An efficient method for statistical circuit simulation

The dynamic behavior of a VLSI circuit can be described by a system of differential-algebraic equations. When some circuit elements are affected by process variations, the dynamic behavior of the circuit will deviate from its nominal trajectory. Monte-Carlo-type random sampling methods are widely used to estimate the trajectory deviation. However they can be quite time-consuming when the dimension of the parameter space is large. This paper offers an alternative solution by casting the problem into the theoretic frame work of non-linear non-Gaussian filtering. To estimate the mean and variance of the time-dependent circuit trajectory, we develop a method based on unscented transformation, which is an efficient Bayesian analysis sampling technique. Theoretically the method has linear runtime complexity. Experimental results show that compared to traditional Monte-Carlo methods, the new method can achieve over 10times speedup with less than 2% error.