Synthesis of a Class of n-Port Networks

The properties of a class of 2n -node networks, called K -networks, are discussed. The characteristic of a K -network is that when any one of its ports is connected to a voltage source keeping all the other ports short circuited, then all the short-circuited ports are at the same potential. The 2n -node network with a pair of equal conductances joining any two ports, as obtained by the presently known procedure for the realization of a dominant conductance matrix, is shown to be a special structure belonging to this general class. It is shown that the realization of a real dominant matrix as the short-circuit conductance matrix Y of an n -port network can be convenientlycarried out using K -networks. Further, the "modified cut-set matrix" of a K -network is of a special form, independent of edge conductances. This property can be made use of in generating a range of equivalent 2n -node n -port networks for a given Y . Examples illustrating the realization procedures are included.