RC-active networks with reduced sensitivity to amplifier gain bandwidth product

A sensitivity analysis for a general second-order multiamplifier RC-active network is described. The conditions for minimized sensitivity to amplifier gain-bandwidth product (GBWP) are established after first formulating the transfer function gain dependence under the assumption of a single-pole representation of the complex amplifier gain. On the basis of a perturbation technique, approximate expressions are presented for the evaluation of the selectivity and frequency sensitivities. By distinguishing a general form of denominator decomposition, the methods available for realization of high Q´s with improved sensitivity are explored. Three special cases of the decomposition are identified; two of these, in common with the general case, suggest the use of twin-T null networks with their attendant high passive sensitivities, but the third gives rise to an additional group of circuits ´realizable as double first-order all-pass sections. By comparison with some previous circuits which require matched amplifiers to achieve a low sensitivity, the proposed configurations are shown to be unconditionally insensitive to variations of the GBWP of the amplifiers.