Internal structure and parametric representation of equivalent resistive n-port networks

The theory of resistive n-port networks has attracted considerable interest during the last decade. This is due, partly, to the fact that results obtained in analysis and synthesis of resistive networks have been applied to many other engineering problems. The field of applications covers all such systems which can be modelised by nets whose branch characteristics may be expressed by real numbers, e.g. communication and probabilistic nets, switching networks etc. In the paper, general equivalence theory of resistive n-port networks is studied. A parametric representation of the whole class of equivalent resistive n-ports corresponding to a given short-circuit admittance matrix is derived. An algebraic-geometric interpretation of this representation is given and some properties pertinent to its continuity and differentiability and to the connectedness of the domain of realisability are then obtained. A special discussion is devoted to certain distinguished subclasses of equivalent resistive n-ports. The results obtained here reveal the internal symmetry inherent in the whole family of equivalent n-ports.