Equivalence in sensitivity calculation between direct differentiation and the method based on Tellegen's theorem

Abstract

The concept of an adjoint network together with Tellegen's theorem has been-extensively used in deriving network sensitivity formulas both in analog circuits and digital filters. However, a direct differentiation of the network or signal-flow graph equations leads exactly to the same algorithm. The equivalence between the two methods is shown and simultaneously the unnecessary complexity of the derivation of the sensitivity formulas, when using Tellegen's theorem and the adjoint network, is emphasized.