1The Electromagnetic Model 1
1-1 Introduction 1
1-2 The Electromagnetic Model 3
1-3 SI Units and Universal Constants 8
Review Questions 10
2Vector Analysis 11
2-1 Introduction 11
2-2 Vector Addition and Subtraction 12
2-3 Products of Vectors 14
2-3.1 Scalar or Dot Product 14
2-3.2 Vector or Cross Product 16
2-3.3 Product of Three Vectors 18
2-4 Orthogonal Coordinate Systems 20
2-4.1 Cartesian Coordinates 23
2-4.2 Cylindrical Coordinates 27
2-4.3 Spherical Coordinates 31
2-5 Integrals Containing Vector Functions 37
2-6 Gradient of a Scalar Field 42
2-7 Divergence of a Vector Field 46
2-8 Divergence Theorem 50
2-9 Curl of a Vector Field 54
2-10 Stokes’s Theorem 58
2-11 Two Null Identities 61
2-11.1 Identity Ⅰ 61
2-11.2 Identity Ⅱ 62
2-12 Helmholtz’s Theorem 63
Review Questions 66
3Static Electric Fields 72
3-1 Introduction 72
3-2 Fundamental Postulates of Electrostatics in Free Space 74
3-3 Coulomb’s Law 77
3-3.1 Electric Field Due to a System of Discrete Charges 82
3-3.2 Electric Field Due to a Continuous Distributionof Charge 84
3-4 Gauss’s Law and Applications 87
3-5 Electric Potential 92
3-5.1 Electric Potential Due to a Charge Distribution 94
3-6 Conductors in Static Electric Field 100
3-7 Dielectrics in Static Electric Field 105
3-7.1 Equivalent Charge Distributions ofPolarized Dielectrics 106
3-8 Electric Flux Density and Dielectric Constant 109
3-8.1 Dielectric Strength 114
3-9 Boundary Conditions for Electrostatic Fields 116
3-10 Capacitance and Capacitors 121
3-10.1 Series and Parallel Connections of Capacitors 126
3-10.2 Capacitances in Multiconductor Systems 129
3-10.3 Electrostatic Shielding 132
3-11 Electrostatic Energy and Forces 133
3-11.1 Electrostatic Energy in Terms of Field Quantities 137
3-11.2 Electrostatic Forces 140
Review Questions 143
Problems 145
4Solution of Electrostatic Problems 152
4-1 Introduction 152
4-2 Poisson’s and Laplace’s Equations 152
4-3 Uniqueness of Electrostatic Solutions 157
4-4 Method of Images 159
4-4.1 Point Charge and Conducting Planes 161
4-4.2 Line Charge and Parallel Conducting Cylinder 162
4-4.3 Point Charge and Conducting Sphere 170
4-4.4 Charged Sphere and Grounded Plane 172
4-5 Boundary-Value Problems in Cartesian Coordinates 174
4-6 Boundary-Value Problems in Cylindrical Coordinates 183
4-7 Boundary-Value Problems in Spherical Coordinates 188
Review Questions 192
Problems 193
5Steady Electric Currents 198
5-1 Introduction 198
5-2 Current Density and Ohm’s Law 199
5-3 Electromotive Force and Kirchhoff’s Voltage Law 205
5-4 Equation of Continuity and Kirchhoff’s Current Law 208
5-5 Power Dissipation and Joule’s Law 210
5-6 Boundary Conditions for Current Density 211
5-7 Resistance Calculations 215
Review Questions 219
Problems 220
6Static Magnetic Fields 225
6-1 Introduction 225
6-2 Fundamental Postulates of Magnetostatics in Free Space 226
6-3 Vector Magnetic Potential 232
6-4 The Biot-Savart Law and Applications 234
6-5 The Magnetic Dipole 239
6-5.1 Scalar Magnetic Potential 242
6-6 Magnetization and Equivalent Current Densities 243
6-6.1 Equivalent Magnetization Charge Densities 247
6-7 Magnetic Field Intensity and Relative Permeability 249
6-8 Magnetic Circuits 251
6-9 Behavior of Magnetic Materials 257
6-10 Boundary Conditions for Magnetostatic Fields 262
6-11 Inductances and Inductors 266
6-12 Magnetic Energy 277
6-12.1 Magnetic Energy in Terms of Field Quantities 279
6-13 Magnetic Forces and Torques 281
6-13.1 Hall Effect 282
6-13.2 Forces and Torques on Current-Carrying Conductors 283
6-13.3 Forces and Torques in Terms of StoredMagnetic Energy 289
6-13.4 Forces and Torques in Terms of Mutual Inductance 292
Review Questions 294
Problems 296
7Time-Varying Fields and Maxwell’s Equations 307
7-1 Introduction 307
7-2 Faraday’s Law of Electromagnetic Induction 308
7-2.1 A Stationary Circuit in a Time-VaryingMagnetic Field 309
7-2.2 Transformers 310
7-2.3 A Moving Conductor in a Static Magnetic Field 314
7-2.4 A Moving Circuit in a Time-Varying Magnetic Field 317
7-3 Maxwell’s Equations 321
7-3.1 Integral Form of Maxwell’s Equations 323
7-4 Potential Functions 326
7-5 Electromagnetic Boundary Conditions 329
7-5.1 Interface between Two Lossless Linear Media 330
7-5.2 Interface between a Dielectric and aPerfect Conductor 331
7-6 Wave Equations and Their Solutions 332
7-6.1 Solution of Wave Equations for Potentials 333
7-6.2 Source-Free Wave Equations 334
7-7 Time-Harmonic Fields 335
7-7.1 The Use of Phasors—A Review 336
7-7.2 Time-Harmonic Electromagnetics 338
7-7.3 Source-Free Fields in Simple Media 340
7-7.4 The Electromagnetic Spectrum 343
Review Questions 346
Problems 347
8Plane Electromagnetic Waves 354
8-1 Introduction 354
8-2 Plane Waves in Lossless Media 355
8-2.1 Doppler Effect 360
8-2.2 Transverse Electromagnetic Waves 361
8-2.3 Polarization of Plane Waves 364
8-3 Plane Waves in Lossy Media 367
8-3.1 Low-Loss Dielectrics 368
8-3.2 Good Conductors 369
8-3.3 Ionized Gases 373
8-4 Group Velocity 375
8-5 Flow of Electromagnetic Power and the Poynting Vector 379
8-5.1 Instantaneous and Average Power Densities 382
8-6 Normal Incidence at a Plane Conducting Boundary 386
8-7 Oblique Incidence at a Plane Conducting Boundary 390
8-7.1 Perpendicular Polarization 390
8-7.2 Parallel Polarization 395
8-8 Normal Incidence at a Plane Dielectric Boundary 397
8-9 Normal Incidence at Multiple Dielectric Interfaces 401
8-9.1 Wave Impedance of the Total Field 403
8-9.2 Impedance Transformation with Multiple Dielectrics 404
8-10 Oblique Incidence at a Plane Dielectric Boundary 406
8-10.1 Total Reflection 408
8-10.2 Perpendicular Polarization 411
8-10.3 Parallel Polarization 414
Review Questions 417
Problems 419
9Theory and Applications of Transmission Lines 427
9-1 Introduction 427
9-2 Transverse Electromagnetic Wave along a Parallel-Plate Transmission Line 429
9-2.1 Lossy Parallel-Plate Transmission Lines 433
9-2.2 Microstrip Lines 435
9-3 General Transmission-Line Equations 437
9-3.1 Wave Characteristics on an InfiniteTransmission Line 439
9-3.2 Transmission-Line Parameters 444
9-3.3 Attenuation Constant from Power Relations 447
9-4 Wave Characteristics on Finite Transmission Lines 449
9-4.1 Transmission Lines as Circuit Elements 454
9-4.2 Lines with Resistive Termination 460
9-4.3 Lines with Arbitrary Termination 465
9-4.4 Transmission-Line Circuits 467
9-5 Transients on Transmission Lines 471
9-5.1 Reflection Diagrams 474
9-5.2 Pulse Excitation 478
9-5.3 Initially Charged Line 480
9-5.4 Line with Reactive Load 482
9-6 The Smith Chart 485
9-6.1 Smith-Chart Calculations for Lossy Lines 495
9-7 Transmission-Line Impedance Matching 497
9-7.1 Impedance Matching by Quarter-Wave Transformer 497
9-7.2 Single-Stub Matching 501
9-7.3 Double-Stub Matching 505
Review Questions 509
Problems 512
10Waveguides and Cavity Resonators 520
10-1 Introduction 520
10-2 General Wave Behaviors along Uniform Guiding Structures 521
10-2.1 Transverse Electromagnetic Waves 524
10-2.2 Transverse Magnetic Waves 525
10-2.3 Transverse Electric Waves 529
10-3 Parallel-Plate Waveguide 534
10-3.1 TM Waves between Parallel Plates 534
10-3.2 TE Waves between Parallel Plates 539
10-3.3 Energy-Transport Velocity 541
10-3.4 Attenuation in Parallel-Plate Waveguides 543
10-4 Rectangular Waveguides 547
10-4.1 TM Waves in Rectangular Waveguides 547
10-4.2 TE Waves in Rectangular Waveguides 551
10-4.3 Attenuation in Rectangular Waveguides 555
10-4.4 Discontinuities in Rectangular Waveguides 559
10-5 Circular Waveguides 562
10-5.1 Bessel’s Differential Equation andBessel Functions 563
10-5.2 TM Waves in Circular Waveguides 567
10-5.3 TE Waves in Circular Waveguides 569
10-6 Dielectric Waveguides 572
10-6.1 TM Waves along a Dielectric Slab 572
10-6.2 TE Waves along a Dielectric Slab 576
10-6.3 Additional Comments onDielectric Waveguides 579
10-7 Cavity Resonators 582
10-7.1 Rectangular Cavity Resonators 582
10-7.2 Quality Factor of Cavity Resonator 586
10-7.3 Circular Cavity Resonator 589
Review Questions 592
Problems 594
11Antennas and Radiating Systems 600
11-1 Introduction 600
11-2 Radiation Fields of Elemental Dipoles 602
11-2.1 The Elemental Electric Dipole 602
11-2.2 The Elemental Magnetic Dipole 605
11-3 Antenna Patterns and Antenna Parameters 607
11-4 Thin Linear Antennas 614
11-4.1 The Half-Wave Dipole 617
11-4.2 Effective Antenna Length 619
11-5 Antenna Arrays 621
11-5.1 Two-Element Arrays 622
11-5.2 General Uniform Linear Arrays 625
11-6 Receiving Antennas 631
11-6.1 Internal Impedance and Directional Pattern 632
11-6.2 Effective Area 634
11-6.3 Backscatter Cross Section 637
11-7 Transmit-Receive Systems 639
11-7.1 Friis Transmission Formula and Radar Equation 639
11-7.2 Wave Propagation near Earth’s Surface 642
11-8 Some Other Antenna Types 643
11-8.1 Traveling-Wave Antennas 643
11-8.2 Helical Antennas 645
11-8.3 Yagi-Uda Antenna 648
11-8.4 Broadband Antennas 650
11-9 Aperture Radiators 655
References 661
Review Questions 662
Problems 664
Appendixes 671
A Symbols and Units 671
A-1 Fundamental SI （Rationalized MKSA） Units 671
A-2 Derived Quantities 671
A-3 Multiples and Submultiples of Units 673
B Some Useful Material Constants 674
B-1 Constants of Free Space 674
B-2 Physical Constants of Electron and Proton 674
B-3 Relative Permittivities （Dielectric Constants） 675
B-4 Conductivities 675
B-5 Relative Permeabilities 676
C Index of Tables 677
General Bibliography 679
Answers to Selected Problems 681
Index 693