Sensitivity of third- and higher-order filters

Abstract

For any realization of a network function F(s) = N(s)/D(s), the sensitivities that can be most readily calculated are those of the coefficients in N(s) and D(s). A simple relationship is derived that enables one to calculate the root (pole and zero) sensitivities of F(s) in terms of the coefficient sensitivities. The root sensitivities, in turn, enable one to calculate the root pair Q and root frequency sensitivities, which can be used to characterize and compare different realizations of F(s). Application to 3rd- and 4th-order filters reveals formulations that are more elegant than those already known in the literature.