Transmission Losses in 2n-Terminal Networks

Abstract

The semipositive character of the dissipation function of any physical 2n-terminal network imposes some restrictions on the realizability of prescribed transmission losses between the various pairs of terminals when they are connected to given impedances. These restrictions are most easily expressed in terms of elements of the efficiency matrix of the network, which is defined in the first part of this paper. Discussions of the application of matrix calculus to the solution of reactive and resistive, transformer-type, and general 2n-terminal networks are presented. A very useful tool in solving telephone transmission problems is the conventional theory of 4-terminal transducers, often called 4-pole networks. Although this theory is sufficient for the study of most circuits, some problems involve networks with a larger number of terminals, which are often referred to as 2n-terminal, or 2n-pole networks. This paper is a contribution to their theory. The particular point that will be considered in this paper is the restriction imposed by physical realizability on the arbitrary choice of transmission losses between various pairs of terminals connected to a given set of terminating (generator or receiver) impedances.