Real amplifier influence on impedance tapered 2nd-order filters

In this paper, an influence of real parameters of operational amplifier to the impedance tapered filter transfer function is analyzed. As an example, a second-order low-pass (LP) and high-pass (HP) Sallen and Key filters with Butterworth and Chebyshev transfer function approximations are considered. Design tables with normalized element values for both cases are given. The filter elements were calculated using three different design criteria: equal resistors, capacitors and impedance tapered elements. Filter transfer functions are obtained using ideal and real operational amplifier. Real model of common operational amplifier is presented. Active sensitivities for all presented filters are shown. The results obtained by the analyses show significant influence of real amplifier in the frequency ranges higher than 100kHz. Reduction of active sensitivities is obtained using impedance tapering, which fortunately, reduces the passive sensitivities as well.