Stochastic formulation of SPICE-type electronic circuit simulation with polynomial chaos

Abstract

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.

Review of Polynomial Chaos-Based Methods for Uncertainty Quantification in Modern Integrated Circuits

“…Hence, different PC-based techniques have been developed over the years by the research community tailored on the types of devices or components considered: lumped element circuits [42][43][44], multiconductor transmission lines [45][46][47], generic linear multiport systems [37,39,48], and nonlinear systems [38,[49][50][51][52][53]. Additional details are given in the next section, where a review of the main applications of the PC method in electrical and electronics problem is presented.…”

A Comprehensive and Modular Stochastic Modeling Framework for the Variability-Aware Assessment of Signal Integrity in High-Speed Links

“…Many techniques based on the polynomial chaos (PC) method [1], [2] have been recently developed to tackle this problem [3]- [14], and are able to perform variability analysis with high accuracy and efficiency compared to MC-based approaches. Each method is tailored for a specific class of circuits, like lumped-element circuits [3], transmissionline circuits [4], [5], arbitrary passive linear systems [6]- [8], or nonlinear circuits [9]- [14].…”

“…Each method is tailored for a specific class of circuits, like lumped-element circuits [3], transmissionline circuits [4], [5], arbitrary passive linear systems [6]- [8], or nonlinear circuits [9]- [14]. However, a general and comprehensive modeling framework, capable of including heterogeneous stochastic components appears yet to be missing.…”

Uncertainty quantification of silicon photonic devices with correlated and non-Gaussian random parameters

“…There is a lack of uncertainty quantification techniques for silicon photonics, however some results have been reported recently for nanometer integrated circuits (IC) [9][10][11][12] and microelectromechanical systems (MEMS) [13,14]. The mainstream stochastic simulation technique in commercial design software is Monte Carlo [15].…”