Hierarchical statistical analysis of performance variation for continuous-time delta-sigma modulators

Statistical analysis has become increasingly important with increasing process parameter variations in manufacturing. Monte Carlo method has been most popular for statistical analysis, but it is not efficient for complex circuits/systems due to overwhelming computational time. In this paper, we present a general hierarchical method for efficient statistical analysis of performance parameter variations for complex circuits/systems and conduct a case study on a 4th order continuous-time Delta Sigma modulator. At circuit-level, we use response surface modeling method to extract quadratic models of circuit- level performance parameters in terms of process parameter variations. Then, at system-level, we use behavioral models to extract statistical distribution of the overall system performance parameter. The method can achieve a good tradeoff between computational efficiency and accuracy.