Richardson extrapolation-based sensitivity analysis in the multi-objective optimization of analog circuits

The feasible solutions provided by a multi-objective evolutionary algorithm (MOEA) in the optimal sizing of analog integrated circuits (ICs) can be very sensitive to process variations. Therefore, to select the optimal sizes of metal–oxide–semiconductor field-effect-transistors (MOSFETs) but with low sensitivities, we propose to perform multi-parameter sensitivity analysis. However, since MOEAs generate feasible solutions without an explicit equation, then we show the application of Richardson extrapolation to approximate the partial derivatives associated to the sensitivities of the performances of an amplifier with respect to the sizes of every MOSFET. The proposed multi-parameter sensitivity analysis is verified through the optimization of a recycled folded cascode (RFC) operational transconductance amplifier (OTA). We show the behavior of the multi-parameter sensitivity approach versus generations. The final results show that the optimal sizes, selected after executing the sensitivity approach, guarantee the lowest sensitivities values while improving the performances of the RFC OTA.