New time-domain sensitivity formulas and their applications

This paper proposes two time-domain tolerance measures: the sum of squared sensitivities of output sample values (SS), and the sum of squared errors of output sample values (SE), in order to investigate the parasitic effect on the impulse responses of linear time-invariant networks. The measure SS is expressed in a Hermitian form with 1) a matrix to be determined uniquely from a transfer function and time parameters, and 2) a vector whose elements are pole and zero sensitivities. In the case of cascade networks, the dependence of SS on an active element contained in a second-order stage can be expressed in terms of a pole sensitivity of this stage. This leads to computational savings. As an application, we present a method of finding the pole sensitivity which provides the lower limit of SS. This method is applicable to various network structures although only one case is discussed here. The measure SE is expressed in a quadratic form, with 1) a matrix to be computed using the formula for SS, and 2) a vector whose elements are relative errors of network parameters. We apply SE to the problem of the optimum tolerance assignment which produces the cheapest network.