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 correspond
s 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 generators 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.
