Neutral delay differential equations from the PEEC circuit solution of Maxwell's equation

Abstract

The purpose of this paper is twofold. First, we present the Partial Element Equivalent Circuit (PEEC) formulation of Maxwell's equations. Second, the resultant system of neutral delay differential equations (NDDEs), arising from the time domain solution of PEEC models, and the stability of these are considered. In the classical PEEC model, single delay approximations were used for the partial elements describing the electric- and magnetic field couplings. It was shown that the resultant system of delay differential equations may become unstable for some time domain applications. In this paper, we present a systematic process for the stability and accuracy enhancement of the time domain PEEC model by improving the evaluation of the partial element based on the subdivision technique and by a filtering process.