On the modeling of highly nonlinear circuits using total-variation-decreasing finite-difference schemes

This paper presents the modeling of highly nonlinear circuits using a total-variation-decreasing (TVD) difference scheme developed for the simulation of problems involving shock phenomena. In contrast to the commonly used leapfrog scheme, a second-order accurate TVD method based on the Lax-Wendroff scheme is applied to one-dimensional nonlinear transient electromagnetic-wave problems. Furthermore, for the analysis of transmission-line-based networks, an adapted inclusion of nonlinear lumped elements in such a TVD scheme is proposed. As an example, both the scattered signals of a linear transmission line loaded with a nonlinear lumped element is investigated and the formation of a shock-wave of a low-loss nonlinear transmission line with distributed diodes is studied. In the simulation results, the modeling of rapidly rising edges occurring in the time signal are demonstrated.