Computational Methods in Electromagnetic Compatibility

Antenna Theory Approach Versus Transmission Line Models
Standards Information Network (Verlag)
  • 1. Auflage
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  • erschienen am 10. Mai 2018
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  • 432 Seiten
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978-1-119-33707-2 (ISBN)
Offers a comprehensive overview of the recent advances in the area of computational electromagnetics

Computational Method in Electromagnetic Compatibility offers a review of the most recent advances in computational electromagnetics. The authors-noted experts in the field-examine similar problems by taking different approaches related to antenna theory models and transmission line methods. They discuss various solution methods related to boundary integral equation techniques and finite difference techniques.

The topics covered are related to realistic antenna systems including antennas for air traffic control or ground penetrating radar antennas; grounding systems (such as grounding systems for wind turbines); biomedical applications of electromagnetic fields (such as transcranial magnetic stimulation); and much more. The text features a number of illustrative computational examples and a reference list at the end of each chapter. The book is grounded in a rigorous theoretical approach and offers mathematical details of the formulations and solution methods. This important text:

Provides a trade-off between a highly efficient transmission line approach and antenna theory models providing analysis of high frequency and transient phenomena
Contains the newest information on EMC analysis and design principles
Discusses electromagnetic field coupling to thin wire configurations and modeling in bioelectromagnetics

Written for engineering students, senior researchers and practicing electrical engineers, Computational Method in Electromagnetic Compatibility provides a valuable resource in the design of equipment working in a common electromagnetic environment.
1. Auflage
  • Englisch
  • USA
John Wiley & Sons Inc
  • Für Beruf und Forschung
  • 30,89 MB
978-1-119-33707-2 (9781119337072)

weitere Ausgaben werden ermittelt
DRAGAN POLJAK, Ph.D., is the Full Professor at Department of Electronics and Computing, Faculty of electrical engineering, mechanical engineering and naval architecture at the University of Split. He is also Adjunct Professor at Wessex Institute of Technology (WIT) and a member of the WIT Board of Directors.

KHALIL EL KHAMLICHI DRISSI, Ing., Ph.D., is the Full Professor at the Department of Electrical Engineering at Clermont Auvergne University in France. In addition, he is senior researcher at Institute Pascal Laboratory and member of National Council of Universities (CNU-63).
Preface xiii

Part I Electromagnetic Field Coupling to ThinWire Configurations of Arbitrary Shape 1

1 Computational Electromagnetics - Introductory Aspects 3

1.1 The Character of Physical Models Representing Natural Phenomena 3

1.1.1 Scientific Method, a Definition, History, Development ... ? 3

1.1.2 Physical Model and the MathematicalMethod to Solve the Problem -The Essence of Scientific Theories 4

1.1.3 Philosophical Aspects Behind Scientific Theories 7

1.1.4 On the Character of Physical Models 8

1.2 Maxwell's Equations 9

1.2.1 Original Form of Maxwell's Equations 9

1.2.2 Modern Form of Maxwell's Equations 10

1.2.3 From the Corner of Philosophy of Science 12

1.2.4 FDTD Solution of Maxwell's Equations 13

1.2.5 Computational Examples 16

1.3 The ElectromagneticWave Equations 19

1.4 Conservation Laws in the Electromagnetic Field 20

1.5 Density of Quantity of Movement in the Electromagnetic Field 22

1.6 Electromagnetic Potentials 25

1.7 Solution of theWave Equation and Radiation Arrow of Time 25

1.8 Complex Phasor Form of Equations in Electromagnetics 27

1.8.1 The Generalized Symmetric Form of Maxwell's Equations 27

1.8.2 Complex Phasor Form of ElectromagneticWave Equations 29

1.8.3 Poynting Theorem for Complex Phasors 29

References 31

2 Antenna Theory versus Transmission Line Approximation - General Considerations 33

2.1 A Note on EMC ComputationalModels 33

2.1.1 Classification of EMC Models 34

2.1.2 Summary Remarks on EMC Modeling 34

2.2 Generalized Telegrapher's Equations for the Field Coupling to Finite LengthWires 35

2.2.1 Frequency Domain Analysis for StraightWires above a Lossy Ground 36 Integral Equation for PECWire of Finite Length above a Lossy Ground 37 Integral Equation for a Lossy Conductor above a Lossy Ground 39 Generalized Telegraphers Equations for PECWires 39 Generalized Telegraphers Equations for Lossy Conductors 42 Numerical Solution of Integral Equations 43 Simulation Results 46 Simulation Results and Comparison with TLTheory 46

2.2.2 Frequency Domain Analysis for StraightWires Buried in a Lossy Ground 51 Integral Equation for Lossy Conductor Buried in a Lossy Ground 51 Generalized Telegraphers Equations for Buried LossyWires 54 Computational Examples 56

2.2.3 Time Domain Analysis for StraightWires above a Lossy Ground 61 Space-Time Integro-Differential Equation for PECWire above a Lossy Ground 61 Space-Time Integro-Differential Equation for Lossy Conductors 65 Generalized Telegraphers Equations for PECWires 66 Generalized Telegrapher's Equations for Lossy Conductors 70

2.2.4 Time Domain Analysis for StraightWires Buried in a Lossy Ground 74 Space-Time Integro-Differential Equation for PECWire below a Lossy Ground 74 Space-Time Integro-Differential Equation for Lossy Conductors 79 Generalized Telegrapher's Equations for BuriedWires 80 Computational Results: BuriedWire Scatterer 82 Computational Results: Horizontal Grounding Electrode 84

2.3 Single HorizontalWire in the Presence of a Lossy Half-Space: Comparison of Analytical Solution, Numerical Solution, and Transmission Line Approximation 86

2.3.1 Wire above a Perfect Ground 88

2.3.2 Wire above an Imperfect Ground 89

2.3.3 Wire Buried in a Lossy Ground 89

2.3.4 Analytical Solution 90

2.3.5 Boundary Element Procedure 92

2.3.6 The Transmission Line Model 93

2.3.7 Modified Transmission Line Model 94

2.3.8 Computational Examples 95 Wire above a PEC Ground 95 Wire above a Lossy Ground 95 Wire Buried in a Lossy Ground 103

2.3.9 Field Transmitted in a Lower Lossy Half-Space 103

2.3.10 Numerical Results 110

2.4 Single VerticalWire in the Presence of a Lossy Half-Space: Comparison of Analytical Solution, Numerical Solution, and Transmission Line Approximation 114

2.4.1 Numerical Solution 117

2.4.2 Analytical Solution 119

2.4.3 Computational Examples 121 Transmitting Antenna 122 Receiving Antenna 122

2.5 Magnetic Current Loop Excitation of ThinWires 132

2.5.1 Delta Gap and Magnetic Frill 134

2.5.2 Magnetic Current Loop 135

2.5.3 Numerical Solution 136

2.5.4 Numerical Results 139

References 146

3 Electromagnetic Field Coupling to OverheadWires 153

3.1 Frequency Domain Models and Methods 154

3.1.1 Antenna Theory Approach: Set of Coupled Pocklington's Equations 154

3.1.2 Numerical Solution 160

3.1.3 Transmission Line Approximation: Telegrapher's Equations in the Frequency Domain 162

3.1.4 Computational Examples 162

3.2 Time Domain Models and Methods 167

3.2.1 The Antenna Theory Model 167

3.2.2 The Numerical Solution 175

3.2.3 The Transmission Line Model 181

3.2.4 The Solution of Transmission Line Equations via FDTD 182

3.2.5 Numerical Results 184

3.3 Applications to Antenna Systems 187

3.3.1 Helix Antennas 187

3.3.2 Log-Periodic Dipole Arrays 190

3.3.3 GPR Dipole Antennas 198

References 202

4 Electromagnetic Field Coupling to BuriedWires 205

4.1 Frequency Domain Modeling 205

4.1.1 Antenna Theory Approach: Set of Coupled Pocklington's Equations for ArbitraryWire Configurations 206

4.1.2 Antenna Theory Approach: Numerical Solution 210

4.1.3 Transmission Line Approximation: 212

4.1.4 Computational Examples 213

4.2 Time Domain Modeling 216

4.2.1 Antenna Theory Approach 216

4.2.2 Transmission Line Model 219

4.2.3 Computational Examples 223

References 223

5 Lightning Electromagnetics 225

5.1 AntennaModel of Lightning Channel 225

5.1.1 Integral Equation Formulation 226

5.1.2 Computational Examples 228

5.2 Vertical AntennaModel of a Lightning Rod 230

5.2.1 Integral Equation Formulation 234

5.2.2 Computational Examples 236

5.3 AntennaModel of aWind Turbine Exposed to Lightning Strike 237

5.3.1 Integral Equation Formulation for Multiple OverheadWires 240

5.3.2 Numerical Solution of Integral Equation Set for Overhead Wires 241

5.3.3 Computational Example: Transient Response of aWT Lightning Strike 242

References 247

6 Transient Analysis of Grounding Systems 253

6.1 Frequency Domain Analysis of Horizontal Grounding Electrode 254

6.1.1 Integral Equation Formulation/Reflection Coefficient Approach 254

6.1.2 Numerical Solution 257

6.1.3 Integral Equation Formulation/Sommerfeld Integral Approach 258

6.1.4 Analytical Solution 260

6.1.5 Modified Transmission Line Method (TLM) Approach 261

6.1.6 Computational Examples 261

6.1.7 Application of Magnetic Current Loop (MCL) Source model to Horizontal Grounding Electrode 284

6.2 Frequency Domain Analysis of Vertical Grounding Electrode 288

6.2.1 Integral Equation Formulation/Reflection Coefficient Approach 288

6.2.2 Numerical Solution 290

6.2.3 Analytical Solution 291

6.2.4 Examples 292

6.3 Frequency Domain Analysis of Complex Grounding Systems 297

6.3.1 Antenna Theory Approach: Set of Homogeneous Pocklington's Integro-Differential Equations for Grounding Systems 298

6.3.2 Antenna Theory Approach: Numerical Solution 300

6.3.3 Modified Transmission Line Method Approach 301

6.3.4 Finite Difference Solution of the Potential Differential Equation for Transient Induced Voltage 301

6.3.5 Computational Examples: Grounding Grids and Rings 304

6.3.6 Computational Examples: Grounding Systems forWTs 311

6.4 Time Domain Analysis of Horizontal Grounding Electrodes 320

6.4.1 Homogeneous Integral Equation Formulation in the Time Domain 321

6.4.2 Numerical Solution Procedure for Pocklington's Equation 322

6.4.3 Numerical Results for Grounding Electrode 323

6.4.4 Analytical Solution of Pocklington's Equation 323

6.4.5 Transmission Line Model 324

6.4.6 FDTD Solution of Telegrapher's Equations 325

6.4.7 The Leakage Current 326

6.4.8 Computational Examples for the Horizontal Grounding Electrode 328

References 331

Part II Advanced Models in Bioelectromagnetics 337

7 Human Exposure to Electromagnetic Fields - General Aspects 339

7.1 Dosimetry 340

7.1.1 Low Frequency Exposures 341

7.1.2 High Frequency Exposures 342

7.2 Coupling Mechanisms 342

7.2.1 Coupling to LF Electric Fields 343

7.2.2 Coupling to LF Magnetic Fields 343

7.2.3 Absorption of Energy from Electromagnetic Radiation 343

7.2.4 Indirect Coupling Mechanisms 344

7.3 Biological Effects 344

7.3.1 Effects of ELF Fields 345

7.3.2 Effects of HF Radiation 345

7.4 Safety Guidelines and Exposure Limits 348

7.5 Some Remarks 351

References 351

8 Modeling of Human Exposure to Static and Low Frequency Fields 353

8.1 Exposure to Static Fields 354

8.1.1 Finite Element Solution 356

8.1.2 Boundary Element Solution 357

8.1.3 Numerical Results 360

8.2 Exposure to Low Frequency (LF) Fields 361

8.2.1 Numerical Results 362

References 363

9 Modeling of Human Exposure to High Frequency (HF) Electromagnetic Fields 365

9.1 Internal Electromagnetic Field DosimetryMethods 366

9.1.1 Solution by the Hybrid Finite Element/Boundary Element Approach 366

9.1.2 Numerical Results for the Human Eye Exposure 368

9.1.3 Solution by the Method of Moments 372

9.1.4 Computational Example for the Brain Exposure 380

9.2 Thermal Dosimetry Procedures 381

9.2.1 Finite Element Solution of Bio-Heat Transfer Equation 381

9.2.2 Numerical Results 382

References 383

10 Biomedical Applications of Electromagnetic Fields 387

10.1 Modeling of Induced Fields due to Transcranial Magnetic Stimulation (TMS) Treatment 388

10.1.1 Numerical Results 391

10.2 Modeling of Nerve Fiber Excitation 392

10.2.1 Passive Nerve Fiber 396

10.2.2 Numerical Results for Passive Nerve Fiber 397

10.2.3 Active Nerve Fiber 397

10.2.4 Numerical Results for Active Nerve Fiber 401

References 403

Index 407

Chapter 1
Computational Electromagnetics - Introductory Aspects

This introductory section deals with the character of a physical model and the corresponding mathematical method to solve the problem of interest. The models are characterized to be simplified imaginary simulations of the real-world systems one attempts to understand. However, models include only those properties and relationships required to understand aspects of real systems that are of interest at the given moment, i.e. those aspects of real systems one knows, or those one is aware of after all. The rest of the information about a real system is simply neglected. Furthermore, this introductory section discusses the fundamental framework to describe electromagnetic phenomena - Maxwell's equations, wave equations, and conservation laws.

1.1 The Character of Physical Models Representing Natural Phenomena

1.1.1 Scientific Method, a Definition, History, Development . ?

Scientists create tools, that's what they do...

C.P. Snow

Science could be considered as an entire set of facts, definitions, theorems, techniques, and relationships, and is tested on phenomena in the real, objective, and external world and, itself, has many elements of imagination, logic, creativity, judgment, metaphor, and instrumentations.

The essence of science is definitely more in research methods and specific way of reasoning, and less in particular facts and results.

Scientific insight starts with observing a certain phenomenon, and then organizing the collected observations in a sort of hypothesis that is tested on additional observations, and if necessary, modified. Then, predictions based on these modified hypotheses are carried out, and some experiments are performed to test the predictions. When the range of predictions provided by the hypothesis is considered to be satisfactory for the scientific community, the hypothesis is referred to as a scientific theory or natural law.

This rather successful methodology, more than four centuries old, is called science or scientific method.

Scientific method was born in the beginning of the seventeenth century with Galileo having abandoned Aristotle's theory of motion. It was Galileo who came up with the principle of the relativity of motion and with the statement that only change in motion required force.

At the same time, a separation of science from philosophy began in the form of shift from consideration of the nature of phenomenon (essence) to explanation of the behavior of a phenomenon. Namely, the Aristotelian essentialistic approach to the explanation of natural phenomena was replaced by the mathematical predictive approach. Instead of asking the question why scientists started to ask how [1]. As once Kelvin pointed out - to know something about phenomena means to measure them and express them in terms of numbers.

What is considered to be one of the crucial issues in the analysis of a natural phenomenon is related to the development and application of a physical model enabling one to predict the behavior of a system with a certain level of accuracy.

One of the crucial aspects of the scientific method and related technological progress is definitely the physical model of a natural phenomenon of interest.

1.1.2 Physical Model and the Mathematical Method to Solve the Problem - The Essence of Scientific Theories

Therefore, the goal of the scientific method is to establish the model of a physical phenomenon and to develop related mathematical methods for the analysis of the given problem.

Various theoretical and experimental procedures are used while developing a model. Models are simplified imaginary simulations of the natural systems one attempts to understand and include only those properties and relationships required to understand aspects of real systems that are currently of interest, i.e. those aspects one knows, or, those one is aware of after all. The rest of the details about a real system are simply neglected from a model.

The concept of physical model represents the essence of reductionistic approach within the scientific method. How much the model of a given physical phenomenon is satisfactory depends on what is required from the model. In the language of mathematics, almost all problems arising in electromagnetics can be formulated in terms of differential, integral, or variational equations.

Generally, there are two basic approaches to solving problems in electromagnetics - the differential (field) approach and the integral (source) approach.

The field approach deals with a solution of a corresponding differential equation with associated initial and boundary conditions, specified at a boundary of a computational domain. Solving some differential equation type one obtains the spatial and temporal distribution of the corresponding field or potential.

Historically, this approach has been developed by Boskovic, Faraday, Maxwell, and others, and is generally very useful for handling the problems with closed domains and clearly specified boundary conditions, the so-called interior field problems.

The source or integral approach is based on the solution of a corresponding integral equation that yields the distribution of electromagnetic filed sources in terms of charge or current distribution, respectively.

In the past, this approach was promoted by Franklin, Cavendish, and Ampere, among others, and is convenient for the treatment of the exterior (unbounded) field problems.

Thus, a classical boundary-value problem can be formulated in terms of the operator equation:


on the domain O with conditions


prescribed on the boundary G.

L is the linear differential operator, u is the solution of the problem, and p is the excitation function representing the known sources inside the domain. Note that u usually represents potentials (such as scalar potential ?) or fields (such as electric field E).

The character of the differential approach is depicted in Figure 1.1 [2].

Figure 1.1 Differential approach concept.

Methods for the solution of the interior field problem are generally referred to as differential methods or field methods.

Essentially, a differential approach isolates the calculation domain from the rest of the world. The interaction of the domain of interest with the rest is expressed (de facto replaced) by a set of prescribed boundary conditions.

If instead of differential operator L one considers an integral operator g, then unknowns are related to field sources (charge or current densities, respectively), distributed along the boundary G´. Namely, it can be written as


where h denotes the excitation function.

Figure 1.2 illustrates the character of the integral approach [2].

Figure 1.2 Integral approach concept.

Solution methods for the exterior field problem are generally referred to as integral methods or source methods. In this case, the domain of interest is unbounded (infinite). However, the source distribution represents all that exists, i.e. all interactions coming from the outer world are neglected. For example, when a basic electromagnetic model is developed for a dipole antenna in engineering electromagnetics the antenna is assumed to be insulated in free space [2].

Finally, for dynamic phenomena the initial condition of a physical system has to be considered. Basically, any law of nature represents physical states in a mathematical form (written in terms of differential, integral, or variational equations). Thus, a prescribed initial condition (behavior of the considered physical quantity at t = 0) by definition implies that nothing exists earlier than t = 0. This is also considered to be the origin of time asymmetry in physical laws.

Generally, techniques for the solution of operator equations can be referred to as analytical, numerical, or hybrid methods. Analytical solution methods provide exact solutions but are, on the other hand, limited to a narrow range of applications, mostly related to canonical problems.

Unfortunately, there are not many realistic scenarios in physics or practical engineering problems that can be worked out using these techniques.

Numerical techniques are applicable to almost all scientific engineering problems, but the main drawbacks are related to the limits governed by the approximation contained in the model itself.

Moreover, the criteria for accuracy, stability, and convergence are not always straightforward and clear to the researcher in a particular area [2].

1.1.3 Philosophical Aspects Behind Scientific Theories

One of the crucial questions in the philosophy of science is how physical models really work, or, more generally, how scientific theories are developed or "upgraded."

Looking back into the history of physics, the development of Maxwell's kinetic theory of gases and electromagnetic field theory was not motivated by experimental findings that were not compatible with the existing paradigm (in the sense of Kuhn [3]), as was...

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