Electromagnetics, microwave circuit and antenna design for communications engineering

Peter Russer's introduction to electromagnetics is intended as a resource for understanding the application of the subject in current, emerging and future broadband communications systems and high-speed analogue and digital electronic circuits and systems.

Author Notes

Peter Russer received his Dipl.-Ing. and Dr. techn. degrees in Electrical Engineering from the Vienna University of Technology.

He is a Professor and Head of the Institute for High Frequency Engineering at Technische Universität München in Germany. He is a Fellow of the IEEE.

050

Preface	p. xvii
Chapter 1 Introduction	p. 1
References	p. 6
Chapter 2 Basic Electromagnetics	p. 9
2.1 The Electromagnetic Field Concept	p. 9
2.2 Field Intensities	p. 12
2.3 Current and Flux Densities	p. 16
2.4 Constitutive Relations	p. 18
2.5 The Charge Density	p. 23
2.6 The Maxwell Puzzle	p. 24
2.7 The Integral Form of Maxwell's Equations	p. 26
2.8 The Electromagnetic Wave	p. 29
2.8.1 The Wave Equation	p. 35
2.8.2 The Polarization of Electromagnetic Waves	p. 36
2.9 Kirchhoff's Laws	p. 38
2.10 Maxwell's Equations in Local Form	p. 41
2.11 Time-Harmonic Electromagnetic Fields	p. 43
2.12 Maxwell's Equations in the Frequency Domain	p. 44
2.13 Curvilinear Coordinates	p. 46
2.14 Boundary Conditions	p. 47
2.15 Problems	p. 56
References	p. 59
Chapter 3 Potentials and Waves	p. 61
3.1 The Electromagnetic Potentials	p. 61
3.2 The Helmholtz Equation	p. 65
3.3 Time-Harmonic Plane Waves	p. 67
3.3.1 Time-Harmonic Plane Waves in Lossless Medium	p. 69
3.3.2 Complex Waves	p. 72
3.4 TM and TE Fields and Waves	p. 74
3.5 Reflection and Transmission of Plane Waves	p. 77
3.5.1 Reflection and Diffraction of a TE Wave at a Plane Boundary	p. 80
3.5.2 Reflection and Diffraction of a TM Wave at a Plane Boundary	p. 83
3.5.3 Total Reflection	p. 86
3.6 Waves in Planar Layered Media	p. 89
3.7 Thin Conducting Sheets	p. 93
3.8 The Vector Wave Equation	p. 94
3.9 Circular Cylindrical Waves	p. 98
3.9.1 Excitation of a Cylindric Wave by a Uniform Current Filament	p. 101
3.10 Spherical Waves	p. 106
3.11 Problems	p. 106
References	p. 107
Chapter 4 Concepts, Methods, and Theorems	p. 109
4.1 Energy and Power	p. 109
4.2 Field Theoretic Formulation of Tellegen's Theorem	p. 116
4.3 Sources of the Electromagnetic Field	p. 118
4.4 The Uniqueness Theorem	p. 120
4.5 The Equivalence Principle	p. 121
4.6 Babinet's Principle	p. 123
4.7 Reciprocity	p. 125
4.7.1 The Lorentz Reciprocity Theorem	p. 125
4.7.2 The Reciprocity Theorem for Impressed Sources	p. 126
4.8 Green's Function	p. 128
4.9 The Integral Equation Method	p. 133
4.10 The Free-Space Green's Dyadic Form	p. 136
4.11 Green's Theorems	p. 136
4.11.1 The Scalar Green's Theorems	p. 136
4.11.2 Green's Theorems in Two Dimensions	p. 138
4.11.3 The Vector Green's Theorems	p. 140
4.12 Integral Formulation of the Equivalence Principle	p. 141
4.13 The Sturm-Liouville Equation	p. 143
4.14 Spectral Representation of Green's Functions	p. 146
4.15 Problems	p. 148
References	p. 148
Chapter 5 Static and Quasistatic Fields	p. 151
5.1 Conditions for Static and Quasistatic Fields	p. 151
5.2 Static and Quasistatic Electric Fields	p. 153
5.2.1 Green's Function for the Static Electric Field	p. 153
5.2.2 Capacitance	p. 155
5.3 Static and Quasistatic Magnetic Fields	p. 161
5.3.1 Green's Function for the Static Magnetic Field	p. 161
5.3.2 Inductance	p. 163
5.4 The Laplace Equation	p. 169
5.4.1 Potential Separation Planes	p. 170
5.4.2 Three-Dimensional Laplace Equation in Cartesian Coordinates	p. 171
5.5 Conformal Mapping	p. 174
5.5.1 Field of an Elliptic Cylindric Line	p. 181
5.5.2 Field of a Coaxial Line	p. 183
5.5.3 Parallel Wire Line	p. 186
5.6 The Schwarz-Christoffel Transformation	p. 191
5.6.1 The Coplanar Line	p. 193
5.6.2 The Coplanar Stripline	p. 196
5.6.3 The Stripline	p. 197
5.7 Problems	p. 201
References	p. 204
Chapter 6 Waves at the Surface of Conducting Media	p. 207
6.1 Transverse Magnetic Surface Waves	p. 208
6.2 Surface Currents	p. 216
6.3 Surface Current Losses	p. 221
6.4 Induced Surface Currents	p. 224
6.5 Problems	p. 227
References	p. 228
Chapter 7 Transmission-Lines and Waveguides	p. 229
7.1 Introduction	p. 229
7.2 Phase and Group Velocity	p. 232
7.3 The Field Components	p. 233
7.4 Waveguides for Transverse Electromagnetic Waves	p. 235
7.5 Multiconductor Transmission-Lines	p. 249
7.6 Quasi-TEM Modes of Transmission-Lines	p. 254
7.6.1 Quasi-TEM Modes of Two-Conductor Transmission-Lines	p. 254
7.6.2 Quasi-TEM Modes of Multiconductor Transmission-Lines	p. 259
7.7 Planar Transmission-Lines	p. 260
7.7.1 The Microstrip Line	p. 260
7.7.2 Quasistatic Approximation for the Microstrip Line	p. 262
7.7.3 Coplanar Waveguide and Coplanar Stripline	p. 265
7.8 Hollow Waveguides	p. 266
7.8.1 TE Modes	p. 266
7.8.2 TM Modes	p. 270
7.8.3 Modal Expansions in Waveguides	p. 272
7.9 Rectangular Waveguides	p. 276
7.9.1 Transverse Electric Modes	p. 276
7.9.2 Transverse Magnetic Modes	p. 282
7.9.3 Power Flow in the Waveguide	p. 284
7.9.4 Orthogonality of the Waveguide Modes	p. 285
7.9.5 Generalized Currents and Voltages in Waveguides	p. 286
7.9.6 Attenuation Due to Conductor Losses	p. 289
7.9.7 Attenuation Due to Dielectric Losses	p. 291
7.10 Circular Cylindric Waveguides	p. 292
7.10.1 The Circular Waveguide Modes	p. 292
7.10.2 Power Flow and Attenuation in the TE[subscript 01] Mode	p. 298
7.11 Radial Waveguides	p. 300
7.11.1 Radial Parallel Plate Waveguide	p. 300
7.11.2 Wedged Radial Parallel Plate Waveguide	p. 307
7.12 Spherical Waveguides	p. 309
7.12.1 Conical Waveguide	p. 311
7.12.2 Biconical Waveguide	p. 313
7.13 Dielectric Waveguides and Optical Fibers	p. 316
7.13.1 Homogeneous Planar Dielectric Waveguides	p. 316
7.13.2 Dielectric Slab with Single-Sided Metallization	p. 320
7.13.3 Circular Dielectric Waveguides with Step Index Profile	p. 322
7.14 Problems	p. 329
References	p. 333
Chapter 8 The Transmission-Line Equations	p. 335
8.1 The Transmission-Line Concept	p. 335
8.2 Generalized Voltages and Currents	p. 337
8.3 Solution of the Transmission-Line Equations	p. 341
8.4 Wave Amplitudes	p. 344
8.5 Reflection Coefficient and Smith Chart	p. 346
8.5.1 Impedance Matching with Lumped Elements	p. 353
8.5.2 Impedance Matching with Stubs	p. 355
8.6 Solution of the Multiconductor Transmission-Line Equations	p. 356
8.7 Multimode Excitation of Uniform Hollow Waveguides	p. 363
8.7.1 The Transverse Field Equations	p. 363
8.7.2 Modal Field Representation	p. 366
8.7.3 Multimode Transmission-Line Equations for Hollow Waveguides	p. 368
8.7.4 Multimode Transmission-Line Equations of Lossless Waveguides without Internal Sources	p. 374
8.8 Green's Functions for Transmission-Lines	p. 375
8.8.1 Green's Function for the Transmission-Line with Matched Terminations	p. 378
8.8.2 Green's Function for the Transmission-Line with Arbitrary Linear Passive Terminations	p. 379
8.9 Problems	p. 381
References	p. 384
Chapter 9 Resonant Circuits and Resonators	p. 385
9.1 The Linear Passive One-Port	p. 385
9.2 The Reactance Theorem	p. 387
9.3 Resonant Circuits	p. 389
9.4 The Transmission-Line Resonator	p. 392
9.5 Cavity Resonators	p. 395
9.5.1 The Rectangular Cavity Resonator	p. 395
9.5.2 The Circular Cylindric Cavity Resonator	p. 399
9.6 Coupling of Resonant Circuits and Resonators	p. 402
9.6.1 The Loaded Quality Factor	p. 402
9.6.2 Termination of a Transmission-Line with a Resonant Circuit	p. 403
9.6.3 Inductive Coupling of Cavity Resonators	p. 405
9.7 Orthogonality of the Resonator Modes	p. 407
9.8 Excitation of Resonators by Internal Sources	p. 409
9.9 Problems	p. 411
References	p. 412
Chapter 10 Passive Microwave Circuits	p. 413
10.1 Linear Multiports	p. 413
10.2 Source-Free Linear Multiports	p. 414
10.2.1 Impedance and Admittance Representations	p. 414
10.2.2 The Chain Matrix	p. 415
10.2.3 The Scattering Matrix	p. 419
10.2.4 The Transmission Matrix	p. 424
10.3 Tellegen's Theorem	p. 425
10.3.1 Connection Networks	p. 428
10.3.2 Tellegen's Theorem for Discretized Fields	p. 429
10.4 The Power Properties	p. 430
10.5 Reciprocal Multiports	p. 431
10.6 Elementary Two-Ports	p. 433
10.7 Signal Flow Graphs	p. 436
10.8 Lumped Element Equivalent Circuits	p. 439
10.8.1 Foster Representation of Reactance Multiports	p. 439
10.8.2 Cauer Representation of Radiating Structures	p. 445
10.9 Obstacles in Waveguides	p. 450
10.10 The Symmetry Properties of Waveguide Junctions	p. 456
10.10.1 Symmetric Three-Port Waveguide Junctions	p. 457
10.10.2 Symmetric Four-Port Waveguide Junctions	p. 460
10.11 Problems	p. 463
References	p. 466
Chapter 11 Periodic Structures and Filters	p. 467
11.1 Periodic Electromagnetic Structures	p. 467
11.1.1 TE Modes in Rectangular Periodic Waveguides	p. 467
11.1.2 Sinusoidal Variation of the Permittivity	p. 472
11.2 Wave Parameter Theory of Two-Ports	p. 474
11.3 Lumped Low-Pass Filter Prototypes	p. 481
11.3.1 The Butterworth Prototype	p. 482
11.3.2 The Chebyshev Prototype	p. 485
11.4 Ladder Filter Networks	p. 488
11.4.1 Butterworth Ladder Networks	p. 489
11.4.2 Chebyshev Ladder Networks	p. 490
11.5 Frequency Transformation	p. 492
11.5.1 Low-Pass to High-Pass Transformation	p. 492
11.5.2 Low-Pass to Band-Pass Transformation	p. 493
11.5.3 Low-Pass to Band-Stop Transformation	p. 495
11.6 Transmission-Line with Periodic Load	p. 497
11.7 Plane Wave Scattering by Periodic Structures	p. 501
11.7.1 Scattering of te Waves by Periodic Structures	p. 501
11.7.2 Scattering of tm Waves by Periodic Structures	p. 505
11.8 Metamaterials	p. 507
11.9 Problems	p. 515
References	p. 517
Chapter 12 Radiation from Dipoles	p. 519
12.1 The Hertzian Dipole	p. 519
12.2 Aperiodic Spherical Waves	p. 524
12.3 Vertically Oriented Electric Dipole over Lossy Half-Space	p. 528
12.3.1 The Far-Field of the Vertical Dipole over Ground	p. 538
12.3.2 The Surface Wave	p. 539
12.4 Horizontally Oriented Electric Dipole over Lossy Half-Space	p. 540
12.5 Problems	p. 544
References	p. 545
Chapter 13 Antennas	p. 547
13.1 Introduction	p. 547
13.2 Linear Antennas	p. 549
13.3 The Integral Equation for the Linear Antenna	p. 555
13.4 The Impedance of the Linear Antenna	p. 558
13.5 The Loop Antenna	p. 560
13.6 Receiving Antennas	p. 563
13.6.1 The Hertzian Dipole as Receiving Antenna	p. 563
13.6.2 The Loop Antenna as Receiving Antenna	p. 564
13.6.3 The Linear Dipole Antenna as Receiving Antenna	p. 565
13.7 Gain and Effective Antenna Aperture	p. 569
13.8 Antenna Arrays	p. 575
13.8.1 Linear Antenna Arrays	p. 575
13.8.2 Circular Antenna Arrays	p. 577
13.9 Aperture Antennas	p. 578
13.9.1 Radiating Apertures	p. 578
13.9.2 Horn Antennas	p. 582
13.9.3 Gain and Effective Area of Aperture Antennas	p. 585
13.9.4 Mirror and Lens Antennas	p. 587
13.9.5 Slot Antennas	p. 589
13.10 Microstrip Antennas	p. 591
13.10.1 Planar Rectangular Patch Antenna	p. 593
13.11 Broadband Antennas	p. 595
13.12 Problems	p. 597
References	p. 601
Chapter 14 Numerical Electromagnetics	p. 603
14.1 Introduction	p. 603
14.2 The Method of Moments	p. 605
14.3 The Transmission-Line Matrix Method	p. 611
14.4 The Mode Matching Method	p. 617
References	p. 623
Appendix A Vectors and Differential Forms	p. 627
A.1 Vectors	p. 627
A.2 Differential Forms	p. 631
A.2.1 Products of Exterior Differential Forms	p. 632
A.2.2 The Contraction	p. 633
A.2.3 The Exterior Derivative	p. 634
A.2.4 The Laplace Operator	p. 635
A.3 Stokes' Theorem	p. 636
A.4 Curvilinear Coordinates	p. 640
A.4.1 General Cylindrical Coordinates	p. 646
A.4.2 Circular Cylindric Coordinates	p. 647
A.4.3 Spherical Coordinates	p. 650
A.4.4 Twisted Forms	p. 653
A.4.5 Integration of Differential Forms by Pullback	p. 653
A.5 Double Differential Forms	p. 654
A.6 Relations between Exterior Calculus and Conventional Vector Notation	p. 656
A.6.1 Differential Operators	p. 656
A.6.2 Maxwell's Equations	p. 656
References	p. 657
Appendix B Special Functions	p. 659
B.1 Ordinary Bessel Functions	p. 659
B.2 Modified Bessel Functions	p. 662
B.3 Spherical Bessel Functions	p. 665
B.4 Legendre Polynomials	p. 667
B.5 Spherical Harmonics	p. 670
References	p. 672
Appendix C Linear Algebra	p. 673
C.1 Unitary Vector Space	p. 673
C.2 Diagonalization of a Matrix	p. 679
C.3 Matrix Functions	p. 681
C.4 The Hilbert Space	p. 683
C.4.1 Linear Operators in Hilbert Space	p. 686
C.4.2 Function Spaces	p. 691
C.4.3 Function Spaces with Biorthogonal Basis	p. 693
References	p. 696
Appendix D Fourier Series and Fourier Transform	p. 697
D.1 The Fourier Series	p. 697
D.2 The Fourier Integral	p. 699
D.3 The Delta Distribution	p. 701
References	p. 704
Appendix E Complex Integration	p. 705
E.1 Analytic Functions	p. 705
E.2 The Residue Theorem	p. 707
E.3 The Saddle-Point Method	p. 708
References	p. 710
List of Symbols	p. 711
About the Author	p. 717
Index	p. 719

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