Sensitivities of six R-C active circuits

The R-C active filters investigated use operational amplifiers as the active element and are capable of realizing second-order network functions with no finite transmission zeros. One of the networks uses positive feedback; another uses negative feedback (from an amplifier of nominally infinite gain); two use both positive and negative feedback (from a paraphase amplifier of nominally infinite gain); the fifth uses a combination of three amplifiers all of nominally infinite gain; the sixth uses a four-amplifier realization of a gyrator, again all of nominally infinite gain. Expressions are given for the sensitivity of the (Q-factor and frequency of location of the `peak¿ to variations in the ratios of the passive elements and to gain. Also the effects on the Q-factor of finite gain and phase shift in the amplifier are observed. The operational amplifiers are assumed to be of infinite input impedance and zero output impedance and to have a gain which is approximated to a first-order lag.