Capacitance ratio approximation in SC filters via genetic algorithm

Accurate capacitance matching is a critical issue for switched-capacitor (SC) filter implementations. Using identical unit capacitors in parallel to form larger capacitances and careful layout design can provide an accuracy of 0.1%. However, this technique can be directly applied only if the filter coefficients are rational numbers. In general, coefficient approximations are required, leading to frequency response errors. In this paper, a new design method, using a genetic algorithm (GA), is proposed to find the optimum capacitance ratio approximations by rational numbers that produce acceptable frequency response errors and minimize the total number of unit capacitors in order to save die area. Design examples in 0.35 μm CMOS are presented and simulated to illustrate the proposed method.