Partitioned Model Order Reduction of Partial Element Equivalent Circuit Models

As very large scale integration circuit speeds and density continue to increase, 3-D electromagnetic methods have become essential for the analysis, design, and verification of high-speed systems. Since such models are commonly used inside standard circuit simulators for time or frequency domain computations, it is imperative to make them as compact as possible without compromising accuracy. To this aim, model-order reduction techniques can be successfully adopted. In this paper, we describe a partitioned Krylov subspace-based method for deriving reduced-order models directly from 3-D quasi-static partial element equivalent circuit models. The multiscale block decomposition method is adopted to speed-up the computation of the projection matrix; furthermore, the adaptive cross approximation and singular value decomposition techniques are used to achieve matrix compression exploiting the low-rank behavior of magnetic and electric field couplings. Results are presented on several examples to demonstrate the capabilities and speed of the proposed new method.