On the Modeling of Highly Nonlinear Circuits Using Total-Variation-Decreasing Finite-Difference Schemes

This paper presents the modeling of highly nonlinearcircuits using a total-variation-decreasing (TVD) differencescheme developed for the simulation of problems involving shockphenomena. In contrast to the commonly used leapfrog scheme,a second-order accurate TVD method based on the Lax–Wen-droff scheme is applied to one-dimensional nonlinear transientelectromagnetic-wave problems. Furthermore, for the analysisof transmission-line-based networks, an adapted inclusion ofnonlinear lumped elements in such a TVD scheme is proposed. Asan example, both the scattered signals of a linear transmission lineloaded with a nonlinear lumped element is investigated and theformation of a shock-wave of a low-loss nonlinear transmissionline with distributed diodes is studied. In the simulation results,the modeling of rapidly rising edges occurring in the time signalare demonstrated.