Electromagnetic Pulse Simulations Using Finite-difference Time-domain Method

Discover the utility of the FDTD approach to solving electromagnetic problems with this powerful new resource

Electromagnetic Pulse Simulations Using Finite-Difference Time-Domain Method delivers a comprehensive overview of the generation and propagation of ultra-wideband electromagnetic pulses. The book provides a broad cross-section of studies of electromagnetic waves and their propagation in free space, dielectric media, complex media, and within guiding structures, like waveguide lines, transmission lines, and antennae.

The distinguished author offers readers a fresh new approach for analyzing electromagnetic modes for pulsed electromagnetic systems designed to improve the reader’s understanding of the electromagnetic modes responsible for radiating far-fields. The book also provides a wide variety of computer programs, data analysis techniques, and visualization tools with state-of-the-art packages in MATLAB^® and Octave.

Following an introduction and clarification of basic electromagnetics and the frequency and time domain approach, the book delivers explanations of different numerical methods frequently used in computational electromagnetics and the necessity for the time domain treatment. In addition to a discussion of the Finite-difference Time-domain (FDTD) approach, readers will also enjoy:

• A thorough introduction to electromagnetic pulses (EMPs) and basic electromagnetics, including common applications of electromagnetics and EMP coupling and its effects
• An exploration of time and frequency domain analysis in electromagnetics, including Maxwell’s equations and their practical implications
• A discussion of electromagnetic waves and propagation, including waves in free space, dielectric mediums, complex mediums, and guiding structures
• A treatment of computational electromagnetics, including an explanation of why we need modeling and simulations

Perfect for undergraduate and graduate students taking courses in physics and electrical and electronic engineering, Electromagnetic Pulse Simulations Using Finite-Difference Time-Domain Method will also earn a place in the libraries of scientists and engineers working in electromagnetic research, RF and microwave design, and electromagnetic interference.

Shahid Ahmed, PhD, is Research Associate Professor at Norfolk State University in Virginia, United States. He is Adjunct Faculty in Physics at Tidewater Community College and the Art Institute at Virginia Beach. He has published forty scholarly papers on various aspects of electromagnetics in peer-reviewed journals.

Acknowledgments xiii

Preface xv

1 Electromagnetic Pulse 1

1.1 Sources of EMP 1

1.2 EMP Coupling and its Effects 3

1.3 EMP Simulators 3

1.4 Review of Earlier Work 5

1.5 Overview of this Book 10

1.6 Summary 12

2 Time and Frequency Domain Analysis 13

2.1 Introduction 13

2.2 Nuclear Electromagnetic Pulse 14

2.2.1 Differences of Two Exponentials Times in a Unit Step Function 14

2.2.1.1 Time-Domain 15

2.2.1.2 Frequency-Domain 15

2.2.2 Reciprocal of the Sum of Two Exponentials 17

2.2.2.1 Time-Domain Characteristics 18

2.2.2.2 Frequency-Domain 19

2.3 Summary 22

3 Simulations Using FDTD Method 23

3.1 Introduction 23

3.2 Need for FDTD Analysis of an EMP Simulator 24

3.2.1 Choice of Method for Self-consistent Analysis 25

3.3 Maxwell’s Equations and the Yee Algorithm 25

3.4 FDTD Implementation 27

3.5 Numerical Issues 29

3.6 Summary 31

4 Electromagnetic Pulse in Free Space and Material Media 32

4.1 Introduction 32

4.2 Input Waveform 32

4.2.1 MATLAB^® Script for Visualization: Listing #1 33

4.2.2 Execution of MATLAB/OCTAVE Code 35

4.3 One-dimension Approach 36

4.3.1 Free Space 36

4.3.1.1 MATLAB Code Listing #1: EM Wave Propagation in Free-space 38

4.3.2 Data Recording and Visualization 41

4.3.2.1 MATLAB Script for Visualization: Listing #2 41

4.3.3 Dielectric Medium 43

4.3.3.1 Lossless Dielectric Medium 44

4.3.3.2 MATLAB Code Listing #2: EM Wave in Air and Lossless-dielectric Medium 45

4.3.3.3 Lossy Dielectric Medium 49

4.3.3.4 MATLAB Code Listing #3: EM Wave in Air and Lossy-dielectric Medium 51

4.3.3.5 MATLAB Code Listing #4: Analytical Approach for Wave in Lossy Medium 55

4.3.4 Perfect Electric Conductor (PEC) 56

4.3.4.1 MATLAB Code Listing #5: EM Wave in Air-PEC Half-space 57

4.4 Summary 61

Exercises 61

5 Simulation of Capacitor Bank 63

5.1 Introduction 63

5.2 Details of Model 64

5.2.1 Description of Geometry 64

5.2.2 Method of Charging 65

5.2.3 Method for Calculating FDTD Charge and Capacitance 66

5.2.4 FDTD Model of Closing Switch 68

5.2.5 Discharging a Charged Capacitor 69

5.3 Results and Discussion 70

5.3.1 Charge Deposition on Plates 70

5.3.2 Stabilization of Charge Density Distribution 71

5.3.3 Determination of Characteristic Discharge Time 72

5.4 Cross-check of FDTD Results Using Method-of-Moments 73

5.4.1 Check of Capacitance 74

5.4.2 Edge Effects on Charge Density Distribution 75

5.4.3 Check of Charge Density Distribution 76

5.5 Effect of Boundary Condition 78

5.6 Summary 80

Exercises 81

6 Bounded Wave Simulator for Electromagnetic Pulses 83

6.1 Introduction 83

6.1.1 Organization of This Chapter 83

6.2 Geometry and Computational Model 85

6.2.1 Idealizations 85

6.2.2 Geometry 86

6.2.3 FDTD Model 87

6.3 Validation of TEM Structure Geometry 88

6.3.1 Analytical Check 88

6.3.2 Numerical Check 88

6.4 FDTD Model of Closing Switch 91

6.5 Choice of Distance to Domain Boundary 93

6.6 Electric Field within TEM Structure 93

6.6.1 Effect of Switch Closure Time 94

6.6.2 Pulse Fidelity 95

6.7 Flow of Current through Simulator Plates 96

6.8 Prepulse 96

6.9 Effect of Test Object 99

6.10 Validation Checks for FDTD Analysis 101

6.11 Summary 102

Exercises 103

7 Electromagnetic Modes Inside Bounded Wave Simulators 104

7.1 Introduction 104

7.1.1 Choice of Method for Modal Analysis 104

7.1.2 Organization of This Chapter 105

7.2 Details of Model 105

7.2.1 FDTD Model 105

7.2.2 Qualitative Discussion of Mode Structure 106

7.2.3 Application of SVD for Modal Analysis 108

7.2.4 Validation of SVD Results 109

7.2.5 Sample Calculation 109

7.3 Modal Analysis of Simulator Without Test Object 111

7.4 Modal Analysis of Simulator With Test Object 119

7.4.1 Qualitative Analysis 120

7.4.2 Quantitative Analysis Using SVD of E_x Data 122

7.4.3 Quantitative Analysis Using SVD of E_z Data 127

7.5 Physical Interpretation for Electric Field Increase 131

7.6 Summary 135

Exercises 136

8 Parametric Study of Radiation Leakage from a Bounded-Wave Simulator 138

8.1 Introduction 138

8.2 Details of Computational Model 139

8.3 Sensitivity to Length of Parallel-plate Extension 140

8.4 Sensitivity to Angle Between Tapered Plates 141

8.5 Effect of Type of Termination 143

8.6 Sensitivity to Closure Time of Switch 147

8.7 Effect of Test Object 150

8.8 Physical Interpretation 150

8.9 Summary 153

Exercises 154

9 Modal Perspective of Radiation Leakage from a Bounded-Wave Simulator 155

9.1 Introduction 155

9.2 Calculation Procedure 156

9.3 Effect of Angle of Inclination Between Tapered Plates 156

9.3.1 Correlation Study 157

9.3.2 Physical Interpretation 159

9.3.3 Variation of Leakage with Plate Angle 161

9.4 Effect of Pulse Compression 162

9.4.1 Effect on Radiation Leakage 162

9.4.2 Explanation in Terms of Mode Structure 163

9.5 Summary 165

Exercises 167

10 Spatial Mode Filter for Reducing Radiation Leakage 168

10.1 Introduction 168

10.2 Suppression of Higher Order Modes 168

10.2.1 Optimal Value of Longitudinal Resistance 170

10.2.2 Optimal Length of Suppressor Inside Test Volume 173

10.2.3 Mode Structure with Suppressor in Presence of Test Object 174

10.3 Summary 176

Exercises 177

11 EMP Interaction with Biological Tissues 178

11.1 Introduction 178

11.2 Model Description 179

11.3 Results and Discussion 181

11.3.1 Pulse Evolution in the TEM Cell 181

11.3.2 Interaction of EMP with Human Body 182

11.4 Summary 186

Exercises 186

12 FDTD Computer Program 187

12.1 Introduction 187

12.2 Computer Code Details 187

12.3 Sample Output 246

12.4 Summary 325

References 326

Index 331

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