Heaviside Condition Applied to Lossy Transmission Lines Terminated by RLC-Circuits

Authors : Vasil G. Angelov.

Volume/Issue : Volume 3 - 2018, Issue 10 - October

Scribd : https://goo.gl/qptVc6

Thomson Reuters ResearcherID : https://goo.gl/KTXLC3

Abstract : Here we consider lossy transmission lines terminated by a circuit consisting of linear and nonlinear RCL-elements. Using the Kirchhoff’s laws we derive boundary conditions and formulate the mixed problem for hyperbolic system describing the lossy transmission line. Then we reduce the mixed problem to an initial value problem on the boundary. To obtain a distortionless propagation we change variables and formulate a mixed problem for the hyperbolic system with respect to the new variables. The nonlinear characteristics of the RLC-elements generate nonlinearity in the equations of neutral type on the boundary. Since we are not able to eliminate some transitional currents and voltages we have to consider a system of 6 equations for 6 unknown functions. Under Heaviside conditions we show that natural solutions are distortionless ones. By means of fixed point technique we prove existence-uniqueness of an oscillatory solution.

Keywords : fixed point method, Heaviside condition, hyperbolic system, lossy transmission line, oscillatory solution, RLC-circui.

Here we consider lossy transmission lines terminated by a circuit consisting of linear and nonlinear RCL-elements. Using the Kirchhoff’s laws we derive boundary conditions and formulate the mixed problem for hyperbolic system describing the lossy transmission line. Then we reduce the mixed problem to an initial value problem on the boundary. To obtain a distortionless propagation we change variables and formulate a mixed problem for the hyperbolic system with respect to the new variables. The nonlinear characteristics of the RLC-elements generate nonlinearity in the equations of neutral type on the boundary. Since we are not able to eliminate some transitional currents and voltages we have to consider a system of 6 equations for 6 unknown functions. Under Heaviside conditions we show that natural solutions are distortionless ones. By means of fixed point technique we prove existence-uniqueness of an oscillatory solution.

Keywords : fixed point method, Heaviside condition, hyperbolic system, lossy transmission line, oscillatory solution, RLC-circui.