Electromagnetic Fields in Cavities: Deterministic and Statistical Theories / Edition 1

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A thorough and rigorous analysis of electromagnetic fields in cavities

This book offers a comprehensive analysis of electromagnetic fields in cavities of general shapes and properties.

Part One covers classical deterministic methods to conclude resonant frequencies, modal fields, and cavity losses; quality factor; mode bandwidth; and the excitation of cavity fields from arbitrary current distributions for metal-wall cavities of simple shape.

Part Two covers modern statistical methods to analyze electrically large cavities of complex shapes and properties.

Electromagnetic Fields in Cavities combines rigorous solutions to Maxwell's equations with conservation of energy to solve for the statistics of many quantities of interest: penetration into cavities (and shielding effectiveness), field strengths far from and close to cavity walls, and power received by antennas within cavities. It includes all modes and shows you how to utilize fairly simple statistical formulae to apply to your particular problem, whether it's interference calculations, electromagnetic compatibility testing in reverberation chambers, measurement of shielding materials using multiple cavities, or efficiency of test antennas. Electromagnetic Fields in Cavities is a valuable resource for researchers, engineers, professors, and graduate students in electrical engineering.

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Product Details

Meet the Author

David A. Hill is a Guest Researcher at the National Institute of Standards and Technology (NIST) specializing in cavity theory and reverberation chamber applications. Previously, he held project leader positions with the Institute for Telecommunication Sciences and NIST. Since 1980, he has been an Adjunct Professor in the Department of Electrical and Computer Engineering at the University of Colorado at Boulder, where he teaches graduate courses in electromagnetics and advises graduate students on master's and PhD theses. Dr. Hill is an IEEE Life Fellow and a member of URSI Commissions A, B, E, and F. He has won IEEE EMC Society Prize Paper Awards for "Out-of-Band Response of Antenna Arrays" in 1987 and "On Determining the Maximum Emissions from Electrically Large Sources" in 2002.
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Table of 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

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 DensityFunctions 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

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

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

Appendlx C Spherical Bessel Functions 241

Appendix D The Role of Chaos In cavity Fields 243

Appendix E Short Electric Dipole Response 245

Appendtx F Small Loop Antenna Response 247

Appendix G Ray Theory for Chamber Analysis 249

Appendtx H Absorption by a Homogeneous Sphere 251

Appendlx I Transmission Cross Section of a Small Circular Aperture 255

Appendix J Scaling 257

References 261

Index 277

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