LOSSY TRANSMISSION LINES TERMINATED BY PARALLEL CONNECTED RLC-ELEMENTS WITHOUT THE HEAVISIDE’S CONDITION

Abstract

The paper deals with analysis of propagation of transverse electromagnetic waves along lossy transmission lines terminated by a circuit consisting of parallel connected RLCelements. Using the Kirchhoff’s laws we derive boundary conditions and formulate the mixed problem for hyperbolic system describing the lossy transmission line. Without the Heaviside's condition, we cannot guarantee the distortionless propagation of waves and hence we cannot apply the known methods. That is why we apply a different method and obtain conditions for existence-uniqueness of generalized solution. 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. We propose an operator presentation of the mixed problem for transmission line system and by means of fixed point technique we prove existence-uniqueness of a generalized solution.