Active filters with zero transfer function sensitivity with respect to the time constants of operational amplifiers

Most second-order RC active filters show a marked dependence on the gain-bandwidth product (GB) of operational amplifiers (OA's) when the
\omega_0
to be realized is greater than 1 percent of GB and
Q > 10
. Here designs are given that are virtually independent of OA's when
\omega_0<0.01
GB and
Q < 10
. Even for
\omega_0=0.05
GB and
Q=10
, the center frequency shift due to OA's is less than 0.1 percent. This desirable result is achieved by designing filter amplifiers which have zero first-order sensitivities with respect to the time constant
\tau = 1/GB
of the OA's used in the design. As a result, the filter transfer function has also zero first-order sensitivity with respect to
\tau
. General criteria for such designs are given. Experimental results show excellent agreement with theory.