Some further sensitivity theorems in active equivalent - network theory

The relevance of various sensitivity measures in the study of active equivalent networks is investigated. It is known that the summed differential sensitivity of the passive components in an active RC network is invariant under the transformation; it is now shown that the similar sums of large-change sensitivities and the large-change multiparameter sensitivity are both invariant for component changes within specified bounds. Even more practical sensitivity measures derive from integral definitions over a specified frequency interval. It is demonstrated that the sums of integral sensitivities are noninvariant under transformation but the integral of the multiparameter sensitivity function again remains invariant. These results are of significance in any attempted optimisation of the sensitivities of active-filter structures.