Interconnect Macromodelling and Approximation of Matrix Exponent

Abstract

The simplest interconnection model for an integrated circuit is a discrete RC-circuit governed by a system Ri′ + Di e u′ of differential equations with positive definite matrices R and D. Such a system usually has a high dimension, so it is natural to solve it approximately. Traditionally it is investigated by means of Krylov subspace methods. In this article a close approach is discussed. This approach admits an effective estimation of accuracy. It is based on the approximation of the main factor eAt (here A e −R−1D) in the impulse response H(t) e eAt R−1 by a polynomial r(A, t) e a0(t)1 + a1(t)A + ··· +an(t)An with the coefficients ak(t) depending on t or by a rational function of a similar form.