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 Handel's model, the noise depends on the resonator volume under the electrodes and the unloaded quality factor of the resonator. Handel's 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.