Analysis of resonance phenomena in Josephson interferometer devices

Approximate formulas that yield the resonance amplitude of symmetric two-junction interferometers have been derived using step-by-step linearizations and approximations based on physical arguments. The resonance amplitude is found to strongly depend on the device Q. It increases as Q increases, reaches a peak, and subsequently decreases again. In the low-Q region, the resonance step is very broad and largely independent of rapid changes in device current. This is not the case in the high-Q region where the resonance amplitude increases with decreasing device current rise time. In the range of validity of the approximations, the results were compared to computer solutions, and reasonable agreement was found for arbitrarily chosen test cases. Although derived for two-junction interferometers, the results can be extended directly to certain symmetric three-junction interferometers.