Equipotential shells for efficient partial inductance extraction

The shift-truncate potential method was introduced as an approach to sparsify the partial inductance matrix while maintaining the stability and symmetry. This was accomplished with the use of spherical return shells around point-like current segments. In this paper we propose the use of filament current distributions for the same purpose. Ellipsoidal shells are introduced to model the equipotential surfaces for filament currents. Importantly, we prove that the positive definiteness of the resulting sparse partial inductance matrix is preserved for this and all other potential-shell models when the compensating currents are placed on equipotential surfaces of the original current distribution. The utility and efficiency of this ellipsoidal shell partial inductance approximation are demonstrated for both on-chip and system-level extraction examples.