Generalised exact nonuniform transmission lines and their characteristic functions

A new category of nonuniform transmission lines, called `exact nonuniform transmission lines¿, may be obtained, if the linear second-order differential equation representing the variation of voltage (or current) along any of the lines of the new category, satisfies the condition of exactness for a linear second-order differential equation. The paper introduces two generalised subclasses of such exact nonuniform transmission lines. For ease in distinguishing these two subclasses from other solvable nonuniform lines, expressions for the distributions of line-parameters, the propagation factor and the characteristic impedance, for each of the subclasses, are presented in terms of two mutually independent and arbitrary functions of the distance variable. If one of the functions is taken to define the arbitrarily chosen distribution of one of the line parameters, the other function stands for the independent variable of the generalised form of the voltage (or current) differential equation governing the line. The 2-port characteristic functions of each subclass, required to express all the matrix parameters in convenient form, are tabulated.