Analysis of transmission lines non linear loaded using Galerkin method

In this paper a new numerical technique, based on the Galerkin method, is proposed for simulating linear lossy transmission lines with terminal nonlinear resistors. Two complementary formulations of the transmission line equations are considered for estimating the errors due to the numerical approximation. Each of the two formulations enforces one of the two canonical transmission line equations exactly, whereas the remaining canonical equation first, is rewritten in the weak form, and, then, is discretized in the space by means of the Galerkin method. The Galerkin equations obtained in this way are solved in time by a fourth order Runge-Kutta method. This technique appears computationally less cumbersome than that based on the convolution method, especially when the analysis of multiconductor transmission lines is considered