Automatic synthesis of uncertain models for linear circuit simulation: A polynomial chaos theory approach

A generalized and automated process for the evaluation of system uncertainty using computer simulation is presented. Wiener–Askey polynomial chaos and generalized polynomial chaos expansions along with Galerkin projections, are used to project a resistive companion system representation onto a stochastic space. Modifications to the resistive companion modeling method that allow for individual models to be produced independently from one another are presented. The results of the polynomial chaos system simulation are compared to Monte Carlo simulation results from PSPICE and C++. The comparison of the simulation results from the various methods demonstrates that polynomial chaos circuit simulation is accurate and advantageous. The algorithms and processes presented in this paper are the basis for the creation of a computer-aided design (CAD) simulator for linear networks containing uncertain parameters.