Modified Numerical Inversion of Laplace Transform Methods for the Time-Domain Analysis of Retarded Partial Elements Equivalent Circuit Models

This article presents a new method for the simulation of the retarded partial element equivalent circuit (PEEC), which is used to model the EM phenomena at the circuit level. The new method adapts a recently introduced approach for numerical inversion of the Laplace transform (NILT). The conventional NILT approach is equivalent to a high-order stable differential equation solver. Its application in the context of PEEC circuits eliminated late-time instability issues. However, the recent development in NILT (known as NILTn) further reduced the approximation error by several orders of magnitude for roughly the same computational cost as in the conventional NILT, thereby permitting a significant increase in the length of the time step with lower computational cost. The approach proposed in this article further develops the ideas in NILTn so that it can be applied to the simulation of PEEC circuits in the time-domain. The new approach, therefore, combines the desirable late-time stability of NILT with a reduced computational cost. Furthermore, this article also utilizes an interpolation approach to reproduce the desired circuit waveforms between the points evaluated by NILTn.