Transient analysis of transmission lines with time-dependent terminations and general input

In this paper an exact time-domain solution for the wave equation in lossless TEM transmission lines with time-dependent boundary conditions in the input and output terminals will be presented. First a mathematical closed form time-domain solution for the wave equation in lossless TEM transmissions lines subject to arbitrary terminations will be presented, then this general solution will be specialized for some time dependent resistive terminations. Fundamentals of transient analysis of transmission lines with random inputs such as white noise was also briefly considered in this paper. In the latter situation the results are in the form of some statistical parameters, such as, correlation function, mean, variance and spectral density of the voltage or current stochastic processes, in the line as a function of time and distance