Stochastic Analog Circuit Behavior Modeling by Point Estimation Method

Stochastic device parameter variations have dramatically increased beyond the scale of 65nm and can significantly lead to large mismatch for analog circuits. To estimate unknown analog circuit behavior in performance space under the given stochastic variations in parameter space, many state-of-art approaches have been developed recently. However, either Gaussian distribution or response surface model (RSM) with analytical formulae has to be assumed when connecting performance space and parameter space. A novel point-estimation based approach has been proposed in this paper to capture arbitrary stochastic distributions for analog circuit behaviors in performance space. First, to evaluate high-order moments of circuit behavior in an accurate fashion, the point-estimation method has been applied with only a few number of simulations. Then, probability density function (PDF) of circuit behavior can be efficiently extracted by the obtained high-order moments. This method is further extended for multiple parameters under linear complexity. Extensive numerical experiments on a number of different circuits have demonstrated that the proposed point-estimation method can provide up to 181X runtime speedup with the same accuracy, when compared with Monte Carlo method. Moreover, it can further achieve up to 15X speedup over the RSM-based method such as APEX with the similar accuracy.