Frequency readout of relaxation oscillation superconducting quantum interference devices in the GHz regime

The output of relaxation oscillation superconducting quantum interference devices (ROSs) consists of a sequence of voltage pulses with a frequency that depends on the flux that is applied to the ROS. In this paper, a theoretical model for the flux-to-frequency conversion of a ROS is presented, and this model is validated in practice for oscillation frequencies up to 7 GHz. The experiments have been performed on more than ten different ROSs and the model was able to fit all measured data, which illustrates the versatility of the model. Furthermore, a simple flux locked loop based on frequency readout of a ROS in the GHz regime is presented. The measured flux noise, √SΦ=2.5μΦ0/√Hz, corresponding to an energy resolution ε≊600h, is probably not intrinsic to the ROSs, but due to the readout electronics.