Analysis of Multiconductor Transmission Lines (Wiley Series in Microwave & Optical Engineering, 28)

ANALYSIS OF MULTICONDUCTOR TRANSMISSION LINES......Page 1
Series......Page 5
Title page......Page 6
Copyright page......Page 7
Dedication......Page 8
Contents......Page 9
Preface......Page 17
1 Introduction......Page 21
1.1 Examples of Multiconductor Transmission-Line Structures......Page 24
1.2 Properties of the Transverse ElectroMagnetic (TEM) Mode of Propagation......Page 27
1.3.1 Derivation from the Integral Form of Maxwell's Equation......Page 33
1.3.2 Derivation from the Diflerential Form of Maxwell's Equations......Page 41
1.3.3 Derivatipn from the Per-Unit-Length Equivalent Circuit......Page 42
1.3.4 Properties of the Per-Unit-Length Parameters......Page 44
1.4 Classification of Transmission Lines......Page 46
1.5.1.1 The Infinite Parallel-Plate Transmission Line......Page 50
1.5.1.2 The Coaxial Transmission Line......Page 56
1.5.2 Transmission-Line Currents vs. Antenna Currents......Page 57
References......Page 60
Problems......Page 62
2.1 Derivation from the Integral Form of Maxwell's Equations......Page 66
2.2 Derivation from the Per-Unit-Length Equivalent Circuit......Page 76
2.3 Summary of the MTL Equations......Page 77
2.4 Properties of the Per-Unit-Length Parameter Matrices L, C, G......Page 78
Problems......Page 82
3 The Per-Unit-Length Parameters......Page 84
3.1.1 The Per-Unit-Length Inductance Matrix, L......Page 85
3.1.2 The Per-Unit-Length Capacitance Matrix, C......Page 89
3.1.3 The Per-Unit-Length Conductance Matrix, G......Page 92
3.1.4 The Generalized Capacitance Matrix, C......Page 93
3.2.1.1 Magnetic Flux Due to a Filament of Current......Page 97
3.2.1.2 Voltage Due to a Filament of Charge......Page 100
3.2.1.3 The Method of Images......Page 102
3.2.2.1 Two Wires......Page 103
3.2.2.2 One Wire Above an Infinite, Perfectly Conducting Plane......Page 109
3.2.2.3 The Coaxial Cable......Page 110
3.2.3 Wide-Separation Approximations for Wires in Homogeneous Media......Page 112
3.2.3.2 n Wires Above an Infinite, Perfectly Conducting Plane......Page 113
3.2.3.3 n Wires Within a Perfectly Conducting Shield......Page 116
3.2.4 Numerical Methods for the General Case......Page 117
3.2.4.1 Applications to Inhomogeneous Dielectric Media......Page 123
3.2.5 Computed Results: Ribbon Cables......Page 129
3.3 Multiconductor Lines Having Conductors of Rectangular Cross Section......Page 133
3.3.1 Method of Moments (MOM) Techniques......Page 135
3.3.1.1 Applications to Printed Circuit Boards......Page 144
3.3.1.2 Computed Results: Printed Circuit Boards......Page 155
3.3.2 Finite Difference Techniques......Page 160
3.3.3 Finite Element Techniques......Page 166
3.4 Miscellaneous Additional Techniques......Page 173
3.4.1 Conformal Mapping Techniques......Page 174
3.4.2 Spectral-Domain Techniqucs......Page 175
3.5 Shielded Unes......Page 176
3.6 Incorporaron of Losses; Calculation of R, Lh and G......Page 177
3.6.1 Calculation of the Per-Unit-Length Conductance Matrix, G......Page 178
3.6.2 Representation of Conductor Losses......Page 181
3.6.2.1 Surface Impedance of Plane Conductors......Page 182
3.6.2.2 Resistance and Internal Inductance of Wires......Page 184
3.6.2.3 Internal Impedance of Rectangular Cross Section Conductors......Page 188
3.6.2.4 Approximate Representation of Conductor Internal Impedances in the Frequency Domain......Page 197
References......Page 200
Problems......Page 202
4.1 The MTL Equations for Sinusoidal Steady-State Excitation......Page 206
4.2 Solutions for Two-Conductor Lines......Page 209
4.3 General Solution for an (n + 1)-Conductor Line......Page 214
4.3.1 Analogy of the MTL Equations to the State-Variable Equations......Page 215
4.3.2 Decoupling the MTL Equations by Similarity Transformations......Page 220
4.3.3 Characterizing the Line as a 2n Port with the Chain Parameter Matrix......Page 225
4.3.4 Properties of the Chain Parameter Matrix......Page 226
4.3.5 Incorporating the Terminal Conditions......Page 229
4.3.5.1 The Generalized Thévenin Equivalent......Page 230
4.3.5.2 The Generalized Norton Equivalent......Page 233
4.3.5.3 Mixed Representations......Page 234
4.3.6 Approximating Nonuniform Lines......Page 236
4.4 Solution for Line Categories......Page 239
4.4.1 Perfect Conductors in Homogeneous Media......Page 240
4.4.2 Lossy Conductors in Homogeneous Media......Page 242
4.4.3 Perfect Conductors in Inhomogeneous Media......Page 244
4.4.5 Cyclic Symmetric Structures......Page 245
4.5 Lumped-Circuit Iterative Approximate Characterizations......Page 251
4.6 Alternative 2n-Port Characterizations......Page 254
4.7 Power and the Reflection Coefficient Matrix......Page 256
4.8 Computed Results......Page 258
4.8.1 Ribbon Cables......Page 259
4.8.2 Printed Circuit Boards......Page 261
Problems......Page 266
5 Time-Domain Analysis......Page 272
5.1 Two-Conductor Lossless Lines......Page 273
5.1.1 Graphical Solutions......Page 277
5.1.2 The Method of Characteristics (Branin's Method)......Page 286
5.1.3 The Bergeron Diagram......Page 290
5.2 Multiconductor Lossless Lines......Page 295
5.2.1 Decoupling the MTL Equations......Page 297
5.2.1.1 Lossless Lines in Homogeneous Media......Page 299
5.2.1.2 Lossless Lines in Inhomogeneous Media......Page 300
5.2.1.3 Incorporating the Terminal Conditions via the SPICE Program......Page 303
5.2.2 Extension of Branin's Method to Lossless Multiconductor Lines in Homogeneous Media......Page 308
5.2.3 Time-Domain to Frequency-Domain Transformations......Page 312
5.2.5 Finite Difference-Time Domain (FDTD) Methods......Page 315
5.2.6 Computed Results......Page 329
5.2.6.1 Ribbon Cable......Page 331
5.2.6.2 Printed Circuit Board......Page 337
5.3 Incorporation of Losses......Page 340
5.3.1 Two-Conductor Lossy Lines......Page 343
5.3.1.1 Lumped-Circuit Approximate Characterizations......Page 344
5.3.1.2 Time-Domain to Frequency-Domain Transformations......Page 345
5.3.1.3 Finite Difference-Time Domain (FDTD) Methods......Page 346
5.3.1.4 Direct Solution via Inversion of the Laplace Transform......Page 354
5.3.1.5 Time-Domain Characterization of the Line as a Two Port......Page 357
5.3.2 Multiconductor Lines......Page 363
5.3.3 Computed Results......Page 367
5.3.3.1 Ribbon Cable......Page 368
References......Page 371
Problems......Page 374
6 Literal (Symbollc) Solutions for Three-Conductor Lines......Page 379
6.1 Frequency-Domain Solution......Page 383
6.1.1 Inductive and Capacitive Coupling......Page 387
6.1.2 Common-Impedance Coupling......Page 389
6.2 Time-Domain Solution......Page 391
6.2.1 Explicit Solution......Page 393
6.2.2 Weakly Coupled Lines......Page 395
6.2.3 Inductive and Capacitive Coupling......Page 398
6.2.4 Common-Impedance Coupling......Page 402
6.3.1 A Three-Wire Ribbon Cable......Page 403
6.3.2 A Three-Conductor Printed Circuit Board......Page 408
References......Page 413
Problems......Page 414
7.1 Derivation of the MTL Equations for Incident-Field Excitation......Page 415
7.1.1 Equivalence of Source Representations......Page 422
7.2 Frequency-Domain Solutions......Page 425
7.2.1 Solution of the MTL Equations......Page 426
7.2.1.1 Simplified Forms of the Excitations......Page 427
7.2.2 Incorporaron of the Terminal Conditions......Page 430
7.2.2.1 Lossless Lines in Homogeneous Media......Page 433
7.2.3 Lumped-Circuit Iterative Approximate Characterizations......Page 435
7.2.4 Uniform Plane-Wave Excitation of the Line......Page 436
7.2.5 Two-Conductor Lines......Page 443
7.2.5.1 Uniform Plane-Wave Excitation of the Line......Page 445
7.2.5.2 Special Cases......Page 446
7.2.5.3 One Conductor Above a Oround Plane......Page 449
7.2.5.4 Electrically Short Lines......Page 453
7.2.6.1 Comparison with Predictions of the Method of Moments Codes......Page 455
7.2.6.2 A Three-Wire Line in an Incident Uniform Plane Wave......Page 460
7.3 Time-Domain Solutions......Page 464
7.3.1.1 The General Solution via the Method of Characteristics......Page 466
7.3.1.2 The General Solution via the Frequency Domain......Page 468
7.3.1.3 Uniform Plane-Wave Excitation of the Line......Page 473
7.3.1.4 Electrically Short Lines......Page 479
7.3.1.5 A SPICE Equivalent Circuit......Page 480
7.3.1.6 Computed Results......Page 483
7.3.2 Multiconductor Lines......Page 486
7.3.2.1 Decoupling the MTL Equations......Page 487
7.3.2.2 A SPICE Equivalent Circuit......Page 490
7.3.2.4 Time-Domain to Frequency-Domain Transformations......Page 495
7.3.2.5 Finite Difference-Time Domain Methods......Page 497
7.3.2.6 Computed Results......Page 500
References......Page 506
Problems......Page 507
8 Transmission-Line Networks......Page 509
8.2 Representation with Lumped-Circuit Iterative Models......Page 512
8.3 Representation via the Admittance or Impedance Parameters......Page 514
8.4 Representation with the BLT Equations......Page 528
8.5 Direct Time-Domain Solutions in terms of Traveling Waves......Page 537
References......Page 542
Problems......Page 543
Publications by the Author Concerning Transmission Lines......Page 545
Appendix A Description of Computer Software......Page 551
A.l Programs for Calculation of the Per-Unit-Length Parameters......Page 552
A. 1.1 Wide-Separation Approximations for Wires: WIDESEP.FOR......Page 553
A.1.2 Ribbon Cables: RIBBON.FOR......Page 556
A.1.3 Printed Circuit Boards: PCB.FOR, PCBGAL.FOR......Page 559
A.1.4 Coupled Microstrip Structures: MSTRP.FOR, MSTRPGAL.FOR......Page 561
A.2.1 General: MTL.FOR......Page 562
A.3.1 Time-Domain to Frequency-Domain Transformaron: TIMEFREQ.FOR......Page 563
A.3.4 Finite Difference-Time Domain Method: FDTDLOSS.FOR......Page 564
A.4.2 Lumped-pi Circuit, ¡Lossless Lines: SPICELPI.FOR......Page 565
A.5 Incident Field Excitation......Page 567
A.5.1 Frequency-Domain Program: INCIDENT.FOR 547 A.5.2 SPICE/PSPICE Subcircuit Model: SPICEINC.FOR......Page 568
A.5.3 Finite Diffcrence-Time Domain (FDTD) Model: FDTDINCFOR......Page 570
References......Page 571
B......Page 572
C......Page 573
D......Page 576
E......Page 577
F......Page 578
G......Page 581
I......Page 582
L......Page 584
M......Page 585
P......Page 587
Q......Page 589
S......Page 590
T......Page 592
V......Page 594
W......Page 595