Two-port representation of a linear transmission line in the time domain

Abstract

Abstract : This report discusses the adaptation of a linear section transmission line to a time-domain code. The linear section is described by frequency-domain parameters appropriately transformed into the time domain. On both ends of the linear section, the time-domain code employs difference equations to describe regions which may exhibit a nonlinear response. The interface between the linear and potentially nonlinear sections of cable produce boundary conditions joining the variant mathematical descriptions of the regions. This document reports on the formulation (in the time domain) of a two-part representation for a linear transmission line, and the joining of this result to a nonlinear, time-domain, transmission-line code. In general, the nonlinearities can occur in two regions: The first, or primary breakdown region, close to the burst, results from the high intensity fields associated with the nuclear device. The second, or secondary breakdown region, can occur at a discontinuity in the line far from the area of detonation. These are caused by signals propagated by the line and reflected at the discontinuity. These two regions are separated by a linear section of cable. Of course, this central line section is quite compatible with the nonlinear codes; that is, the difference equations representing the transmission-line equations are compatible with linear, as well as nonlinear, line behavior.