The Sensitivity Function in Variability Analysis

Methods of variability analysis include deterministic approaches, e.g., ``worst case'' methods, ``Shmoo Plots,'' and probabilistic approaches (Monte Carlo and Moment methods). Most of these use as a point of departure the Taylor Series expansion of the performance function about the nominal operating point with all but first-order terms neglected. The coefficients of the series are the partial derivatives of the performance function with respect to the components evaluated at the nominal operating point. These derivatives when properly normalized become the sensitivity functions used extensively in the study of feedback systems. The purpose of this paper is to bring together various results concerning sensitivity which are of direct use in variability analysis. One of the most useful of these is a relation concerning sensitivity sums which furnishes a valuable check on sensitivity calculation for homogeneous functions. Enough errors have been noted in recent literature to indicate that use of this check should become a routine part of variability analysis wherever it is applicable. Also included are applications to pole-zero sensitivity of electrical networks.