CMCal: An Accurate Analytical Approach for the Analysis of Process Variations with Non-Gaussian Parameters and Nonlinear Functions

Abstract

As technology rapidly scales, performance variations (delay, power etc.) arising from process variation are becoming a significant problem. The use of linear models has been proven to be very critical in many today's applications. Even for well-behaved performance functions, linearising approaches as well as quadratic model provide serious errors in calculating expected value, variance and higher central moments. This paper presents a novel approach to analyse the impacts of process variations with low efforts and minimum assumption. Circuit performance was formulated as a function of the random parameters and approximated it by Taylor expansion up to 4th order. Taking advantage of the knowledge about higher moments, the Taylor series was converted to characteristics of performance distribution. The experiments show that this approach provides extremely exact results even in strongly non-linear problems with large process variations. Its simplicity, efficiency and accuracy make this approach a promising alternative to the Monte Carlo method in most practical applications