Leapfrogging solitary waves are characterized in two capacitively coupled transmission lines that are periodically loaded with Schottky varactors, called coupled nonlinear transmission lines (NLTLs). The coupling implies that a nonlinear solitary wave moving on one of the lines is bounded with the wave moving on the other line, which results in the periodic amplitude/phase oscillation called leapfrogging. In this study, we clarify how the leapfrogging frequency depends on the physical parameters of coupled NLTLs using a numerical model validated through measuring test lines and demonstrate the relaxation of leapfrogging. In addition, coupled Korteweg-de Vries equations are derived by applying the reductive perturbation method to the transmission equations of coupled NLTLs. Using perturbation theory based on the inverse scattering transform, a closed-form expression of leapfrogging frequency is obtained and the parameter values that simulate the properties well are examined. Engineering applications based on leapfrogging are finally discussed.
Abstract:We investigate the three-wave mixing process that is induced by nonlinear envelope pulse collisions in composite right-and left-handed transmission lines with regularly spaced Schottky varactors. For left-handed waves, the wave number decreases as the frequency increases; this results in the resonant interaction of colliding left-and right-moving waves. In this study, we introduce design criteria for the generation efficiency of sum frequency waves using the derivative expansion method; we also introduce a method of generating pulsed second-harmonic waves.
A method of the generation of an electrical short pulse, which uses the Schottky line periodically loaded with electronic switches as a key device, is proposed. As is well known, the Schottky line, which means a transmission line periodically loaded with Schottky diodes, simulates the Toda lattice. When a pulse with the longer temporal duration than the inverse of the Bragg frequency of the line is inputted, it is split to be several solitons. Moreover, these solitons have in general shorter temporal duration than the input pulse. We consider the case in which an electronic switch (the switch is open for voltages greater than some fixed threshold, and closed otherwise) is put in parallel with each Schottky diode. Once the input pulse crosses the threshold voltage of the shunt switches, this multiple solitons are all attenuated at the voltages below the threshold by the finite conductance. However, it is found that the larger solitons are less attenuated than the smaller ones. Thus, it is possible to obtain only the largest soliton among the multiple ones, when we obtain the output after the appropriate transmission of the pulse on the proposed nonlinear transmission line. In this paper, we describe the principle of the operation of the proposed method and quantify how well the method succeeds in the generation of short pulses through both the perturbative characterization and the numerical integration of the transmission equation of the line.
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