Simplified Multiple Parameter Sensitivity Calculation and Continuously Equivalent Networks

Abstract

A method of efficiently calculating the sensitivity functions of a single output variable with respect to all the parameters in a reciprocal network is described. The method reduces the problem of obtaining these sensitivity functions to the simple problem of solving one additional network easily derived from the given network. A distinct advantage of the method is that currently available digital computer network analysis programs can be used with little modification and calculation of the sensitivity functions. Next, the frequency dependence of the sensitivity of continuously equivalent networks is examined. The results of this study allows one to make three hypotheses about continuously equivalent networks. 1) The continuously equivalent network resulting from a minimization of the sum of the magnitudes squared of the sensitivity functions at a given frequency is the network with minimum sum of the magnitudes squared of the sensitivity function at all frequencies. 2) The sum of the magnitudes squared of the sensitivity functions decreases as the number of elements increases in continuously equivalent networks. 3) The sum of the sensitivity functions is invariant with respect to the various equivalent networks. The most important hypothesis is the first since if true for all continuously equivalent networks, then a great simplification of the computation problem results. Even if a limited class of continuously equivalent networks exhibit this property, then the result is worthwhile. Experimental results show that such a class does exist. These experimental results do not prove that all continuously equivalent networks have these three properties.