Electromagnetic modeling of composite metallic and dielectric structures

This practical, new book provides a wide choice of analytical solutions to problems faced by antenna design engineers and researchers working in electromagnetic modeling. Based on leading-edge method-of-moments procedures, the book presents new theories and techniques that help professionals optimize performance in numerical analysis of composite metallic and dielectric structures in the complex frequency domain. For the first time, comparisons and new combinations of techniques bring the elements of flexibility, ease of implementation, accuracy, and efficiency into clear focus for all practitioners. A wide range of examples are given - from simple to complex - including scatterers, antennas and microwave circuits. Intricate models include TV UHF pannels, horn, parabolic, microstrip patch antennas, and many others.

Author Notes

Antonije Djordjevic earned his D.Sc. and M.Sc. in electromagnetic fields, and B.Sc. in electrical engineering at the University of Belgrade.

Djordevic is a professor at the School of Electrical Engineering, University of Belgrade.

050

1 Introduction	p. 1
1.1 MoM as a General Approach to Solving Electromagnetic-Field Problems	p. 2
1.2 MoM/SIE, MoM/VIE, and FEM	p. 4
1.3 Basic Classes of Composite Metallic and Dielectric Structures (Material Structures)	p. 6
1.4 Methods for the Analysis of Thin-Wire Structures	p. 8
1.5 Methods for the Analysis of Metallic Structures	p. 11
1.6 Methods for the Analysis of Composite Metallic and Dielectric Structures	p. 14
1.7 What Is New in This Book?	p. 15
1.8 Survey of Chapters	p. 18
References	p. 20
2 MoM	p. 27
2.1 Formulation of Deterministic-Field Problems	p. 27
2.2 Linear Operator Equation	p. 30
2.3 Solution of Integral Equations	p. 33
2.3.1 Approximation of Unknown Function	p. 33
2.3.2 Point-Matching Method	p. 35
2.3.3 Data Postprocessing	p. 36
2.3.4 Estimation of the Solution Quality	p. 39
2.3.5 Least-Squares Method	p. 43
2.3.6 Inner Product	p. 45
2.3.7 Rayleigh-Ritz Method	p. 47
2.3.8 Galerkin Method	p. 49
2.3.9 MoM	p. 54
2.3.10 Weighted Point-Matching Method	p. 55
2.3.11 Memory and Analysis-Time Requirements	p. 57
2.3.12 Choice of Test Procedure	p. 59
2.3.13 Choice of Basis Functions	p. 60
2.3.14 Adaptive Methods	p. 63
2.4 Solution of Differential Equations	p. 66
2.4.1 Approximation of Unknown Function	p. 66
2.4.2 FD Method	p. 70
2.4.3 Sparse Matrices	p. 73
2.4.4 Iterative Procedure	p. 75
2.4.5 FEM Via the Galerkin Method	p. 79
2.5 Choosing the Optimal Method	p. 82
2.6 Summary	p. 83
References	p. 84
3 Electromagnetic Theory	p. 87
3.1 Maxwell's Equations	p. 87
3.1.1 Maxwell's Equations in the Frequency Domain	p. 89
3.2 Retarded Potentials	p. 93
3.3 Field Vectors	p. 95
3.3.1 Basic Integral Expressions	p. 95
3.3.2 Alternative Expressions for the Electric Field	p. 97
3.3.3 Definition of L and K Operators	p. 100
3.3.4 Expressions for Fields Due to Surface Current	p. 100
3.3.5 Far-Field Expressions	p. 104
3.4 Volume Equivalence Principle	p. 105
3.5 Duality Relations Between Electric and Magnetic Quantities	p. 107
3.6 Boundary Conditions	p. 108
3.7 Formulation of the Basic Field Problem in the Frequency Domain	p. 113
3.8 Poynting Theorem	p. 115
3.9 Surface Equivalence Principle	p. 116
3.10 Uniqueness Theorem	p. 119
3.10.1 Single Region	p. 119
3.10.2 Multiple Region	p. 123
3.11 Summary	p. 125
References	p. 126
4 Field Integral Equations	p. 127
4.1 BIEs for Metallic Structures	p. 128
4.1.1 EFIEs and MFIEs	p. 132
4.1.2 Generalized Scalar Formulation of the EFIE and MFIE	p. 134
4.1.3 Equivalent Sources and EBCs	p. 136
4.1.4 Spurious Resonances	p. 139
4.1.5 AFIE	p. 143
4.1.6 CFIE	p. 144
4.1.7 Generalized Scalar Formulation of CFIE	p. 146
4.1.8 CSIE	p. 149
4.1.9 Thin-Plate Approximation	p. 151
4.1.10 Thin-Wire Approximation	p. 154
4.1.11 Hallen Equation	p. 158
4.1.12 IBC-IE	p. 160
4.1.13 Optimal Choice of BIEs for Analysis of Metallic Structures	p. 161
4.2 BIEs for Combined Metallic and Dielectric Structures	p. 162
4.2.1 EFIE, MFIE, and CFIE for Multiple-Region Problems	p. 167
4.2.2 CRIEs	p. 169
4.2.3 Muller Formulation	p. 170
4.2.4 PMCHW Formulation	p. 171
4.2.5 Thin Plate at an Interface Between Two Regions	p. 174
4.2.6 Optimal Choice of BIEs for Analysis of Multiple-Region Problems	p. 175
4.3 CIEs	p. 176
4.3.1 VIEs	p. 178
4.3.2 Metallic Surfaces with Distributed Loadings	p. 179
4.3.3 Wires with Distributed Loadings	p. 182
4.3.4 Wires with Concentrated Loadings	p. 185
4.4 Hybrid Methods	p. 188
4.4.1 Surface/Volume Integral Formulation	p. 188
4.4.2 MoM and FEM	p. 189
4.4.3 MoM and Green's-Function Techniques	p. 190
4.4.4 MoM and Asymptotic High-Frequency Techniques	p. 193
4.5 Summary	p. 196
References	p. 197
5 Geometrical Modeling	p. 203
5.1 Wire Structures	p. 204
5.1.1 Generalized Wires	p. 204
5.1.2 Approximation of Wires by Spline Curves	p. 205
5.1.3 Right Truncated Cones	p. 207
5.1.4 Piecewise Cylindrical (Conical) Approximation of Wires	p. 210
5.1.5 Equivalent Radius of Wire Curvature	p. 210
5.2 Metallic and Dielectric Surfaces	p. 214
5.2.1 Generalized Quadrilaterals and Triangles	p. 214
5.2.2 Unitary Vectors and Related Quantities	p. 217
5.2.3 Exact Modeling of Surfaces by Generalized Quadrilaterals	p. 218
5.2.4 Approximations of Surfaces by Spline Quadrilaterals	p. 219
5.2.5 Bilinear Surfaces and Flat Triangles	p. 221
5.2.6 Piecewise Almost-Flat Approximation of Surfaces	p. 223
5.2.7 Concept of Equivalent Radius for Surfaces	p. 224
5.3 Dielectric Volumes	p. 226
5.4 Wire-to-Plate Junctions and Related Structures	p. 229
5.4.1 Attachment Modes	p. 230
5.4.2 General Localized Junction Model	p. 231
5.4.3 Protrusion of a Wire Through a Dielectric Surface	p. 233
5.5 Automatic Parameterization of 3-D Geometries	p. 234
5.6 Automatic Segmentation of Electrically Large Surface Patches	p. 238
5.7 Summary	p. 243
References	p. 245
6 Approximation of Currents and Fields	p. 251
6.1 Approximation of Currents Along Wires	p. 252
6.1.1 Subdomain Basis Functions	p. 253
6.1.2 Entire-Domain Basis Functions	p. 258
6.1.3 Inclusion of KCL into Basis Functions	p. 260
6.1.4 Combined Polynomial and Trigonometric Expansions	p. 264
6.1.5 Quasistatic Treatment of Wire Ends and Interconnections	p. 266
6.1.6 Basis Functions in Terms of Simplex Coordinates	p. 269
6.2 Approximation of Currents over Generalized Quadrilaterals	p. 271
6.2.1 Subdomain Approximation	p. 272
6.2.2 Approximate and Exact Formulation of Surface Doublets	p. 275
6.2.3 Rooftop Basis Functions (Exact Formulation)	p. 277
6.2.4 Entire-Domain Basis Functions	p. 278
6.2.5 Inclusion of Continuity Equation into Basis Functions	p. 280
6.2.6 Single and Multiple Metallic Junctions	p. 283
6.2.7 Single and Multiple Dielectric Junctions	p. 285
6.2.8 Composite Metallic and Dielectric Junctions	p. 289
6.2.9 Inclusion of Quasistatic Relation (Edge Effect) into Basis Functions	p. 291
6.2.10 Square Scatterer Benchmark	p. 293
6.3 Approximation of Currents over (Generalized) Triangles	p. 297
6.3.1 Doublets and Rooftop Basis Functions	p. 297
6.3.2 Entire-Domain Approximation in Simplex Coordinates	p. 299
6.4 Generalized Hexahedrons	p. 304
6.4.1 Basis Functions That Maintain Normal Continuity (VIE)	p. 304
6.4.2 Basis Functions That Maintain Tangential Continuity (FEM)	p. 307
6.5 Generalized Tetrahedrons	p. 310
6.6 Approximation of Currents and Fields Across Junctions of Incompatible Building Elements	p. 311
6.7 Comparison of MoM/SIE, MoM/VIE, and FEM Based on Topological Analysis	p. 314
6.8 Summary	p. 318
References	p. 319
7 Treatment of Excitations	p. 323
7.1 Free-Space Waves	p. 323
7.2 Voltage and Current Generators	p. 325
7.2.1 Delta-Function Generator	p. 326
7.3 Guided Waves	p. 329
7.3.1 Exact Modeling	p. 329
7.3.2 TEM Magnetic-Current Frill	p. 333
7.4 Transfer of Excitation	p. 337
7.5 Summary	p. 339
References	p. 339
8 Test Procedure	p. 341
8.1 Testing of Vector Equations in Nonorthogonal Coordinate Systems	p. 341
8.2 Weighted Point-Matching Method	p. 344
8.2.1 Choice of Matching (Integration) Points and Weighting Coefficients	p. 345
8.2.2 Field Integrals of Currents over Generalized Quadrilaterals	p. 348
8.2.3 Reduced Kernel in Field Integrals of Currents Along Generalized Wires	p. 350
8.3 Galerkin Method	p. 354
8.3.1 Choice of the SIE Form	p. 354
8.3.2 Impedance Integrals Due to Currents over Generalized Quadrilaterals	p. 357
8.3.3 Simplified Testing Based on Generalized Scalar Formulation of SIEs	p. 362
8.4 Choice of Optimal Test Procedure	p. 365
8.5 Summary	p. 367
References	p. 367
9 Practical Examples	p. 369
9.1 TV-UHF Panel Antenna with Radome	p. 370
9.2 Horn Antennas	p. 373
9.3 Paraboloidal Reflector Antenna with Feed and Feed Struts	p. 377
9.4 Stacked Patch Antenna Mounted on an Airplane	p. 380
9.5 Base-Station Antenna with Cosecant Characteristic at 60 GHz	p. 383
9.6 Summary	p. 388
References	p. 388
About the Authors	p. 391
Index	p. 393

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