Statistical and behavioural modelling of analogue integrated circuits

Abstract

A full statistical model for the behavioural parameters of an analogue cell is presented. The parameter variations with respect to manufacturing tolerances are approximated by response surfaces which allow the mean, standard deviation, correlation of parameter pairs and the actual distribution to be estimated. The parameters are characterised from either measurements of fabricated devices or from circuit simulation of the analogue cell. An efficient method of mapping between the performance space and the behavioural parameter space which requires no a priori assumption about the analytical maping is demonstrated. By combining the mapping with statistical methods we can include tolerance information in the behavioural model. Such models can then be used for simulation and yield estimation at a higher circuit level. This procedure is demonstrated on the behavioural model of a switched-capacitor integrator by considering the effect of tolerances derived from both simulations and actual measurements. The accuracy of results obtained with the characterised behavioural model relative to the circuit-level simulation is considered.