Realizability constraints for third-order impedance-tapered allpole filters

It is shown that allpole filters of second- and third-order can be significantly desensitized to component tolerances by so-called impedance tapering, i.e., successively impedance-scaling upwards the L-sections of a resistance-capacitance ladder network in the forward and feedback path of a single-amplifier active filter. In order to obtain a realizable filter, certain constraints on the design equations must be observed. These constraints are derived here, and the resulting conditions necessary for the design of realizable third-order impedance tapered allpole filters are given.