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E-raamat: Transmission Lines and Lumped Circuits: Fundamentals and Applications

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(University of Cassino and Southern Lazio, Cassino, Italy), (Universita di Napoli Federico II, Italy)
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  • Sari: Electromagnetism
  • Ilmumisaeg: 23-Feb-2001
  • Kirjastus: Academic Press Inc
  • Keel: eng
  • ISBN-13: 9780080519593
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Transmission Lines and Lumped Circuits: Fundamentals and ApplicationsSuurem pilt
  • Formaat: PDF+DRM
  • Sari: Electromagnetism
  • Ilmumisaeg: 23-Feb-2001
  • Kirjastus: Academic Press Inc
  • Keel: eng
  • ISBN-13: 9780080519593
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The theory of transmission lines is a classical topic of electrical engineering. Recently this topic has received renewed attention and has been a focus of considerable research. This is because the transmisson line theory has found new and important applications in the area of high-speed VLSI interconnects, while it has retained its significance in the area of power transmission. In many applications, transmission lines are connected to nonlinear circuits. For instance, interconnects of high-speed VLSI chips can be modelled as transmission lines loaded with nonlinear elements. These nonlinearities may lead to many new effects such as instability, chaos, generation of higher order harmonics, etc. The mathematical models of transmission lines with nonlinear loads consist of the linear partial differential equations describing the current and voltage dynamics along the lines together with the nonlinear boundary conditions imposed by the nonlinear loads connected to the lines. These nonlinear boundary conditions make the mathematical treatment very difficult. For this reason, the analysis of transmission lines with nonlinear loads has not been addressed adequately in the existing literature. The unique and distinct feature of the proposed book is that it will present systematic, comprehensive, and in-depth analysis of transmission lines with nonlinear loads.

* A unified approach for the analysis of networks composed of distributed and lumped circuits
* A simple, concise and completely general way to present the wave propagation on transmission lines, including a thorough study of the line equations in characteristic form
* Frequency and time domain multiport representations of any linear transmission line
* A detailed analysis of the influence on the line characterization of the frequency and space dependence of the line parameters
* A rigorous study of the properties of the analytical and numerical solutions of the network equations
* The associated discrete circuits and the associated resisitive circuits of transmission lines
* Periodic solutions, bifurcations and chaos in transmission lines connected to noninear lumped circuits

Muu info

* A unified approach for the analysis of networks composed of distributed and lumped circuits * A simple, concise and completely general way to present the wave propagation on transmission lines, including a thorough study of the line equations in characteristic form * Frequency and time domain multiport representations of any linear transmission line * A detailed analysis of the influence on the line characterization of the frequency and space dependence of the line parameters * A rigorous study of the properties of the analytical and numerical solutions of the network equations * The associated discrete circuits and the associated resisitive circuits of transmission lines * Periodic solutions, bifurcations and chaos in transmission lines connected to noninear lumped circuits
Foreword xix
Preface xxi
Introduction 1(2)
A Survey of the Problem
3(2)
The Idea of the Book
5(10)
Transmission Line Equations and Properties
15(34)
Transmission Line Model
16(5)
Two-Conductor Transmission Line Equations
21(5)
Ideal Transmission Lines
21(1)
Lossy Transmission Lines
22(1)
Nonuniform Transmission Lines
23(1)
Transmission Lines with Distributed Sources
23(1)
Transmission Lines with Frequency-Dependent Parameters
24(2)
Multiconductor Transmission Line Equations
26(6)
Ideal Multiconductor Transmission Lines
26(2)
Lossy Multiconductor Transmission Lines
28(2)
Multiconductor Transmission Lines with Distributed Sources
30(1)
Multiconductor Transmission Lines with Frequency-Dependent Parameters
30(2)
Poynthing's Theorem for Lines with Frequency Independent Parameters
32(2)
Two-Conductor Transmission Lines
32(1)
Multiconductor Transmission Lines
33(1)
Uniqueness of the Solution of Transmission Lines Equations
34(3)
Two-Conductor Transmission Lines
34(2)
Multiconductor Transmission Lines
36(1)
Poynting's Theorem for Lines in the Frequency Domain
37(2)
Two-Conductor Transmission Lines
37(1)
Multiconductor Transmission Lines
38(1)
Uniqueness of the Solution of Transmission Lines Equations with Frequency-Dependent Parameters
39(2)
Two-Conductor Transmission Lines
39(2)
Multiconductor Transmission Lines
41(1)
Transmission Line Equations in the Laplacde Domain
41(1)
Reciprocity Theorems for Two-Conductor Transmission Lines
42(2)
The First Form of the Reciprocity Theorem
42(2)
The Second Form of the Reciprocity Theorem
44(1)
The Third Form of the Reciprocity Theorem
44(1)
Reciprocity Theorems for Multiconductor Transmission Lines
44(5)
The First Form of the Reciprocity Theorem
45(2)
The Second Form of the Reciprocity Theorem
47(1)
The Third Form of the Reciprocity Theorem
47(1)
Reciprocity Theorem for a Semi-infinite Transmission Lines
47(2)
Ideal Two-Conductor Transmission Lines Connected to Lumped Circuits
49(44)
d'Alembert Solution of Two-Conductor Transmission Lines Equations
50(3)
Some Elementary Networks
53(11)
An Infinite Line
53(1)
A Semi-infinite Line Connected to an Ideal Current Source
54(2)
A Semi-infinite Line Connected to a Linear Resistor; Reflection Coefficient
56(2)
A Semi-infinite Line Connected to a Linear Capacitor
58(2)
A Semi-infinite Line Connected to a Nonlinear Resistor
60(3)
A Semi-infinite Line Connected to a Nonlinear Resistor in Parallel with a Linear Capacitor
63(1)
Natural Frequencies of a Finite Length Transmission Lines Connected to Short Circuits
64(2)
Two-Conductor Transmission Lines as Two-Ports
66(5)
State Variables of the Line
67(1)
Transmission Line Behaviour at the Ends
67(4)
The Input-Output Description
71(1)
The Input-State-Output Description, and Equivalent Circuits of Thevenin and Norton Type
72(3)
Lines Connected to Linear Lumped Circuits
75(9)
State Equations in Normal Form
77(1)
Natural Frequencies of the Network
78(1)
Solution in the Laplace Domain
79(5)
A Glimpse at a Transmission Lines Connected to a Nonlinear One-Port: State Equations in Normal Form
84(4)
A Line Connected to a Nonlinear Resistor
85(1)
A Line Connected to a Nonlinear Resistor in Parallel with a Linear Capacitor
86(2)
Ideal Two-Conductor Transmission Lines with Distributed Sources
88(5)
A Particular Solution of the Line Equations With Distributed Sources
88(3)
Characterization as Two-Ports
91(2)
Ideal Multiconductor Transmission Lines
93(36)
d'Alembert Solution for Ideal Multiconductor Transmission Lines
93(10)
Properties and Diagonalization of the Matrices LC and CL
95(4)
Characteristic Resistance and Conductance Matrices
99(2)
Natural Modes of Propagation
101(2)
Infinite Multiconductor Transmission Lines
103(1)
Semi-infinite Multiconductor Transmission Lines and Equivalent Circuits
104(2)
Ideal Multiconductor Transmission Lines as Multiports
106(6)
Characterization of the Transmission Line Behavior at the Ends
108(4)
The Input-State-Output Description and the Equivalent Circuits of Thevenin and Norton Type
112(3)
Multiconductor Lines with Homogeneous Dielectric
115(2)
Characterization of the Transmission Line Behavior at the Ends
116(1)
Multiconductor Transmission Line Connected to Linear Resistive Multiports
117(4)
Natural Frequencies of the Network
120(1)
A Particular Solution of the Ideal Multiconductor Transmission Line Equations with Distributed Sources
121(4)
Transversally Homogeneous Lines
124(1)
Properties of the Characteristic Conductance Matrix Gc and Resistance Matrix Rc
125(4)
Lossy Two-Conductor Transmission Lines
129(52)
Lossy Transmission Lines are Dispersive
130(2)
The Heaviside Condition
131(1)
Solution of the Lossy Transmission Line Equations in the Laplace Domain
132(4)
The Propagation Along a Lossy Transmission Line
136(5)
Semi-infinite Lossy Line Connected to an Ideal Current Source
141(7)
Properties of the Characteristic Impedance Zc(s) and of the Impulse Response Zc(t)
142(3)
A Fast Convolution Algorithm
145(3)
Representation of Lossy Two-Conductor Lines as Two-Ports
148(6)
Terminal Behaviour of the Line in the Laplace Domain: the Describing Functions Zc(s) and P(s)
149(3)
Properties of the Global Propagation Operator P(s) and of the Impulse Response p(t)
152(2)
The Input-State-Output Description
154(6)
Laplace Domain Equivalent Circuits of Thevenin and Norton Type
154(2)
Time Domain Thevenin Description
156(2)
Time Domain Norton Description
158(2)
Input-Output Descriptions in Explicit Form
160(8)
The Impedance Matrix
160(4)
The Admittance Matrix
164(1)
The Hybrid Matrices
165(1)
The Transmission Matrices
166(2)
A Lossy Transmission Line Connecting Two Linear Resistive One-Ports
168(4)
Numerical Solution of Volterra Integral Equations of the Second Kind
171(1)
The Matching Problem for Lossy Lines
172(2)
Lossy Transmission Lines with Distributed Sources
174(4)
Particular Solution of Line Equations with Distributed Sources
175(2)
Two-port Characterisation
177(1)
Characterization of the Terminal Behavior of the Line Through the Scattering Parameters
178(3)
Lossy Two-Conductor Transmission Lines with Frequency-Dependent Parameters
181(34)
Introduction
181(3)
Frequency Behavior of the Per-Unit-Length Admittance Y(s)
184(9)
Homogeneous Embedding Medium
187(3)
Nonhomogeneous Embedding Medium
190(2)
Asymptotic Expression of Y(s)
192(1)
Frequency Behavior of the Per-Unit-Length Impedance Z(s)
193(7)
Skin Effect
196(2)
Anomalous Skin Effect
198(1)
Superconducting Transmission Lines
199(1)
A Single Wire Above a Finite Conductivity Ground plane
200(1)
Properties of the Describing Functions P(s), Zc(s), and Yc(s)
200(6)
Asymptotic Expression of Zc
203(1)
Asymptotic Expression of P
204(1)
Asymptotic Behaviour of Yc
205(1)
Qualitative Behavior of the Impulse Responses p(t), zc(t), and Yc(s)
206(9)
Inverse Laplace Transform of Functions Behaving as s-1 for s → ∞
206(1)
Qualitative Behavior of the Impulse Responses zc and yc
207(1)
Qualitative Behavior of the Impulse Response p
208(2)
A Numerical Experiment
210(5)
Lossy Multiconductor Transmission Lines
215(50)
Introduction
215(2)
Lossy Multiconductor Lines Exhibiting a Structural Symmetry
217(2)
Lossy Multiconductor Line Equations in the Laplace Domain
219(5)
The Eigenvalues and Eigenvectors of the Matrices Λ = ZY/s2 and Π = YZ/s2
219(2)
The General Solution
221(3)
Lossy Multiconductor Transmission Line as Multiports in the Laplace Domain
224(4)
The Input-State-Output Description and the Equivalent Representations of Thevenin and Norton Type
228(3)
Laplace Domain
228(2)
Time Domain
230(1)
Input-Output Descriptions in Explicit Form
231(4)
The Impedance Matrix
231(1)
The Admittance Matrix
232(1)
The Hybrid Matrices
233(1)
The Transmission Matrices
234(1)
The Problem of the Inverse Laplace Transform of the Matrix Operators P(s), Zc(s), and Yc(s)
235(5)
Study of the Asymptotic Behavior of the Matrix Operator Λ(s) Through the Rayleigh-Schrodinger Method
240(6)
The Eigenvalues of Λ(0) = LC Are Nondegenerate
242(1)
The Eigenvalues of Λ(0) = LC Are Degenerate
243(2)
A Particular Case of Degeneracy: Lines with Transverse Homogeneous Dielectric
245(1)
Asymptotic Expressions for the Matrix Operators A(s) and Tv(s)
246(1)
Evaluation of the Impulse Responses for Lossy Multiconductor Lines with Frequency-Independent Parameters
247(7)
Asymptotic Expressions for the Describing Functions P(s), Zc(s), and Yc(s)
248(2)
Evaluation of the Principal Parts of the Impulse Responses p(t), zc(t), and yc(t)
250(2)
An Application to a Three-Conductor Line
252(2)
Evaluation of the Impulse Responses of Lossy Multiconductor Lines with Frequency-Dependent Parameters
254(11)
Multiconductor Lines with Skin Effect
254(6)
Application to a Three-Conductor Line
260(2)
Per-Unit-Length Impedance and Admittance Matrices with Arbitrary Frequency Dependence
262(3)
Nonuniform Transmission Lines
265(40)
Introduction
265(4)
Equations for Nonuniform Lossless Transmission Lines
The Dyson Series
269(2)
Analytical Solutions for Lines with Transversally Homogeneous Dielectric and Particular Profiles of L(x)
271(8)
Exponential Profile
271(2)
Linear Profile
273(1)
Gaussian Profile
274(3)
General Solution of the Traveling Wave Type
277(2)
Representation of Nonuniform Transmission Lines as Two-Ports in the Laplace Domain
279(6)
Terminal Behavior of the Line
280(3)
The Input-State-Output Description and an Equivalent Circuit of Thevenin Type
283(1)
Input-Output Descriptions in Explicit Form
284(1)
The Equivalent Circuit of Thevenin Type in the Time Domain
285(10)
Asymptotic Behavior of the Describing Functions
286(2)
Impulse Responses
288(7)
The Solution of the Line Equations for a Generic Profile of L(x) and C(x)
295(10)
Study of the Asymptotic Behavior of the Solution Through the Liouville-Green Transformation
295(3)
Semianalytical Evaluation of Traveling Wave Solutions Based on the WKB Method
298(7)
Transmission Line Equations in Characteristic Form
305(32)
Introduction
305(1)
A First-order Wave Equation in Characteristic Form and the Characteristic Curves
306(6)
The Domain of Dependence of the Solution
309(1)
The Transport of the Irregularities
309(3)
The Characteristic Form Equations for Lines with Frequency Independent Parameters
312(11)
The Domain of Dependence of the Solution
317(4)
The Transport of the Discontinuities
321(1)
The Riemann Variables
321(2)
The Characteristic Form Equations for Lines with Frequency-Dependent Parameters
323(6)
Characteristic Equations for Multiconductor Lines
329(3)
Stepwise Integration of the Transmission Line Equations in Characteristic Form
332(5)
Lumped Nonlinear Networks Interconnected by Transmission Lines
337(40)
Introduction
337(1)
Time Domain Formulation of the Network Equations
338(3)
A Glimpse at the Uniqueness Problem for Ideal Two-Conductor Transmission Lines
341(8)
An Ill-Posed Problem
344(1)
A Circuit with an Additional Parasitic Reactance
345(4)
A Glimpse at the Uniqueness Problem for Imperfect Two-Conductor Transmission Lines: Associated Resistive Circuit
349(5)
The Volterra Integral Equation of the Second Kind in Normal Form
349(1)
Uniqueness Condition for Imperfect Lines
350(2)
A Circuit with an Additional Parasitic Reactance
352(2)
A Glimpse at the Numerical Solution for Imperfect Two-Conductor Transmission Lines: Associated Discrete Circuit
354(9)
Effects of an Additional Parasitic Reactance
358(2)
Numerical Solution of an Ill-Posed Circuit by Artificially Enforcing the Continuity of the Terminal Voltage
360(3)
Well-Posedness of the Network Equations
363(5)
Numerical Solution of the Network Equations
368(3)
Lumped Circuits Connected Through Multiconductor Transmission Lines
371(6)
Associated Resistive Circuit
372(1)
Lines Connecting Resistive Multiports
372(3)
Associated Discrete Circuit
375(2)
Qualitative Analysis of an Ideal Two-Conductor Line Connected to Nonlinear Resistors: Periodic Solutions, Bifurcations and Chaos
377(58)
Introduction
377(3)
State Equations in Normal Form for an Ideal Two-Conductor Line Connected to Nonlinear Resistors: Formulation in Terms of a Scalar Map un + 1 = f(un)
380(4)
A Glimpse at the Scalar Maps
384(11)
Stair-Step Diagrams
386(1)
Linear Map
387(2)
Affine Linear Map
389(1)
Bounded Solutions and Stability
390(2)
Steady-State Solution
392(3)
Passivity, Eventual Passivity, and Local Passivity
395(3)
Some General Properties of the Dynamics
398(6)
Study of the Boundedness of the Solution Through the Liapunov Function Method
399(1)
Local Behavior of the Map un + 1 = f(un)
400(2)
Qualitative Behavior of the Solution for Locally Passive Resistors
402(2)
Qualitative Behavior of the Solution for Locally Active Resistors: A Glimpse at the Bifurcations
404(6)
Pitchwork Bifurcation of a Nonhyperbolic Fixed Point
407(1)
Period-Doubling Bifurcation of a Nonhyperbolic Fixed Point
408(2)
A Glimpse at the Behaviour of Noninvertible Maps: Chaotic Dynamics
410(19)
A Tent Map
410(6)
The Lyapunov Exponent and Chaotic Transients
416(2)
A Unimodal Map
418(6)
The Logistic Map
424(5)
The Spatio-Temporal Chaos
429(1)
Lossy Transmission Lines
429(6)
Appendix A Some Useful Notes on the Matrix Operators 435(10)
A1 Preliminary Definitions
435(1)
A2 The Eigenvalue Problem Au = λu
436(3)
A3 The Generalized Eigenvalue Problem Au = λBu
439(1)
A4 Function of a Matrix Operator
440(1)
A5 Perturbation of a Matrix Operator: Asymptotic Behavior of the Eigenvalues
441(4)
Appendix B Some Useful Notes on the Laplace Transformation 445(8)
B1 General Considerations
445(5)
B2 Asymptotic Behavior of the Object Function for t → ∞
450(3)
Appendix C Some a-priori Estimates 453(4)
C1 a-priori Estimates for the Solution of Equation (9.8)
453(1)
C2 a-priori Estimates for the Solution of Equation (9.18)
454(3)
Appendix D Tables of Equivalent Representations of Transmission Lines 457(6)
References 463(8)
Index 471


Antonio Maffucci is Associate Professor of Electrical Engineering at the University of Cassino and Southern Lazio. Since 2014, he has also been associated to the INFN, Frascati National Laboratories. His research focuses on issues of electromagnetic and circuit modeling, computational electromagnetics, electromagnetic compatibility, nanotechnology. He is the author of 160 international publications, 3 reviews, 1 book, 7 book chapters and 4 receiverships.
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