Dynamics of Josephson junctions and single-flux-quantum networks with   superconductor-insulator-normal metal junction shunts
  Within the framework of the microscopic model of tunneling, we modelled the behavior of the Josephson junction shunted by the Superconductor-Insulator-Normal metal (SIN) tunnel junction. We found that the electromagnetic impedance of the SIN junction yields both the frequency-dependent damping and dynamic reactance which leads to an increase in the effective capacitance of the circuit. We calculated the dc I-V curves and transient characteristics of these circuits and explained their quantitative differences to the curves obtained within the resistively shunted junction model. The correct operation of the basic single-flux-quanta circuits with such SIN-shunted junctions, i.e. the Josephson transmission line and the toggle flip-flop, have also been modelled. 
A.B. Zorin, E.M. Tolkacheva, M.I. Khabipov, F.-I. Buchholz, J.   Niemeyer