Low-Cost Error Estimation for Fast and Stable Circuit Simulation Using Modified Inversion of the Laplace Transform

Abstract

The modified numerical inversion of the Laplace transform (NILT <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> ) has been recently proposed as a fast and provably stable numerical simulation for general circuits. However, its efficiency has revealed challenges that are not typically seen in the conventional circuit simulators that rely on the classical SPICE engine. More particularly, the issue of estimating the approximation error is one problem that has not been adequately addressed using efficient approaches. The work presented in this article addresses this issue by deriving a formula that is used to estimate the approximation error for a given length of the time step. The proposed method is based on the relation between NILT <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$n$ </tex-math></inline-formula> and NILT0, which allows the error to be estimated via a series of forward/backward substitutions. The numerical simulations show the accuracy of the proposed method to predict the approximation error at an incremental computational cost.