FDTD analysis of lossy, multiconductor transmission linesterminated in arbitrary loads

A hybrid method is presented for incorporating general terminations into the solution of lossy multiconductor transmission lines (MTLs). The terminations are characterized by a state-variable formulation which allows a general characterization of dynamic as well as nonlinear elements in the termination networks. The method combines the second-order accuracy of the finite difference-time domain (FDTD) algorithm for the MTL with the absolutely stable, backward Euler discretization of the state-variable representations of the termination networks. A compact matrix formulation of the recursion relations at the interface between the MTL and the termination networks allows a straightforward coding of the algorithm. Skin effect losses of the line conductors as well as the effect of an incident field are easily incorporated into the algorithm. Several numerical examples are given which contain dynamic and nonlinear elements in the terminations. These examples demonstrate the validity of the method and show that the temporal and spatial step sizes can be maximized, thereby minimizing the computational burden