Characteristic functions for different 2-port configurations of solvable nonuniform transmission lines

The voltage-current matrix parameters for a network may always be expressed in terms of its six characteristic functions, which were originally introduced by Matthaei and subsequently used by Chirlian. This paper outlines a simple procedure by which the derivation of the [Z] parameters alone, for the common 2-port configuration of a nonuniform transmission line, is shown to be sufficient for the evaluation of all the characteristic functions for three 2-port configurations of the line. It is shown that each of the characteristic functions can be expressed in terms of the two linearly independent functions of the distance variable x which constitute the general solution of the telegrapher´s equation governing the line. The characteristic functions for the three different configurations of a nonuniform line are derived and tabulated. The characteristic functions for the common 2-port configuration of three classes of generalised nonuniform lines, with their voltage solutions in closed forms, are tabulated, and their usefulness is shown by examples. The potential field of application for these functions is in the evaluation of the responses of integrated circuits which have the forms of the tabulated classes of nonuniform line. Since it has been shown by Bolinder that all types of wave parameter, e.g. scatting matrix, may be expressed in terms of voltage-current matrix parameters, the concept of characteristic functions of nonuniform lines may be employed to obtain these wave parameters for any device which employs TEM wave propagation in an isotropic medium.