Using a Genetic Algorithm to Optimize Capacitance Ratio Approximations in SC Filters

Accurate capacitance matching is one of the main design issues in switched-capacitor (SC) filters. Using identical unit capacitors in parallel to implement each filter capacitor, combined with a careful layout design, can provide an accuracy of 0.1% in the filter coefficients. The disadvantage of this technique is the fact that it can be directly applied only if the coefficients can be expressed as ratios of integer numbers. As a result, coefficient approximations are required, leading to frequency response errors. In this paper, a genetic algorithm (GA) is used to find the optimum capacitance ratio approximations by rational numbers that minimize the total number of unit capacitors for a given error tolerance in the frequency response. Design examples in 0.35 μm CMOS are presented and simulated to illustrate the proposed approach and verify its effectiveness.