Modified Inversion of the Laplace Transform for Fast and Stable Time-Domain Simulation of Nonlinear Circuits

This article introduces a novel method for simulating nonlinear circuits in the time domain. The approach leverages the numerical inversion of the Laplace transform (NILT) to create a high-order, stable time-stepping scheme suitable for general circuit simulations. This method involves splitting the circuit into linear and nonlinear parts, then matching time-domain derivatives at their interface using NILT and rooted tree (RT) techniques. The approach utilizes an advanced form of NILT, called NILTn, which provides improved accuracy per time step compared with the conventional NILT, referred to as NILT0. Numerical simulations reveal significant speed improvements over both traditional and recent NILT0-based methods.