Generalised patterns of nonuniformity for solvable algebraic and transcendental transmission lines

The aim of this letter is to show that, on transforming the independent variable x of the telegrapher's equation for nonuniform lines to another independent variable w=F(x) which is some function of the distance variable x, and then constraining the transformed equation, so obtained, to represent either Su's trigonometric or his hyperbolic line, a generalised pattern of nonuniformity, expressible either in terms of any arbitrary w=F(x), or in terms of another arbitrary f(x) [where f(x)=Z(x)/Z0, Z0 being an impedance constant, defines the distribution of nonuniformity for the series impedance Z(x) per unit length] may be obtained. In addition, the generalised expressions for the distributions of nonuniformity for a prototype of Cheby̅shev line are derived, and it is shown that the Cheby̅shev line is a subclass of Hellstrom's generalised proportional line.