A Ladder Network Theorem

Abstract

The theorem of this paper gives four-terminal representation of ladder networks satisfying a prescribed condition on the side impedances, in terms of the three parameters specifying the network connected as a transducer, the driving-point impedance between short-circuited transducer terminal pairs, and an impedance ratio involving the side impedances only. This mode of representation has a special advantage in applications to electric railway networks in that the transducer parameters which alone involve the ladder shunt impedances (under the stated conditions) may be calculated in a relatively simple fashion, and extensive networks reduced to manageable form. The theorem is stated and proved, and its applications are sketched in some detail.