Reviews the fundamental concepts behind the theory and computation of electromagnetic fields The book is divided in two parts. The first part covers both fundamental theories (such as vector analysis, Maxwell s equations, boundary condition, and transmission line theory) and advanced topics (such as wave transformation, addition theorems, and fields in layered media) in order to benefit students at all levels. The second part of the book covers the major computational methods for numerical analysis of electromagnetic fields for engineering applications. These methods include the three fundamental approaches for numerical analysis of electromagnetic fields: the finite difference method (the finite difference time–domain method in particular), the finite element method, and the integral equation–based moment method. The second part also examines fast algorithms for solving integral equations and hybrid techniques that combine different numerical methods to seek more efficient solutions of complicated electromagnetic problems. Theory and Computation of Electromagnetic Fields, Second Edition: Provides the foundation necessary for graduate students to learn and understand more advanced topics Discusses electromagnetic analysis in rectangular, cylindrical and spherical coordinates Covers computational electromagnetics in both frequency and time domains Includes new and updated homework problems and examples Theory and Computation of Electromagnetic Fields, Second Edition is written for advanced undergraduate and graduate level electrical engineering students. This book can also be used as a reference for professional engineers interested in learning about analysis and computation skills. INDICE: Preface xv .Acknowledgments xxi .PART I Electromagnetic Field Theory 1 .1 Basic Electromagnetic Theory 3 .1.1 Review of Vector Analysis, 3 .1.1.1 Vector Operations and Integral Theorems, 4 .1.1.2 Symbolic Vector Method, 6 .1.1.3 Helmholtz Decomposition Theorem, 9 .1.1.4 Green s Theorems, 9 .1.2 Maxwell s Equations in Terms of Total Charges and Currents, 11 .1.2.1 Maxwell s Equations in Integral Form, 12 .1.2.2 Maxwell s Equations in Differential Form, 17 .1.2.3 Current Continuity Equation, 17 .1.2.4 The Lorentz Force Law, 18 .1.3 Constitutive Relations, 18 .1.3.1 Electric Polarization, 19 .1.3.2 Magnetization, 21 .1.3.3 Electric Conduction, 22 .1.3.4 Classification of Media, 23 .1.4 Maxwell s Equations in Terms of Free Charges and Currents, 25 .1.5 Boundary Conditions, 27 .1.6 Energy, Power, and Poynting s Theorem, 31 .1.7 Time–Harmonic Fields, 33 .1.7.1 Time–Harmonic Fields, 33 .1.7.2 Fourier Transforms, 35 .1.7.3 Complex Power, 37 .1.7.4 Complex Permittivity and Permeability, 42 .References, 46 .Problems, 46 .2 Electromagnetic Radiation in Free Space 53 .2.1 Scalar and Vector Potentials, 53 .2.1.1 Static Fields, 54 .2.1.2 Time–Harmonic Fields and the Lorenz Gauge Condition, 58 .2.2 Solution of Vector Potentials in Free Space, 61 .2.2.1 Delta Function and Green s Function, 61 .2.2.2 Green s Function in Free Space, 62 .2.2.3 Field Source Relations in Free Space, 63 .2.2.4 Why Use Auxiliary Potential Functions, 64 .2.2.5 Free–Space Dyadic Green s Functions, 66 .2.3 Electromagnetic Radiation in Free Space, 69 .2.3.1 Infinitesimal Electric Dipole, 69 .2.3.2 Finite Electric Dipole, 72 .2.3.3 Far–Field Approximation and the Sommerfeld Radiation Condition, 73 .2.3.4 Circular Current Loop and Magnetic Dipole, 76 .2.4 Radiation by Surface Currents and Phased Arrays, 78 .2.4.1 Radiation by a Surface Current, 78 .2.4.2 Radiation by a Phased Array, 81 .References, 84 .Problems, 85 .3 Electromagnetic Theorems and Principles 89 .3.1 Uniqueness Theorem, 90 .3.2 Image Theory, 94 .3.2.1 Basic Image Theory, 94 .3.2.2 Half–Space Field Source Relations, 99 .3.3 Reciprocity Theorems, 101 .3.3.1 General Reciprocity Theorem, 101 .3.3.2 Lorentz Reciprocity Theorem, 102 .3.3.3 Rayleigh Carson Reciprocity Theorem, 103 .3.4 Equivalence Principles, 107 .3.4.1 Surface Equivalence Principle, 107 .3.4.2 Application to Scattering by a Conducting Object, 109 .3.4.3 Application to Scattering by a Dielectric Object, 114 .3.4.4 Volume Equivalence Principle, 116 .3.5 Duality Principle, 120 .3.6 Aperture Radiation and Scattering, 121 .3.6.1 Equivalent Problems, 121 .3.6.2 Babinet s Principle, 124 .3.6.3 Complementary Antennas, 127 .References, 128 .Problems, 129 .4 Transmission Lines and Plane Waves 135 .4.1 Transmission Line Theory, 135 .4.1.1 Governing Differential Equations and General Solutions, 135 .4.1.2 Reflection and Transmission, 138 .4.1.3 Green s Function and Eigenfunction Expansion, 140 .4.2 Wave Equations and General Solutions, 144 .4.2.1 Wave Equations and Solution by Separation of Variables, 144 .4.2.2 Characteristics of a Plane Wave, 146 .4.2.3 Wave Velocities and Attenuation, 147 .4.2.4 Linear, Circular, and Elliptical Polarizations, 151 .4.2.5 Wave Propagation in Metamaterials, 154 .4.3 Plane Waves Generated by a Current Sheet, 156 .4.4 Reflection and Transmission, 159 .4.4.1 Reflection and Transmission at Normal Incidence, 159 .4.4.2 Reflection and Transmission at Oblique Incidence, 161 .4.4.3 Total Transmission and Total Reflection, 164 .4.4.4 Transmission into a Left–Handed Medium, 168 .4.4.5 Plane Waves Versus Transmission Lines, 170 .4.5 Plane Waves in Anisotropic and Bi–Isotropic Media, 174 .4.5.1 Plane Waves in Uniaxial Media, 174 .4.5.2 Plane Waves in Gyrotropic Media, 179 .4.5.3 Plane Waves in Chiral Media, 183 .References, 190 .Problems, 191 .5 Fields and Waves in Rectangular Coordinates 199 .5.1 Uniform Waveguides, 199 .5.1.1 General Analysis, 200 .5.1.2 General Characteristics, 204 .5.1.3 Uniform Rectangular Waveguide, 208 .5.1.4 Losses in Waveguides and Attenuation Constant, 215 .5.2 Uniform Cavities, 220 .5.2.1 General Theory, 221 .5.2.2 Rectangular Cavity, 223 .5.2.3 Material and Geometry Perturbations, 226 .5.3 Partially Filled Waveguides and Dielectric Slab Waveguides, 229 .5.3.1 General Theory, 229 .5.3.2 Partially Filled Rectangular Waveguide, 231 .5.3.3 Dielectric Slab Waveguide on a Ground Plane, 236 .5.4 Field Excitation in Waveguides, 241 .5.4.1 Excitation by Planar Surface Currents, 242 .5.4.2 Excitation by General Volumetric Currents, 243 .5.5 Fields in Planar Layered Media, 245 .5.5.1 Spectral Green s Function and Sommerfeld Identity, 245 .5.5.2 Vertical Electric Dipole above a Layered Medium, 247 .5.5.3 Horizontal Electric Dipole above a Layered Medium, 249 .5.5.4 Dipoles on a Grounded Dielectric Slab, 251 .References, 257 .Problems, 257 .6 Fields and Waves in Cylindrical Coordinates 261 .6.1 Solution of Wave Equation, 261 .6.1.1 Solution by Separation of Variables, 262 .6.1.2 Cylindrical Wave Functions, 263 .6.2 Circular and Coaxial Waveguides and Cavities, 266 .6.2.1 Circular Waveguide, 267 .6.2.2 Coaxial Waveguide, 273 .6.2.3 Cylindrical Cavity, 276 .6.3 Circular Dielectric Waveguide, 279 .6.3.1 Analysis of Hybrid Modes, 279 .6.3.2 Characteristics of Hybrid Modes, 283 .6.4 Wave Transformation and Scattering Analysis, 287 .6.4.1 Wave Transformation, 288 .6.4.2 Scattering by a Circular Conducting Cylinder, 289 .6.4.3 Scattering by a Circular Dielectric Cylinder, 293 .6.4.4 Scattering by a Circular Multilayer Dielectric Cylinder, 296 .6.5 Radiation by Infinitely Long Currents, 300 .6.5.1 Line Current Radiation in Free Space, 300 .6.5.2 Radiation by a Cylindrical Surface Current, 304 .6.5.3 Radiation in the Presence of a Circular Conducting Cylinder, 306 .6.5.4 Radiation in the Presence of a Conducting Wedge, 309 .6.5.5 Radiation by a Finite Current, 312 .References, 319 .Problems, 320 .7 Fields and Waves in Spherical Coordinates 325 .7.1 Solution of Wave Equation, 325 .7.1.1 Solution by Separation of Variables, 325 .7.1.2 Spherical Wave Functions, 328 .7.1.3 TEr and TMr Modes, 329 .7.2 Spherical Cavity, 331 .7.3 Biconical Antenna, 335 .7.3.1 Infinitely Long Model, 335 .7.3.2 Finite Biconical Antenna, 339 .7.4 Wave Transformation and Scattering Analysis, 341 .7.4.1 Wave Transformation, 342 .7.4.2 Expansion of a Plane Wave, 344 .7.4.3 Scattering by a Conducting Sphere, 347 .7.4.4 Scattering by a Dielectric Sphere, 352 .7.4.5 Scattering by a Multilayer Dielectric Sphere, 357 .7.5 Addition Theorem and Radiation Analysis, 360 .7.5.1 Addition Theorem for Spherical Wave Functions, 360 .7.5.2 Radiation of a Spherical Surface Current, 362 .7.5.3 Radiation in the Presence of a Sphere, 368 .7.5.4 Radiation in the Presence of a Conducting Cone, 370 .References, 377 .Problems, 377 .PARTII Electromagnetic Field Computation 383 .8 The Finite Difference Method 385 .8.1 Finite Differencing Formulas, 385 .8.2 One–Dimensional Analysis, 387 .8.2.1 Solution of the Diffusion Equation, 387 .8.2.2 Solution of the Wave Equation, 389 .8.2.3 Stability Analysis, 390 .8.2.4 Numerical Dispersion Analysis, 392 .8.3 Two–Dimensional Analysis, 393 .8.3.1 Analysis in the Time Domain, 393 .8.3.2 Analysis in the Frequency Domain, 395 .8.4 Yee s FDTD Scheme, 397 .8.4.1 Two–Dimensional Analysis, 397 .8.4.2 Three–Dimensional Analysis, 399 .8.5 Absorbing Boundary Conditions, 402 .8.5.1 One–Dimensional ABC, 403 .8.5.2 Two–Dimensional ABCs, 404 .8.5.3 Perfectly Matched Layers, 406 .8.6 Modeling of Dispersive Media, 417 .8.6.1 Recursive Convolution Approach, 417 .8.6.2 Auxiliary Differential Equation Approach, 420 .8.7 Wave Excitation and Far–Field Calculation, 422 .8.7.1 Modeling of Wave Excitation, 422 .8.7.2 Near–to–Far–Field Transformation, 426 .8.8 Summary, 427 .References, 428 .Problems, 429 .9 The Finite Element Method 433 .9.1 Introduction to the Finite Element Method, 434 .9.1.1 The General Principle, 434 .9.1.2 One–Dimensional Example, 435 .9.2 Finite Element Analysis of Scalar Fields, 439 .9.2.1 The Boundary–Value Problem, 439 .9.2.2 Finite Element Formulation, 440 .9.2.3 Application Examples, 446 .9.3 Finite Element Analysis of Vector Fields, 450 .9.3.1 The Boundary–Value Problem, 450 .9.3.2 Finite Element Formulation, 452 .9.3.3 Application Examples, 456 .9.4 Finite Element Analysis in the Time Domain, 465 .9.4.1 The Boundary–Value Problem, 465 .9.4.2 Finite Element Formulation, 466 .9.4.3 Application Examples, 470 .9.5 Discontinuous Galerkin Time–Domain Method, 472 .9.5.1 Basic Idea, 473 .9.5.2 Central–Flux DGTD Method, 475 .9.5.3 Upwind–Flux DGTD Method, 478 .9.5.4 Application Example, 481 .9.6 Absorbing Boundary Conditions, 483 .9.6.1 Two–Dimensional ABCs, 483 .9.6.2 Three–Dimensional ABCs, 486 .9.6.3 Perfectly Matched Layers, 488 .9.7 Some Numerical Aspects, 494 .9.7.1 Mesh Generation, 494 .9.7.2 Matrix Solvers, 494 .9.7.3 Higher–Order Elements, 495 .9.7.4 Curvilinear Elements, 496 .9.7.5 Adaptive Finite Element Analysis, 496 .9.8 Summary, 497 .References, 497 .Problems, 499 .10 The Method of Moments 505 .10.1 Introduction to the Method of Moments, 506 .10.2 Two–Dimensional Analysis, 510 .10.2.1 Formulation of Integral Equations, 510 .10.2.2 Scattering by a Conducting Cylinder, 514 .10.2.3 Scattering by a Conducting Strip, 518 .10.2.4 Scattering by a Homogeneous Dielectric Cylinder, 522 .10.3 Three–Dimensional Analysis, 523 .10.3.1 Formulation of Integral Equations, 523 .10.3.2 Scattering and Radiation by a Conducting Wire, 528 .10.3.3 Scattering by a Conducting Body, 532 .10.3.4 Scattering by a Homogeneous Dielectric Body, 538 .10.3.5 Scattering by an Inhomogeneous Dielectric Body, 542 .10.4 Analysis of Periodic Structures, 544 .10.4.1 Scattering by a Planar Periodic Conducting Patch Array, 544 .10.4.2 Scattering by a Discrete Body–of–Revolution Object, 549 .10.5 Analysis of Microstrip Antennas and Circuits, 551 .10.5.1 Formulation of Integral Equations, 552 .10.5.2 The Moment–Method Solution, 556 .10.5.3 Evaluation of Green s Functions, 556 .10.5.4 Far–Field Calculation and Application Examples, 561 .10.6 The Moment Method in the Time Domain, 561 .10.6.1 Time–Domain Integral Equations, 563 .10.6.2 Marching–On–in–Time Solution, 564 .10.7 Summary, 568 .References, 568 .Problems, 571 .11 Fast Algorithms and Hybrid Techniques 575 .11.1 Introduction to Fast Algorithms, 576 .11.2 Conjugate Gradient FFT Method, 578 .11.2.1 Scattering by a Conducting Strip or Wire, 578 .11.2.2 Scattering by a Conducting Plate, 579 .11.2.3 Scattering by a Dielectric Object, 585 .11.3 Adaptive Integral Method, 591 .11.3.1 Planar Structures, 592 .11.3.2 Three–Dimensional Objects, 596 .11.4 Fast Multipole Method, 602 .11.4.1 Two–Dimensional Analysis, 602 .11.4.2 Three–Dimensional Analysis, 606 .11.4.3 Multilevel Fast Multipole Algorithm, 610 .11.5 Adaptive Cross–Approximation Algorithm, 614 .11.5.1 Low–Rank Matrix, 615 .11.5.2 Adaptive Cross–Approximation, 617 .11.5.3 Application to the Moment–Method Solution, 619 .11.6 Introduction to Hybrid Techniques, 623 .11.7 Hybrid Finite Difference Finite Element Method, 624 .11.7.1 Relation Between FETD and FDTD, 625 .11.7.2 Hybridization of FETD and FDTD, 627 .11.7.3 Application Example, 629 .11.8 Hybrid Finite Element Boundary Integral Method, 630 .11.8.1 Traditional Formulation, 631 .11.8.2 Symmetric Formulation, 635 .11.8.3 Numerical Examples, 638 .11.9 Summary, 642 .References, 643 .Problems, 649 .12 Concluding Remarks on Computational Electromagnetics 651 .12.1 Overview of Computational Electromagnetics, 651 .12.1.1 Frequency–Versus Time–Domain Analysis, 651 .12.1.2 High–Frequency Asymptotic Techniques, 653 .12.1.3 First–Principle Numerical Methods, 654 .12.1.4 Time–Domain Simulation Methods, 656 .12.1.5 Hybrid Techniques, 658 .12.2 Applications of Computational Electromagnetics, 659 .12.3 Challenges in Computational Electromagnetics, 670 .References, 671 .Appendix A Vector Identities, Integral Theorems, and Coordinate Transformation 681 .A.1 Vector Identities, 681 .A.2 Integral Theorems, 682 .A.3 Coordinate Transformation, 682 .Appendix B Bessel Functions 683 .B.1 Definition, 683 .B.2 Series Expressions, 683 .B.3 Integral Representation, 685 .B.4 Asymptotic Expressions, 685 .B.5 Recurrence and Derivative Relations, 685 .B.6 Symmetry Relations, 686 .B.7 Wronskian Relation, 686 .B.8 Useful Integrals, 686 .Appendix C Modified Bessel Functions 687 .C.1 Definition, 687 .C.2 Series Expressions, 687 .C.3 Integral Representations, 688 .C.4 Asymptotic Expressions, 688 .C.5 Recurrence and Derivative Relations, 689 .C.6 Symmetry Relations, 690 .C.7 Wronskian Relation, 690 .C.8 Useful Integrals, 690 .Appendix D Spherical Bessel Functions 691 .D.1 Definition, 691 .D.2 Series Expressions, 692 .D.3 Asymptotic Expressions, 693 .D.4 Recurrence and Derivative Relations, 693 .D.5 Symmetry Relations, 694 .D.6 Wronskian Relation, 695 .D.7 Riccati Bessel Functions, 695 .D.8 Modified Spherical Bessel Functions, 695 .Appendix E Associated Legendre Polynomials 697 .E.1 Definition, 697 .E.2 Series Expression, 698 .E.3 Special Values, 700 .E.4 Symmetry Relations, 701 .E.5 Recurrence and Derivative Relations, 701 .E.6 Orthogonal Relations, 702 .E.7 Fourier Legendre Series, 702 .Index 703
- ISBN: 978-1-119-10804-7
- Editorial: Wiley–Blackwell
- Encuadernacion: Cartoné
- Páginas: 744
- Fecha Publicación: 09/10/2015
- Nº Volúmenes: 1
- Idioma: Inglés