[Show abstract][Hide abstract] ABSTRACT: This paper introduces a novel compact implicit model for a probabilistic set of waveforms (PSoW) which arise as representations for uncertain signal waveforms in Statistical Static Timing Analysis (SSTA). In traditional SSTA tools, signals are just represented as (distributions of) arrival time and slew. In our approach, to increase accuracy, PSoW's are used instead. However, to represent PSoW's explicitly, a very large amount of data is necessary, which can be problematic. To solve this problem, a compact implicit model is introduced, which can be characterized with just a handful of parameters. The results obtained show that the implicit model can generate real-life PSoW's with high accuracy.
[Show abstract][Hide abstract] ABSTRACT: Monte Carlo methods and simulation are often used to estimate the mean, variance, and higher order statistical moments of circuit properties like delay and power. 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 a uniform sampling technique and a weighted sample estimator. The proposed method needs significantly fewer 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 show that the proposed method needs 100× fewer simulations iterations than Monte Carlo runs for accurate moments estimation of delay and power for standard cells in 45 nm and 32 nm technologies.
Full-text · Article · Nov 2010 · Journal of Low Power Electronics