Window-based susceptance models for large-scale RLC circuit analyses

Due to the increasing operating frequencies and the manner in which the corresponding integrated circuits and systems must be designed, the extraction, modeling and simulation of the magnetic couplings for final design verification can be a daunting task. In general, when modeling inductance and the associated return paths, one must consider the on-chip conductors as well as the system packaging. This can result in an RLC circuit size that is impractical for traditional simulators. In this paper we demonstrate a localized, window-based extraction and simulation methodology that employs the recently proposed susceptance (the inverse of inductance matrix) concept. We provide a qualitative explanation for the efficacy of this approach, and demonstrate how it facilitates pre-manufacturing simulations that would otherwise be intractable. A critical aspect of this simulation efficiency is owed to a susceptance-based circuit formation that we prove to be symmetric positive definite. This property, along with the sparsity of the susceptance matrix, enables the use of some advanced sparse matrix solvers. lye demonstrate this extraction and simulation methodology on some industrial examples