Hierarchical statistical analysis of complex analog and mixed-signal systems

With increasing process parameter variations in nanometre regime, circuits and systems encounter significant performance variations and therefore statistical analysis has become increasingly important. For complex analog and mixed-signal circuits and systems, efficient yet accurate statistical analysis has been a challenge mainly due to significant simulation and modelling time. In the past years, there have been various approaches proposed for statistical analysis of analog and mixed-signal circuits. A recent work is reported to address statistical analysis for continuous-time Delta-Sigma modulators. In this article, we generalise that method and present a hierarchical method for efficient statistical analysis of complex analog and mixed-signal circuits while maintaining reasonable accuracy. At circuit level, we use the response surface modelling method to extract quadratic models of circuit-level performance parameters in terms of process parameters. Then at system level, we use behavioural models and apply the Monte-Carlo method for statistical evaluation of system performance parameters. We illustrate and validate the method on a continuous-time Delta–Sigma modulator and an analog filter.