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```TABLE OF CONTENTS
Preface
Chapter 1	Introduction
1.1	Examples of Multiconductor Transmission-Line Structures
1.2	Properties of the Transverse ElectroMagnetic (TEM) Mode of Propagation
1.3	The Transmission-Line Equations: a Preview
1.3.1	Unique Definition of Voltage and Current for the TEM Mode of Propagation
1.3.2	Defining the Per-Unit-Length Parameters
1.3.3	Obtaining the Transmission-Line Equations from the Transverse Electromagnetic Field Equations
1.3.4	Properties of the Per-Unit-Length Parameters
1.4	Classification of Transmission Lines
1.4.1	Uniform vs. Nonuniform Lines
1.4.2	Homogeneous vs. Inhomogeneous Surrounding Media
1.4.3	Lossless vs. Lossy Lines
1.5	Restrictions on the Applicability of the Transmission-Line Equation Formulation
1.5.1	Higher-Order Modes
1.5.1.1	The Infinite, Parallel-Plate Transmission Line
1.5.1.2	The Coaxial Transmission Line
1.5.1.3	Two-Wire Lines
1.5.2	Transmission-Line Currents vs. Antenna Currents
1.6	The Time Domain vs. the Frequency Domain
1.6.1	The Fourier Series and Transform
1.6.2	Spectra and Bandwidth of Digital Waveforms
1.6.3	Computing the Time-Domain Response of Transmission Lines Having Linear Terminations Using Fourier Methods and Superposition
References
Problems
Chapter 2	The Transmission-Line Equations for Two-Conductor Lines
2.1	Derivation of the Transmission-Line Equations from the Integral Form of Maxwell's Equations
2.2	Derivation of the Transmission-Line Equations from the Per-Unit-Length Equivalent Circuit
2.3	Properties of the Per-Unit-Length Parameters
2.4	Incorporating Frequency-Dependent Losses
2.4.1	Properties of the Frequency-Domain Per-Unit-Length Impedance and Admittance
References
Problems
Chapter 3	The Transmission-Line Equations for Multiconductor Lines
3.1	Derivation of the Multiconductor Transmission-Line Equations from the Integral Form of Maxwell's Equations
3.2	Derivation of the Multiconductor Transmission-Line Equations from the Per-Unit-Length Equivalent Circuit
3.3	Summary of the MTL Equations
3.4	Incorporating Frequency-Dependent Losses
3.5	Properties of the Per-Unit-Length Parameter Matrices L, C, G
References
Problems
Chapter 4	The Per-Unit-Length Parameters for Two-Conductor Lines
4.1	Definitions of the Per-Unit-Length Parameters l, c, and g
4.2	Lines Having Conductors of Circular, Cylindrical Cross Section (Wires)
4.2.1	Fundamental Subproblems for Wires
4.2.1.1	The Method of Images
4.2.2	Per-Unit-Length Inductance and Capacitance for Wire-Type Lines
4.2.3	Per-Unit-Length Conductance and Resistance for Wire-Type Lines
4.3	Lines Having Conductors of Rectangular Cross Section (PCB Lands)
4.3.1	Per-Unit-Length Inductance and Capacitance for PCB-Type Lines
4.3.2	Per-Unit-Length Conductance and Resistance for PCB-Type Lines
References
Problems
Chapter 5	The Per-Unit-Length Parameters for Multiconductor Lines
5.1	Definitions of the Per-Unit-Length Parameter Matrices L, C, and G
5.1.1	The Generalized Capacitance Matrix,
5.2	Multiconductor Lines Having Conductors of Circular, Cylindrical Cross Section (Wires)
5.2.1	Wide-Separation Approximations for Wires in Homogeneous Media
5.2.1.1	(n+1) Wires
5.2.1.2	n Wires Above an Infinite, Perfectly-Conducting Plane
5.2.1.3	n Wires Within a Perfectly-Conducting, Cylindrical Shield
5.2.2	Numerical Methods for the General Case
5.2.2.1	Applications to Inhomogeneous Dielectric Media
5.2.3	Computed Results: Ribbon Cables
5.3	Multiconductor Lines Having Conductors of Rectangular Cross Section
5.3.1	Method of Moments (MoM) Techniques
5.3.1.1	Applications to Printed Circuit Boards
5.3.1.2	Applications to Coupled Microstrip Lines
5.3.1.3	Applications to Coupled Striplines
5.4	Finite Difference Techniques
5.5	Finite Element Techniques
References
Problems
Chapter 6	Frequency-Domain Analysis of Two-Conductor Lines
6.1	The Transmission-Line Equations in the Frequency Domain
6.2	The General Solution for Lossless Lines
6.2.1	The Reflection Coefficient and Input Impedance
6.2.2	Solutions for the Terminal Voltages and Currents
6.2.3	The SPICE (PSPICE) Solution for Lossless Lines
6.2.4	Voltage and Current as a Function of Position on the Line
6.2.5	Matching and VSWR
6.2.6	Power Flow on a Lossless Line
6.3	The General Solution for Lossy Lines
6.3.1	The Low-Loss Approximation
6.4	Lumped-Circuit Approximate Models of the Line
6.5	Alternative Two-Port Representations of the Line
6.5.1	The Chain Parameters
6.5.2	Approximating Abruptly Nonuniform Lines with the Chain Parameter Matrix
6.5.3	The Z and Y Parameters
Problems
Chapter 7	Frequency-Domain Analysis of Multiconductor Lines
7.1	The MTL Transmission-Line Equations in the Frequency Domain
7.2	The General Solution for an (n+1)-Conductor Line
7.2.1	Decoupling the MTL Equations by Similarity Transformations
7.2.2	Solution for Line Categories
7.2.2.1	Perfect Conductors in Lossy, Homogeneous Media
7.2.2.2	Lossy Conductors in Lossy, Homogeneous Media
7.2.2.3	Perfect Conductors in Lossless, Inhomogeneous Media
7.2.2.4	The General Case: Lossy Conductors in Lossy, Inhomogeneous Media
7.2.2.5	Cyclic-Symmetric Structures
7.3	Incorporating the Terminal Conditions
7.3.1	The Generalized Thevenin Equivalent
7.3.2	The Generalized Norton Equivalent
7.3.3	Mixed Representations
7.4	Lumped-Circuit Approximate Characterizations
7.5	Alternative 2n-Port Characterizations
7.5.1	Analogy of the Frequency-Domain MTL Equations to State-Variable Equations
7.5.2	Characterizing the Line as a 2n-Port with the Chain Parameter Matrix
7.5.3	Properties of the Chain Parameter Matrix
7.5.4	Approximating Nonuniform Lines with the Chain Parameter Matrix
7.5.5	The Impedance and Admittance Parameter Matrix Characterizations
7.6	Power Flow and the Reflection Coefficient Matrix
7.7	Computed and Experimental Results
7.7.1	Ribbon Cables
7.7.2	Printed Circuit Boards
References
Problems
Chapter 8	Time-Domain Analysis of Two-Conductor Lines
8.1	The Solution for Lossless Lines
8.1.1	Wave Tracing and the Reflection Coefficients
8.1.2	Series Solutions and the Difference Operator
8.1.3	The Method of Characteristics and a Two-Port Model of the Line
8.1.4	The SPICE (PSPICE) Solution for Lossless Lines
8.1.5	The Laplace Transform Solution
8.1.5.1	Lines with Capacitive and Inductive Loads
8.1.6	Lumped-Circuit Approximate Models of the Line
8.1.6.1	When is the Line Electrically Short in the Time Domain?
8.1.7	The Time-Domain to Frequency-Domain (TDFD) Transformation Method
8.1.8	The Finite-Difference, Time-Domain (FDTD) Method
8.1.8.1	The Magic Time Step
8.1.9	Matching for Signal Integrity
8.1.9.1	When is Matching Not Required?
8.1.9.2	Effects of Line Discontinuities
8.2	Incorporation of Losses
8.2.1	Representing Frequency-Dependent Losses
8.2.1.1	Representing Losses in the Medium
8.2.1.2	Representing Losses in the Conductors and Skin Effect
8.2.1.3	Convolution with Frequency-Dependent Losses
8.2.2	The Time-Domain to Frequency-Domain (TDFD) Transformation Method
8.2.3	The Finite-Difference, Time-Domain (FDTD) Method
8.2.3.1	Including Frequency-Independent Losses
8.2.3.2	Including Frequency-Dependent Losses
8.2.3.3	Prony?s Method for Representing a Function
8.2.3.4	Recursive Convolution
8.2.3.5	An Example: A High-Loss Line
8.2.3.6	A Correction for the FDTD Errors
8.2.4	Lumped-Circuit Approximate Characterizations
8.2.5	The Use of Macromodels in Modeling the Line
8.2.6	Representing Frequency-Dependent Functions in the Time Domain Using Pade? Methods
Chapter 9	Time-Domain Analysis of Multiconductor Lines
9.1	The Solution for Lossless Lines
9.1.1	The Recursive Solution for MTLs
9.1.2	Decoupling the MTL Equations
9.1.2.1	Lossless Lines in Homogeneous Media
9.1.2.2	Lossless Lines in Inhomogeneous Media
9.1.2.3	Incorporating the Terminal Conditions via the SPICE Program
9.1.3	Lumped-Circuit Approximate Characterizations
9.1.4	The Time-Domain to Frequency-Domain (TDFD) Transformation Method
9.1.5	The Finite-Difference, Time-Domain (FDTD) Method
9.1.5.1	Including Dynamic and/or Nonlinear Terminations in the FDTD Analysis
9.2	Incorporation of Losses
9.2.1	The Time-Domain to Frequency-Domain (TDFD) Transformation Method
9.2.2	Lumped-Circuit Approximate Characterizations
9.2.3	The Finite-Difference, Time-Domain (FDTD) Method
9.2.4	Representation of the Lossy MTL with the Generalized Method of Characteristics
9.2.5	Model Order Reduction (MOR) Methods
9.2.5.1	Pade? Approximation of the Matrix Exponential
9.2.5.2	Asymptotic Waveform Evaluation (AWE)
9.2.5.3	Complex Frequency Hopping (CFH)
9.2.5.4	Vector Fitting and MOR
9.3	Computed and Experimental Results
9.3.1	Ribbon Cables
9.3.2	Printed Circuit Boards
References
Problems
Chapter 10	Literal (Symbolic) Solutions for Three-Conductor Lines
10.1	The Literal, Frequency-Domain Solution for a Homogeneous Medium
10.1.1	Inductive and Capacitive Coupling
10.1.2	Common Impedance Coupling
10.2	The Literal, Time-Domain Solution for a Homogeneous Medium
10.2.1	Explicit Solution
10.2.2	Weakly Coupled Lines
10.2.3	Inductive and Capacitive Coupling
10.2.4	Common Impedance Coupling
10.3	Computed and Experimental Results
10.3.1	A Three-Wire Ribbon Cable
10.3.2	A Three-Conductor Printed Circuit Board
References
Problems
Chapter 11	Incident Field Excitation of Two-Conductor Lines
11.1	Derivation of the Transmission-Line Equations for Incident-Field Excitation
11.1.1	Equivalence of Source Representations
11.2	The Frequency-Domain Solution
11.2.1	Solution of the Transmission-Line Equations
11.2.2	Simplified Forms of the Excitations
11.2.3	Incorporating the Line Terminations
11.2.4	Uniform Plane-Wave Excitation of the Line
11.2.4.1	Special Cases
11.2.4.2	One Conductor Above a Ground Plane
11.2.5	Comparison With Predictions of the Method of Moments
11.3	The Time-Domain Solution
11.3.1	The Laplace Transform Solution
11.3.2	Uniform Plane-Wave Excitation of the Line
11.3.3	A SPICE Equivalent Circuit
11.3.4	The Time-Domain to Frequency-Domain (TDFD) Transformation Method
11.3.5	The Finite-Difference, Time-Domain (FDTD) Solution Method
11.3.6	Computed Results
Chapter 12	Incident Field Excitation of Multiconductor Lines
12.1	Derivation of the MTL Equations for Incident-Field Excitation
12.1.1	Equivalence of Source Representations
12.2	The Frequency-Domain Solution
12.2.1	Solution of the MTL Equations
12.2.2	Simplified Forms of the Excitations
12.2.3	Incorporating the Line Terminations
12.2.3.1	Lossless Lines in Homogeneous Media
12.2.4	Lumped-Circuit Approximate Characterizations
12.2.5	Uniform Plane Wave Excitation of the Line
12.3	The Time-Domain Solution
12.3.1	Decoupling the MTL Equations
12.3.2	A SPICE Equivalent Circuit
12.3.3	Lumped-Circuit Approximate Models
12.3.4	The Time-Domain to Frequency-Domain (TDFD) Transformation
12.3.5	The Finite-Difference, Time-Domain (FDTD) Solution Method
12.4	Computed Results
References
Problems
Chapter 13	Transmission-Line Networks
13.1	Representation of Lossless Lines with the SPICE Model
13.2	Representation with Lumped-Circuit Approximate Models
13.3	Representation via the Admittance or Impedance 2n-Port Parameters
13.4	Representation with the BLT Equations
13.5	Direct, Time-Domain Solutions in terms of Traveling Waves
13.6	A Summary of Methods for Analyzing Multiconductor Transmission Lines
References
Problems
Publications by the Author Concerning Transmission Lines
Appendix A.	Description of Computer Software
A.1	Programs for Calculation of the Per-Unit-Length Parameters
A.1.1	Wide-Separation Approximations for Wires: WIDESEP.FOR
A.1.2	Ribbon Cables: RIBBON.FOR
A.1.3	Printed Circuit Boards: PCB.FOR
A.1.4	Coupled Microstrip Structures: MSTRP.FOR
A.1.5	Coupled Stripline Structures: STRPLINE.FOR
A.2	Frequency-Domain Analysis
A.2.1	General: MTL.FOR
A.3	Time-Domain Analysis
A.3.1	Time-Domain to Frequency-Domain Transformation: TIMEFREQ.FOR
A.3.2	Branin?s Method Extended to Multiconductor Transmission Lines: BRANIN.FOR
A.3.3	Finite-Difference, Time-Domain Method: FINDIF.FOR
A.3.4	Finite-Difference, Time-Domain Method: FDTDLOSS.FOR
A.4	SPICE/PSPICE Subcircuit Generation Programs
A.4.1	General Solution, Lossless Lines: SPICEMTL.FOR
A.4.2	Lumped-Pi Circuit, Lossless Lines: SPICELPI.FOR
A.4.3	Inductive-Capacitive Coupling Model: SPICELC.FOR
A.5	Incident Field Excitation
A.5.1	Frequency-Domain Program: INCIDENT.FOR
A.5.2	SPICE/PSPICE Subcircuit Model: SPICEINC.FOR
A.5.3	Finite-Difference, Time-Domain Method: FDTDINC.FOR
References
Appendix B.	A SPICE(PSPICE) Tutorial
B.1	Creating the SPICE or PSPICE Program
B.2	Circuit Description
B.3	Execution Statements
B.4	Output Statements
B.5	Examples
B.6	The Subcircuit Model
References
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Library of Congress Subject Headings for this publication:

Multiconductor transmission lines.
Electric circuit analysis -- Data processing.