Design of single-voltage amplifier active filters for minimum open-loop gain sensitivity

The pole sensitivity with reference to the open-loop gainbandwidth product
|\omega_{a}|
of the amplifier for a large class of single-voltage amplifier
RC
networks is examined. Both finite gain and operational amplifier networks are considered under the assumption that the amplifier openloop gain effectively has a one-pole rolloff frequency characteristic. For
p=\omega_{0}(-1/2Q+j\sqrt{1-1/4Q^{2}})
a nominal pole of the transfer function, general expressions for
dp/d(1/ \omega_{a}), dQ/d(1/ \omega_{a})
, and
d \omega_{0}/d(1 / \omega_{a})
are presented in terms of certain parameters of the
RC
network. It is shown that these parameters may generally be found by inspection from the
RC
openand short-circuit time constants and the high-frequency current gain of the passive
RC
network. The second-order transfer function case is considered in detail and the optimum choices of the pertinent passive
RC
network parameters for minimum sensitivity magnitude under various constraints are presented. A simple expression for the minimum possible magnitude of
dp / d(1 / \omega_{a})
for a given second-order transfer function is derived. Finally, the application of these criteria to existing synthesis schemes in order to minimize
dp/d(1/ \omega_{a})
or achieve other sensitivity properties, such as zero
Q
sensitivity, is discussed.