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 amplifierRCnetworks 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. Forp=omega_{0}(-1/2Q+jsqrt{1-1/4Q^{2}})a nominal pole of the transfer function, general expressions fordp/d(1/ omega_{a}), dQ/d(1/ omega_{a}), andd omega_{0}/d(1 / omega_{a})are presented in terms of certain parameters of theRCnetwork. It is shown that these parameters may generally be found by inspection from theRCopenand short-circuit time constants and the high-frequency current gain of the passiveRCnetwork. The second-order transfer function case is considered in detail and the optimum choices of the pertinent passiveRCnetwork parameters for minimum sensitivity magnitude under various constraints are presented. A simple expression for the minimum possible magnitude ofdp / 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 minimizedp/d(1/ omega_{a})or achieve other sensitivity properties, such as zeroQsensitivity, is discussed.