Energy Theory of Sensitivity in LCR Networks

Abstract

Relationships between the classical sensitivity functions in resistively terminated LC <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> -port networks and the reactive energy stored in each L or C under the harmonic excitation are discussed. The results show that the mean value of the energy stored in a reactive element can be expressed in terms of the imaginary parts of the sensitivity functions of the scattering parameters with respect to the element. Further, the modulus of the sensitivity function of a scattering parameter with respect to a reactive element is the geometric mean of two mean values of energy stored in the element in the forward and the backward transmission. Some additional remarks, especially on the analytical properties and upper bounds of the sensitivity functions of resistively terminated LC two-port networks, are described.