Statistical Moment Estimation in Circuit Simulation

Monte Carlo methods and simulation are often used to estimate the mean, variance, and higher order statistical moments of signal properties like delay and slew. The main issues with Monte Carlo methods are the required long run time and the need for prior detailed knowledge of the distribution of the variations. Additionally, most of available circuit simulation tools can run Monte Carlo analysis for Gaussian, lognormal and uniform distribution only. In this paper, in order to estimate these statistical moments, we propose a new method based on the uniform sampling technique and weighted sample estimator. The proposed method needs significantly less simulation runs, and does not need detailed prior knowledge of the variation distributions. Furthermore, it can be used for any type of probability distribution irrespective of the circuit simulation tool used for the analysis. The results obtained shows that the proposed method needs 100× fewer simulations iterations than Monte Carlo runs for the moments estimation of the delay for standard cells in 45nm and 32nm technologies.