An Extended Solution to the Equations Describing a 3-Conductor Transmission Line

Abstract

The full derivation of the generalized and extended solution to the equations describing threeconductor Transmission line is given in this paper; the brief results are presented in a previous paper. The Considerations proceed from the c. Paul formulation of lossless transmission lines terminated by linear loads. In contrast to c. Paul, the conjoint interaction between the two lines is considered here and the influence of the Receptor line is not neglected, that is the weak-coupling approximation is not applied. In result, an extended and Generalized mathematical model compared the original model of c. Paul is obtained. In particular, a mixed Problem for the hyperbolic system describing the three-conductor transmission line is formulated. It is shown That the formulated mixed problem is equivalent to an initial value problem for a functional system on the Boundary of hyperbolic system’s domain with voltages and currents as the unknown functions in this system Are the lines’. The system of functional equations can be resolved by a fixed-point method that enables us to Find an approximated but explicit solution. The method elaborated in this paper might be applied also for linear As well as nonlinear boundary conditions.