A Graphical and Analytical Method to Determine the Transient Response for an Ideal Transmission Line, Loaded by a Time-Varying Impedance

Based on Bergeron's theory, a graphical and analytical method has been worked out to determine the dynamic load characteristic and load transients for a time-varying load impedance, pulsed by a lossless transmission line. The analytical solution has been compared with the numerical solution of the network analysis code SCEPTRE. A parametric study for a time-decreasing load function, demonstrated by the example of a vacuum-discharge flash X-ray tube, reveals that the dynamic load characteristic IL[UL(t), U0, Z0, T] and the transients UL(t, U0, Z0, T) and IL(t, U0, Z0, T) are dependent on the diode function ZL(t) as well as on the charging voltage U0 and the characteristics T and Z0 of the line.