VHDL-AMS Statistical Analysis for marginal probabilities

The impact of parameter variations on components´ and systems´ characteristics, especially in the area of IC design, has been discussed for several years. To investigate the influence of parameter variations on system characteristics, standard Monte Carlo simulation is often used when exact results cannot be obtained using a deterministic algorithm. However, this procedure may require a huge number of simulation runs if marginal probabilities are estimated. This paper shows how importance sampling as a variance reduction technique can be used for estimating small probabilities in simulation experiments based on the SAE J 2748 VHDL-AMS Statistical Analysis Package. Furthermore, application examples are presented to show how the use of parameter sensitivities can help creating random variable distributions for importance sampling.