Improved Stochastic Macromodeling of Electrical Circuits via Rational Polynomial Chaos Expansions

This paper introduces the use of a rational polynomial chaos expansions (PCE) for the stochastic macromodeling of network responses affected by parameter variability, as a more suitable alternative to classical PCEs, The new formulation is motivated by the intrinsic form of the response of a linear and lumped network, which is indeed known to be a rational function of both frequency and parameters. As a matter of fact, the proposed representation is exact for lumped circuits, provided that a suitable expansion order and truncation is used. Moreover, it is shown that the rational PCE provides a better approximation also for distributed networks. An iterative and re-weighed linear least-square regression is used to estimate the model coefficients. It is also found that their calculation is less sensitive to the number of regression samples, compared to the classical PCE, Two application examples, concerning a lumped and a distributed system, illustrate and validate the advocated methodology.