Generalized Confluent Hypergeometric and Hypergeometric Transmission Lines

1 August 1969

journal article
Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Circuit Theory

Vol. 16 (3) , 289-294
https://doi.org/10.1109/tct.1969.1082981

Abstract

A proliferation of exact closed-form solutions of the telegrapher's equationV_{xx} - Z_{x}Z^{-1}V_{x} - kZ Y V = 0for the voltageV(x)in anRCor lossless transmission line, with distributed series impedanceZ(x)and shunt admittanceY(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 forZ(x), Y(x), orZ(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.

Keywords

This publication has 19 references indexed in Scilit:

Raised trigonometric and hyperbolic power lines
Electronics Letters, 1968
On generalized nonuniform lines
Proceedings of the IEEE, 1967
Nonuniform RC and Lossless Transmission Lines
IEEE Transactions on Circuit Theory, 1966
Generalized Nonuniform Transmission Lines
IEEE Transactions on Circuit Theory, 1966
Hermite lines
Proceedings of the IEEE, 1966
Dual distributions of solvable nonuniform lines
Proceedings of the IEEE, 1966
Tapered Distributed RC Networks with Similar Immittances
IEEE Transactions on Circuit Theory, 1965
Transfer characteristics of a class of distributed RC networks
Proceedings of the IEEE, 1965
Some Exactly Solvable Nonuniform RC Lines
IEEE Transactions on Circuit Theory, 1965
Tapered Distributed Filters
IRE Transactions on Circuit Theory, 1962