Analysis of Multiconductor Transmission Lines, 2nd EditionISBN: 9780470131541
780 pages
October 2007, WileyIEEE Press

The increasing use of highspeed digital technology requires that all electrical engineers have a working knowledge of transmission lines. However, because of the introduction of computer engineering courses into alreadycrowded fouryear undergraduate programs, the transmission line courses in many electrical engineering programs have been relegated to a senior technical elective, if offered at all.
Now, Analysis of Multiconductor Transmission Lines, Second Edition has been significantly updated and reorganized to fill the need for a structured course on transmission lines in a senior undergraduate or graduatelevel electrical engineering program. In this new edition, each broad analysis topic, e.g., perunitlength parameters, frequencydomain analysis, timedomain analysis, and incident field excitation, now has a chapter concerning twoconductor lines followed immediately by a chapter on MTLs for that topic. This enables instructors to emphasize twoconductor lines or MTLs or both.
In addition to the reorganization of the material, this Second Edition now contains important advancements in analysis methods that have developed since the previous edition, such as methods for achieving signal integrity (SI) in highspeed digital interconnects, the finitedifference, timedomain (FDTD) solution methods, and the timedomain to frequencydomain transformation (TDFD) method. Furthermore, the content of Chapters 8 and 9 on digital signal propagation and signal integrity application has been considerably expanded upon to reflect all of the vital information current and future designers of highspeed digital systems need to know.
Complete with an accompanying FTP site, appendices with descriptions of numerous FORTRAN computer codes that implement all the techniques in the text, and a brief but thorough tutorial on the SPICE/PSPICE circuit analysis program, Analysis of Multiconductor Transmission Lines, Second Edition is an indispensable textbook for students and a valuable resource for industry professionals.
Chapter 1: Introduction.
1.1 Examples of Multiconductor TransmissionLine Structures.
1.2 Properties of the Transverse ElectroMagnetic (TEM) Mode of Propagation.
1.3 The TransmissionLine Equations: a Preview.
1.3.1 Unique Definition of Voltage and Current for the TEM Mode of Propagation.
1.3.2 Defining the PerUnitLength Parameters.
1.3.3 Obtaining the TransmissionLine Equations from the Transverse Electromagnetic Field Equations.
1.3.4 Properties of the PerUnitLength 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 TransmissionLine Equation Formulation.
1.5.1 HigherOrder Modes.
1.5.1.1 The Infinite, ParallelPlate Transmission Line.
1.5.1.2 The Coaxial Transmission Line.
1.5.1.3 TwoWire Lines.
1.5.2 TransmissionLine 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 TimeDomain Response of Transmission Lines Having Linear Terminations Using Fourier Methods and Superposition.
References.
Problems.
Chapter 2: The TransmissionLine Equations for TwoConductor Lines.
2.1 Derivation of the TransmissionLine Equations from the Integral Form of Maxwell's Equations.
2.2 Derivation of the TransmissionLine Equations from the PerUnitLength Equivalent Circuit.
2.3 Properties of the PerUnitLength Parameters.
2.4 Incorporating FrequencyDependent Losses.
2.4.1 Properties of the FrequencyDomain PerUnitLength Impedance and Admittance .
References.
Problems.
Chapter 3: The TransmissionLine Equations for Multiconductor Lines.
3.1 Derivation of the Multiconductor TransmissionLine Equations from the Integral Form of Maxwell's Equations.
3.2 Derivation of the Multiconductor TransmissionLine Equations from the PerUnitLength Equivalent Circuit.
3.3 Summary of the MTL Equations.
3.4 Incorporating FrequencyDependent Losses.
3.5 Properties of the PerUnitLength Parameter Matrices L, C, G.
References.
Problems.
Chapter 4: The PerUnitLength Parameters for TwoConductor Lines.
4.1 Definitions of the PerUnitLength 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 PerUnitLength Inductance and Capacitance for WireType Lines.
4.2.3 PerUnitLength Conductance and Resistance for WireType Lines.
4.3 Lines Having Conductors of Rectangular Cross Section (PCB Lands).
4.3.1 PerUnitLength Inductance and Capacitance for PCBType Lines.
4.3.2 PerUnitLength Conductance and Resistance for PCBType Lines.
References.
Problems.
Chapter 5: The PerUnitLength Parameters for Multiconductor Lines.
5.1 Definitions of the PerUnitLength 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 WideSeparation Approximations for Wires in Homogeneous Media.
5.2.1.1 (n+1) Wires.
5.2.1.2 n Wires Above an Infinite, PerfectlyConducting Plane.
5.2.1.3 n Wires Within a PerfectlyConducting, 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: FrequencyDomain Analysis of TwoConductor Lines.
6.1 The TransmissionLine 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 LowLoss Approximation.
6.4 LumpedCircuit Approximate Models of the Line.
6.5 Alternative TwoPort 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: FrequencyDomain Analysis of Multiconductor Lines.
7.1 The MTL TransmissionLine 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 CyclicSymmetric 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 LumpedCircuit Approximate Characterizations.
7.5 Alternative 2nPort Characterizations.
7.5.1 Analogy of the FrequencyDomain MTL Equations to StateVariable Equations.
7.5.2 Characterizing the Line as a 2nPort 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: TimeDomain Analysis of TwoConductor 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 TwoPort 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 LumpedCircuit Approximate Models of the Line.
8.1.6.1 When is the Line Electrically Short in the Time Domain?.
8.1.7 The TimeDomain to FrequencyDomain (TDFD) Transformation Method.
8.1.8 The FiniteDifference, TimeDomain (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 FrequencyDependent 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 FrequencyDependent Losses.
8.2.2 The TimeDomain to FrequencyDomain (TDFD) Transformation Method.
8.2.3 The FiniteDifference, TimeDomain (FDTD) Method.
8.2.3.1 Including FrequencyIndependent Losses.
8.2.3.2 Including FrequencyDependent 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 HighLoss Line.
8.2.3.6 A Correction for the FDTD Errors.
8.2.4 LumpedCircuit Approximate Characterizations.
8.2.5 The Use of Macromodels in Modeling the Line.
8.2.6 Representing FrequencyDependent Functions in the Time Domain Using Pade' Methods.
Chapter 9: TimeDomain 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 LumpedCircuit Approximate Characterizations.
9.1.4 The TimeDomain to FrequencyDomain (TDFD) Transformation Method.
9.1.5 The FiniteDifference, TimeDomain (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 TimeDomain to FrequencyDomain (TDFD) Transformation Method.
9.2.2 LumpedCircuit Approximate Characterizations.
9.2.3 The FiniteDifference, TimeDomain (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 ThreeConductor Lines.
10.1 The Literal, FrequencyDomain Solution for a Homogeneous Medium.
10.1.1 Inductive and Capacitive Coupling.
10.1.2 Common Impedance Coupling.
10.2 The Literal, TimeDomain 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 ThreeWire Ribbon Cable.
10.3.2 A ThreeConductor Printed Circuit Board.
References.
Problems.
Chapter 11: Incident Field Excitation of TwoConductor Lines.
11.1 Derivation of the TransmissionLine Equations for IncidentField Excitation.
11.1.1 Equivalence of Source Representations.
11.2 The FrequencyDomain Solution.
11.2.1 Solution of the TransmissionLine Equations.
11.2.2 Simplified Forms of the Excitations.
11.2.3 Incorporating the Line Terminations.
11.2.4 Uniform PlaneWave 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 TimeDomain Solution.
11.3.1 The Laplace Transform Solution.
11.3.2 Uniform PlaneWave Excitation of the Line.
11.3.3 A SPICE Equivalent Circuit.
11.3.4 The TimeDomain to FrequencyDomain (TDFD) Transformation Method.
11.3.5 The FiniteDifference, TimeDomain (FDTD) Solution Method.
11.3.6 Computed Results.
Chapter 12: Incident Field Excitation of Multiconductor Lines.
12.1 Derivation of the MTL Equations for IncidentField Excitation.
12.1.1 Equivalence of Source Representations.
12.2 The FrequencyDomain 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 LumpedCircuit Approximate Characterizations.
12.2.5 Uniform Plane Wave Excitation of the Line.
12.3 The TimeDomain Solution.
12.3.1 Decoupling the MTL Equations.
12.3.2 A SPICE Equivalent Circuit.
12.3.3 LumpedCircuit Approximate Models.
12.3.4 The TimeDomain to FrequencyDomain (TDFD) Transformation.
12.3.5 The FiniteDifference, TimeDomain (FDTD) Solution Method.
12.4 Computed Results.
References.
Problems.
Chapter 13: TransmissionLine Networks.
13.1 Representation of Lossless Lines with the SPICE Model.
13.2 Representation with LumpedCircuit Approximate Models.
13.3 Representation via the Admittance or Impedance 2nPort Parameters.
13.4 Representation with the BLT Equations.
13.5 Direct, TimeDomain 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 PerUnitLength Parameters.
A.1.1 WideSeparation 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 FrequencyDomain Analysis.
A.2.1 General: MTL.FOR.
A.3 TimeDomain Analysis.
A.3.1 TimeDomain to FrequencyDomain Transformation: TIMEFREQ.FOR.
A.3.2 Branin’s Method Extended to Multiconductor Transmission Lines: BRANIN.FOR.
A.3.3 FiniteDifference, TimeDomain Method: FINDIF.FOR.
A.3.4 FiniteDifference, TimeDomain Method: FDTDLOSS.FOR.
A.4 SPICE/PSPICE Subcircuit Generation Programs.
A.4.1 General Solution, Lossless Lines: SPICEMTL.FOR.
A.4.2 LumpedPi Circuit, Lossless Lines: SPICELPI.FOR.
A.4.3 InductiveCapacitive Coupling Model: SPICELC.FOR.
A.5 Incident Field Excitation.
A.5.1 FrequencyDomain Program: INCIDENT.FOR.
A.5.2 SPICE/PSPICE Subcircuit Model: SPICEINC.FOR.
A.5.3 FiniteDifference, TimeDomain 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.
Clayton R. Paul, PhD, is Professor and the Sam Nunn Eminent Professor of Aerospace Systems Engineering in the Department of Electrical Engineering and Computer Engineering at Mercer University in Macon, Georgia. He is also Emeritus Professor of Electrical Engineering at the University of Kentucky. Dr. Paul is the author of numerous textbooks on EE subjects and technical papers, the majority of which are in his primary research area of EMC of electronic systems. He is a Fellow of the IEEE and an Honorary Life Member of the IEEE EMC Society.
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