State-variable biquads with optimum integrator sensitivities

Abstract

We show how to derive state-variable biquadratic sections with lowest possible sensitivity to their integrators. The resulting structures turn out to satisfy the condition for optimum dynamic range given by Mullis and Roberts [1]. The sensitivity optimum obtained is very ‘strong’ in the sense that these biquads simultaneously attain lower bounds for several practical measures of sensitivity. Furthermore, it is shown that this class of filters exhibits sensitivities that are either equal to or lower than those of doubly-terminated LC ladders.