Transmission Lines and Lumped Circuits: Fundamentals and Applications

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 circuitsA simple, concise and completely general way to present the wave propagation on transmission lines, including a thorough study of the line equations in characteristic formFrequency and time domain multiport representations of any linear transmission lineA detailed analysis of the influence on the line characterization of the frequency and space dependence of the line parametersA rigorous study of the properties of the analytical and numerical solutions of the network equationsThe associated discrete circuits and the associated resisitive circuits of transmission linesPeriodic solutions, bifurcations and chaos in transmission lines connected to noninear lumped circuits

Transmission Line Equations and Properties
Ideal Two-Conductor Transmission Lines Connected to Lumped Circuits
Ideal Multiconductor Transmission Lines
Lossy Two-Conductor Transmission Lines
Lossy Two-Conductor Transmission Lines with Frequency-Dependent Parameters
Lossy Multiconductor Transmission Lines
Nonuniform Transmission Lines
Transmission Line Equations in Characteristic Form
Lumped Nonlinear Networks Interconnected by Transmission Lines
Qualitative Analysis of an Ideal Two-Conductor Line Connected to Nonlinear Resistors: Periodic Solutions, Bifurcations and Chaos
Appendix A: Some Useful Notes on the Matrix Operators
Appendix B: Some Useful Notes on the Laplace Transformation
Appendix C: Some a-priori Estimates
Appendix D: Tables of Equivalent Representations of Transmission Lines