State-space synthesis of optimum active biquads

A state-space technique recently developed for the synthesis of optimum integrator sensitivity active filters [2, 3] is extended to further optimise the active-RC biquads. It is found that the optimum sensitivity active biquad, which, having an asymmetric normal system matrix, has optimally distributed sensitivity both to the coefficient of the integrators, as well as to the effect of the finite gain/bandwidth product of the op amps. The normal integrator loop thus has two leaky integrators with equal damping coefficients and equal gains. The normal loop, however, can provide only the lowpass characteristic at the output of either integrator. Any other output characteristic with optimum sensitivity can only be obtained using nonzero output feed-forward coefficients c1 and c2.