Small and large signal analyses of Josephson nonlinear inductance for superconductive parametric amplifier

Due to the inherent nonlinearity in the Josephson junction (JJ) element, there is great potential to develop nonlinear parametric devices, such as amplifiers and mixers. In this paper, we investigate the time domain small-signal and large-signal analysis on the nonlinear flux-current characteristics of an array of lumped JJs. The procedure is similar to that applied on the nonlinear current-voltage characteristics of a semiconductor p-n junction diode, and results are presented in closed-form equations. The gain improvement due to parametric interaction of the pump with the signal is also discussed at the end of the paper.