Element sensitivity and energy storage of a passive impedance

The sensitivity of a passive impedance (admittance) to variations of its individual elements is discussed using Vratsanos´ (Cohn´s) theorem. The measure of the overall sensitivity which arises naturally is the sum of the magnitudes of the sensitivities to individual elements. For reciprocal realizations the sensitivity magnitude sums over resistances and reactances are separately related to the total power dissipation and the energy storage of the network. To minimize sensitivity, the energy storage must be minimized. Previous results for the energy storage of a one-port are used and extended to discuss further the minimum sensitivity problem. In certain cases it is shown how to find a synthesis having minimum sensitivity at all frequencies. The wider class of networks containing gyrators is also discussed, using an extension of Vratsanos´ theorem. In this case the results obtained are weaker, since the properties of the actual realization, and that of the conjugate realization obtained by gyrator coupling reversals, are involved symmetrically. Bounds in terms of total power dissipations and energy storage are found for the sensitivity magnitude sums over resistances and reactances. The general results are illustrated by particular examples. It is shown by example that the sensitivity magnitude sum over resistances in a nonreciprocal network can be lower than the universal value imposed on reciprocal networks.