Transmission Lines and Lumped Circuits: Fundamentals and ApplicationsThe 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 highspeed 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 highspeed 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 indepth analysis of transmission lines with nonlinear loads.

Contents
1  
15  
Chapter 2 Ideal TwoConductor Transmission Lines Connected to Lumped Circuits  49 
Chapter 3 Ideal Multiconductor Transmission Lines  93 
Chapter 4 Lossy TwoConductor Transmission Lines  129 
Chapter 5 Lossy TwoConductor Transmission Lines with FrequencyDependent Parameters  181 
Chapter 6 Lossy Multiconductor Transmission Lines  215 
Chapter 7 Nonuniform Transmission Lines  265 
Chapter 9 Lumped Nonlinear Networks Interconnected by Transmission Lines  337 
Periodic Solutions Bifurcations and Chaos  377 
Appendix A Some Useful Notes on the Matrix Operators  435 
Appendix B Some Useful Notes on the Laplace Transformation  445 
Appendix C Some apriori Estimates  453 
Appendix D Tables of Equivalent Representations of Transmission Lines  457 
463  
471  
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Common terms and phrases
amplitude analytically assume asymptotic behavior backward behavior bounded branch Chapter characteristic characteristic curves characterized circuit complex conductor consequence consider constant continuous controlled corresponding defined depend described determine distributed domain dynamics effect eigenvalues eigenvectors electrical equal equations equivalent circuit evaluated existence expression Figure fixed point forward frequency function given hence ideal impedance impulse responses independent initial conditions integral interval introduced inverse known Laplace domain Laplace transform line ends line equations linear losses lossy lumped circuits matrix method nonlinear numerical obtain operator orbit parameters particular passive perunitlength periodic positive possible problem propagation properties relations representation represented resistive resistor respectively satisfied shown in Fig solution solved sources stable term terminal transmission lines uniform uniqueness variables voltage voltage wave wave whereas zero
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Page 464  Arbitrary Pulse Shape Synthesis via Nonuniform Transmission Lines,
Page 23  India. where /4 is the magnetic permeability and a is the electrical conductivity of the fluid.
Page xxii  In particular, we appreciate the support for the development of this text from the Department of Electrical Engineering of the University of Naples, Federico II.