Time-Domain Computation of Full-Wave Partial Inductances Based on the Modified Numerical Inversion of Laplace Transform Method

The partial inductance is a very well known concept in electromagnetic modeling that allows us to ascribe the properties of inductance to an isolated piece of conductor and of a mutual inductance to a couple of finite-size conductors, not necessarily constituting a closed loop as it is required for the standard concept of inductance. Although, its computation has been widely studied in the static case and in the frequency domain for the dynamic case, its computation in the time domain (TD) has been only partially addressed. This article aims to fill this gap also pointing out their use in the framework of a TD solver. In particular, the modified numerical inversion of the Laplace transform (NILT) is adopted to compute the time samples of the partial inductance avoiding the cumbersome inverse Fourier transform (IFT). It will be shown that, in addition to the high accuracy, the delayed implementation of the NILT method strictly preserves the causality of the magnetic coupling. Furthermore, the use of Hermite interpolation allows us to significantly reduce the computational effort. The proposed method is tested by comparison with analytical formulas existing for coplanar zero-thickness regions and with IFT techniques for the both orthogonal and nonorthogonal geometries.