Surface Impedance Boundary Conditions: A Comprehensive Approach / Edition 1

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Surface Impedance Boundary Conditions is perhaps the first effort to formalize the concept of SIBCs or to extend them to higher orders by providing a comprehensive, consistent, and thorough approach to the subject.

The product of nearly 12 years of research on surface impedance, this book takes the mystery out of the largely overlooked SIBCs. It provides an understanding that will help practitioners select, use, and develop these efficient modeling tools for their own applications. Use of SIBCs has often been viewed as an esoteric issue, and they have been applied in a very limited way, incorporated in computation as an ad hoc means of simplifying the treatment for specific problems.

Apply a Surface Impedance "Toolbox" to Develop SIBCs for Any Application

The book not only outlines the need for SIBC but also offers a simple, systematic method for constructing SIBCs of any order based on a perturbation approach. The formulation of SIBCs within common numerical techniques is discussed in detail and elucidated with specific examples.

Since SIBCs are often shunned because their implementation usually requires extensive modification of existing software, the authors have mitigated this problem by developing their own SIBCs, which can be incorporated within existing software without system modification.

The authors also present:

Conditions of applicability and errors to be expected from SIBC inclusion

Analysis of theoretical arguments and mathematical relationships

Well-known numerical techniques and formulations of SIBCs

A practical set of guidelines for evaluating SIBC feasibility and maximum errors its use will produce

A careful mix of theory and practical aspects, this is an excellent tool to help anyone acquire a solid grasp of SIBCs and maximize their implementation potential.

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Product Details

  • ISBN-13: 9781420044898
  • Publisher: CRC Press
  • Publication date: 9/15/2009
  • Edition number: 1
  • Pages: 410
  • Product dimensions: 6.30 (w) x 9.30 (h) x 1.10 (d)

Meet the Author

Sergey Yuferev was born in St. Petersburg, Russia, in 1964. He received his MSc in computational fluid mechanics from St. Petersburg Technical University, St. Petersburg, in 1987, and his Ph.D. in computational electromagnetic from the A.F. Ioffe Institute, St. Petersburg, in 1992. From 1987 to 1998, he worked at with the Dense Plasma Dynamics Laboratory, A.F. Ioffe Institute. From 1999 to 2000, he was a visiting associate professor at the University of Akron, Akron, Ohio. Since 2000, he has been with the Nokia Corporation, Tampere, Finland. His current research interests include numerical and analytical methods of computational electromagnetics and their application to electromagnetic compatibility and electromagnetic interference problems of mobile phones.

Nathan Ida is currently a distinguished professor of electrical and computer engineering at the University of Akron, Akron, Ohio. He teaches electromagnetics, antenna theory, electromagnetic compatibility, sensing and actuation, and computational methods and algorithms. His current research interests include numerical modeling of electromagnetic fields, electromagnetic wave propagation, theoretical issues in computation, and nondestructive testing of materials at low and microwave frequencies as well as in communications, especially, in low-power remote control and wireless sensing. He has published extensively on electromagnetic field computation, parallel and vector algorithms and computation, nondestructive testing of materials, surface impedance boundary conditions, and other topics. He is the author of three books and co-author of a fourth. Dr. Ida is a fellow of the IEEE and the American Society of Nondestructive Testing.

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Table of Contents

Introduction xv

1 Classical Surface Impedance Boundary Conditions 1

1.1 Introduction 1

1.2 Skin Effect Approximation 2

1.3 SIBCs of the Order of Leontovich's Approximation 8

1.4 High-Order SIBCs 10

1.4.1 Mitzner's Approach 10

1.5 Rytov's Approach 17

1.5.1 General 17

1.5.2 Calculation of the Field inside the Conductor 18

1.5.3 Boundary Conditions at the Conductor Surface 21

1.5.4 Particular Case of a Planar Interface 22

1.5.5 Notes on Applicability of the Method 23

References 25

2 General Perturbation Approach to Derivation of Surface Impedance Boundary Conditions 27

2.1 Introduction 27

2.2 Local Coordinates 28

2.3 Perturbation Technique 35

2.4 Tangential Components 41

2.5 Normal Components 45

2.6 Normal Derivatives 49

2.7 Components of the Curl Operator 52

2.8 Surface Impedance "Toolbox" Concept 57

2.9 Numerical Example 65

Appendix 2.A.1 Calculation of 73

References 76

3 SIBCs in Terms of Various Formalisms 79

3.1 Introduction 79

3.2 Basic Equations 79

3.3 Electric Field-Magnetic Field Formalism 80

3.4 Magnetic Scalar Potential Formalism 89

3.5 Magnetic Vector Potential Formalism 95

3.6 Common Representation of Various SIBCs Using a Surface Impedance Function 102

3.7 Surface Impedance near Corners and Edges 105

References 113

4 Calculation of the Electromagnetic Field Characteristics in the Conductor's Skin Layer 115

4.1 Introduction 115

4.2 Distributions across the Skin Layer 116

4.3 Resistance and Internal Inductance 127

4.4 Forces Acting on the Conductor 131

5 Derivation of SIBCs for Nonlinear and Nonhomogeneous Problems 135

5.1 Introduction 135

5.2 Coupled Electromagnetic-Thermal Problems 136

5.3 Magnetic Materials 143

5.4 Nonhomogeneous Conductors 156

5.4.1 PEC-Backed Lossy Dielectric Layer 156

5.4.2 Two-Layer Conducting Structure 159

References 165

6 Implementation of SIBCs for the Boundary Integral Equation Method: Low-Frequency Problems 167

6.1 Introduction 167

6.2 Two-Dimensional Problems 169

6.2.1 E-H Formalism 169

6.2.2 A-K Formalism 176

6.2.3 Common Representation 182

6.3 Three-Dimensional Problems 187

6.4 Properties of the Surface Impedance Function 193

6.5 Boundary Element Formulations for Two- and Three-Dimensional Problems in Invariant Form 195

6.6 Numerical Examples 204

6.7 Quasi-Three-Dimensional Integro-Differential Formulation for Symmetric Systems of Conductors 209

References 218

7 Implementation of SIBCs for the Boundary Integral Equation Method: High-Frequency Problems 221

7.1 Introduction 221

7.2 Integral Representations of High-Frequency Electromagnetic Fields 222

7.3 SIBCs for Lossy Dielectrics 227

7.4 Direct Implementation of SIBCs into the Surface Integral Equations 232

7.5 Implementation Using the Perturbation Technique 237

7.6 Numerical Example 248

Appendix 7.A.1 Efficient Evaluation of Time Convolution Integrals 255

References 260

8 Implementation of SIBCs for Volume Discretization Methods 263

8.1 Introduction 263

8.2 Statement of the Problem 264

8.3 Finite-Difference Time-Domain Method 265

8.4 Finite Integration Technique 280

8.5 Finite-Element Method 290

Appendix 8.A.1 Basics of Contour-Path FDTD Method 294

References 296

9 Application and Experimental Validation of the SIBC Concept 299

9.1 Introduction 299

9.2 Selection of the Surface Impedance Boundary Conditions for a Given Problem 299

9.2.1 Characteristic Values of the Problem 300

9.2.2 Asymptotic Expansions 301

9.2.3 Methodology 302

9.3 Experimental Validation of SIBCs 315

9.3.1 Physical Configuration 316

9.3.2 Example: Reconstruction of Currents from Measured Magnetic Fields 322

9.3.3 Example: Calculation of p.u.l. Parameters in Multiconductor Transmission Lines 328

References 335

Appendix A Review of Numerical Methods 337

A.1 Introduction 337

A.2 Finite-Element Method 338

A.2.1 Physical Equations 339

A.2.2 Discretization 341

A.2.3 Approximation 342

A.2.4 Minimization 345

A.2.5 Solution 352

A.2.6 Postprocessing 353

A.3 Finite-Difference Time-Domain Method 353

A.4 Boundary-Element Method 356

References 362

Index 367

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