Analysis of the Power Transfer to a Nonlinear Transmission Line

The input current of a nonlinear transmission line (NLTL), driven by a step voltage pulse, was analyzed theoretically. As specific results of the analysis, two basic parameters of NLTLs were formulated for the first time: the energy injected to NLTLs and their characteristic impedance. The energy delivered to an NLTL by a square voltage source, with a series resistance of R
_S
, is given by a closed-form formula, which depends on the NLTL parameters and the input pulse characteristics. Considering the importance of the problem of the determining the injected energy content in a wide variety of the different applications of NLTLs, the obtained result will be of great importance, facilitating the design procedure and removing the need for a lot of trial-and-error efforts. Moreover, the characteristic impedance of NLTLs was derived by theoretical analysis, and was shown to be equal to the voltage-to-current ratio, either at the beginning of the line or at any other point throughout the line. The results of the developed theory were verified through simulation and exactly performed experimental tests, showing excellent agreement between the theoretical, simulation, and experimental results.