Theory of waveguides and transmission lines

Cover......Page 1
Half Title......Page 2
Title Page......Page 4
Copyright Page......Page 5
Dedication......Page 6
Contents......Page 8
Preface......Page 18
Author......Page 20
 1.1 Introduction......Page 22
 1.2 Classical Transmission Line (Distributed Constant Model)......Page 24
  1.2.2 Example: An Unconventional Transmission Line......Page 31
  1.2.3 Example: A Backward Wave Transmission Line......Page 33
 1.3 Reflected Waves, the Smith Chart and Chain Parameters......Page 34
  1.3.1 Example: Reflection and Transmission At A Section Of Mismatched Line......Page 38
 1.4 Transmission Lines As Models For Plane Wave Propagation......Page 39
  1.4.1 Example: Reflection and Transmission At An Interface......Page 42
  1.5.1 Lowest Order Wkb Approximation......Page 43
  1.5.2 First Order (Rayleigh Bremmer) Wkb Approximation......Page 46
  1.5.3 Turning Points......Page 48
 1.6 Notes and References......Page 51
 1.7 Problems......Page 54
  2.1.1 Impedance and Admittance Matrices......Page 62
  2.1.2 Chain Matrices......Page 65
  2.1.3 Hybrid and Image Parameters......Page 68
  2.1.4 The Scattering Matrix and Related Representations......Page 69
  2.1.5 Example: Equivalent Network For A Length Of Classical Transmission Line......Page 73
  2.1.6 Example: Use Of Chain Matrices......Page 74
  2.1.7 Example: Realization Of A 1:2 Ideal Transformer......Page 75
  2.1.8 Example: A Two Terminal Antenna As A Two Port......Page 76
 2.2 Multiport Networks......Page 77
  2.2.1 Example: Analysis Of Baluns......Page 78
  2.2.2 Analysis Of Four Ports By Even and Odd Excitation......Page 81
  2.2.3 Example: Ring and Hybrid Networks......Page 83
 2.3 Power and Energy Relations......Page 86
  2.3.1 Example: Lossless, Reciprocal Two Port Network......Page 88
 2.4 Notes and References......Page 89
 2.5 Problems......Page 91
  3.1.1 Thevenin and Norton Equivalent Circuits......Page 98
  3.1.2 Huygens (Wave) Sources......Page 99
 3.2 Excitation Of A Classical Transmission Line......Page 102
  3.2.1 Modeling Of Lumped Sources......Page 105
  3.2.2 Equivalent Circuits For Distributed Sources......Page 106
  3.3.1 Matrix Telegrapher’S Equations......Page 108
  3.3.2 Modes Of Multiconductor Lines......Page 110
  3.3.3 Propagating Modes On Lossless Multiconductor Lines......Page 114
  3.3.4 Total Voltages and Currents On A Multiconductor Line......Page 115
  3.3.5 Reflection On A Multiconductor Line......Page 116
  3.3.7 Example: The Symmetric Three Conductor Line......Page 117
 3.4 Notes and References......Page 120
 3.5 Problems......Page 123
 4.2 The Fourier Transform and The Analytic Signal......Page 130
  4.2.1 Energy Moments and Pulse Widths Of Signals......Page 134
  4.2.2 Band Limited Signals......Page 135
 4.3 Narrowband Pulse Distortion By A Linear Time Invariant Network......Page 136
  4.3.1 Quasi Stationary Approximation (Qsa)......Page 137
  4.3.2 Example: Am Gaussian Pulse (Qsa)......Page 139
  4.3.3 Quasi Gaussian Approximation (Qga)......Page 140
  4.3.4 Example: Am Gaussian Pulse (Qga)......Page 142
  4.3.5 Change Of Pulse Center and Duration By A Lossless Network......Page 144
 4.4 Propagation and Distortion Of Pulses; Group Velocity......Page 145
  4.4.1 Propagation Of Arbitrary Pulses......Page 146
 4.5 Multimode Broadening Of Narrowband Pulses......Page 147
 4.6 Distortion Factor and Fidelity Factor......Page 149
  4.6.1 Example: Exponential Pulse in A Low Pass Filter......Page 150
 4.7 Wavefront Distortion......Page 151
 4.8 Moment Matching and Awe......Page 152
  4.8.1 Example......Page 155
 4.9 Notes and References......Page 156
 4.10 Problems......Page 160
 5.1 The Parallel Plate Waveguide......Page 164
  5.2.1 Modes......Page 168
  5.2.2 Reduced Maxwell Equations For Modes......Page 169
  5.2.3 Forward and Reverse Modes......Page 170
  5.2.4 Normalized Mode Fields, Power and Stored Energy......Page 171
  5.2.5 Example: The Parallel Plate Waveguide......Page 173
 5.3 “Hollow” Metallic Waveguides Of Arbitrary Cross Section......Page 174
  5.4.1 Tm Modes......Page 176
  5.4.3 The Eigenvalues......Page 177
  5.4.4 Power Flow and Stored Energy......Page 178
 5.5 Circular Waveguides (Method Of Separation Of Variables)......Page 179
  5.5.1 Normalized Mode Fields......Page 184
  5.5.2 Example: A Variable Attenuator......Page 186
 5.6 Rectangular Waveguides (Ray Description Of The Modes)......Page 187
  5.6.1 Normalized Mode Fields......Page 190
 5.7 Dielectric Losses in Hollow Waveguides......Page 191
 5.8 Notes and References......Page 193
 5.9 Problems......Page 194
 6.1 Introduction......Page 200
 6.2 Dielectric Slab Waveguides––The Ray Description......Page 202
 6.3 Dielectric Slab Waveguides––Field Analysis......Page 207
 6.4 Dielectric Slab Waveguides––The Eigenvalue Equation For Te Modes......Page 210
  6.4.1 Near Cutoff and Far From Cutoff Approximations......Page 214
 6.5 Tm Modes Of The Dielectric Slab......Page 216
 6.6 The Grounded Dielectric Slab......Page 217
 6.7 Circular Optical Fibers......Page 218
  6.7.1 The Weakly Guiding Fiber......Page 223
 6.8 Step Index Fibers Of Other Cross Sections......Page 229
  6.9.1 The Radiation Modes......Page 230
  6.9.2 Location Of Mode Propagation Coefficients......Page 232
 6.10 Notes and References......Page 233
 6.11 Problems......Page 235
  7.1.1 Te Modes......Page 240
 7.2 Graded Index Profiles......Page 243
  7.2.1 Example: A Diffused Slab Waveguide......Page 245
 7.3 Loaded Rectangular Waveguides......Page 247
  7.3.1 Ridged, Grooved and Finned Rectangular Metallic Waveguides......Page 250
 7.4 Quasi Optical Microstrip......Page 254
 7.5 Dielectric Rib Waveguide: The Effective Index Method......Page 259
 7.6 Notes and References......Page 263
 7.7 Problems......Page 265
 8.1 Introduction......Page 270
 8.2 Tem Modes......Page 272
  8.2.1 Power, Energy and Normalization Of Tem Modes......Page 278
  8.2.2 Multiconductor Tem Modes......Page 279
  8.3.1 The Coaxial Transmission Line......Page 282
  8.3.2 Two Wire Transmission Line......Page 283
  8.3.3 Open Stripline......Page 284
 8.4 Distributed Circuit Model Of Non Tem Modes......Page 286
  8.4.1 Definitions Of Line Parameters For Non Tem Modes......Page 289
  8.5.1 “Approximately” Tem Modes and The Quasi Tem Limit......Page 293
  8.5.2 Quasi Tem Modes On Lines Having Air and One Other Dielectric......Page 295
 8.6 Example: Open Microstrip......Page 296
  8.7.1 Open Coplanar Waveguide (Cpw)......Page 300
 8.8 Dispersion......Page 302
  8.8.1 Dispersion In Microstrip......Page 303
  8.8.2 Dispersion In Coplanar Transmission Lines......Page 304
 8.9 Pseudo Tem Modes......Page 305
  8.9.1 The Goubau Line......Page 307
  8.9.2 The Slot Line......Page 308
 8.10 Qualitative Analysis Of Open Planar Waveguides......Page 311
 8.11 Notes and References......Page 314
 8.12 Problems......Page 320
 9.1 Reciprocity and Reaction......Page 330
  9.1.1 Example......Page 333
 9.2 Orthogonality......Page 334
  9.2.1 Orthogonality Of Modes On Lossless Waveguides......Page 336
 9.3 Power Flow In Lossless Waveguides: Equivalent Transmission Line Model......Page 337
 9.4 Dielectric Losses In Waveguides......Page 339
  9.4.1 Example: Dielectric Loss For Quasi Tem Modes......Page 340
  9.4.2 Example: Dielectric Loss In Step Index, Weakly Guiding Waveguides......Page 341
 9.5 Wall Losses In Waveguides......Page 342
  9.5.1 Example: The Te01 Mode Of A Hollow Circular Waveguide......Page 345
  9.5.2 The Incremental Inductance Rule......Page 346
  9.5.3 Example: Conductor Loss In Coaxial Line......Page 348
 9.7 Notes and References......Page 349
 9.8 Problems......Page 352
 10.1 Impressed Sources Versus Induced Currents For Electromagnetic Fields......Page 360
 10.2 Equivalence Principles......Page 361
  10.2.1 Example: Impressed and Induced Sources At A Perfectly Conducting Surface......Page 363
  10.2.2 Example: Thevenin and Norton Types Of Equivalence Theorems For Electromagnetic Fields......Page 364
  10.2.3 Example: Large Apertures and The Kirchhoff Approximation......Page 365
  10.2.4 Example: Tangential Magnetic and Normal Electric Surface Sources......Page 366
  10.2.5 Example: Equivalent Dipoles For Electrically Small Objects......Page 367
  10.2.6 Example: Equivalent Dipoles For Electrically Small Apertures......Page 368
  10.2.7 Electrically Small Apertures In A Thick Conductor......Page 372
  10.2.8 Example: Plane Wave Incident At A Small Aperture......Page 373
 10.3 Equivalent Transmission Lines––Normalization and Characteristic Impedance......Page 374
 10.4 Expansion Of The Field As A Sum Of Modes......Page 375
  10.4.1 Representation Of The Longitudinal Field......Page 379
  10.4.2 Optimizing Excitation Of A Given Mode......Page 380
 10.5 Excitation By Given Arbitrary Aperture Fields......Page 381
  10.5.1 Example: Plane Wave Excitation Of A Dielectric Slab......Page 383
  10.5.3 Example: Excitation Of Microstrip By A Slot In The Ground Plane......Page 385
 10.6 Excitation By Electric And Magnetic Dipoles and Related Scattering Problems......Page 386
  10.6.1 Example: Dipole Excitation Of A Coaxial Cable......Page 387
  10.6.2 Example: Scattering By A Small Obstacle In A Rectangular Waveguide......Page 388
  10.6.3 Example: Diaphragm With A Small Aperture In A Rectangular Waveguide......Page 390
 10.7 Notes and References......Page 392
 10.8 Problems......Page 396
 11.1 Introduction......Page 402
 11.2 The Mode Matching Method......Page 406
  11.2.1 Generalized Scattering Matrix (Gsm)......Page 410
  11.2.2 Example: Parallel Plate Waveguide Step In Height......Page 412
  11.2.3 Example: Rectangular Waveguide Step In Width......Page 416
 11.3 One Port Equivalent Networks......Page 418
  11.4.1 The Open Ended Two Wire Line......Page 421
  11.4.2 A Microstrip Patch Antenna......Page 423
  11.4.3 Truncated Dielectric Slab Waveguide......Page 424
 11.5 Two Port and Multiport Networks......Page 425
  11.6.1 Transverse Diaphragm With Small Aperture In A Rectangular Waveguide......Page 426
  11.6.2 Capacitive Diaphragm; Partitioning Of Equivalent Networks......Page 427
  11.6.3 Right Angle Bend In Microstrip......Page 429
  11.7.1 Use Of Physical Symmetry–The E Plane and H Plane T–Junctions In A Rectangular Waveguide......Page 430
  11.7.2 90......Page 431
  11.7.4 Intersecting Dielectric Waveguides......Page 433
 11.8 Notes and References......Page 434
 11.9 Problems......Page 438
 12.1 Coupling Of Closed Metallic Waveguides......Page 442
  12.1.1 Example: Rectangular Waveguides Coupled Through A Continuous Slot In The Broad Wall......Page 445
 12.2 Coupled Wave Equations......Page 448
 12.3 Field Analysis Of Proximity Coupled Waveguides......Page 451
 12.4 Dielectric Waveguide Coupling......Page 454
  12.5.1 Adiabatic Coupling......Page 457
  12.5.2 Periodic and Contradirectional Coupling......Page 458
 12.6 Notes and References......Page 459
 12.7 Problems......Page 463
 13.1 Introduction......Page 466
 13.2 Lumped Element Resonators......Page 467
  13.2.1 Natural Modes Of An Isolated Resonator......Page 468
  13.2.2 Internal Excitation Of A Resonator......Page 469
  13.2.3 Natural Modes Of A Loaded Resonator......Page 472
  13.2.5 Example:......Page 475
 13.3 Cavity Resonators From Sections Of Metallic Waveguide......Page 477
  13.3.1 Example: Short Circuited Section Of Lossy Transmission Line......Page 479
  13.3.2 Mirror Resonators......Page 480
  13.3.3 Natural Modes Of Resonators Coupled To External Circuits......Page 481
  13.3.4 Steady State Excitation......Page 483
 13.4 Cavities Of Other Shapes......Page 488
  13.4.1 Orthogonality and Normalization......Page 489
  13.4.2 Excitation Of Cavities By Impressed Sources......Page 490
  13.4.3 Wall Losses In Cavity Resonators......Page 491
 13.5 Dielectric Resonators......Page 492
 13.6 Split Ring Resonators and Related Structures......Page 493
 13.7 Notes and References......Page 495
 13.8 Problems......Page 499
  A.1.1 Topological Laws (Kvl and Kcl)......Page 504
  A.1.2 Constitutive (Element) Laws......Page 506
  A.2.1 Lumped Networks......Page 507
  A.3.1 Lumped Networks......Page 508
  A.3.2 Transmission Lines......Page 511
  A.3.3 Decibels (Db)......Page 512
 A.4 Notes and References......Page 513
 B.1 Vectors......Page 514
 B.2 Matrices......Page 516
 B.3 Dyadics Or Tensors......Page 518
 B.4 Problems......Page 519
 C.1 Bessel Functions......Page 520
  C.1.1 Modified Bessel Functions......Page 524
  C.1.3 Integral Formulas......Page 526
 C.2 The Gamma Function......Page 527
 C.3 The Elliptic Integrals......Page 528
 C.4 The Lambert......Page 530
 C.5 A Function Arising In Microstrip Analysis......Page 531
 C.6 Notes and References......Page 532
 C.7 Problems......Page 533
 D.1 Maxwell’S Equations and Boundary Conditions......Page 534
 D.3 Poynting’S Theorem......Page 535
 D.4 Elementary Dipoles......Page 538
 D.5 Image Theory......Page 539
 D.6 Notes and References......Page 540
 E.1 Permittivity and Conductivity......Page 542
 E.2 Notes and References......Page 544
 F.1 The Exponential Line......Page 546
 F.2 The Bessel Line......Page 547
  F.2.1 Propagating Waves On A Bessel Line......Page 548
  F.2.2 Attenuating Waves On A Bessel Line......Page 550
 F.3 Chain Parameters, Reflection and Transmission At A Turning Point......Page 552
 F.4 Notes and References......Page 556
 F.5 Problems......Page 557
 G.1 Fourier Transforms......Page 558
 G.2 Laplace Transforms......Page 560
  G.2.1 Heaviside’S First Expansion Theorem......Page 561
 G.5 Notes and References......Page 562
Appendix H: Modes In Hollow Waveguides With Zero Cutoff Frequency......Page 564
Appendix I: Field Line Plotting......Page 566
 J.1 Identities For General, Lossy Waveguides......Page 568
 J.2 Identities For Modes In Lossless Waveguides......Page 571
 J.4 Expressions For Filling Factors......Page 573
 J.5 Bounds On Phase and Group Velocities......Page 575
 J.6 Notes and References......Page 577
 K.2 Newton’S Method......Page 580
 K.3 Iterative Methods......Page 581
 K.4 Notes and References......Page 582
Appendix L: Derivation Of The Surface Impedance For A Good Conductor......Page 584
 References......Page 585
Appendix M: Change In Inductance Due To Deformation Of Boundary......Page 586
Appendix N: Correction Of Small Obstacle and Small Hole Theory For Boundary Effects......Page 590
 References......Page 592
Appendix O: Overlap Integrals For Coupled Mode Theory......Page 594
 References......Page 595
Bibliography......Page 596
Index......Page 604