We report on the measurement and characterization of power to frequency conversion in the resonant mode of a cryogenic sapphire loaded cavity resonator, which is used as the frequency discriminating element of a loop oscillator circuit. Fluctuations
of power incident on the resonator leads to changes in radiation pressure and temperature in the sapphire dielectric, both of which contribute to a shift in the resonance frequency. We measure a modulation and temperature independent radiation pressure induced power to frequency sensitivity of -0.15 Hz/mW and find that this is the primary factor limiting the stability of the resonator frequency.
Two nominally identical ultra-stable cryogenic microwave oscillators are compared. Each incorporates a dielectric-sapphire resonator cooled to near 6 K in an ultra-low vibration cryostat using a low-vibration pulse-tube cryocooler. The phase noise fo
r a single oscillator is measured at -105 dBc/Hz at 1 Hz offset on the 11.2 GHz carrier. The oscillator fractional frequency stability is characterized in terms of Allan deviation by 5.3 x 10^-16 tau^-1/2 + 9 x 10^-17 for integration times 0.1 s < tau < 1000 s and is limited by a flicker frequency noise floor below 1 x 10^-16. This result is better than any other microwave source even those generated from an optical comb phase-locked to a room temperature ultra-stable optical cavity.
Here we present the design and implementation of a novel frequency synthesizer based on low phase noise digital dividers and a direct digital synthesizer. The synthesis produces two low noise accurate and tunable signals at 10 MHz and 100 MHz. We rep
ort on the measured residual phase noise and frequency stability of the synthesizer, and estimate the total frequency stability, which can be expected from the synthesizer seeded with a signal near 11.2 GHz from an ultra-stable cryocooled sapphire oscillator. The synthesizer residual single sideband phase noise, at 1 Hz offset, on 10 MHz and 100 MHz signals, respectively, were measured to be -135 dBc/Hz and -130 dBc/Hz. Their intrinsic frequency stability contributions, on the 10 MHz and 100 MHz signals, respectively, were measured as sigma_y = 9 x 10^-15 and sigma_y = 2.2 x 10^-15, at 1 s integration time. The Allan Deviation of the total fractional frequency noise on the 10 MHz and 100 MHz signals derived from the synthesizer with the cryocooled sapphire oscillator, may be estimated as sigma_y = 5.2 x 10^-15 tau ^-1 + 3.6 x 10^-15 tau ^-1/2 + 4 x 10^-16 and sigma_y = 2 x 10^-15 tau ^-1/2 + 3 x 10^-16, respectively, for 1 s < tau < 10^4 s. We also calculate the coherence function, (a figure of merit in VLBI) for observation frequencies of 100 GHz, 230 GHz and 345 GHz, when using the cryocooled sapphire oscillator and an hydrogen maser. The results show that the cryocooled sapphire oscillator offers a significant advantage at frequencies above 100 GHz.
A low maintenance long-term operational cryogenic sapphire oscillator has been implemented at 11.2 GHz using an ultra-low-vibration cryostat and pulse-tube cryocooler. It is currently the worlds most stable microwave oscillator employing a cryocooler
. Its performance is explained in terms of temperature and frequency stability. The phase noise and the Allan deviation of frequency fluctuations have been evaluated by comparing it to an ultra-stable liquid-helium cooled cryogenic sapphire oscillator in the same laboratory. Assuming both contribute equally, the Allan deviation evaluated for the cryocooled oscillator is sigma_y = 1 x 10^-15 tau^-1/2 for integration times 1 < tau < 10 s with a minimum sigma_y = 3.9 x 10^-16 at tau = 20 s. The long term frequency drift is less than 5 x 10^-14/day. From the measured power spectral density of phase fluctuations the single side band phase noise can be represented by L_phi(f) = 10^-14.0/f^4+10^-11.6/f^3+10^-10.0/f^2+10^-10.2/f+ 10^-11.0 for Fourier frequencies 10^-3<f<10^3 Hz in the single oscillator. As a result L_phi approx -97.5 dBc/Hz at 1 Hz offset from the carrier.
A Cryogenic Sapphire Oscillator has been implemented at 11.2 GHz using a low-vibration design pulse-tube cryocooler. Compared with a state-of-the-art liquid helium cooled CSO in the same laboratory, the square root Allan variance of their combined fr
actional frequency instability is $sigma_y = 1.4 times 10^{-15}tau^{-1/2}$ for integration times $1 < tau < 10$ s, dominated by white frequency noise. The minimum $sigma_y = 5.3 times 10^{-16}$ for the two oscillators was reached at $tau = 20$ s. Assuming equal contributions from both CSOs, the single oscillator phase noise $S_{phi} approx -96 ; dB ; rad^2/Hz$ at 1 Hz offset from the carrier.
