EMC ANALYSIS METHODS AND
COMPUTATIONAL MODELS
by
Dr. Frederick M. Tesche
EMC Consultant
Dallas, Texas, USA
 
Prof. Michel Ianoz
Ecole Polytechnique Federale de Lausanne
Lausanne, Switzerland
 
Dr. Torbjörn Karlsson
EMICON
Linköping, Sweden

1997, John Wiley & Sons, Inc
ISBN 0-471-15573-X


TABLE OF CONTENTS Chapters:

1. INTRODUCTION TO MODELING AND EMC

2. SYSTEM DECOMPOSITION FOR EMC MODELING

3. LUMPED-PARAMETER CIRCUIT MODELS

4. RADIATION MODELS FOR WIRE ANTENNAS

5. RADIATION, DIFFRACTION AND SCATTERING MODELS FOR APER

6. TRANSMISSION LINE THEORY

7. FIELD COUPLING USING TRANSMISSION LINE THEORY

8. EFFECTS OF A LOSSY GROUND ON TRANSMISSION LINES

9. SHIELDED CABLES

10. SHIELDING

PREFACE

ACKNOWLEDGMENTS

LIST OF ACRONYMS

PART 1 -- PRELIMINARIES

1. INTRODUCTION TO MODELING AND EMC

1.1 THE CONCEPT OF MODELING

1.2 VALIDATION OF MODELS

1.2.1 Example of Experimental Model Validation

1.2.2 Model Validation Using Non-Experimental Methods

1.3 BUILDING MODELS IN ELECTROMAGNETICS

1.4 EMC MODELING: A HISTORICAL OVERVIEW

1.5 CONSIDERATIONS FOR EMC MODELING

1.5.1 Classification of EMC Problems

1.5.2 EMC Problems Amenable to Modeling

1.5.3 Types of Signals in EMC Models

1.5.3.1 Evaluation of the Frequency Spectra 1.5.4 Limits of Modeling

1.6 WHO IS USING MODELING AND TO WHOM IS MODELING USEFUL

CHAPTER 1 REFERENCES

PROBLEMS FOR CHAPTER 1

2. SYSTEM DECOMPOSITION FOR EMC MODELING 2.1 APPLICATION OF ANALYTICAL METHODS IN EMC

2.1.1 System Design Phase

2.1.2 System Construction Phase

2.1.3 EMC Verification

2.1.3.1 Immunity Testing

2.1.3.2 Emission Testing

2.1.4 Summary of the Use of Analytical Models

2.2 TOPOLOGICAL DESCRIPTION OF SYSTEMS

2.2.1 Electromagnetic Topology

2.2.1.1 Topological Diagram

2.2.1.2 Electromagnetic Energy Points of Entry

2.2.1.3 EMC Design

2.2.2 Electromagnetic Interaction with the System 2.2.2.1.1 Interaction Sequence Diagram 2.2.3 Generalized EMC Design Principles Based on EM Topology

2.3 MODELING ACCURACY

2.3.1 Errors Inherent in the Analysis

2.3.2 Balanced Accuracy of Analysis

CHAPTER 2 REFERENCES

PROBLEMS FOR CHAPTER 2

PART 2 -- LOW-FREQUENCY CIRCUIT MODELS

3. LUMPED-PARAMETER CIRCUIT MODELS

3.1 INTRODUCTION

3.2 CONDUCTED DISTURBANCES IN CIRCUITS

3.2.1 Thévenin and Norton Representations

3.2.2 Models for Passive Two-Port Circuits

3.2.2.1 Open-Circuit Impedance Parameters

3.2.2.2 Short-circuit Admittance Parameters

3.2.2.3 Chain Parameters

3.2.2.4 Two-Port Parameter Relationships

3.2.2.5 Other Two-Port Representations

3.2.3 Two-Port Models for Circuits with Sources

3.2.4 Treatment of Multiport Circuits

3.2.5 Example of Conducted Disturbances in Electrical Power Systems

3.2.5.1 Generation of Harmonic Currents

3.2.5.2 Determination of the Mains Impedance

3.2.5.3 Estimation of the Harmonic Current Source

3.3 DISTURBANCES IN CIRCUITS INDUCED BY ELECTROMAGNETIC FIELDS

3.3.1 Magnetic Field Coupling

3.3.1.1 Weak Coupling Approximations

3.3.1.2 Calculation of Mutual and Self Inductances

3.3.2 Electric Field Coupling 3.3.2.1 Weak Coupling Approximations

3.3.2.2 Calculation of Mutual and Self Capacitances

3.3.3 General Field Coupling at Low Frequencies 3.3.3.1 Example: Cross-Talk Between Two Parallel Traces on a Printed Circuit Board 3.3.4 General Methods of Reducing Low-Frequency Interference

3.3.5 Specific Measures To Reduce Capacitive Coupling

3.3.5.1 Effect of a Cylindrical Shield Around a Conductor

3.3.5.2 Discussion

3.3.6 Specific Measures To Reduce Inductive Coupling

3.4 DISTURBANCES CAUSED BY COMMON GROUND RETURNS

3.5 EXTENSION OF CIRCUIT MODELING TO HIGH FREQUENCIES

CHAPTER 3 REFERENCES

PROBLEMS FOR CHAPTER 3

PART 3 -- HIGH FREQUENCY AND BROADBAND COUPLING MODELS

4. RADIATION MODELS FOR WIRE ANTENNAS

4.1 INTRODUCTION

4.2 RADIATION OF ELECTROMAGNETIC FIELDS IN THE FREQUENCY DOMAIN

4.2.1 Overview

4.2.2 Radiation from Elementary Sources

4.2.2.1 Electric Dipole

4.2.2.2 Magnetic Dipole

4.2.3 Radiation from Extended Sources 4.2.3.1 Center-Fed Wire Antenna

4.2.3.2 Integral Equation for the Wire Antenna

4.2.3.2.1 Solution by the Method of Moments

4.2.3.2.2 Approximate Solution for the Antenna problem

4.2.4 Dipole Radiation in the Presence of Other Bodies 4.2.4.1 Electric Dipoles Over a Perfect Ground

4.2.4.2 Electric Dipoles in a Parallel-Plate Region

4.2.4.3 Electric Dipoles in a Cavity

4.2.4.3.1 Solution by the Method of Images

4.2.4.3.2 Eigenmode Solution

4.2.4.4 Electric Dipoles near a Sphere

4.2.4.5 Electric Dipoles over an Imperfectly Conducting Earth

4.2.5 Evaluation of Magnetic Field Components

4.3 RECEPTION AND SCATTERING OF ELECTROMAGNETIC FIELDS IN THE FRCY DOMAIN

4.3.1 General Considerations

4.3.2 Approximate Solution for the Thin Wire

4.3.2.1 Determination of the Induced Current

4.3.2.2 Scattered Field

4.4 ELECTRIC-FIELD INTEGRAL EQUATIONS IN THE TIME-DOMAIN

4.4.1 Overview

4.4.2 The Integrodifferential Equation

4.4.3 Extension to a Wire over a Lossy the Ground

4.4.4 Numerical Solution for the EFIE for Thin Wires in the Time Domain

4.5 SINGULARITY EXPANSION METHOD

4.5.1 Background

4.5.2 Mathematical Description of SEM

4.5.3 SEM Representation of the Antenna Current

4.5.4 SEM Representation of the Scattering Current

4.5.5 SEM Representation of the Radiated Fields

4.5.6 SEM Representation of Scattered Fields

4.5.7 Example of SEM Applied to the Approximate Antenna Analysis

4.5.7.1 Induced Current for the Antenna Problem

4.5.7.2 Induced Current for the Scattering Problem

CHAPTER 4 REFERENCES

PROBLEMS FOR CHAPTER 4

5. RADIATION, DIFFRACTION AND SCATTERING MODELS FOR APER 5.1 INTRODUCTION

5.2 EM FIELD PENETRATION THROUGH APERTURES

5.2.1 Scalar Diffraction Theory

5.2.1.1 Kirchoff Approximation

5.2.1.2 Dirichlet Solution

5.2.1.3 Neumann Solution

5.2.1.4 Discussion of the Scalar Solutions

5.2.1.4.1 Rectangular Aperture

5.2.1.4.2 Circular Aperture

5.2.2 General Vector Field Diffraction 5.2.2.1 Fundamentals

5.2.2.2 Application to the Aperture Penetration Problem

5.2.3 Far-Field Vector Field Diffraction 5.2.3.1 Example for a Rectangular Aperture 5.2.4 The Aperture Integral Equation 5.2.4.1 Example of Aperture Field Calculation 5.2.5 Equivalent Area of an Aperture

5.3 RADIATION FROM EXTENDED ANTENNAS

5.4 THE LOW FREQUENCY APPROXIMATION

5.4.1 Dipole Moments

5.4.2 Aperture Polarizabilities

5.4.2.1 Corrections of the Polarizabilities for Aperture Loading 5.5 WIDEBAND AND TRANSIENT RESPONSES OF APERTURES

5.5.1 Wideband Responses

5.5.2 Direct Time-Domain Calculations

CHAPTER 5 REFERENCES

PROBLEMS FOR CHAPTER 5

PART 4 -- TRANSMISSION LINE MODELS

6. TRANSMISSION LINE THEORY 6.1 OVERVIEW OF TRANSMISSION LINE MODELS

6.1.1 Lumped and Distributed Circuit Parameters

6.1.2 Lumped and Distributed Excitations

6.1.2.1 Examples of System Excitation 6.1.3 Two-Conductor and Multiconductor Systems

6.1.4 Transmission Line and Antenna Mode Responses

6.1.5 Telegrapher's Equations for a Two-Conductor System

6.1.5.1 Evaluation of the Line Parameters 6.2 FREQUENCY DOMAIN RESPONSES

6.2.1 Solution of the Telegrapher's Equations for a Two-Conductor Line

6.2.1.1 Chain Parameter Representation of a Two-Wire Line

6.2.1.2 Other Two-Port Representations for the Two-Wire Line

6.2.1.3 Applications of Two-Port Representations

6.2.1.4 The P and T Equivalent Circuits of the Two-Wire Line

6.2.2 Lumped Source Excitation of Transmission Lines

6.2.3 Terminated Lines: The Voltage Reflection Coefficient

6.2.4 General Solution for a Terminated Line

6.2.4.1 Example of Line Response for a Voltage Source Excitation 6.2.5 Load Responses for a Finite Line 6.2.5.1 BLT Equation

6.2.5.2 Example of Frequency-Domain Voltage Response of a Line

6.2.5.3 Validation of the Transmission Line Models

6.2.6 Multiconductor Transmission Lines 6.2.6.1 Impedance and Admittance Matrices

6.2.6.2 Natural Propagation Modes

6.2.6.3 Diagonalization of the [P] and [R] Matrices

6.2.6.4 Modal Voltages and Currents

6.2.6.5 Solution of the Modal Equations

6.2.6.6 Calculation of the Propagation Matrix and Diagonalization Matrix Elements

6.2.6.7 Open-Circuit Voltage of a Semi-Infinite Multiconductor Line Excited by a Voltage22

6.2.6.8 Simplified Modeling by the Equal-Velocity Assumption

6.2.7 BLT Equation for Multiconductor Lines 6.2.7.1 Simplifications of the BLT Equation 6.2.8 Chain Parameters for a Multiconductor Line

6.2.9 Example of the Use of Multiconductor Line Models

6.3 TIME-DOMAIN TRANSMISSION LINE RESPONSES

6.3.1 Time-Harmonic Excitation

6.3.2 Nonsinusoidal Traveling Waves

6.3.3 Analytical Transformation from the Frequency Domain to the Time Domain

6.3.4 Numerical Transformation of the Solution from the Frequency to the Time Domain

6.3.5 Numerical Solution of the Telegrapher’s Equations in the Time Domain

6.3.6 Inductive and Capacitive Terminations in the Time Domain

6.3.7 Bergeron's Graphical Solution in the Time Domain

6.3.7.1 Principle of Bergeron’s Method

6.3.7.2 Numerical Application of Bergeron's Method

6.3.7.3 Solution of the Nodal Matrix Equation

6.3.7.4 Example: Transient State of a Circuit after Closing Two Interrupters

6.3.8 The Electromagnetic Transients Program 6.3.8.1 Transmission Line Response Using EMTP

6.3.8.2 Modeling of a Test Installation with Two Parallel Lines

6.4 DETERMINATION OF LINE INDUCTANCE PARAMETERS

6.4.1 Inductance Measurement

6.4.2 Analytical Inductance Evaluation

6.4.2.1 Geometrical Mean Distance Between Two Circuits

6.4.2.2 Mutual Inductance per Unit Length

6.4.2.3 Self Inductance per Unit Length

6.4.2.4 Mutual and Self-Inductances of Lines with the Earth as a Return Conductor

6.4.2.4.1 Mutual and Self-Inductances of Lines Over Perfectly Conducting Ground52
6.5 DETERMINATION OF LINE CAPACITANCE PARAMETERS

6.5.1 Measurement of the Capacitance Parameters

6.5.2 Analytical Capacitance Evaluation

6.5.2.1 Partial Capacitances

6.5.2.2 Static Capacitances

6.5.2.2.1 Sign of the Partial Capacitances
6.5.3 Calculation of the Static Capacitances 6.5.3.1 Conductors in a Homogeneous Medium over the Ground

6.5.3.2 Transmission Lines in Nonhomogeneous Media

6.5.3.3 Use of the Finite Element Method to Calculate Partial Capacitances

6.5.3.4 Integral Equation Evaluation of the Per-Unit-Length Capacitance Matrix

6.5.3.5 Capacitance Calculation Using Inductance Values

CHAPTER 6 REFERENCES

PROBLEMS FOR CHAPTER 6

7. FIELD COUPLING USING TRANSMISSION LINE THEORY 7.1 INTRODUCTION

7.2 TWO-WIRE TRANSMISSION LINE

7.2.1 Derivation of the Telegrapher’s Equations with an External Excitation

7.2.1.1 First Telegrapher’s Equation

7.2.1.2 Second Telegrapher’s Equation

7.2.1.3 Modification of the Telegrapher’s Equations for a Finitely Conducting Wire

7.2.1.4 Modification for a Lossy Medium Surrounding the Line

7.2.2 Alternate Forms of the Telegrapher’s Equations 7.2.2.1 Total Voltage Formulation

7.2.2.2 Scattered Voltage Formulation

7.2.2.3 Numerical Example of the Two Formulations

7.2.3 Solution for the Line Current and Voltage

7.2.4 Solution for the Load Currents and Voltages: The BLT Equation

7.2.5 Load Responses for Plane-Wave Excitation

7.2.6 Examples of Line Responses

7.2.6.1 Frequency Domain Responses

7.2.6.2 Transient Response

7.3 SINGLE LINE OVER A PERFECTLY CONDUCTING GROUND PLANE

7.3.1 Derivation of the Telegrapher’s Equations

7.3.1.1 Total Voltage Formulation

7.3.1.2 Scattered Voltage Formulation

7.3.1.3 Comments on the Line Excitation from an EM Scattering Viewpoint

7.3.1.4 Modifications of the Telegrapher’s Equations

7.3.2 Solution to the Telegrapher’s Equations for Load Responses 7.3.2.1 BLT Sources 7.3.3 Load Responses for Plane-Wave Excitation 7.3.3.1 Comparison with the Two-Wire Results 7.3.4 Validation of the Coupling

7.3.5 Load Response for a Non-Plane-Wave Excitation

7.4 TREATMENT OF HIGHLY RESONANT STRUCTURES

7.4.1 Single-Wire Line

7.4.1.1 Numerical Example

7.4.1.2 Expansion of the BLT Resonance Matrix

7.4.2 Extension to Multiconductor Lines

7.5 RADIATION FROM TRANSMISSION LINES

7.5.1 Reciprocity Theorem

7.5.2 Radiating Transmission Line

7.5.3 Example of the Radiation from a Transmission Line

7.6 TRANSMISSION NETWORKS

7.6.1 Network Analysis by Thévenin Transformations

7.6.1.1 Example of a Network Response Using Thévenin Transformations 7.6.2 Development of the Network BLT Equation

7.7 TRANSMISSION LINES WITH NONLINEAR LOADS

7.7.1 Volterra Integral Equation

7.7.2 Example of a Single Transmission Line with a Nonlinear Load Impedance

CHAPTER 7 REFERENCES

PROBLEMS FOR CHAPTER 7

8. EFFECTS OF A LOSSY GROUND ON TRANSMISSION LINES 8.1 INTRODUCTION

8.2 DERIVATION OF THE TELEGRAPHER EQUATIONS

8.2.1 Total Voltage Formulation

8.2.1.1 First Telegrapher’s Equation

8.2.1.2 Second Telegrapher’s Equation

8.2.2 Scattered Voltage Formulation

8.2.3 Termination Conditions

8.2.3.1 V-I Relationships

8.2.3.2 Ground Impedance

8.2.4 Solution of the Telegrapher’s Equations

8.3 PER-UNIT-LENGTH LINE PARAMETERS

8.3.1 Equivalent Circuit for the Line

8.3.2 Frequency-Domain Representations for the Ground Impedance

8.3.3 Time-Domain Representation of the Ground Impedance

8.4 REFLECTED AND TRANSMITTED PLANE-WAVE FIELDS

8.4.1 Plane-Wave Reflection and Transmission from the Earth

8.4.1.1 General Expressions for the Fields

8.4.1.2 Excitation Fields for a Transmission Line

8.4.2 Transient Field Reflected from the Ground 8.4.2.1 Transient Fields Evaluated by the FFT

8.4.2.2 Direct Evaluation of the Transient Reflected E-Field

8.5 EXAMPLES OF ABOVEGROUND TRANSMISSION LINE RESPONSES

8.5.1 Variations in Earth Conductivity

8.5.2 Variations with Angle of Incidence

8.5.3 Variations with Line Height

8.6 BURIED CABLES

8.6.1 Summary of Rigorous Solution

8.6.1.1 Integral Equation

8.6.1.2 Soil Impedance

8.6.1.3 Cable Impedance

8.6.1.4 Solution for the Current

8.6.2 Transmission Line Approximation

8.6.3 Additional Simplifications to the TL Solution

8.6.4 Example of Current Responses on an Infinite Buried Cable

8.6.5 Application to Buried Lines of Finite Length

CHAPTER 8 REFERENCES

PROBLEMS FOR CHAPTER 8

PART 5 -- SHIELDING MODELS

9. SHIELDED CABLES 9.1 INTRODUCTION

9.2 FUNDAMENTALS OF CABLE SHIELD COUPLING

9.2.1 Definitions of Transfer Impedance and Transfer Admittance

9.2.2 Relative Importance of Z't and Y't

9.3 EM COUPLING THROUGH A SOLID TUBULAR SHIELD

9.3.1 Transfer Impedance

9.3.2 Transfer Admittance

9.4 MODELS FOR BRAIDED SHIELDS

9.4.1 EM Field Penetration and Diffraction into Braided Shields

9.4.2 Single Aperture Excitation

9.4.3 Multiple Apertures

9.4.4 Expressions for the Aperture Polarizabilities

9.4.5 Shield Transfer Characteristics in Terms of Braid Weave Parameters

9.4.5.1 Transfer Impedance

9.4.5.2 Transfer Admittance

9.4.5.3 Dielectric Filling in the Cable

9.4.5.4 Comparison with Measurements

9.4.6 Improved Expressions for the Transfer Impedance of Braided Shields 9.4.6.1 Tyni’s Model

9.4.6.2 Demoulin’s model

9.4.6.3 Kley’s model

9.4.6.4 Comparison of Demoulin's and Kley's models

9.4.7 Effect of an Axial Magnetic Field Component

9.4.8 Alternate Expression for the Transfer Admittance of Braided Shields

9.5 CALCULATED RESPONSES OF A BRAIDED CABLE

9.5.1 External Transmission Line

9.5.2 Internal Excitation Sources

9.5.3 Internal Load Responses

9.5.4 Numerical Example of a Shielded Cable System

9.6 CABLES WITH SHIELD INTERRUPTIONS

9.6.1 Introduction

9.6.2 Cable Connectors

9.6.3 Pigtail Terminations

9.6.4 Discontinuous Shields

9.6.5 Example of an Interrupted Cable Shield

CHAPTER 9 REFERENCES

PROBLEMS FOR CHAPTER 9

10. SHIELDING 10.1 INTRODUCTION

10.2 GENERALIZED SHIELD CONCEPT

10.3 SHIELDING MECHANISMS

10.3.1 Shielding of Static Fields

10.3.1.1 Electrical Shielding

10.3.1.2 Magnetostatic Shielding

10.3.2 Shielding of Time Varying Fields: Eddy Current Shielding 10.3.2.1 General Concepts

10.3.2.2 Skin Effect and Skin Depth

10.3.2.3 Plane-Wave Shielding by an Infinite Metal Plate

10.3.2.4 Plane-Wave Shielding by Two Infinite Parallel Plates

10.3.2.5 Plane-Wave Shielding by A Conducting Mesh

10.3.3 Summary of Shielding Dependence on Frequency

10.4 VOLUMETRIC SHIELDS

10.4.1 The Closed, Homogeneous Metal Shield

10.4.1.1 Shielding of Time-Harmonic Fields 10.4.1.1.1 Evaluation of the H-Field Shielding Effectiveness

10.4.1.1.2 Limitations of the Shielding Expressions

10.4.1.1.3 Examples of the H-Field Shielding Effectiveness

10.4.1.1.4 Determination of the E-Field Shielding Effectiveness

10.4.1.2 Shielding of Transient Electromagnetic Fields
10.4.2 Closed Metallic Mesh Shield 10.4.2.1 Induced Responses Within a Mesh-Protected Shield 10.5 SHIELDING OF NON-PLANE-WAVE FIELDS

10.5.1 Overview of Near-Field Shielding

10.5.2 Shielding Between Two Circular Loops

CHAPTER 10 REFERENCES

PROBLEMS FOR CHAPTER 10

Appendix A: Tables of Physical Constants

Appendix B: Vector Analysis and Functions

Appendix C: Per-Unit-Length Line Parameters

Appendix D: Grounding Resistance Parameters

Appendix E: Coaxial Cable and Connector Data

Appendix F: Computer Software

F1 NULINE Transmission Line Code

F2 RISER Transmission Line Coupling Code

F3 LTLINE Transmission Line Code

F4 TOTALFLD Field Code

Index

Author Biographies