  An application-specific Josephson generator is being developed as an on-chip
calibration source for single-microwave-photon detectors operating below $T
\sim $100 mK in the frequency range from 110 to 170 GHz. The targeted
calibration power corresponds to the photon detection rate of 0.01 to 10 counts
per second. We analyze the Josephson oscillations within the framework of the
tunnel junction microscopic (TJM) model and find the corrections to be made to
a standard RSJ model of the junction, operating as a quasi-monochromatic source
of microwaves. Experimentally, we implemented a number of aluminium-based
two-junction interferometers connected to the leads via microstripline
resistors made of partly oxidized titanium films. The $I$-$V$ curves exhibit a
behaviour ensuring generation of the microwave signal in the frequency range
required. By setting the biasing point $\bar{V}$ and applying the magnetic
field, one can tune the generator's frequency and power, respectively. A small
oscillation linewidth, down to a few GHz, and a low level of black-body
radiation emitted by hot parts of the circuit are predicted, using the
experimental parameters.
