GENERALIZED CONFLUENT HYPERGEOMETRIC AND HYPERGEOMETRIC TRANSMISSION LINES

A proliferation of exact closed-form solutions of the telegrapher's equation Vxx — ZxZ-1Vx — kZ Y V = 0 for the voltage V(x) in an RC or lossless transmission line, with distributed series impedance Z(x) and shunt admittance Y(x), respectively, have emerged in recent years. Generalizations of known solutions have been constructed, sometimes using ad hoc methods. A systematic method is described for deriving exact solutions in terms of standard transcendental functions, which yields far more general profiles for Z(x), Y(x), ot Z(x)/Y(x) than previously given. Examples of the procedure are given based upon Bessel's, Whittaker's, and the hypergeometric equation, and previously derived profiles emerge as special cases of the analysis. © 1961, IEEE. All Rights Reserved.