  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.
