Systematic method for determining the minimality of an RC network

Abstract

It is always difficult to tell whether a given RC one-port network is realized in the minimal form, and to what extent the number of elements can be reduced if it is not minimal. In this paper, two operators are defined to denote the parallel and series combinations of circuit elements. The network is represented in a form of expression similar to that of boolean algebra. Some theorems are established to provide a systematic method of determining the minimality of a given network. The mechanism involved is to reduce all the redundant elements by converting the network to its minimal form, which, in general, is Foster's first or second form. In this procedure of network minimization, we are concerned only with the structures of the networks, and are not interested in the actual synthesis procedure.