Macromodeling of general linear systems under stochastic variations

In this paper, a stochastic modeling approach is proposed for time-domain variability analysis of general linear and passive systems with uncertain parameters. Starting from the polynomial chaos (PC) expansion of the scattering parameters, the Galerkin projections (GP) method is adopted to build an augmented scattering matrix which describes the relationship between the corresponding PC coefficients of the input and output port signals. The Vector Fitting (VF) algorithm is then used to obtain a stable and passive state-space model of such augmented matrix. As a result, a stochastic system is described by an equivalent deterministic macro model and the time-domain variability analysis can be performed by means of one time-domain simulation. The feasibility, efficiency and accuracy of the proposed technique are verified by comparison with conventional Monte Carlo (MC) approach for a suitable numerical example.