Stable time domain solutions for EMC problems using PEEC circuit models

Abstract

Time domain solutions for electromagnetic problems are important for many EMC applications like ESD and integrated circuit EMI. The most common solution formulation for such problems is based on integral equations. The instabilities in the solution associated with integral equation techniques in the time domain are well known. In this paper we show that the instability may be either due to the numerical technique used for the time integration or due to problems created by the discrete representation for the solution of the problem by the numerical integration technique. We use the Partial Element Equivalent Circuit (PEEC) formulation of the EFIE integral equation for small model problems and some popular integration techniques to give specific examples of instabilities in the time domain solution. Importantly, we introduce techniques which lead to stable results.