A discrete optimization method of switched capacitor filters

When constructed on a monolithic IC, switched capacitor filters (SCF's) composed of capacitors whose values are integer multiples of a unit value are desirable for miniaturization and reduction of power consumption, since high‐precision capacitance ratios are realized using a small unit capacitance value. This paper describes a discrete optimization method of SCF. Variables which are effective to optimization are selected based on “normalized sensitivities,” which are sensitivities at a certain sampled frequency point divided by the absolute sum of sensitivities at all sampled frequency points. The min‐max method which minimizes the maximum deviation is used to evaluate the optimization error. Initial discrete values of capacitances are determined by multiplying the pre‐quantization capacitance by a positive constant and then minimizing the mean square error of their ratios. Finally, this optimization is applied to an 8th‐order biquad bandpass filter and a 5th‐order leapfrog lowpass filter and its effectiveness is confirmed.