Switching Time Versus DC Current Overdrive of a Josephson Junction Sampler

The time resolution of a Josephson junction sampler depends on the switching time of the junction. This switching time depends on the junctions’ plasma frequency and McCumber parameter, but also on the amount of overdrive current applied. An approximate closed form expression is derived for the switching time as a function of the overdrive, excluding damping or noise. A key result is that the switching time depends logarithmically on the overdrive. Numeric simulations are used to justify the approximations made and reveal the dependence on damping. Comparisons are made between the analytic expression and a numeric simulation of the switching time. Application of the results to a Josephson sampler is presented.