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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. [ABSTRACT FROM AUTHOR]

This paper addresses for the first time the issue of passivity of the circuit models produced by means of the generalized polynomial chaos technique in combination with the stochastic Galerkin method. This approach has been used in literature to obtain statistical information through the simulation of an augmented but deterministic instance of a stochastic circuit, possibly including distributed transmission-line elements. However, transient simulations raise the critical question as to whether such an augmented network is passive or not. This paper discusses the general requirements for the augmented circuits to be passive and provides a sufficient condition for their passivity. Some numerical examples illustrate the theoretical results and conclude the paper. [ABSTRACT FROM PUBLISHER]