Expansion Theorems for Ladder Networks

The well-known expansion theorem of Heaviside applies to circuits whose current-electromotive force relations may be expressed through differential equations, whereas in some networks such as filters and artificial lines, in which the network consists of a repeated pattern or mesh, the relations give what are known as difference equations. These are equations involving the mesh number of the network. The solutions of such networks are given in this paper in the form of expansion theorems similar to Heaviside's expansion theorem and its extensions.