  A quantum-limited electrometer based on charge modulation of the Josephson
supercurrent in the Bloch transistor inserted into a superconducting ring is
proposed. As this ring is inductive coupled to a high-Q resonance tank circuit,
the variations of the charge on the transistor island (input signal) are
converted into variations of amplitude and phase of radio-frequency
oscillations in the tank. These variations are amplified and then detected. The
output noise, the back-action fluctuations and their cross-correlation are
computed. It is shown that our device enables measurements of the charge with a
sensitivity which is determined by the energy resolution of its amplifier, that
can be reduced down to the standard quantum limit of \hbar/2. On the basis of
this setup a "back-action-evading" scheme of the charge measurements is
proposed.
