A Useful Network Theorem

A theorem is developed for finding the steady-state voltage between two points 0 and 0' of a network having the following characteristics. Any number of (linear bilateral) impedances meet at the junction 0'. The voltages from 0 to the opposite ends of these impedances are known. These voltages and impedances are all that need be specified about the network. The theory is both simple to remember and simple to apply in problems where either a literal or a numerical solution is desired. In complicated networks it is a considerable timesaver over the more conventional method involving the simultaneous solution of a number of Kirchhoff's mesh equations. The theorem should find wide application, particularly in many linear-amplifier problems. The method of using the theorem and the relative simplicity with which results can be obtained is illustrated by considering five physically different (although mathematically quite similar) types of networks; namely, a T network, an unbalanced three-phase Y-connected network, a triode amplifier (account being taken of its interelectrode capacitances), the conventional resistance-capacitance coupled amplifier, and a two-stage parallel-feedback amplifier.