Explicit upwind schemes for lossy MTLs with linear terminations

Abstract

The time domain multiconductor transmission line (MTL) equations are written as a general first order system of partial differential equations and a characteristic decomposition is used to obtain first order and second order accurate upwind differencing schemes. Linear boundary conditions in the form of generalized Thevenin equivalent sources are incorporated into the scheme. These schemes are compared with the standard time-space centered second order accurate leapfrog scheme where the current and voltage variables are interlaced in space and time. For any general explicit numerical scheme, for a given MTL, only the fastest propagating TEM mode can be solved for at the Courant limit of the scheme. This causes the other slower modes to disperse. The results of our comparisons, show that at the Courant number both upwind schemes produce less numerical dispersion for the slower propagating modes than the standard leapfrog scheme under the same conditions. In addition, the Courant number of the second order upwind scheme is twice that of the leapfrog scheme. These advantages make the upwind schemes better tools to model inhomogeneous MTLs with linear terminations.