On the uniqueness of the numerical solution of non-linearly loaded lossy transmission lines

The purpose of this paper is to investigate the uniqueness of the solution of lossy lines with frequency-dependent parameters terminated with non-line ar resistors. Several solutions that satisfy the same initial conditions ma y exist if the terminal resistors are locally active. In these cases the un iqueness of solution is assured adding parasitic capacitances in parallel t o the voltage controlled resistors and parasitic inductances in series to t he current controlled resistors. In this way, among all the possible soluti ons, the only one that assures the time continuity of the current and volta ge waveforms at the ends of the line is captured. In the light of these res ults, the properties of numerical models of these distributed circuits base d on convolution techniques have been studied, and conditions assuring the uniqueness of the numerical solution have been found. Numerical simulations , when based on qualitative information of this type, enable us to obtain t he quantitative properties in an efficient manner. In particular, a simple numerical method that enforces artificially the time continuity of the solu tion is proposed to circumvent the need of adding parasitics. Copyright (C) 1999 John Wiley & Sons, Ltd.