OPTIMAL CAPACITANCE ASSIGNMENT OF SWITCHED-CAPACITOR BIQUADS

An algorithm is presented for the optimal capacitance assignment of co nventional switched-capacitor biquads. It maximizes the dynamic range and minimizes the total capacitance simultaneously, with results prese nted 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-dom ain prototype; 2) the keg parameters of the bilinear-transformed z-dom ain transfer function; and 3) the capacitance ratios of the final swit ched capacitor realization. Analytical results are derived and compare d with those from using existing assignment techniques. This shows a r eduction 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.