Influence and evaluation of parasitic inductance in shunted Josephson junctions

The shunt resistors used in many Josephson junction circuits contain an inductive component that can significantly degrade high-frequency performance. Numerical simulations reveal complex dynamical behaviour, including relaxation oscillations, period-doubling sequences, and chaos, all of which are serious problems for applications as high-frequency sources and detectors. This complex AC behaviour creates features in the simulated DC current-voltage characteristics. Since these simulations closely match experimental data, they can be used to investigate the high-frequency AC behaviour of real junctions. Thus, we are able to use simple DC measurements to observe evidence of complex high-frequency dynamics. The inductance of the shunt branch can be accurately determined by comparing simulations to measurements. Simulations also allow us to map regions of the parameter space which exhibit complicated behaviour. These regions should be avoided when a nearly sinusoidal voltage waveform is desired, as is the case for Josephson junction-based oscillators.