J. Imbaud

Losses in high quality quartz crystal resonators at cryogenic temperatures

Measurement of the mechanical losses of quartz crystal is a topic of interest for communities dealing with the gravitational wave detectors and also the time and frequency domain. About the latter, the authors describe Q-factor measurements of quartz crystal resonators at cryogenic temperatures under 10 K, thanks to a cryocooler-based experimental set-up. A Q-factor of 325 millions at 4 K, on the fifth overtone of the quasilongitudinal mode at 15.9 MHz, has been recorded. As shown, the acoustic wave trapping is suspected to limit the Landau–Rumer regime below 6 K [Landau and Rumer, Phys. Z. Sowjetunion 11, 18 (1937)].

Recent investigations on BAW resonators at cryogenic temperatures

This work presents the results of investigations on different aspects of cryogenic operation of BAW resonators. For the quartz crystal resonators the losses mechanisms, the temperature sensitivity, the amplitude-frequency effect are described for liquid helium temperatures. The corresponding problems are discussed. To overcome some of these problems, the possible solution of operation at higher modes is considered. Some of these higher modes exhibit outstanding quality factors. The highest (for BAW resonators) quality factor value and quality factor-frequency product are measured for the 11th and 13th overtones respectively. In addition, two LGT resonators have been characterized in a wide temperature range. Finally, some preliminary results on utilization of cryogenic quartz resonators as a part of a frequency stabilization closed loop system are given.

Advances in development of quartz crystal oscillators at liquid helium temperatures

Abstract This work presents some recent results in the field of liquid helium bulk acoustic wave oscillators. The discussion covers the whole development procedure starting from component selection and characterisation and concluding with actual phase noise measurements. The associated problems and limitations are discussed. The unique features of obtained phase noise power spectral densities are explained with a proposed extension of the Leeson effect.

About Quartz Crystal Resonator Noise: Recent Study

The first step, before investigating physical origins of noise in resonators, is to investigate correlations between external measurement parameters and the resonator noise. Tests and measurements are mainly performed on an advanced phase noise measurement system, recently set up. The resonator noise is examined as a function of the sensitivity to the drive level, the temperature operating point and the tuning capacitor.

Investigations on LGS and LGT crystals to realize BAW resonators

The LGS family are promising materials for the design of high quality bulk acoustic wave resonators. We have manufactured many plano-convex 10 MHz 5th overtone Y-cut resonators using langasite (LGS, La3Ga5SiO14) and langatate (LGT, La3Ga5.5Ta0.5O14) crystals. We observed that the quality factor strongly depends on the polishing method, the supplier of the material, and on the energy trapping. For quartz crystals, we have found that resulting IR spectra exhibit absorption peaks more or less deep, linked to defects. These predominant criteria are not surprising, but they have to be defined in manner similar to that used for quartz crystal. A satisfying machining and polishing method has been first applied to elaborate high Q resonators, and a comparison between samples of LGS and LGT materials from different suppliers is established. In addition, LGT resonators are characterized by their motional parameters and frequency-temperature curves. Nevertheless, one of the main results is that the measured Q times f product is not the expected one. We present results of Q-factor versus radius of curvature: it appears that an optimization should be performed and that this last one cannot be directly transposed from that of quartz crystal resonator. Currently, the best resonator that we have made has a Q times f product of 1.4 times 1013 on its 5th overtone (1.7 times 1013 on its 9th overtone). This result is slightly higher than the similar parameter obtained on a state-of-the-art SC-cut quartz crystal resonator working at the same frequency.

Fluctuation-dissipation theorem and 1/f noise of bulk acoustic wave cavities

The short time stability in quartz crystal ultra-stable oscillators is limited by some intrinsic frequency fluctuations with a 1/f power spectral density. The physical origin of this 1/f noise is still unknown. In this paper, the fluctuation dissipation theorem is used to numerically evaluate the importance of the contribution of internal damping of thickness fluctuations on the level of noise for bulk acoustic wave cavities. A 1/f contribution to the power spectral density of frequency noise for the shear mode usually used is obtained. Its study provides a possible explanation for the fact that, for the best resonators, the 1/f noise amplitude is usually disconnected from the quality factor measured at resonance.

Some considerations on acoustic resonator phase noise modeling and recent short-term stability experimental results

This paper presents a critical review of different acoustic resonator models exposed in the past, in the light of recent experimental results. Among the few models attempting to explain the 1/f behavior of the quartz crystal resonator, the 1/f quantum noise theory of P. Handel and the thermal boson theory of M. Planat, are recalled. The latest published experimental results are analyzed taking into account these models. In the case of Handels model, the noise depends on the resonator volume under the electrodes and the unloaded quality factor of the resonator. Handels model is supposed to give an order of magnitude of the lowest possible noise level, but now some experimental results are under its prediction. An approach using the vibrating volume of the resonator is proposed to renew the lowest noise level estimation and found to be compatible with the latest experimental results.

The effect of power-drive level on the calibration of the bridge instrument for the measurement of the quartz stability

In this paper, it is shown that the amplitude-frequency effect, a well known phenomenon in quartz crystal resonator, questions the short-term stability results of quartz crystal resonators computed from phase noise measurement in passive interferometer systems. This equipment allows one to measure the inherent phase stability of quartz crystal resonators in a passive circuit without the noise usually associated with an active oscillator. The short-term stability of the resonator given by the Allan standard deviation is usually computed with the Leeson frequency. A new method to characterize the short-term stability of crystal resonators by a phase bridge system is given.

Development of a 10 MHz oscillator working with an LGT crystal resonator: Preliminary results

Presently, to our knowledge, measurement of the noise of langatate (LGT) crystal oscillators has not previously been reported. First results of such a measurement are given in this paper. They have been obtained from 10 MHz resonator prototypes tested with a dedicated electronics. The main steps of the resonator manufacturing are described in this paper. Good quality factors, close to 1.4 106, have already been achieved on the 5th overtone of the thickness shear mode of LGT Y cuts, even if the energy trapping should still be optimized. The motional parameters of these resonator prototypes are quite different from those of usual quartz crystal resonators. As a consequence, dedicated sustaining electronics have been designed. The explored options are reported to justify the implemented one. Moreover, the high thermal sensitivity of LGT crystal resonators (parabolic f-T curve) requires that particular attention be paid to the oven thermal stability. This important feature is also pointed out in the paper. The preliminary version of the resulting system exhibits a relative frequency stability of 6 10-2.

Study on the origin of 1/f noise in quartz resonators

Intrinsic frequency fluctuations with a