Volume dependence in handel's model of quartz crystal resonator noise

Abstract

-Though criticized by many, Handel's quantum model for 1/f noise remains the only model giving a quantitative estimation of the level of intrinsic 1/f noise in quartz crystal resonators, compatible with the best experimental results. In this paper, we reconsider the volume dependence in this model. We first argue that an acoustic volume, representing the volume in which the vibration energy is trapped, should be used instead of the geometrical volume between the electrodes. Then, we show that since there is an implicit dependence of the quality factor of the resonator with its thickness, the net effect of Handel's formula is not an increase of noise proportionally to the thickness of the resonator, as could be naively expected, but a net decrease when thickness increases. Finally, we show that a plot of Q 4 S y versus the acoustic volume, instead of the usual S y plot, could be useful to compare the quality of acoustic resonators having very different resonance frequencies.

Low-frequency noise in downscaled silicon transistors: Trends, theory and practice

“…, (384) where V k are the harmonic amplitudes and v(φ)=V(φ)/V 1 is the normalized signal in eq. ( 375), from which the impulse sensitivity function ISF(φ) is…”

“…for lasers, by different mathematical treatment. Later works [383,384,385], however, indicated that vibration-wave nature of the crystals can produce 1/f noise, and, perhaps, there will soon be a reassessment of the approach for quantum noise, since some of the down-scaled devices are with dimensions similar to quantum devices, such as quantum dots and wires (e.g. CNT), and the noise in these devices is very large, see again Figure 51.…”

Phase noise and jitter in digital electronics

“…The idea that the phase noise coefficient b −1 is proportional to 1/V, where V is the active volume, has been around for a while. In quartz resonators, this appears either directly or as a side effect of the larger size at lower frequency [27,28,29,30,31,32]. In ultrastable Fabry-Perot cavities, flicker is powered by thermal noise and proportional to the reciprocal of the length [33,34] which is approximately equivalent to 1/V after mechanical design rules.…”