The lumped equivalent circuit model of a superconducting tunnel junction with a voltage-dependent normal conductance current represented by Ir = I0(V/V0)n is analyzed for the cases n = 2 and n → ∞. Analytic expressions for the hysteresis parameter as a function of the damping factor are obtained. The time-averaged voltage-current characteristics for n = 2 are given in closed form. The results are qualitatively similar to the linear conductance case where n = 1, but the hysteresis is more pronounced for larger n.
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William C. Stewart (1974) studied this question.
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