Applied Frequency–Domain Electromagnetics

Prof Robert Paknys, Concordia University, Canada Robert Paknys received the B.Eng. Degree from McGill University in 1979, and the M.Sc. and Ph.D. degrees from Ohio State University in 1982 and 1985, respectively, all in electrical engineering. He joined the Concordia ECE Department as a faculty member in 1989, and is a full professor. He served the department as the undergraduate program director, associate chair, and department chair. He teaches courses in electromagnetics, antennas and microwaves. His research interest is in electromagnetics, with applications to antennas. He has served as a consultant to the government and industry. Dr. Paknys is a member of ACES, a member of CNC-URSI Commission B, a senior member of the IEEE, a registered professional engineer, and a past associate editor (2004-2010) for the IEEE Transactions on Antennas and Propagation.

Preface xv Acknowledgements xvii 1 Background 1 1.1 Field Laws 1 1.2 Properties of Materials 2 1.3 Types of Currents 3 1.4 Capacitors, Inductors 4 1.5 Differential Form 6 1.6 Time-Harmonic Fields 8 1.7 Sufficient Conditions 9 1.8 Magnetic Currents, Duality 9 1.9 Poynting?s Theorem 10 1.10 Lorentz Reciprocity Theorem 13 1.11 Friis and Radar Equations 14 1.12 Asymptotic Techniques 16 1.13 Further Reading 17 References 18 Problems 18 2 TEM Waves 21 2.1 Introduction 21 2.2 Plane Waves 22 2.3 Oblique Plane Waves 28 2.4 Plane Wave Reflection and Transmission 29 2.5 Multilayer Slab 36 2.6 Impedance Boundary Condition 38 2.7 Transmission Lines 44 2.8 Transverse Equivalent Network 60 2.9 Absorbers 62 2.10 Phase and Group Velocity 63 2.11 Further Reading 65 References 66 Problems 66 3 Waveguides 71 3.1 Separation of Variables 71 3.2 Rectangular Waveguide 73 3.3 Cylindrical Waves 80 3.4 Circular Waveguide 81 3.5 Waveguide Excitation 84 3.6 2D Waveguides 85 3.7 Transverse Resonance Method 94 3.8 Other Waveguide Types 98 3.9 Waveguide Discontinuities 101 3.10 Mode Matching 107 3.11 Waveguide Cavity 114 3.12 Perturbation Method 121 3.13 Further Reading 127 References 127 Problems 127 4 Potentials, Concepts, and Theorems 135 4.1 Vector Potentials A and F 135 4.2 Hertz Potentials 140 4.3 Vector Potentials and Boundary Conditions 141 4.4 Uniqueness Theorem 148 4.5 Radiation Condition 151 4.6 Image Theory 151 4.7 Physical Optics 153 4.8 Surface Equivalent 154 4.9 Love?s Equivalent 158 4.10 Induction Equivalent 161 4.11 Volume Equivalent 162 4.12 Radiation by Planar Sources 164 4.13 2D Sources and Fields 165 4.14 Derivation of Vector Potential Integral 168 4.15 Solution Without Using Potentials 170 4.16 Further Reading 171 References 171 Problems 172 5 Canonical Problems 177 5.1 Cylinder 177 5.2 Wedge 184 5.3 The Relation Between 2D and 3D Solutions 188 5.4 Spherical Waves 192 5.5 Method of Stationary Phase 199 5.6 Further Reading 201 References 202 Problems 202 6 Method of Moments 209 6.1 Introduction 209 6.2 General Concepts 209 6.3 2D Conducting Strip 212 6.4 2D Thin Wire MoM 220 6.5 Periodic 2D Wire Array 224 6.6 3D Thin Wire MoM 228 6.7 EFIE and MFIE 234 6.8 Internal Resonances 236 6.9 PMCHWT Formulation 237 6.10 Basis Functions 238 6.11 Further Reading 240 References 240 Problems 241 7 Finite Element Method 245 7.1 Introduction 245 7.2 Laplace?s Equation 246 7.3 Piecewise-planar Potential 246 7.4 Stored Energy 248 7.5 Connection of Elements 248 7.6 Energy Minimization 250 7.7 Natural Boundary Conditions 252 7.8 Capacitance, Inductance 255 7.9 Computer Program 257 7.10 Poisson?s Equation 258 7.11 Scalar Wave Equation 262 7.12 Galerkin?s Method 266 7.13 Vector Wave Equation 270 7.14 Other Element Types 270 7.15 Radiating Structures 274 7.16 Further Reading 278 References 278 Problems 278 8 Uniform Theory of Diffraction 283 8.1 Fermat?s Principle 283 8.2 2D Fields 284 8.3 Scattering and GTD 292 8.4 3D Fields 294 8.5 Curved Surface Reflection 306 8.6 Curved Wedge Face 308 8.7 Non-Metallic Wedge 308 8.8 Slope Diffraction 309 8.9 Double Diffraction 310 8.10 GTD Equivalent Edge Currents 311 8.11 Surface-Ray Diffraction 315 8.12 Further Reading 324 References 325 Problems 326 9 Physical Theory of Diffraction 337 9.1 PO and an Edge 337 9.2 Asymptotic Evaluation 338 9.3 Reflector Antenna 344 9.4 RCS of a Disc 347 9.5 PTD Equivalent Edge Currents 351 9.6 Further Reading 351 References 352 Problems 352 10 Scalar and Dyadic Green?s Functions 355 10.1 Impulse Response 355 10.2 Green?s Function for A 357 10.3 2D Field Solutions Using Green?s Functions 358 10.4 3D Dyadic Green?s Functions 362 10.5 Some Dyadic Identities 363 10.6 Solution Using a Dyadic Green?s Function 364 10.7 Symmetry Property of G 365 10.8 Interpretation of the Radiation Integrals 367 10.9 Free Space Dyadic Green?s Function 367 10.10Dyadic Green?s Function Singularity 368 10.11Dielectric Rod 370 10.12Further Reading 372 References 372 Problems 372 11 Green?s Functions Construction I 375 11.1 Sturm Liouville Problem 375 11.2 Green?s Second Identity 376 11.3 Hermitian Property 376 11.4 Particular Solution 377 11.5 Properties of the Green?s Function 377 11.6 UT Method 378 11.7 Discrete and Continuous Spectra 382 11.8 Generalized Separation of Variables 388 11.9 Further Reading 396 References 396 Problems 396 12 Green?s Functions Construction II 401 12.1 Sommerfeld Integrals 401 12.2 The Function ?(?) = uk2 ? ?2 402 12.3 The Transformation ? = k sinw 405 12.4 Saddle Point Method 406 12.5 SDP Branch Cuts 415 12.6 Grounded Dielectric Slab 417 12.7 Half Space 426 12.8 Circular Cylinder 435 12.9 Strip Grating on a Dielectric Slab 443 12.10Further Reading 455 References 456 Problems 456 Appendix A Constants and Formulas 461 A.1 Constants 461 A.2 Definitions 461 A.3 Trigonometry 462 A.4 The Impulse Function 462 References 463 B Coordinates and Vector Calculus 465 B.1 Coordinate Transformations 466 B.2 Volume and Surface Elements 466 B.3 Vector Derivatives 468 B.4 Vector Identities 469 B.5 Integral Relations 470 References 472 C Bessel?s Differential Equation 473 C.1 Bessel Functions 473 C.2 Roots of 476 C.3 Integrals 476 C.4 Orthogonality 477 C.5 Recursion Relations 477 C.6 Gamma Function 478 C.7 Wronskians 478 C.8 Spherical Bessel Functions 479 References 480 D Legendre?s Differential Equation 481 D.1 Legendre Functions 481 D.2 Associated Legendre Functions 482 D.3 Orthogonality 482 D.4 Recursion Relations 483 D.5 Spherical Form 483 References 483 E Complex Variables 485 E.1 Residue Calculus 485 E.2 Branch Cuts 486 References 487 F Compilers and Programming 489 F.1 Getting Started 489 F.2 Fortran 90 491 F.3 More on the OS 499 F.4 Plotting 501 F.5 Further Reading 502 References 502 G Numerical Methods 503 G.1 Numerical Integration 503 G.2 Root Finding 507 G.3 Matrix Equations 509 G.4 Matrix Eigenvalues 510 G.5 Bessel Functions 511 G.6 Legendre Polynomials 511 References 512 H Software Provided 513 Index 515