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

286 Pages·2009·5.61 MB·English

by  David A. Hill

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.
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ISBN: 978 0 470 46590 5
Printed in the United States of America.
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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