We study a circuit where a mesoscopic Josephson junction (JJ) is embedded in an environment consisting of a large bias resistor and a normal-insulator-superconductor (NIS) junction. The effective Coulomb blockade of the JJ can be controlled by the tunneling current through the NIS junction leading to transistor-like characteristics. We show using phase correlation theory and numerical simulations that substantial current gain with low current noise (in≲1 fA/Hz) and noise temperature (≲0.1 K) can be achieved. Good agreement between our numerical simulations and experimental results is obtained.

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