A Gaussian mixture model for statistical timing analysis

This paper introduces a Gaussian mixture model to represent delay and slew distributions in the statistical static timing analysis, and proposes algorithms for propagating them on a given circuit graph. The Gaussian mixture model can represent a non-Gaussian distribution due to the statistical max operation properly, and any correlation efficiently, since it consists of plural Gaussian distributions. Therefore, not only topological correlations caused by re-convergent paths but also the correlation between each element and the critical delay, which is useful for circuit optimization, are calculated easily. The propagated slews are used to compute delay distributions of circuit elements dynamically so as to improve the accuracy. The proposed Gaussian mixture model is evaluated by comparing with Monte Carlo simulation, and the results show its effectiveness.