titles as well as reissues and revisions of recognized classics in electromagnetic waves and applications which maintain long term archival significance. Series Editor Andreas Cangellaris University of Illinois at Urbana Champaign Advisory Board Robert E. Collin Case Western Reserve University Akira Ishimaru Douglas S. Jones University of Washington University of Dundee Associate Editors ELECTROMAGNETIC THEORY, SCATTERING, INTEGRAL EQUATION METHODS AND DIFFRACTION Donald R. Wilton Ehud Heyman University of Houston Tel AvivUniversity DIFFERENTIAL EQUATIONMETHODS ANTENNAS, PROPAGATION, ANDMICROWAVES Andreas C. Cangellaris David R. Jackson University of Illinois at Urbana Champaign University of Houston BOOKS IN THE IEEE PRESS SERIES ON ELECTROMAGNETIC WAVE THEORY Chew, W. C., Waves and Fields in Inhomogeneous Media Christopoulos, C., The Transmission Line Modeling Methods; TLM Clemmow, P. C., The Plane Wave Spectrum Representation of Electromagnetic Fields Collin, R. E., Field Theory for Guided Waves, Second Edition Collin, R. E., Foundations for Microwave Engineering, Second Edition Dudley, D. G., Mathematical Foundations for Electromagnetic Theory Elliott, R. S., Antenna Theory and Design. Revised Edition Elliott, R. S., Electromagnetics: History, Theory, and Applications Felsen, L. B., and Marcuvitz, N., Radiation and Scattering of Waves Harrington, R. F., Field Computation by Moment Methods Harrington, R. F, Time Harmonic Electromagnetic Fields Hansen, T. B., and Yaghjian, A. D., Plane Wave Theory of Time Domain Fields Hill, D. A., Electromagnetic Fields in Cavities: Deterministic and Statistical Theories Ishimaru, A., Wave Propagation and Scattering in Random Media Jones, D. S., Methods in Electromagnetic Wave Propagation, Second Edition Josefsson, L., and Persson, P., Conformal Array Antenna Theory and Design Lindell I. V., Methods for Electromagnetic Field Analysis Lindell, I. V., Differential Forms in Electromagnetics Stratton, J. A., Electromagnetic Theory, A Classic Reissue Tai, C. T., Generalized Vector and Dyadic Analysis, Second Edition Van Bladel, J, G., Electromagnetic Fields, Second Edition Van Bladel, J. G., Singular Electromagnetic Fields and Sources Volakis, et al., Finite Element Method for Electromagnetics Zhu, Y., and Cangellaris, A., Multigrid Finite Element Methods for Electromagnetic Field Modeling ELECTROMAGNETIC FIELDS IN CAVITIES DETERMINISTIC AND STATISTICAL THEORIES David A. Hill Electromagnetics Division National Institute of Standards and Technology IEEE Press 445 Hoes Lane Piscataway, NJ 08854 IEEE Press Editorial Board Lajos Hanzo, Editor in Chief R. Abari T. Chen B.M. Hammerli J. Anderson T.G. Croda O. Malik S. Basu M. El Hawary S. Nahavandi A. Chatterjee S. Farshchi W. Reeve Kenneth Moore, Director of IEEE Book and Information Services (BIS) Jeanne Audino, Project Editor Copyright Ó 2009 by Institute of Electrical and Electronics Engineers. All rights reserved. Published by John Wiley & Sons, Inc., Hoboken, New Jersey. Published simultaneously in Canada. No part of this publicationmay 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 ofWarranty: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 orwritten salesmaterials. The advice and strategies containedhereinmaynot 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 CustomerCareDepartmentwithin theUnitedStates at (800)762 2974,outside theUnitedStates 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 maynot be available in electronic formats. Formore information aboutWileyproducts, visit ourweb site at www.wiley.com. Library of Congress Cataloging-in-Publication Data is available. ISBN: 978 0 470 46590 5 Printed in the United States of America. 10 9 8 7 6 5 4 3 2 1 To Elaine CONTENTS PREFACE xi PART I. DETERMINISTIC THEORY 1 1. Introduction 3 1.1 Maxwell’s Equations 3 1.2 Empty Cavity Modes 5 1.3 Wall Losses 8 1.4 Cavity Excitation 12 1.5 Perturbation Theories 16 1.5.1 Small-Sample Perturbation of a Cavity 16 1.5.2 Small Deformation of Cavity Wall 20 Problems 23 2. Rectangular Cavity 25 2.1 Resonant Modes 25 2.2 Wall Losses and Cavity Q 31 2.3 Dyadic Green’s Functions 33 2.3.1 Fields in the Source-Free Region 36 2.3.2 Fields in the Source Region 37 Problems 38 3. Circular Cylindrical Cavity 41 3.1 Resonant Modes 41 3.2 Wall Losses and Cavity Q 47 3.3 Dyadic Green’s Functions 49 3.3.1 Fields in the Source-Free Region 51 3.3.2 Fields in the Source Region 52 Problems 52 4. Spherical Cavity 55 4.1 Resonant Modes 55 4.2 Wall Losses and Cavity Q 63 vii viii CONTENTS 4.3 Dyadic Green’s Functions 66 4.3.1 Fields in the Source-Free Region 68 4.3.2 Fields in the Source Region 69 4.4 Schumann Resonances in the Earth-Ionosphere Cavity 69 Problems 73 PART II. STATISTICAL THEORIES FOR ELECTRICALLY LARGE CAVITIES 75 5. Motivation for Statistical Approaches 77 5.1 Lack of Detailed Information 77 5.2 Sensitivity of Fields to Cavity Geometry and Excitation 78 5.3 Interpretation of Results 79 Problems 80 6. Probability Fundamentals 81 6.1 Introduction 81 6.2 Probability Density Function 82 6.3 Common Probability Density Functions 84 6.4 Cumulative Distribution Function 85 6.5 Methods for Determining Probability Density Functions 86 Problems 88 7. Reverberation Chambers 91 7.1 Plane-Wave Integral Representation of Fields 91 7.2 Ideal Statistical Properties of Electric and Magnetic Fields 94 7.3 Probability Density Functions for the Fields 98 7.4 Spatial Correlation Functions of Fields and Energy Density 101 7.4.1 Complex Electric or Magnetic Field 101 7.4.2 Mixed Electric and Magnetic Field Components 106 7.4.3 Squared Field Components 107 7.4.4 Energy Density 110 7.4.5 Power Density 111 7.5 Antenna or Test-Object Response 112 7.6 Loss Mechanisms and Chamber Q 115 7.7 Reciprocity and Radiated Emissions 122 7.7.1 Radiated Power 122 7.7.2 Reciprocity Relationship to Radiated Immunity 123 7.8 Boundary Fields 127 7.8.1 Planar Interface 128 CONTENTS ix 7.8.2 Right-Angle Bend 132 7.8.3 Right-Angle Corner 138 7.8.4 Probability Density Functions 142 7.9 Enhanced Backscatter at the Transmitting Antenna 143 7.9.1 Geometrical Optics Formulation 144 7.9.2 Plane-Wave Integral Formulation 147 Problems 148 8. Aperture Excitation of Electrically Large, Lossy Cavities 151 8.1 Aperture Excitation 151 8.1.1 Apertures of Arbitrary Shape 152 8.1.2 Circular Aperture 153 8.2 Power Balance 155 8.2.1 Shielding Effectiveness 155 8.2.2 Time Constant 157 8.3 Experimental Results for SE 158 Problems 163 9. Extensions to the Uniform-Field Model 165 9.1 Frequency Stirring 165 9.1.1 Green’s Function 165 9.1.2 Uniform-Field Approximations 167 9.1.3 Nonzero Bandwidth 169 9.2 Unstirred Energy 173 9.3 Alternative Probability Density Function 176 Problems 180 10. Further Applications of Reverberation Chambers 181 10.1 Nested Chambers for Shielding Effectiveness Measurements 181 10.1.1 Initial Test Methods 182 10.1.2 Revised Method 183 10.1.3 Measured Results 186 10.2 Evaluation of Shielded Enclosures 192 10.2.1 Nested Reverberation Chamber Approach 192 10.2.2 Experimental Setup and Results 193 10.3 Measurement of Antenna Efficiency 196 10.3.1 Receiving Antenna Efficiency 197 10.3.2 Transmitting Antenna Efficiency 198 10.4 Measurement of Absorption Cross Section 199 Problems 201 x CONTENTS 11. Indoor Wireless Propagation 203 11.1 General Considerations 203 11.2 Path Loss Models 204 11.3 Temporal Characteristics 205 11.3.1 Reverberation Model 205 11.3.2 Discrete Multipath Model 208 11.3.3 Low-Q Rooms 211 11.4 Angle of Arrival 217 11.4.1 Reverberation Model 217 11.4.2 Results for Realistic Buildings 218 11.5 Reverberation Chamber Simulation 220 11.5.1 A Controllable K-Factor Using One Transmitting Antenna 222 11.5.2 A Controllable K-Factor Using Two Transmitting Antennas 222 11.5.3 Effective K-Factor 223 11.5.4 Experimental Results 225 Problems 230 APPENDIX A. VECTOR ANALYSIS 231 APPENDIX B. ASSOCIATED LEGENDRE FUNCTIONS 237 APPENDIX C. SPHERICAL BESSEL FUNCTIONS 241 APPENDIX D. THE ROLE OF CHAOS IN CAVITY FIELDS 243 APPENDIX E. SHORT ELECTRIC DIPOLE RESPONSE 245 APPENDIX F. SMALL LOOP ANTENNA RESPONSE 247 APPENDIX G. RAY THEORY FOR CHAMBER ANALYSIS 249 APPENDIX H. ABSORPTION BY A HOMOGENEOUS SPHERE 251 APPENDIX I. TRANSMISSION CROSS SECTION OF A SMALL CIRCULAR APERTURE 255 APPENDIX J. SCALING 257 REFERENCES 261 INDEX 277

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