Rational Polynomial Chaos Expansions for the Stochastic Macromodeling of Network Responses

This paper introduces rational polynomial chaos expansions for the stochastic modeling of the frequency-domain responses of linear electrical networks. The proposed method models stochastic network responses as a ratio of polynomial chaos expansions, rather than the standard single polynomial expansion. This approach is motivated by the fact that network responses are best represented by rational functions of both frequency and parameters. In particular, it is proven that the rational stochastic model is exact for lumped networks. The model coefficients are computed via an iterative re-weighted linear least-square regression. Several application examples, concerning both lumped and a distributed systems, illustrate and validate the advocated methodology.