Equivalent Single-Junction Model of Superconducting Quantum Interference Devices in the Presence of Time-Varying Fields

The reduced dynamical model of a two-junction quantum interference device is generalized to the case of time-varying externally applied fluxes with a d. c. component and an oscillating addendum whose frequency is comparable with the inverse of the characteristic time for flux dynamics within the superconducting system. From the resulting effective single-junction model for null inductance of the superconducting loop, it can be seen that the critical current of the device shows a dependence on the frequency and amplitude of the oscillating part of the applied flux. It can therefore be argued that the latter quantities can be considered as control parameters in the voltage versus applied flux curves of superconducting quantum interference devices.