  We have designed an experiment and performed extensive simulations and
preliminary measurements to identify a set of realistic circuit parameters that
should allow the observation of constant-current steps at I=2ef in short arrays
of small Josephson junctions under external AC drive of frequency f.
Observation of these steps demonstrating phase lock of the Bloch oscillations
with the external drive requires a high-impedance environment for the array,
which is provided by on-chip resistors close to the junctions. We show that the
width and shape of the steps crucially depend on the shape of the drive and the
electron temperature in the resistors.
