A hybrid Quasi Monte Carlo method for yield aware analog circuit sizing tool

Efficient yield estimation methods are required by yield aware automatic sizing tools, where many iterative variability analyses are performed. Quasi Monte Carlo (QMC) is a popular approach, in which samples are generated more homogeneously, hence faster convergence is obtained compared to the conventional MC. However, since QMC is deterministic and has no natural variance, there is no convenient way to obtain estimation error bounds. To determine the confidence interval of the estimated yield, scrambled QMC, in which samples are randomly permuted, is run multiple times to obtain stochastic variance by sacrificing computational cost. To palliate this challenge, this paper proposes a hybrid method, where a single QMC is performed to determine infeasible solutions in terms of yield, which is followed by a few scrambled QMC analyses providing variance and confidence interval of the estimated yield. Yield optimization is performed considering the worst case of the current estimation, thus the optimizer guarantees that the solution will satisfy the confidence interval. Furthermore, a yield ranking mechanism is also developed to enforce the optimizer to search for more robust solutions.