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Oscillations in Lossy Transmission Lines Terminated By Exponential R-Load

Vasil G. Angelov*, Dafinka Angelova**

* Department of Mathematics, University of Mining and Geology, Bulgaria.

** Department of Mechanics and Mathematics, Higher School of Civil Engineering, Bulgaria

Periodicity:October - December'2012
DOI : https://doi.org/10.26634/jmat.1.4.2047

Abstract

This present paper is devoted to investigation of lossy transmissions lines terminated by a nonlinear resistive element. The transmission line is terminated by an R-element with exponential nonlinearity in the V-I characteristic. The reducing of the mixed problem for Telegrapher hyperbolic system to an initial value problem for a nonlinear neutral equation on the boundary is made in [3]. The nonlinearity in the boundary condition is transferred to the neutral equation on the boundary. Then we introduce a suitable operator whose fixed point is an oscillatory solution of the neutral equation. The main existence-uniqueness theorem contains conditions which guarantee that the operator mentioned is contractive one in a uniform space. Finally, we demonstrate how to apply the results obtained to the circuit design.

Keywords

Lossy Transmission Lines, Oscillatory Solutions, Neutral Equations, Fixed Point Theorem.

How to Cite this Article?

Angelov, V., and Angelova, D. (2012). Oscillations In Lossy Transmission Lines Terminated By Exponential R-Load. i-manager’s Journal on Mathematics, 1(4), 22-33. https://doi.org/10.26634/jmat.1.4.2047

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