A general method of transient analysis for lossless transmission lines and its analytical solution to time-varying resistive terminations

A general solution of the problem of transients on lossless transmission lines has been formulated that is based on the classical analysis of the forward and reflected waves on the line. The problem of transients on a lossless line with arbitrary boundary conditions at the end of the line is then investigated. Transients on a line terminated by a time-varying resistance with arbitrary time dependence are obtained analytically. In the special case where the time dependence is a ramp function, the problem is solved by the Laplace transform method and it is shown that the two solutions are identical.