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.