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

The paper deals with analysis of propagation of transverse electromagnetic waves alonglossy transmission lines terminated by a circuit consisting of parallel connected RLCelements. Using the Kirchhoff’s laws we derive boundary conditions and formulate themixed problem for hyperbolic system describing the lossy transmission line. Without theHeaviside's condition, we cannot guarantee the distortionless propagation of waves andhence we cannot apply the known methods. That is why we apply a different method andobtain conditions for existence-uniqueness of generalized solution. We change variablesand formulate a mixed problem for the hyperbolic system with respect to the newvariables. The nonlinear characteristics of the RLC-elements generate nonlinearity in theequations of neutral type on the boundary. We propose an operator presentation of themixed problem for transmission line system and by means of fixed point technique weprove existence-uniqueness of a generalized solution.