UNIQUENESS OF SOLUTION FOR LINEAR TRANSMISSION-LINES WITH NONLINEAR TERMINAL RESISTORS

Linear transmission lines with nonlinear terminal resistors are consid ered. Each resistor is assumed to be voltage controlled or current con trolled and weakly active. These distributed circuits are shown to hav e a unique solution, which passes at a given instant through a given v alue, if the characteristics of the terminal resistors satisfy certain inequalities. In particular, if the resistors are locally passive, th en the solution is unique. Transmission lines with terminal resistors that are locally active may admit several solutions that have the same initial value. In these cases, the uniqueness of solution is obtained adding ''small'' capacitances in parallel to the voltage controlled r esistors and ''small'' inductances in series to the current controlled resistors.