Electromagnetic Pulse Simulations Using Finite-Difference Time-Domain Method
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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.
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Shahid Ahmed, PhD, is a Senior Application Engineer at ANSYS, Inc. He has taught undergrad and graduate-level courses in physics, electrical, and electronics engineering. His research included experiments as well as computational modeling and simulations. He has published forty scholarly papers on various aspects of electromagnetics in peer-reviewed journals and conferences.
Content
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 Ex Data 122
7.4.3 Quantitative Analysis Using SVD of Ez 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
1
Electromagnetic Pulse
Various natural and artificial processes, such as lightning discharges and nuclear explosions, can produce a strong pulse of broad-band electromagnetic radiation called an electromagnetic pulse (EMP). EMP has been the subject of research since World War II, as Fermi anticipated the electromagnetic effects resulting from a nuclear explosion [1]. The large electric fields in such a pulse can cause damage to electronic and control equipment. The generation of EMP during nuclear tests was first observed in the 1950s, where it sometimes resulted in instrumentation failure [2]. EMP occurring in lightning discharges, and during fast switching of high-voltage circuits, is also known to cause damage to electrical and electronics systems. The experimental and theoretical study of different sources of EMP, and their effects on systems, is an active field of study around the world [2].
1.1 Sources of EMP
There are various natural and artificial sources of EMP. A common natural source is lightning. Artificial sources include high-voltage fast switches, power stations and distribution systems, nuclear explosions, ultra-wideband radar, etc. EMP generated by lightning is called lightning electromagnetic pulse (LEMP), while that due to nuclear explosions is called nuclear electromagnetic pulse (NEMP). More details are available in [3].
Figure 1.1 illustrates the basic mechanism of NEMP generation. A nuclear detonation releases a stream of energetic gamma-ray photons. This primary gamma, , produces Compton electrons following a collision with free electrons available in the atmosphere. The current channel formed by the Compton electrons gives rise to a large d, producing NEMP [1].
Figure 1.2 shows the temporal as well as spectral waveforms of LEMP and NEMP. This figure is adapted from [4]. The electromagnetic fields in a NEMP follow a double-exponential temporal waveform given by [5]:
where , and are constants that govern the amplitude, inverse of rise and fall times, respectively. The rise-time and pulse-width of NEMP are of the order of nanoseconds and microseconds. For LEMP, these parameters are typically microsecond and millisecond, respectively. Both have an ultra-wideband nature.
Figure 1.1 Schematic of basic mechanism for NEMP generation.
Figure 1.2 Temporal and spectral waveform of different kinds of EMP [4].
1.2 EMP Coupling and its Effects
We have seen that EMP from different sources covers a broad range of the electromagnetic spectrum, with frequencies ranging from a few hertz to hundreds of megahertz. This corresponds to a wide range of free-space wavelengths. The longer wavelengths can couple to large objects such as overhead transmission lines, while small wavelengths couple to small objects such as control equipment and semiconductor devices. The coupling mechanism can be divided into two broad types, viz. "front door" and "back door" coupling. Front door coupling refers to energy that enters through the antennas of systems containing a receiver or transmitter. Back door coupling denotes energy that leaks into systems through apertures and seams in their enclosures [6].
The amount of front-door coupling depends upon the design frequency of the antenna and is maximum around its bandwidth. Back-door coupling through apertures and vents is maximum for wavelengths of the order of the aperture size and falls off steadily with increase in the wavelength. Figure 1.3 shows a schematic of front- and back- door coupling of EMP generated following a nuclear detonation, to electronic and electrical equipment [3]. EMP can enter the enclosure through overhead and underground transmission lines, telephone lines, windows, as well as utility ducts.
The high-intensity transient voltages and currents induced in electrical/electronic appliances can cause damage. The damage can be either temporary or permanent, depending upon the intensity of the incident pulse and the hardness of the exposed system [3].
1.3 EMP Simulators
A number of laboratories around the world have developed EMP simulators that can produce pulses of different types, with the objective of testing the susceptibility of systems exposed to EMP [7]. These are generally driven by a high-voltage pulsed-power source, e.g. a Marx capacitor bank. These simulators are used in two ways. The first is for assessing the effects of EMP on systems. The second is for testing the effectiveness of shielding ("hardening") of these systems.
Simulators can be divided into two broad categories: bounded-wave (closed) and radiate-wave (open). In a radiate-wave simulator, an ultra-wideband antenna, e.g. transverse electro-magnetic (TEM) horn, is used to radiate the electromagnetic field. This type of EMP simulator is used when systems to be tested are spread over a wide area [8]. Bounded-wave type simulators, with which this study is concerned, concentrate energy within the workspace of the system itself [9].
Figure 1.3 Schematic showing EMP coupling to electrical and electronics. This schematic is taken from [3].
(Source: Ghose [3]. 1984, Don White Consultants.)
A bounded-wave EMP simulator, in its simplest form, consists of two electrically conducting triangular plates, making up a TEM structure, separated by a parallel plate region [10]. This is illustrated schematically in Figure 1.4.
The front plate, which displays a near-constant impedance over a wide frequency range, plays a significant role in determining the EMP waveform, while the middle and rear plates serve to guide the signal [10]. The object to be tested is mounted in the bounded volume of the parallel-plate region.
There are several variants of the geometry shown in Figure 1.4. Some simulators do not have the rear plate, while others dispense with the parallel-plate section as well. The tapered section could also have some other shape, e.g. conical.
Figure 1.5 shows the setup of a bounded-wave EMP simulator, details of which have been reported in Ref. [9]. Only the tapered section of the simulator is shown here - the test section consists of a parallel-plate section, several meters in length.
Figure 1.4 Schematic of parallel-plate transmission-line type of EMP simulator.
(Source: Adapted from Giri et al. [11].)
Figure 1.5 Experimental setup of a bounded-wave EMP simulator.
(Source: Adapted from Schilling et al. [9].)
1.4 Review of Earlier Work
In this section, we examine earlier work in different areas relevant to modeling of EMP simulators.
We first consider earlier work involving overall analysis of bounded-wave simulator performance. Several time- and frequency-domain models have been reported. However, these analyses are based on several simplifying assumptions. For example, the conducting plates of a simulator have been approximated by wire grids or meshes. The current induced on the wires has been solved in the time-domain using a space-time-domain technique [12]. It has also been solved in the frequency domain using the method-of-moments (MOM) [13].
The transient electromagnetic field distribution inside a simulator has been studied through a space-time-domain technique [12]. The problem was formulated in terms of the radiation of a transient waveform from perfectly conducting wires, which involves the computation of the induced currents on the wires. This has been solved using the space-time-integral equation [14]. King and others [10, 15] have theoretically analyzed the transient behavior of a rhombic EMP simulator. In their simplified model, simulator plates are approximated by a hexagonal wire structure which is located along the edge of the metal plates. This approximation is based upon the fact that the largest current density in the parallel-plate simulator is found along the edge of the metal plates. Klaasen [16] has numerically analyzed the transient behavior of a bounded-wave simulator using a space-time-domain technique. The basic waveform of the current induced in the wire has been taken from [10]. As compared to King and workers [15], that study more accurately models the plates by increasing the number of wires in the calculation.
Hoo [13] has used MOM for the numerical analysis of a transmission line EMP simulator using a known waveform of electric field excitation. The electromagnetic field structure inside the bounded volume of the simulator was calculated by approximating the current waveform through a triangular basis function. As a check on the numerical method, the input impedance of a triangular dipole was calculated, which shows a fairly good match with experiments.
These methods are not suited for detailed analysis of simulators with test objects, for two...
