ADVANCED MODELING IN COMPUTATIONAL ELECTROMAGNETIC COMPATIBILITY
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1 ADVANCED MODELING IN COMPUTATIONAL ELECTROMAGNETIC COMPATIBILITY DRAGAN POLJAK, PhD Department of Electronics University of Split, Croatia BICENTENNIAL 1 8 O 7 WILEY 2 O O 7 ICENTENNIAL WILEY-INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION
2 CONTENTS PREFACE PART I: FUNDAMENTAL CONCEPTS IN COMPUTATIONAL ELECTROMAGNETIC COMPATIBILITY 1 1. Introduction to Computational Electromagnetics and Electromagnetic Compatibility Historical Note on Modeling in Electromagnetics Electromagnetic Compatibility and Electromagnetic Interference EMC Computational Models and Solution Methods Classification of EMC Models Summary Remarks on EMC Modeling References 8 2. Fundamentals of Electromagnetic Theory Differential Form of Maxwell Equations Integral Form of Maxwell Equations Maxwell Equations for Moving Media The Continuity Equation Ohm's Law Conservation Law in the Electromagnetic Field The Electromagnetic Wave Equations Boundary Relationships for Discontinuities in Material Properties The Electromagnetic Potentials Boundary Relationships for Potential Functions Potential Wave Equations Coulomb Gauge 36
3 viii CONTENTS Diffusion Gauge Lorentz Gauge Retarded Potentials General Boundary Conditions and Uniqueness Theorem Electric and Magnetic Walls The Lagrangian Form of Electromagnetic Field Laws Lagrangian Formulation and Hamilton Variational Principle Lagrangian Formulation and Hamilton Variational Principle in Electromagnetics Complex Phasor Notation of Time-Harmonic Electromagnetic Fields Poyinting Theorem for Complex Phasors Complex Phasor Form of Electromagnetic Wave Equations The Retarded Potentials for the Time-Harmonic Fields Transmission Line Theory Field Coupling Using Transmission Line Models Derivation of Telegrapher's Equation for the Two-Wire Transmission Line Plane Wave Propagation Radiation Radiation Mechanism Hertzian Dipole Fundamental Antenna Parameters Linear Antennas References 79 3 Introduction to Numerical Methods in Electromagnetics Analytical Versus Numerical Methods Frequency and Time Domain Modeling Overview of Numerical Methods: Domain, Boundary, and Source Simulation Modeling of Problems via the Domain Methods: FDM and FEM Modeling of Problems via the BEM: Direct and Indirect Approach 85
4 CONTENTS ix 3.3 The Finite Difference Method One-Dimensional FDM Two-Dimensional FDM The Finite Element Method Basic Concepts of FEM One-Dimensional FEM Two-Dimensional FEM The Boundary Element Method Integral Equation Formulation Boundary Element Discretization Computational Example for 2D Static Problem References Static Field Analysis Electrostatic Fields Magnetostatic Fields Modeling of Static Field Problems Integral Equations in Electrostatics Using Sources Computational Example: Modeling of a Lightning Rod References Quasistatic Field Analysis Introduction Formulation of the Quasistatic Problem Integral Equation Representation of the Helmholtz Equation Computational Example Analytical Solution of the Eddy Current Problem Boundary Element Solution of the Eddy Current Problem References Electromagnetic Scattering Analysis The Electromagnetic Wave Equations Complex Phasor Form of the Wave Equations Two-Dimensional Scattering from a Perfectly Conducting Cylinder of Arbitrary Cross-Section 154
5 X CONTENTS 6.4 Solution by the Indirect Boundary Element Method Constant Element Case Linear Elements Case Numerical Example References 162 PART II: ANALYSIS OF THIN WIRE ANTENNAS AND SCATTERERS Wire Antennas and Scatterers: General Considerations Frequency Domain Thin Wire Integral Equations Time Domain Thin Wire Integral Equations Modeling in the Frequency and Time Domain: Computational Aspects References Wire Antennas and Scatterers: Frequency Domain Analysis Thin Wires in Free Space Single Straight Wire in Free Space Boundary Element Solution of Thin Wire Integral Equation Calculation of the Radiated Electric Field and the Input Impedance of the Wire Numerical Results for Thin Wire in Free Space Coated Thin Wire Antenna in Free Space The Near Field of a Coated Thin Wire Antenna Boundary Element Procedures for Coated Wires Numerical Results for Coated Wire Thin Wire Loop Antenna Boundary Element Solution of Loop Antenna Integral Equation Numerical Results for a Loop Antenna Thin Wire Array in Free Space: Horizontal Arrangement Boundary Element Analysis of Horizontal Antenna Array Radiated Electric Field of the Wire Array 201
6 CONTENTS xi Numerical Results for Horizontal Wire Array Boundary Element Analysis of Vertical Antenna Array: Modeling of Radio Base Station Antennas Numerical Procedures for Vertical Array Numerical Results Thin Wires Above a Lossy Half-Space Single Straight Wire Above a Dissipative Half-Space Loaded Antenna Above a Dissipative Half-Space Electric Field and the Input Impedance of a Single Wire Above a Half-Space Boundary Element Analysis for Single Wire Above a Real Ground Treatment of Sommerfeld Integrals Calculation of Electric Field and Input Impedance Numerical Results for a Single Wire Above a Real Ground Multiple Straight Wire Antennas Over a Lossy Half-Space Electric Field of a Wire Array Above a Lossy Half-Space Boundary Element Analysis of Wire Array Above a Lossy Ground Near-Field Calculation for Wires Above Half-Space Computational Examples for Wires Above a Lossy Half-Space References Wire Antennas and Scatterers: Time Domain Analysis Thin Wires in Free Space Single Wire in Free Space Single Wire Far Field Loaded Straight Thin Wire in Free Space Two Coupled Identical Wires in Free Space Measures for Postprocessing of Transient Response 263
7 XII CONTENTS Computational Procedures for Thin Wires in Free Space Numerical Results for Thin Wires in Free Space Thin Wires in a Presence of a Two-Media Configuration Single Straight Wire Above a Real Ground Far Field Equations Loaded Straight Thin Wire Above a Lossy Half-Space Two Coupled Horizontal Wires in a Two Media Configuration Thin Wire Array Above a Real Ground Computational Procedures for Horizontal Wires Above a Dielectric Half-Space Computational Examples References 333 PART III: COMPUTATIONAL MODELS IN ELECTROMAGNETIC COMPATIBILITY Transmission Lines of Finite Length: General Considerations Transmission Line Theory Method Antenna Models of the Transmission Lines Above-Ground Transmission Lines Below-Ground Transmission Lines References Electromagnetic Field Coupling to Overhead Lines: Frequency Domain and Time Domain Analysis Frequency Domain Analysis: Derivation of Generalized Telegrapher's Equations Frequency Domain Computational Results Single Wire Above an Imperfect Ground Multiple Wire Transmission Line Above an Imperfect Ground Time Domain Analysis Time Domain Computational Examples 359
8 xiii Single Wire Transmission Line Two Wire Transmission Line Three Wire Transmission Line References The Electromagnetic Field Coupling to Buried Cables: Frequency- and Time-Domain Analysis The Frequency-Domain Approach Formulation in the Frequency Domain Numerical Solution of the Integral Equation The Calculation of Transient Response Numerical Results Time-Domain Approach Formulation in the Time Domain Time-Domain Energy Measures Time-Domain Numerical Solution Procedures Computational Examples References Simple Grounding Systems Vertical Grounding Electrode Integral Equation Formulation for the Vertical Grounding Electrode The Evaluation of the Input Impedance Spectrum Numerical Procedures for Vertical Grounding Electrode Calculation of the Transient Impedance Numerical Results Horizontal Grounding Electrode Integral Equation Formulation for the Horizontal Electrode The Evaluation of the Input Impedance Spectrum Numerical Procedures for Horizontal Electrode The Transient Impedance Calculation Numerical Results Transmission Line Method Versus Antenna Theory Approach Transmission Line Method (TLM) Approach to Modeling of Horizontal Grounding Electrode 438
9 CONTENTS Computational Examples Measures for Quantifying the Transient Response of Grounding Electrodes Transient Response Assessment Measures for Quantifying the Transient Response Computational Examples References Human Exposure to Electromagnetic Fields Environmental Risk of Electromagnetic Fields: General Considerations Nonionizing and Ionizing Radiation Electrosmog or Radiation Pollution at Low and High Frequencies The Effects of Low Frequency Fields The Effects of High Frequency Fields Remarks on Electromagnetic Fields and Related Possible Hazard to Humans Assessment of Human Exposure to Electromagnetic Fields: Frequency and Time Domain Approach Frequency Domain Cylindrical Antenna Model Realistic Models of the Human Body for ELF Exposures Human Exposure to Transient Electromagnetic Fields Human Exposure to Extremely Low Frequency (ELF) Electromagnetic Fields Parasitic Antenna Representation of the Human Body Realistic Modeling of the Human Body Exposure of Humans to Transient Radiation: Cylindrical Model of the Human Body Time Domain Model of the Human Body Measures of the Transient Response References 489
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