A Network Theorem

It is shown that any relation between any of the commonly used parameters of a linear passive network (of any complexity) with two pairs of terminals is the equivalent of some other equally true relation which, by a simple rule for symbol substitution, may be obtained from, but is not necessarily algebraically contained in, the original expression. This symbol substitution theorem applies not only to transducer parameters but also to those quantities which describe the action of the transducer with load, with one exception. Distinguishing between the theorem and the rule for symbol substitution included in it, the rule may be used arbitrarily in cases where the theorem does not apply. By such a process it is shown that there is a closer relationship between certain structures than has heretofore been known. As an incidental to bringing the so-called general circuit parameters under the theorem, these have been expressed in terms of other parameters in such a way that certain minor theorems roughly analogous to Thevenin´s theorem result.