Stochastic Modeling of Nonlinear Circuits via SPICE-Compatible Spectral Equivalents

This paper presents a systematic approach for the statistical simulation of nonlinear networks with uncertain circuit elements. The proposed technique is based on spectral expansions of the elements' constitutive equations (I–V characteristics) into polynomial chaos series and applies to arbitrary circuit components, both linear and nonlinear. By application of a stochastic Galerkin method, the stochastic problem is cast in terms of an augmented set of deterministic constitutive equations relating the voltage and current spectral coefficients. These new equations are given a circuit interpretation in terms of equivalent models that can be readily implemented in SPICE-type simulators, as such allowing to take full advantage of existing algorithms and available built-in models for complex devices, like diodes and MOSFETs. The pertinent statistical information of the entire nonlinear network is retrieved via a single simulation. This approach is both accurate and efficient with respect to traditional techniques, such as Monte Carlo sampling. Application examples, including the analysis of a diode rectifier, a CMOS logic gate and a low-noise amplifier, validate the methodology and conclude the paper.