Generalized Decoupled Polynomial Chaos for Nonlinear Circuits With Many Random Parameters

Abstract

This letter proposes a general and effective decoupled technique for the stochastic simulation of nonlinear circuits via polynomial chaos. According to the standard framework, stochastic circuit waveforms are still expressed as expansions of orthonormal polynomials. However, by using a point-matching approach instead of the traditional stochastic Galerkin method, a transformation is introduced that renders the polynomial chaos coefficients decoupled and therefore obtainable via repeated non-intrusive simulations and an inverse linear transformation. As discussed throughout the letter, the proposed technique overcomes several limitations of state-of-the-art methods. In particular, the scalability is hugely improved and tens of random parameters can be simultaneously treated within the polynomial chaos framework. Validating application examples are provided that concern the statistical analysis of microwave amplifiers with up to 25 random parameters.