Analysis of Multiconductor Transmission Lines, 2E (Wiley Series in Microwave & Optical Engineering)

ANALYSIS OF MULTICONDUCTOR TRANSMISSION LINES, 2E......Page 1
Title page......Page 6
Copyright page......Page 7
Dedication......Page 8
Contents......Page 9
Preface......Page 19
1 Introduction......Page 25
1.1 Examples of Multiconductor Transmission-Line Structures......Page 29
1.2 Properties of the TEM Mode of Propagation......Page 32
1.3 The Transmission-Line Equations: A Preview......Page 42
1.3.1 Unique Definition of Voltage and Current for the TEM Mode of Propagation......Page 43
1.3.2 Defining the Per-Unit-Length Parameters......Page 46
1.3.3 Obtaining the Transmission-Line Equations from the Transverse Electromagnetic Field Equations......Page 52
1.3.4 Properties of the Per-Unit-Length Parameters......Page 54
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1.4 Classification of Transmission Lines......Page 56
1.4.1 Uniform versus Nonuniform Lines......Page 57
1.4.2 Homogeneous versus Inhomogeneous Surrounding Media......Page 59
1.4.3 Lossless versus Lossy Lines......Page 60
1.5 Restrictions on the Applicability of the Transmission-Line Equation Formulation......Page 61
1.5.1.1 The Infinite, Parallel-Plate Transmission Line......Page 62
1.5.1.2 The Coaxial Transmission Line......Page 67
1.5.1.3 Two-Wire Lines......Page 68
1.5.2 Transmission-Line Currents versus Antenna Currents......Page 69
1.6 The Time Domain versus the Frequency Domain......Page 71
1.6.1 The Fourier Series and Transform......Page 74
1.6.2 Spectra and Bandwidth of Digital Waveforms......Page 76
1.6.3 Computing the Time-Domain Response of Transmission Lines Having Linear Terminations Using Fourier Methods and Superposition......Page 80
Problems......Page 85
References......Page 93
2.1 Derivation of the Transmission-Line Equations from the Integral Form of Maxwell’s Equations......Page 95
2.2 Derivation of the Transmission-Line Equations from the Per-Unit-Length Equivalent Circuit......Page 101
2.3 Properties of the Per-Unit-Length Parameters......Page 102
2.4 Incorporating Frequency-Dependent Losses......Page 103
2.4.1 Properties of the Frequency-Domain Per-Unit-Length Impedance ˆz(w) and Admittance ˆy(w)......Page 105
Problems......Page 109
References......Page 112
3.1 Derivation of the Multiconductor Transmission-Line Equations from the Integral Form of Maxwell’s Equations......Page 113
3.2 Derivation of the Multiconductor Transmission-Line Equations from the Per-Unit-Length Equivalent Circuit......Page 123
3.3 Summary of the MTL Equations......Page 125
3.4 Incorporating Frequency-Dependent Losses......Page 126
3.5 Properties of the Per-Unit-Length Parameter Matrices L, C, G......Page 127
Problems......Page 132
References......Page 133
4 The Per-Unit-Length Parameters for Two-Conductor Lines......Page 134
4.1 Definitions of the Per-Unit-Length Parameters l, c, and g......Page 135
4.2.1 Fundamental Subproblems for Wires......Page 137
4.2.1.1 The Method of Images......Page 142
4.2.2 Per-Unit-Length Inductance and Capacitance for Wire-Type Lines......Page 143
4.2.3 Per-Unit-Length Conductance and Resistance for Wire-Type Lines......Page 154
4.3 Lines Having Conductors of Rectangular Cross Section (PCB Lands)......Page 168
4.3.1 Per-Unit-Length Inductance and Capacitance for PCB-Type Lines......Page 169
4.3.2 Per-Unit-Length Conductance and Resistance for PCB-Type Lines......Page 172
Problems......Page 180
References......Page 182
5 The Per-Unit-Length Parameters for Multiconductor Lines......Page 184
5.1 Definitions of the Per-Unit-Length Parameter Matrices L, C, and G......Page 185
5.1.1 The Generalized Capacitance Matrix C......Page 191
5.2.1 Wide-Separation Approximations for Wires in Homogeneous Media......Page 195
5.2.1.2 n Wires Above an Infinite, Perfectly Conducting Plane......Page 197
5.2.1.3 n Wires Within a Perfectly Conducting Cylindrical Shield......Page 198
5.2.2 Numerical Methods for the General Case......Page 200
5.2.2.1 Applications to Inhomogeneous Dielectric Media......Page 205
5.2.3 Computed Results: Ribbon Cables......Page 211
5.3 Multiconductor Lines Having Conductors of Rectangular Cross Section......Page 213
5.3.1 Method of Moments (MoM) Techniques......Page 214
5.3.1.1 Applications to Printed Circuit Boards......Page 223
5.3.1.2 Applications to Coupled Microstrip Lines......Page 235
5.3.1.3 Applications to Coupled Striplines......Page 243
5.4 Finite Difference Techniques......Page 247
5.5 Finite-Element Techniques......Page 253
Problems......Page 261
References......Page 263
6 Frequency-Domain Analysis of Two-Conductor Lines......Page 264
6.1 The Transmission-Line Equations in the Frequency Domain......Page 265
6.2 The General Solution for Lossless Lines......Page 266
6.2.1 The Reflection Coefficient and Input Impedance......Page 268
6.2.2 Solutions for the Terminal Voltages and Currents......Page 271
6.2.3 The SPICE (PSPICE) Solution for Lossless Lines......Page 274
6.2.4 Voltage and Current as a Function of Position on the Line......Page 276
6.2.5 Matching and VSWR......Page 279
6.2.6 Power Flow on a Lossless Line......Page 280
6.3 The General Solution for Lossy Lines......Page 282
6.3.1 The Low-Loss Approximation......Page 284
6.4 Lumped-Circuit Approximate Models of the Line......Page 289
6.5 Alternative Two-Port Representations of the Line......Page 293
6.5.1 The Chain Parameters......Page 294
6.5.2 Approximating Abruptly Nonuniform Lines with the Chain-Parameter Matrix......Page 297
6.5.3 The Z and Y Parameters......Page 299
Problems......Page 302
7.1 The MTL Transmission-Line Equations in the Frequency Domain......Page 306
7.2.1 Decoupling the MTL Equations by Similarity Transformations......Page 308
7.2.2 Solution for Line Categories......Page 315
7.2.2.1 Perfect Conductors in Lossy, Homogeneous Media......Page 316
7.2.2.2 Lossy Conductors in Lossy, Homogeneous Media......Page 317
7.2.2.3 Perfect Conductors in Lossless, Inhomogeneous Media......Page 320
7.2.2.5 Cyclic-Symmetric Structures......Page 322
7.3.1 The Generalized Thevenin Equivalent......Page 329
7.3.2 The Generalized Norton Equivalent......Page 332
7.3.3 Mixed Representations......Page 334
7.4 Lumped-Circuit Approximate Characterizations......Page 336
7.5.1 Analogy of the Frequency-Domain MTL Equations to State-Variable Equations......Page 338
7.5.2 Characterizing the Line as a 2n-Port with the Chain-Parameter Matrix......Page 340
7.5.3 Properties of the Chain-Parameter Matrix......Page 342
7.5.4 Approximating Nonuniform Lines with the Chain-Parameter Matrix......Page 346
7.5.5 The Impedance and Admittance Parameter Matrix Characterizations......Page 347
7.6 Power Flow and the Reflection Coefficient Matrix......Page 351
7.7.1 Ribbon Cables......Page 356
7.7.2 Printed Circuit Boards......Page 359
Problems......Page 362
References......Page 366
8 Time-Domain Analysis of Two-Conductor Lines......Page 367
8.1 The Solution for Lossless Lines......Page 368
8.1.1 Wave Tracing and the Reflection Coefficients......Page 370
8.1.2 Series Solutions and the Difference Operator......Page 380
8.1.3 The Method of Characteristics and a Two-Port Model of the Line......Page 385
8.1.4 The SPICE (PSPICE) Solution for Lossless Lines......Page 389
8.1.5 The Laplace Transform Solution......Page 392
8.1.5.1 Lines with Capacitive and Inductive Loads......Page 394
8.1.6 Lumped-Circuit Approximate Models of the Line......Page 397
8.1.6.1 When is the Line Electrically Short in the Time Domain?......Page 398
8.1.7 The Time-Domain to Frequency-Domain (TDFD) Transformation Method......Page 399
8.1.8 The Finite-Difference, Time-Domain (FDTD) Method......Page 403
8.1.8.1 The Magic Time Step......Page 409
8.1.9 Matching for Signal Integrity......Page 416
8.1.9.1 When is Matching Required?......Page 422
8.1.9.2 Effects of Line Discontinuities......Page 423
8.2 Incorporation of Losses......Page 430
8.2.1.1 Representing Losses in the Medium......Page 432
8.2.1.2 Representing Losses in the Conductors and Skin Effect......Page 434
8.2.1.3 Convolution with Frequency-Dependent Losses......Page 439
8.2.2 The Time-Domain to Frequency-Domain (TDFD) Transformation Method......Page 445
8.2.3.1 Including Frequency-Independent Losses......Page 447
8.2.3.2 Including Frequency-Dependent Losses......Page 451
8.2.3.3 Prony’s Method for Representing a Function......Page 455
8.2.3.4 Recursive Convolution......Page 458
8.2.3.5 An Example: A High-Loss Line......Page 463
8.2.3.6 A Correction for the FDTD Errors......Page 467
8.2.4 Lumped-Circuit Approximate Characterizations......Page 471
8.2.5 The Use of Macromodels in Modeling the Line......Page 474
8.2.6 Representing Frequency-Dependent Functions in the Time Domain Using Pade Methods......Page 477
Problems......Page 485
References......Page 491
9.1 The Solution for Lossless Lines......Page 494
9.1.1 The Recursive Solution for MTLs......Page 495
9.1.2 Decoupling the MTL Equations......Page 500
9.1.2.1 Lossless Lines in Homogeneous Media......Page 502
9.1.2.2 Lossless Lines in Inhomogeneous Media......Page 503
9.1.2.3 Incorporating the Terminal Conditions via the SPICE Program......Page 506
9.1.3 Lumped-Circuit Approximate Characterizations......Page 511
9.1.5 The Finite-Difference, Time-Domain (FDTD) Method......Page 512
9.1.5.1 Including Dynamic and/or Nonlinear Terminations in the FDTD Analysis......Page 514
9.2 Incorporation of Losses......Page 520
9.2.2 Lumped-Circuit Approximate Characterizations......Page 522
9.2.3 The Finite-Difference, Time-Domain (FDTD) Method......Page 523
9.2.4 Representation of the Lossy MTL with the Generalized Method of Characteristics......Page 525
9.2.5.1 Pade Approximation of the Matrix Exponential......Page 536
9.2.5.2 Asymptotic Waveform Evaluation (AWE)......Page 539
9.2.5.4 Vector Fitting......Page 542
9.3 Computed and Experimental Results......Page 548
9.3.1 Ribbon Cables......Page 550
9.3.2 Printed Circuit Boards......Page 554
Problems......Page 561
References......Page 565
10 Literal (Symbolic) Solutions for Three-Conductor Lines......Page 568
10.1 The Literal Frequency-Domain Solution for a Homogeneous Medium......Page 572
10.1.1 Inductive and Capacitive Coupling......Page 578
10.1.2 Common-Impedance Coupling......Page 580
10.2 The Literal Time-Domain Solution for a Homogeneous Medium......Page 582
10.2.1 Explicit Solution......Page 584
10.2.2 Weakly Coupled Lines......Page 586
10.2.3 Inductive and Capacitive Coupling......Page 588
10.3 Computed and Experimental Results......Page 591
10.3.1 A Three-Wire Ribbon Cable......Page 592
10.3.2 A Three-Conductor Printed Circuit Board......Page 593
Problems......Page 599
References......Page 600
11.1 Derivation of the Transmission-Line Equations for Incident Field Excitation......Page 602
11.1.1 Equivalence of Source Representations......Page 609
11.2.1 Solution of the Transmission-Line Equations......Page 610
11.2.2 Simplified Forms of the Excitations......Page 616
11.2.3 Incorporating the Line Terminations......Page 618
11.2.4 Uniform Plane-Wave Excitation of the Line......Page 622
11.2.4.1 Special Cases......Page 626
11.2.4.2 One Conductor Above a Ground Plane......Page 630
11.2.5 Comparison with Predictions of Method of Moments Codes......Page 634
11.3.1 The Laplace Transform Solution......Page 635
11.3.2 Uniform Plane-Wave Excitation of the Line......Page 644
11.3.3 A SPICE Equivalent Circuit......Page 649
11.3.5 The Finite-Difference, Time-Domain (FDTD) Solution Method......Page 652
11.3.6 Computed Results......Page 659
Problems......Page 662
References......Page 663
12 Incident Field Excitation of Multiconductor Lines......Page 665
12.1 Derivation of the MTL Equations for Incident Field Excitation......Page 666
12.1.1 Equivalence of Source Representations......Page 672
12.2 Frequency-Domain Solutions......Page 674
12.2.1 Solution of the MTL Equations......Page 675
12.2.2 Simplified Forms of the Excitations......Page 677
12.2.3 Incorporating the Line Terminations......Page 679
12.2.3.1 Lossless Lines in Homogeneous Media......Page 682
12.2.5 Uniform Plane-Wave Excitation of the Line......Page 684
12.3 The Time-Domain Solution......Page 691
12.3.1 Decoupling the MTL Equations......Page 692
12.3.2 A SPICE Equivalent Circuit......Page 698
12.3.4 The Time-Domain to Frequency-Domain (TDFD) Transformation......Page 705
12.3.5 The Finite-Difference, Time-Domain (FDTD) Solution Method......Page 706
12.4 Computed Results......Page 710
Problems......Page 715
References......Page 716
13 Transmission-Line Networks......Page 717
13.1 Representation of Lossless Lines with the SPICE Model......Page 720
13.3 Representation via the Admittance or Impedance 2n-Port Parameters......Page 723
13.4 Representation with the BLT Equations......Page 736
13.5 Direct Time-Domain Solutions in Terms of Traveling Waves......Page 745
13.6 A Summary of Methods for Analyzing Multiconductor Transmission Lines......Page 750
Problems......Page 751
References......Page 752
Publications by the Author Concerning Transmission Lines......Page 753
Appendix A. Description of Computer Software......Page 760
A.1.1 Wide-Separation Approximations for Wires: WIDESEP.FOR......Page 762
A.1.2 Ribbon Cables: RIBBON.FOR......Page 764
A.1.3 Printed Circuit Boards: PCB.FOR......Page 767
A.1.4 Coupled Microstrip Structures: MSTRP.FOR......Page 769
A.1.5 Coupled Stripline Structures: STRPLINE.FOR......Page 770
A.2.1 General: MTL.FOR......Page 771
A.3.2 Branin’s Method Extended to Multiconductor Lines: BRANIN.FOR......Page 772
A.4 SPICE/PSPICE Subcircuit Generation Programs......Page 773
A.4.2 Lumped-Pi Circuit, Lossless Lines: SPICELPI.FOR......Page 774
A.4.3 Inductive-Capacitive Coupling Model: SPICELC.FOR......Page 775
A.5.1 Frequency-Domain Program: INCIDENT.FOR......Page 776
A.5.2 SPICE/PSPICE Subcircuit Model: SPICEINC.FOR......Page 777
A.5.3 Finite-Difference, Time-Domain (FDTD) Model: FDTDINC.FOR......Page 778
References......Page 779
Appendix B. A SPICE (PSPICE) Tutorial......Page 780
B.1 Creating the SPICE or PSPICE Program......Page 781
B.2 Circuit Description......Page 782
B.3 Execution Statements......Page 787
B.4 Output Statements......Page 789
B.5 Examples......Page 791
B.6 The Subcircuit Model......Page 793
References......Page 795
Index......Page 797