Abstract :
It is shown in the paper that each paramount non-singular matrix of order 3, or alternatively its inverse, may always be ordered into the uniformly tapered form. The network-theory interpretation of this result shows that each resistive 3-port network may be realized by at least one (and sometimes both) of two minimal structures, one with just four vertices and the other one with three independent circuits only. Moreover, there exists a unique parent configuration, a completely connected graph with four vertices, which is applicable to each realizable 3-port. After choosing an arbitrary linear tree on this graph, one is able to obtain any realizable 3-port by one of two methods: by either describing the ports on, or inscribing them into, the edges of this tree and by suitably choosing the values of its elements.
