Advanced Modeling in Computational Electromagnetic Compatibility

DRAGAN POLJAK, PhD, is Professor in the Department of Electronics at the University of Split, Croatia, and Adjunct Professor at Wessex Institute of Technology, United Kingdom. He has developed more than 60,000 lines of research code for the solution of many electromagnetic compatibility problems, with an emphasis on problems involving modeling of wire structures. Dr. Poljak has also written over 200 journal and conference papers.

• PREFACE xvPART I: FUNDAMENTAL CONCEPTS IN COMPUTATIONAL ELECTROMAGNETIC COMPATIBILITY 11. Introduction to Computational Electromagnetics and Electromagnetic Compatibility 31.1 Historical Note on Modeling in Electromagnetics 31.2 Electromagnetic Compatibility and Electromagnetic Interference 51.2.1 EMC Computational Models and Solution Methods 51.2.2 Classification of EMC Models 71.2.3 Summary Remarks on EMC Modeling 81.3 References 82. Fundamentals of Electromagnetic Theory 102.1 Differential Form of Maxwell Equations 102.2 Integral Form of Maxwell Equations 112.3 Maxwell Equations for Moving Media 142.4 The Continuity Equation 172.5 Ohm’s Law 192.6 Conservation Law in the Electromagnetic Field 212.7 The Electromagnetic Wave Equations 242.8 Boundary Relationships for Discontinuities in Material Properties 262.9 The Electromagnetic Potentials 322.10 Boundary Relationships for Potential Functions 332.11 Potential Wave Equations 352.11.1 Coulomb Gauge 362.11.2 Diffusion Gauge 372.11.3 Lorentz Gauge 382.12 Retarded Potentials 402.13 General Boundary Conditions and Uniqueness Theorem 412.14 Electric and Magnetic Walls 412.15 The Lagrangian Form of Electromagnetic Field Laws 422.15.1 Lagrangian Formulation and Hamilton Variational Principle 432.15.2 Lagrangian Formulation and Hamilton Variational Principle in Electromagnetics 452.16 Complex Phasor Notation of Time-Harmonic Electromagnetic Fields 512.16.1 Poyinting Theorem for Complex Phasors 522.16.2 Complex Phasor Form of Electromagnetic Wave Equations 532.16.3 The Retarded Potentials for the Time-Harmonic Fields 542.17 Transmission Line Theory 542.17.1 Field Coupling Using Transmission Line Models 552.17.2 Derivation of Telegrapher’s Equation for the Two-Wire Transmission Line 562.18 Plane Wave Propagation 662.19 Radiation 682.19.1 Radiation Mechanism 682.19.2 Hertzian Dipole 692.19.3 Fundamental Antenna Parameters 712.19.4 Linear Antennas 752.20 References 793 Introduction to Numerical Methods in Electromagnetics 803.1 Analytical Versus Numerical Methods 823.1.1 Frequency and Time Domain Modeling 823.2 Overview of Numerical Methods: Domain, Boundary, and Source Simulation 843.2.1 Modeling of Problems via the Domain Methods: FDM and FEM 843.2.2 Modeling of Problems via the BEM: Direct and Indirect Approach 853.3 The Finite Difference Method 853.3.1 One-Dimensional FDM 863.3.2 Two-Dimensional FDM 883.4 The Finite Element Method 913.4.1 Basic Concepts of FEM 913.4.2 One-Dimensional FEM 923.4.3 Two-Dimensional FEM 983.5 The Boundary Element Method 1093.5.1 Integral Equation Formulation 1093.5.2 Boundary Element Discretization 1143.5.3 Computational Example for 2D Static Problem 1213.6 References 1224 Static Field Analysis 1234.1 Electrostatic Fields 1234.2 Magnetostatic Fields 1244.3 Modeling of Static Field Problems 1264.3.1 Integral Equations in Electrostatics Using Sources 1264.3.2 Computational Example: Modeling of a Lightning Rod 1294.4 References 1355 Quasistatic Field Analysis 1365.1 Introduction 1365.2 Formulation of the Quasistatic Problem 1375.3 Integral Equation Representation of the Helmholtz Equation 1405.4 Computational Example 1435.4.1 Analytical Solution of the Eddy Current Problem 1445.4.2 Boundary Element Solution of the Eddy Current Problem 1465.5 References 1506 Electromagnetic Scattering Analysis 1516.1 The Electromagnetic Wave Equations 1516.2 Complex Phasor Form of the Wave Equations 1546.3 Two-Dimensional Scattering from a Perfectly Conducting Cylinder of Arbitrary Cross-Section 1546.4 Solution by the Indirect Boundary Element Method 1566.4.1 Constant Element Case 1586.4.2 Linear Elements Case 1596.5 Numerical Example 1596.6 References 162PART II: ANALYSIS OF THIN WIRE ANTENNAS AND SCATTERERS 1637 Wire Antennas and Scatterers: General Considerations 1657.1 Frequency Domain Thin Wire Integral Equations 1657.2 Time Domain Thin Wire Integral Equations 1667.3 Modeling in the Frequency and Time Domain: Computational Aspects 1677.4 References 1688 Wire Antennas and Scatterers: Frequency Domain Analysis 1718.1 Thin Wires in Free Space 1718.1.1 Single Straight Wire in Free Space 1728.1.2 Boundary Element Solution of Thin Wire Integral Equation 1748.1.3 Calculation of the Radiated Electric Field and the Input Impedance of the Wire 1808.1.4 Numerical Results for Thin Wire in Free Space 1808.1.5 Coated Thin Wire Antenna in Free Space 1818.1.6 The Near Field of a Coated Thin Wire Antenna 1868.1.7 Boundary Element Procedures for Coated Wires 1878.1.8 Numerical Results for Coated Wire 1908.1.9 Thin Wire Loop Antenna 1918.1.10 Boundary Element Solution of Loop Antenna Integral Equation 1938.1.11 Numerical Results for a Loop Antenna 1968.1.12 Thin Wire Array in Free Space: Horizontal Arrangement 1968.1.13 Boundary Element Analysis of Horizontal Antenna Array 1998.1.14 Radiated Electric Field of the Wire Array 2018.1.15 Numerical Results for Horizontal Wire Array 2018.1.16 Boundary Element Analysis of Vertical Antenna Array: Modeling of Radio Base Station Antennas 2018.1.17 Numerical Procedures for Vertical Array 2078.1.18 Numerical Results 2098.2 Thin Wires Above a Lossy Half-Space 2138.2.1 Single Straight Wire Above a Dissipative Half-Space 2148.2.2 Loaded Antenna Above a Dissipative Half-Space 2208.2.3 Electric Field and the Input Impedance of a Single Wire Above a Half-Space 2228.2.4 Boundary Element Analysis for Single Wire Above a Real Ground 2248.2.5 Treatment of Sommerfeld Integrals 2278.2.6 Calculation of Electric Field and Input Impedance 2298.2.7 Numerical Results for a Single Wire Above a Real Ground 2338.2.8 Multiple Straight Wire Antennas Over a Lossy Half-Space 2378.2.9 Electric Field of a Wire Array Above a Lossy Half-Space 2398.2.10 Boundary Element Analysis of Wire Array Above a Lossy Ground 2408.2.11 Near-Field Calculation for Wires Above Half-Space 2418.2.12 Computational Examples for Wires Above a Lossy Half-Space 2428.3 References 2469 Wire Antennas and Scatterers: Time Domain Analysis 2509.1 Thin Wires in Free Space 2529.1.1 Single Wire in Free Space 2529.1.2 Single Wire Far Field 2569.1.3 Loaded Straight Thin Wire in Free Space 2579.1.4 Two Coupled Identical Wires in Free Space 2599.1.5 Measures for Postprocessing of Transient Response 2639.1.6 Computational Procedures for Thin Wires in Free Space 2659.1.7 Numerical Results for Thin Wires in Free Space 2759.2 Thin Wires in a Presence of a Two-Media Configuration 2909.2.1 Single Straight Wire Above a Real Ground 2909.2.2 Far Field Equations 2949.2.3 Loaded Straight Thin Wire Above a Lossy Half-Space 2969.2.4 Two Coupled Horizontal Wires in a Two Media Configuration 3009.2.5 Thin Wire Array Above a Real Ground 3049.2.6 Computational Procedures for Horizontal Wires Above a Dielectric Half-Space 3079.2.7 Computational Examples 3179.3 References 333PART III: COMPUTATIONAL MODELS IN ELECTROMAGNETIC COMPATIBILITY 33510 Transmission Lines of Finite Length: General Considerations 33710.1 Transmission Line Theory Method 33810.2 Antenna Models of the Transmission Lines 34010.2.1 Above-Ground Transmission Lines 34110.2.2 Below-Ground Transmission Lines 34110.3 References 34211 Electromagnetic Field Coupling to Overhead Lines: Frequency Domain and Time Domain Analysis 34511.1 Frequency Domain Analysis: Derivation of Generalized Telegrapher’s Equations 34511.2 Frequency Domain Computational Results 35111.2.1 Single Wire Above an Imperfect Ground 35111.2.2 Multiple Wire Transmission Line Above an Imperfect Ground 35511.3 Time Domain Analysis 35911.4 Time Domain Computational Examples 35911.4.1 Single Wire Transmission Line 36011.4.2 Two Wire Transmission Line 36711.4.3 Three Wire Transmission Line 36711.5 References 37212 The Electromagnetic Field Coupling to Buried Cables: Frequency- and Time-Domain Analysis 37412.1 The Frequency-Domain Approach 37412.1.1 Formulation in the Frequency Domain 37512.1.2 Numerical Solution of the Integral Equation 37812.1.3 The Calculation of Transient Response 38012.1.4 Numerical Results 38112.2 Time-Domain Approach 38412.2.1 Formulation in the Time Domain 38412.2.2 Time-Domain Energy Measures 39112.2.3 Time-Domain Numerical Solution Procedures 39212.2.4 Computational Examples 39512.3 References 40313 Simple Grounding Systems 40513.1 Vertical Grounding Electrode 40613.1.1 Integral Equation Formulation for the Vertical Grounding Electrode 40713.1.2 The Evaluation of the Input Impedance Spectrum 41113.1.3 Numerical Procedures for Vertical Grounding Electrode 41313.1.4 Calculation of the Transient Impedance 41413.1.5 Numerical Results 41613.2 Horizontal Grounding Electrode 41813.2.1 Integral Equation Formulation for the Horizontal Electrode 42013.2.2 The Evaluation of the Input Impedance Spectrum 42513.2.3 Numerical Procedures for Horizontal Electrode 42713.2.4 The Transient Impedance Calculation 42813.2.5 Numerical Results 42813.3 Transmission Line Method Versus Antenna Theory Approach 43713.3.1 Transmission Line Method (TLM) Approach to Modeling of Horizontal Grounding Electrode 43813.3.2 Computational Examples 43913.4 Measures for Quantifying the Transient Response of Grounding Electrodes 44313.4.1 Transient Response Assessment 44313.4.2 Measures for Quantifying the Transient Response 44413.4.3 Computational Examples 44513.5 References 45114 Human Exposure to Electromagnetic Fields 45314.1 Environmental Risk of Electromagnetic Fields: General Considerations 45314.1.1 Nonionizing and Ionizing Radiation 45414.1.2 Electrosmog or Radiation Pollution at Low and High Frequencies 45414.1.3 The Effects of Low Frequency Fields 45514.1.4 The Effects of High Frequency Fields 45614.1.5 Remarks on Electromagnetic Fields and Related Possible Hazard to Humans 45714.2 Assessment of Human Exposure to Electromagnetic Fields: Frequency and Time Domain Approach 45814.2.1 Frequency Domain Cylindrical Antenna Model 45814.2.2 Realistic Models of the Human Body for ELF Exposures 45914.2.3 Human Exposure to Transient Electromagnetic Fields 45914.3 Human Exposure to Extremely Low Frequency (ELF) Electromagnetic Fields 45914.3.1 Parasitic Antenna Representation of the Human Body 46014.3.2 Realistic Modeling of the Human Body 46714.4 Exposure of Humans to Transient Radiation: Cylindrical Model of the Human Body 47814.4.1 Time Domain Model of the Human Body 47914.4.2 Measures of the Transient Response 48014.5 References 489Index 493

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