A nonuniform transmission line code for pulsed power Z-pinch drivers

Recently, a number of architectures have been proposed for the design of future pulsed power Z-pinch drivers¹. In the architectures nonuniform transmission lines were used to combine the outputs of several-hundred terawatt-level pulse generators to produce a petawatt-level pulse. In general, people obtained the output voltage from a nonuniform transmission line by considering the nonuniform line as a cascaded multiple-section line and then calculating it with the circuit simulation codes such as PSpice or TLCODE. We also treated the nonuniform line as a cascaded multiple-section line, but analyzed it with an analytical method. We found that a mathematical expression of the output voltage from a nonuniform line could be deduced if the impedance profile of the nonuniform line changes continuously and monotonically and each line section of the cascaded multiple-section line is short enough. The output voltage consists of one primary component called first arriving wave and numerous double-reflection components. In comparison with the input voltage wave, the first arriving wave is the same in wave shape and proportional to (Z_out/Z_in)^1/2 in amplitude, where Z_out and Z_in are the output impedance and the input impedance of the nonuniform line, respectively. It was shown that the double reflection components not only lower the output voltage, but also compress the output voltage pulse. The waveform of the output voltage obtained using our mathematical expression is fully overlapping with that obtained from the circuit simulation using PSpice, which indicates that our mathematical expression is correct.