  The Bloch oscillating transistor (BOT) is a device, where single electron
current through a normal tunnel junction can be used to enhance Cooper pair
current in a mesoscopic Josephson junction leading to signal amplification. In
this paper we develop a theory, where the BOT dynamics is described as a
two-level system. The theory is used to predict current-voltage characteristics
and small-signal response. Transition from stable operation into hysteretic
regime is studied. By identifying the two-level switching noise as the main
source of fluctuations, the expressions for equivalent noise sources and the
noise temperature are derived. The validity of the model is tested by comparing
the results with simulations.
