Sensitivity minimization in a single amplifier biquad circuit

The single amplifier biquad (SAB) circuit of J. J. Friend is critically examined with a view to minimize its sensitivity properties. This is shown to involve the proper choice of the free design parameters to achieve a trade off between the contributions due to passive and active element variations. First the bandpass configuration is analyzed. A statistical measure of the overall pole variation due to both passive and active components is formulated. The analysis includes a novel but very simple approach for estimating the effects due to op amp variations which is applicable to many of the active filter topologies known. Using the figure of merit obtained in this fashion, it is shown that a near optimal design exists which permits ready physical realization, and which has the property that the transmission error terms are dominated by the irreducible fixed contribution due to the product which defines the resonant frequency. From the aspect of sensitivity, therefore, it is concluded that no other circuit topology can have superior performance. The frequency range over which these conclusions remain valid are determined by using reasonable estimates of circuit component tolerances. For a simple operational amplifier of the 741-type this range is shown to extend to approximately 2 kHz, while if a more sophisticated two-pole single zero compensation is used for the operational amplifier the range of validity is extended to about 20 kHz. The above results are then shown to hold for all the other important