Optimal capacitance assignment of switched-capacitor biquads

An algorithm is presented for the optimal capacitance assignment of conventional switched-capacitor biquads. It maximizes the dynamic range and minimizes the total capacitance simultaneously, with results presented in analytical forms. This is made possible by the development of a canonical representation of second-order transfer functions in the z-domain, which gives simple relations among three sets of parameters: (1) the pole-and zero-frequencies, and pole- and zero-Q´s of the s-domain prototype; (2) the key parameters of the bilinear-transformed z-domain transfer function; and (3) the capacitance ratios of the final switched-capacitor realization. Analytical results are derived and compared with those from using existing assignment techniques. This shows a reduction of 12% in total capacitance for some biquads. An extension of the algorithm to very large time-constant biquads is also discussed; the improvement is even larger for these circuits