Cryogenic small-signal conversion with relaxation oscillations in Josephson junctions

Broadband detection of small electronic signals from cryogenic devices, with the option of simple implementation for multiplexing, is often a highly desired, although non-trivial task. We investigate and demonstrate a small-signal analog-to-frequency conversion system based on relaxation oscillations in a single Josephson junction. Operation and stability conditions are derived, with special emphasis on noise analysis, showing the dominant noise sources to originate from fluctuation processes in the junction. At optimum conditions the circuit is found to deliver excellent noise performance over a broad dynamic range. Our simple models apply within the regime of classical Josephson junction and circuit dynamics, which we confirm by experimental results. A discussion on possible applications includes a measurement of the response to a cryogenic radiation detector.