Surface Impedance Boundary Conditions is perhaps the first effort to formalize the concept of SIBC or to extend it 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 SIBC. It provides an understanding that will help practitioners select, use, and develop these efficient modeling tools for their own applications. Use of SIBC 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 SIBC of any order based on a perturbation approach. The formulation of the SIBC within common numerical techniquessuch as the boundary integral equations method, the finite element method, and the finite difference methodis discussed in detail and elucidated with specific examples. Since SIBC are often shunned because their implementation usually requires extensive modification of existing software, the authors have mitigated this problem by developing 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 SIBC
A practical set of guidelines for evaluating SIBC feasibility and maximum errors their use will produce
A careful mix of theory and practical aspects, this is an excellent tool to help anyone acquire a solid grasp of SIBC and maximize their implementation potential.
| Introduction |
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xv | |
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Classical Surface Impedance Boundary Conditions |
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1 | (26) |
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1 | (1) |
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Skin Effect Approximation |
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2 | (6) |
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SIBCs of the Order of Leontovich's Approximation |
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8 | (2) |
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10 | (7) |
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10 | (7) |
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17 | (10) |
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17 | (1) |
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Calculation of the Field inside the Conductor |
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18 | (3) |
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Boundary Conditions at the Conductor Surface |
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21 | (1) |
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Particular Case of a Planar Interface |
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22 | (1) |
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Notes on Applicability of the Method |
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23 | (2) |
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25 | (2) |
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General Perturbation Approach to Derivation of Surface Impedance Boundary Conditions |
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27 | (52) |
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27 | (1) |
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28 | (7) |
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35 | (6) |
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41 | (4) |
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45 | (4) |
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49 | (3) |
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Components of the Curl Operator |
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52 | (5) |
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Surface Impedance ``Toolbox'' Concept |
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57 | (8) |
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65 | (14) |
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Calculation of (f3)η, (g2)ξκ, and (g2)η |
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73 | (3) |
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76 | (3) |
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SIBCs in Terms of Various Formalisms |
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79 | (36) |
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79 | (1) |
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79 | (1) |
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Electric Field-Magnetic Field Formalism |
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80 | (9) |
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Magnetic Scalar Potential Formalism |
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89 | (6) |
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Magnetic Vector Potential Formalism |
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95 | (7) |
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Common Representation of Various SIBCs Using a Surface Impedance Function |
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102 | (3) |
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Surface Impedance near Corners and Edges |
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105 | (10) |
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113 | (2) |
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Calculation of the Electromagnetic Field Characteristics in the Conductor's Skin Layer |
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115 | (20) |
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115 | (1) |
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Distributions across the Skin Layer |
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116 | (11) |
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Resistance and Internal Inductance |
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127 | (4) |
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Forces Acting on the Conductor |
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131 | (4) |
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Derivation of SIBCs for Nonlinear and Nonhomogeneous Problems |
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135 | (32) |
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135 | (1) |
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Coupled Electromagnetic-Thermal Problems |
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136 | (7) |
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143 | (13) |
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Nonhomogeneous Conductors |
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156 | (11) |
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PEC-Backed Lossy Dielectric Layer |
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156 | (3) |
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Two-Layer Conducting Structure |
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159 | (6) |
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165 | (2) |
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Implementation of SIBCs for the Boundary Integral Equation Method: Low-Frequency Problems |
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167 | (54) |
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167 | (2) |
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169 | (18) |
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169 | (7) |
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176 | (6) |
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182 | (5) |
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Three-Dimensional Problems |
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187 | (6) |
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Properties of the Surface Impedance Function |
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193 | (2) |
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Boundary Element Formulations for Two-and Three-Dimensional Problems in Invariant Form |
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195 | (9) |
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204 | (5) |
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Quasi-Three-Dimensional Integro-Differential Formulation for Symmetric Systems of Conductors |
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209 | (12) |
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218 | (3) |
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Implementation of SIBCs for the Boundary Integral Equation Method: High-Frequency Problems |
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221 | (42) |
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221 | (1) |
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Integral Representations of High-Frequency Electromagnetic Fields |
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222 | (5) |
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SIBCs for Lossy Dielectrics |
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227 | (5) |
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Direct Implementation of SIBCs into the Surface Integral Equations |
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232 | (5) |
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Implementation Using the Perturbation Technique |
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237 | (11) |
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248 | (15) |
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Efficient Evaluation of Time Convolution Integrals |
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255 | (5) |
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260 | (3) |
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Implementation of SIBCs for Volume Discretization Methods |
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263 | (36) |
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263 | (1) |
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264 | (1) |
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Finite-Difference Time-Domain Method |
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265 | (15) |
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Finite Integration Technique |
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280 | (10) |
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290 | (9) |
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Basics of Contour-Path FDTD Method |
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294 | (2) |
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296 | (3) |
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Application and Experimental Validation of the SIBC Concept |
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299 | (38) |
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299 | (1) |
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Selection of the Surface Impedance Boundary Conditions for a Given Problem |
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299 | (16) |
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Characteristic Values of the Problem |
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300 | (1) |
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301 | (1) |
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302 | (13) |
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Experimental Validation of SIBCs |
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315 | (22) |
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316 | (6) |
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Example: Reconstruction of Currents from Measured Magnetic Fields |
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322 | (6) |
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Example: Calculation of p.u.1. Parameters in Multiconductor Transmission Lines |
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328 | (7) |
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335 | (2) |
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Appendix A: Review of Numerical Methods |
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337 | (30) |
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337 | (1) |
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338 | (15) |
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339 | (2) |
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341 | (1) |
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342 | (3) |
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345 | (7) |
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352 | (1) |
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353 | (1) |
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Finite-Difference Time-Domain Method |
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353 | (3) |
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356 | (11) |
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362 | (5) |
| Index |
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367 | |
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.
