Stability measurements of microwave frequency synthesis with liquid helium cooled cryogenic sapphire oscillators

We report on the evaluation of microwave frequency synthesis using two cryogenic sapphire oscillators developed at the University of Western Australia. A down converter is used to make comparisons between microwave clocks at different frequencies, where the synthesized signal has a stability not significantly different from the reference oscillator. By combining the CSO with a H-maser, a reference source of arbitrary frequency at X-band can be synthesized with a fractional frequency stability of sub-$4 \times 10^{-15}$ for integration times between 1 s and 10,000 s.