ON THE DYNAMIC EQUATIONS OF LINEAR MULTICONDUCTOR TRANSMISSION-LINES WITH TERMINAL NONLINEAR MULTIPORT RESISTORS

Distributed circuits composed of linear multiconductor transmission li nes and terminated with nonlinear weakly active multiport resistors ar e considered. The line is represented as a linear dynamic multiport th rough recursive convolution relations and special considerations are g iven to some general properties of the line impulse responses. The con volution technique allows the mathematical description of these distri buted circuits by means of a sea: of nonlinear algebraic-integral equa tions of Volterra type for the terminal voltages and currents. The con ditions under which these governing equations can he reformulated as a set of Volterra integral equations of second kind in normal form are given with the explicit means for doing so. These conditions also assu re the existence and the uniqueness of the solution. In particular if the terminal multiport resistors are strictly locally passive, then th e normal form exists and the solution is unique. Transmission lines wi th terminal multiport resistors that are locally active may not admit a normal form for the governing equations, and hence, several solution s that have the same initial conditions are possible, In these cases a simple method is presented for revising the original network model so that the normal form exists, and hence, the uniqueness of solution is assured, under mild restrictions.