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 NILT
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) 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 NILT
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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 NILT
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.