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.