Stochastic Testing Method for Transistor-Level Uncertainty Quantification Based on Generalized Polynomial Chaos

TLDR

Uncertainties have become a major concern in integrated circuit design. The paper introduces an intrusive spectral simulator to eliminate the extensive repeated simulations required by conventional Monte Carlo flows. It employs generalized polynomial chaos expansion and an intrusive stochastic testing variant of stochastic collocation to accelerate uncertainty quantification of nonlinear transistor circuits. The proposed ST method produces decoupled deterministic equations, requires fewer samples, allows flexible time steps, and outperforms SG and SC in efficiency, as demonstrated on digital, analog, and RF circuits and applicable to other engineering problems.

Abstract

Uncertainties have become a major concern in integrated circuit design. In order to avoid the huge number of repeated simulations in conventional Monte Carlo flows, this paper presents an intrusive spectral simulator for statistical circuit analysis. Our simulator employs the recently developed generalized polynomial chaos expansion to perform uncertainty quantification of nonlinear transistor circuits with both Gaussian and non-Gaussian random parameters. We modify the nonintrusive stochastic collocation (SC) method and develop an intrusive variant called stochastic testing (ST) method to accelerate the numerical simulation. Compared with the stochastic Galerkin (SG) method, the resulting coupled deterministic equations from our proposed ST method can be solved in a decoupled manner at each time point. At the same time, ST uses fewer samples and allows more flexible time step size controls than directly using a nonintrusive SC solver. These two properties make ST more efficient than SG and than existing SC methods, and more suitable for time-domain circuit simulation. Simulation results of several digital, analog and RF circuits are reported. Since our algorithm is based on generic mathematical models, the proposed ST algorithm can be applied to many other engineering problems.