RC-Amplifier Resonators for Active Filters

Active filters may consist of a cascade of isolated resonators, with each resonator supplying a single pair of complexconjugate poles. This paper supplies a detailed analysis of some
RC
-amplifier resonators whose characteristics are well suited for practical filters. The calculations are facilitated by a set of sensitivity identities. One resonator, taken from the Sallen and Key catalog, is shown to have extremely low passive sensitivities:
S_{Z}^{Q} = \pm \frac{1}{6}
for all passive elements. Active
Q
multiplication is used to extend the usefulness of the circuit. Analysis of the dualintegrator feedback resonator shows that it is notably insensitive to amplifier parasitics. Finally, the dual-integrator concept is realized in a resonator that uses only two amplifiers. The several resonators supply a range of useful pole-
Q
's from low values to several hundred.