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In Series Connected RCL-Elements Loaded on Lossy Transmission Lines without the Heaviside’s Condition

Vasil G. Angelov*

*Department of Mathematics, University of Mining and Geology “St. I. Rilski”, Sofia, Bulgaria.

Periodicity:April - June'2019
DOI : https://doi.org/10.26634/jmat.8.2.16649

Abstract

The main purpose of the present paper is to analyze the processes in a lossy transmission line terminated by in-series connected nonlinear RCL-loads. The distortion less propagation of the TEM-waves along the line under the Heaviside's condition has been investigated in a previous paper. Here we assume that the Heaviside condition is not satisfied. This leads to difficulties which can be overcome by a different type operator presentation of the mixed problem for the lossy transmission line. First, we formulate boundary conditions using the Kirchhoff's law, then transform the system in an operator form, and apply the fixed point method to obtain an existence-uniqueness theorem for a generalized solution. The uniqueness of solution is lost along the whole length of the line. Finally, we demonstrate the conditions of the main theorem on a typical example.

Keywords

Lossy transmission line, Nonlinear loads, Heaviside’s condition, Fixed point method.

How to Cite this Article?

Angelov, G. V. (2019). In Series Connected RCL-Elements Loaded on Lossy Transmission Lines without the Heaviside’s Condition. i-manager's Journal on Mathematics, 8(2), 1-14. https://doi.org/10.26634/jmat.8.2.16649

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