Statistical analysis of RF circuits using combined circuit simulator-full wave field solver approach

As technologies continue to shrink in size, modeling the effect of process variations on circuit performance is assuming profound significance. Process variations affect the on-chip performance of both active and passive components. This necessitates the inclusion of the effect of these variations on distributed interconnect structures in modeling overall circuit performance. In this work, first it is shown through field-solver simulations that larger process variations lead to non-Gaussian PDFs (probability density functions) for the circuit equivalent parameters of distributed passives. Next, a method for accurate statistical analysis of coupled circuit-EM (Electromagnetic) systems without computing the equivalent circuit parameters of EM-modeled objects is demonstrated. This method also obviates the need to generate random variables representing the equivalent circuit parameters, from distributions which are correlated, non-Gaussian and non-closed-form. The proposed approach relies on application of the response surface (RS) methodology to the y-parameters of both the circuit and the distributed structures independently and expressing the eventual performance measures through a suitable combination of the y-parameters. The eventual performance measures are expressed through a hierarchical approach in terms of the underlying Gaussian random variables representing the process parameters. A rapid response surface Monte Carlo (RSMC) analysis on these derived response surfaces furnishes the PDFs and can also be used to predict the yield based on different qualifying criteria and objective functions.