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

The pole sensitivity with reference to the open-loop gainbandwidth product of the amplifier for a large class of single-voltage amplifier 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 a nominal pole of the transfer function, general expressions for , and are presented in terms of certain parameters of the network. It is shown that these parameters may generally be found by inspection from the openand short-circuit time constants and the high-frequency current gain of the passive network. The second-order transfer function case is considered in detail and the optimum choices of the pertinent passive network parameters for minimum sensitivity magnitude under various constraints are presented. A simple expression for the minimum possible magnitude of for a given second-order transfer function is derived. Finally, the application of these criteria to existing synthesis schemes in order to minimize or achieve other sensitivity properties, such as zero sensitivity, is discussed.