Model order reduction techniques for linear systems with large numbers of terminals

This paper addresses the well known difficulty of applying model order reduction (MOR) to linear circuits with a large number of input-output terminals. Traditional MOR techniques substitute the original large but sparse matrices used in the mathematical modeling of linear circuits by models that approximate the behavior of the circuit at its terminals, and use significantly smaller matrices. Unfortunately these small MOR matrices become dense as the number of terminals increases, thus canceling the benefits of size reduction. The paper introduces a model reduction technique suitable for circuits with numerous terminals. The technique exploits the correlation that almost always exists between circuit responses at different terminals. The correlation is rendered explicit through an SVD-based algorithm and the result is a substantial sparsification of the MOR matrices. The proposed sparsification technique is applicable to a large class of problems encountered in the analysis and design of interconnect in VLSI circuits. Relevant examples are used to analyze and validate the method.