Towards a Sparse Partial Inductance Matrix

Abstract — Currently available techniques for extraction and modelling of interconnect related inductance effects are either too restrictive on the geometries to be handled or computationally too demanding to be useful for large scale layout-to-circuit extraction. We present the results of a crit-ical evaluation of the partial inductances which form the building blocks in the PEEC method [1]. The physical origin of the well known passivity problem related to truncation of the partial inductance matrix is identified. This leads in a natural way to a preprocessing procedure of the partial in-ductances, which yields a modified matrix less sensitive to truncation. The proposed method disturbs the symmetry of the matrix, but for the important class of orthogonal systems of conductors symmetry is preserved. Therefore it will be of use for a majority of the circuit components where induc-tance effects are considered to be relevant in the first place (long lines: data, clock, VSS, VDD). Our results quantify the existence of a tubular shell with return currents, as recently suggested by He et al. [2] in a qualitative way. Keywords—Inductance, PEEC method, Passivity,Layout-to-circuit extraction I