Computational Methods in Electromagnetic Compatibility

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 xiiiPart I Electromagnetic Field Coupling to ThinWire Configurations of Arbitrary Shape 11 Computational Electromagnetics – Introductory Aspects 31.1 The Character of Physical Models Representing Natural Phenomena 31.1.1 Scientific Method, a Definition, History, Development ... ? 31.1.2 Physical Model and the MathematicalMethod to Solve the Problem –The Essence of Scientific Theories 41.1.3 Philosophical Aspects Behind Scientific Theories 71.1.4 On the Character of Physical Models 81.2 Maxwell’s Equations 91.2.1 Original Form of Maxwell’s Equations 91.2.2 Modern Form of Maxwell’s Equations 101.2.3 From the Corner of Philosophy of Science 121.2.4 FDTD Solution of Maxwell’s Equations 131.2.5 Computational Examples 161.3 The ElectromagneticWave Equations 191.4 Conservation Laws in the Electromagnetic Field 201.5 Density of Quantity of Movement in the Electromagnetic Field 221.6 Electromagnetic Potentials 251.7 Solution of theWave Equation and Radiation Arrow of Time 251.8 Complex Phasor Form of Equations in Electromagnetics 271.8.1 The Generalized Symmetric Form of Maxwell’s Equations 271.8.2 Complex Phasor Form of ElectromagneticWave Equations 291.8.3 Poynting Theorem for Complex Phasors 29References 312 Antenna Theory versus Transmission Line Approximation – General Considerations 332.1 A Note on EMC ComputationalModels 332.1.1 Classification of EMC Models 342.1.2 Summary Remarks on EMC Modeling 342.2 Generalized Telegrapher’s Equations for the Field Coupling to Finite LengthWires 352.2.1 Frequency Domain Analysis for StraightWires above a Lossy Ground 362.2.1.1 Integral Equation for PECWire of Finite Length above a Lossy Ground 372.2.1.2 Integral Equation for a Lossy Conductor above a Lossy Ground 392.2.1.3 Generalized Telegraphers Equations for PECWires 392.2.1.4 Generalized Telegraphers Equations for Lossy Conductors 422.2.1.5 Numerical Solution of Integral Equations 432.2.1.6 Simulation Results 462.2.1.7 Simulation Results and Comparison with TLTheory 462.2.2 Frequency Domain Analysis for StraightWires Buried in a Lossy Ground 512.2.2.1 Integral Equation for Lossy Conductor Buried in a Lossy Ground 512.2.2.2 Generalized Telegraphers Equations for Buried LossyWires 542.2.2.3 Computational Examples 562.2.3 Time Domain Analysis for StraightWires above a Lossy Ground 612.2.3.1 Space–Time Integro-Differential Equation for PECWire above a Lossy Ground 612.2.3.2 Space–Time Integro-Differential Equation for Lossy Conductors 652.2.3.3 Generalized Telegraphers Equations for PECWires 662.2.3.4 Generalized Telegrapher’s Equations for Lossy Conductors 702.2.4 Time Domain Analysis for StraightWires Buried in a Lossy Ground 742.2.4.1 Space–Time Integro-Differential Equation for PECWire below a Lossy Ground 742.2.4.2 Space–Time Integro-Differential Equation for Lossy Conductors 792.2.4.3 Generalized Telegrapher’s Equations for BuriedWires 802.2.4.4 Computational Results: BuriedWire Scatterer 822.2.4.5 Computational Results: Horizontal Grounding Electrode 842.3 Single HorizontalWire in the Presence of a Lossy Half-Space: Comparison of Analytical Solution, Numerical Solution, and Transmission Line Approximation 862.3.1 Wire above a Perfect Ground 882.3.2 Wire above an Imperfect Ground 892.3.3 Wire Buried in a Lossy Ground 892.3.4 Analytical Solution 902.3.5 Boundary Element Procedure 922.3.6 The Transmission Line Model 932.3.7 Modified Transmission Line Model 942.3.8 Computational Examples 952.3.8.1 Wire above a PEC Ground 952.3.8.2 Wire above a Lossy Ground 952.3.8.3 Wire Buried in a Lossy Ground 1032.3.9 Field Transmitted in a Lower Lossy Half-Space 1032.3.10 Numerical Results 1102.4 Single VerticalWire in the Presence of a Lossy Half-Space: Comparison of Analytical Solution, Numerical Solution, and Transmission Line Approximation 1142.4.1 Numerical Solution 1172.4.2 Analytical Solution 1192.4.3 Computational Examples 1212.4.3.1 Transmitting Antenna 1222.4.3.2 Receiving Antenna 1222.5 Magnetic Current Loop Excitation of ThinWires 1322.5.1 Delta Gap and Magnetic Frill 1342.5.2 Magnetic Current Loop 1352.5.3 Numerical Solution 1362.5.4 Numerical Results 139References 1463 Electromagnetic Field Coupling to OverheadWires 1533.1 Frequency Domain Models and Methods 1543.1.1 Antenna Theory Approach: Set of Coupled Pocklington’s Equations 1543.1.2 Numerical Solution 1603.1.3 Transmission Line Approximation: Telegrapher’s Equations in the Frequency Domain 1623.1.4 Computational Examples 1623.2 Time Domain Models and Methods 1673.2.1 The Antenna Theory Model 1673.2.2 The Numerical Solution 1753.2.3 The Transmission Line Model 1813.2.4 The Solution of Transmission Line Equations via FDTD 1823.2.5 Numerical Results 1843.3 Applications to Antenna Systems 1873.3.1 Helix Antennas 1873.3.2 Log-Periodic Dipole Arrays 1903.3.3 GPR Dipole Antennas 198References 2024 Electromagnetic Field Coupling to BuriedWires 2054.1 Frequency Domain Modeling 2054.1.1 Antenna Theory Approach: Set of Coupled Pocklington’s Equations for ArbitraryWire Configurations 2064.1.2 Antenna Theory Approach: Numerical Solution 2104.1.3 Transmission Line Approximation: 2124.1.4 Computational Examples 2134.2 Time Domain Modeling 2164.2.1 Antenna Theory Approach 2164.2.2 Transmission Line Model 2194.2.3 Computational Examples 223References 2235 Lightning Electromagnetics 2255.1 AntennaModel of Lightning Channel 2255.1.1 Integral Equation Formulation 2265.1.2 Computational Examples 2285.2 Vertical AntennaModel of a Lightning Rod 2305.2.1 Integral Equation Formulation 2345.2.2 Computational Examples 2365.3 AntennaModel of aWind Turbine Exposed to Lightning Strike 2375.3.1 Integral Equation Formulation for Multiple OverheadWires 2405.3.2 Numerical Solution of Integral Equation Set for Overhead Wires 2415.3.3 Computational Example: Transient Response of aWT Lightning Strike 242References 2476 Transient Analysis of Grounding Systems 2536.1 Frequency Domain Analysis of Horizontal Grounding Electrode 2546.1.1 Integral Equation Formulation/Reflection Coefficient Approach 2546.1.2 Numerical Solution 2576.1.3 Integral Equation Formulation/Sommerfeld Integral Approach 2586.1.4 Analytical Solution 2606.1.5 Modified Transmission Line Method (TLM) Approach 2616.1.6 Computational Examples 2616.1.7 Application of Magnetic Current Loop (MCL) Source model to Horizontal Grounding Electrode 2846.2 Frequency Domain Analysis of Vertical Grounding Electrode 2886.2.1 Integral Equation Formulation/Reflection Coefficient Approach 2886.2.2 Numerical Solution 2906.2.3 Analytical Solution 2916.2.4 Examples 2926.3 Frequency Domain Analysis of Complex Grounding Systems 2976.3.1 Antenna Theory Approach: Set of Homogeneous Pocklington’s Integro-Differential Equations for Grounding Systems 2986.3.2 Antenna Theory Approach: Numerical Solution 3006.3.3 Modified Transmission Line Method Approach 3016.3.4 Finite Difference Solution of the Potential Differential Equation for Transient Induced Voltage 3016.3.5 Computational Examples: Grounding Grids and Rings 3046.3.6 Computational Examples: Grounding Systems forWTs 3116.4 Time Domain Analysis of Horizontal Grounding Electrodes 3206.4.1 Homogeneous Integral Equation Formulation in the Time Domain 3216.4.2 Numerical Solution Procedure for Pocklington’s Equation 3226.4.3 Numerical Results for Grounding Electrode 3236.4.4 Analytical Solution of Pocklington’s Equation 3236.4.5 Transmission Line Model 3246.4.6 FDTD Solution of Telegrapher’s Equations 3256.4.7 The Leakage Current 3266.4.8 Computational Examples for the Horizontal Grounding Electrode 328References 331Part II Advanced Models in Bioelectromagnetics 3377 Human Exposure to Electromagnetic Fields – General Aspects 3397.1 Dosimetry 3407.1.1 Low Frequency Exposures 3417.1.2 High Frequency Exposures 3427.2 Coupling Mechanisms 3427.2.1 Coupling to LF Electric Fields 3437.2.2 Coupling to LF Magnetic Fields 3437.2.3 Absorption of Energy from Electromagnetic Radiation 3437.2.4 Indirect Coupling Mechanisms 3447.3 Biological Effects 3447.3.1 Effects of ELF Fields 3457.3.2 Effects of HF Radiation 3457.4 Safety Guidelines and Exposure Limits 3487.5 Some Remarks 351References 3518 Modeling of Human Exposure to Static and Low Frequency Fields 3538.1 Exposure to Static Fields 3548.1.1 Finite Element Solution 3568.1.2 Boundary Element Solution 3578.1.3 Numerical Results 3608.2 Exposure to Low Frequency (LF) Fields 3618.2.1 Numerical Results 362References 3639 Modeling of Human Exposure to High Frequency (HF) Electromagnetic Fields 3659.1 Internal Electromagnetic Field DosimetryMethods 3669.1.1 Solution by the Hybrid Finite Element/Boundary Element Approach 3669.1.2 Numerical Results for the Human Eye Exposure 3689.1.3 Solution by the Method of Moments 3729.1.4 Computational Example for the Brain Exposure 3809.2 Thermal Dosimetry Procedures 3819.2.1 Finite Element Solution of Bio-Heat Transfer Equation 3819.2.2 Numerical Results 382References 38310 Biomedical Applications of Electromagnetic Fields 38710.1 Modeling of Induced Fields due to Transcranial Magnetic Stimulation (TMS) Treatment 38810.1.1 Numerical Results 39110.2 Modeling of Nerve Fiber Excitation 39210.2.1 Passive Nerve Fiber 39610.2.2 Numerical Results for Passive Nerve Fiber 39710.2.3 Active Nerve Fiber 39710.2.4 Numerical Results for Active Nerve Fiber 401References 403Index 407