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Full Description
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.
Contents
Preface xv
Acknowledgments xxi
Part I Electromagnetic Field Theory 1
1 Basic Electromagnetic Theory 3
1.2 Maxwell's Equations in Terms of Total Charges and Currents 11
1.3 Constitutive Relations 18
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
References 46
Problems 46
2 Electromagnetic Radiation in Free Space 53
2.1 Scalar and Vector Potentials 53
2.2 Solution of Vector Potentials in Free Space 61
2.3 Electromagnetic Radiation in Free Space 69
2.4 Radiation by Surface Currents and Phased Arrays 78
References 84
Problems 85
3 Electromagnetic Theorems and Principles 89
3.1 Uniqueness Theorem 90
3.2 Image Theory 94
3.3 Reciprocity Theorems 101
3.4 Equivalence Principles 107
3.5 Duality Principle 120
3.6 Aperture Radiation and Scattering 121
References 128
Problems 129
4 Transmission Lines and Plane Waves 135
4.1 Transmission Line Theory 135
4.2 Wave Equations and General Solutions 144
4.3 Plane Waves Generated by a Current Sheet 156
4.4 Reflection and Transmission 159
4.5 Plane Waves in Anisotropic and Bi-Isotropic Media 174
References 190
Problems 191
5 Fields and Waves in Rectangular Coordinates 199
5.1 Uniform Waveguides 199
5.2 Uniform Cavities 220
5.3 Partially Filled Waveguides and Dielectric Slab Waveguides 229
5.4 Field Excitation in Waveguides 241
5.5 Fields in Planar Layered Media 245
References 257
Problems 257
6 Fields and Waves in Cylindrical Coordinates 261
6.1 Solution of Wave Equation 261
6.2 Circular and Coaxial Waveguides and Cavities 266
6.3 Circular Dielectric Waveguide 279
6.4 Wave Transformation and Scattering Analysis 287
6.5 Radiation by Infinitely Long Currents 300
References 319
Problems 320
7 Fields and Waves in Spherical Coordinates 325
7.1 Solution of Wave Equation 325
7.2 Spherical Cavity 331
7.3 Biconical Antenna 335
7.4 Wave Transformation and Scattering Analysis 341
7.5 Addition Theorem and Radiation Analysis 360
References 377
Problems 377
Part II Electromagnetic Field Computation 383
8 The Finite Difference Method 385
8.1 Finite Differencing Formulas 385
8.2 One-Dimensional Analysis 387
8.3 Two-Dimensional Analysis 393
8.4 Yee's FDTD Scheme 397
8.5 Absorbing Boundary Conditions 402
8.6 Modeling of Dispersive Media 417
8.7 Wave Excitation and Far-Field Calculation 422
8.8 Summary 427
References 428
Problems 429
9 The Finite Element Method 433
9.1 Introduction to the Finite Element Method 434
9.2 Finite Element Analysis of Scalar Fields 439
9.3 Finite Element Analysis of Vector Fields 450
9.4 Finite Element Analysis in the Time Domain 465
9.5 Discontinuous Galerkin Time-Domain Method 472
9.6 Absorbing Boundary Conditions 483
9.7 Some Numerical Aspects 494
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
10.3 Three-Dimensional Analysis 523
10.4 Analysis of Periodic Structures 544
10.5 Analysis of Microstrip Antennas and Circuits 551
10.6 The Moment Method in the Time Domain 561
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
11.3 Adaptive Integral Method 591
11.4 Fast Multipole Method 602
11.5 Adaptive Cross-Approximation Algorithm 614
11.6 Introduction to Hybrid Techniques 623
11.7 Hybrid Finite Difference-Finite Element Method 624
11.8 Hybrid Finite Element-Boundary Integral Method 630
11.9 Summary 642
References 643
Problems 649
12 Concluding Remarks on Computational Electromagnetics 651
12.1 Overview of Computational Electromagnetics 651
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
