On the passivity of polynomial chaos-based augmented models for stochastic circuits

This paper addresses for the first time the issue of passivity of the circuit models produced by means of the generalized polynomial chaos technique in combination with the stochastic Galerkin method. This approach has been used in literature to obtain statistical information through the simulation of an augmented but deterministic instance of a stochastic circuit, possibly including distributed transmission-line elements. However, transient simulations raise the critical question as to whether such an augmented network is passive or not. This paper discusses the general requirements for the augmented circuits to be passive and provides a sufficient condition for their passivity. Some numerical examples illustrate the theoretical results and conclude the paper