Stochastic Formulation of SPICE-Type Electronic Circuit Simulation with Polynomial Chaos

A methodology for efficient tolerance analysis of electronic circuits based on nonsampling stochastic simulation of transients is formulated, implemented, and validated. We model the stochastic behavior of all quantities that are subject to tolerance spectrally with polynomial chaos. A library of stochastic models of linear and nonlinear circuit elements is created. In analogy to the deterministic implementation of the SPICE electronic circuit simulator, the overall stochastic circuit model is obtained using nodal analysis. In the proposed case studies, we analyze the influence of device tolerance on the response of a lowpass filter, the impact of temperature variability on the output of an amplifier, and the effect of changes of the load of a diode bridge on the probability density function of the output voltage. The case studies demonstrate that the novel methodology is computationally faster than the Monte Carlo method and more accurate and flexible than the root-sum-square method. This makes the stochastic circuit simulator, referred to as PolySPICE, a compelling candidate for the tolerance study of reliability-critical electronic circuits.