Evaluation of nonlinear elastic coefficient causing frequency shifts in AT-cut resonators

Hirose, Yasuo; Tsuzuki, Y.

doi:10.1109/freq.1991.145887

Cited by 3 publications

(3 citation statements)

References 9 publications

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“…More recently it has been commonly assumed to be the former, so finding only the latter in AT-and BT-cut VHF resonators is likely to be somewhat controversial. Alternatively, this may account for some of the measurement discrepancies mentioned in the literature for these cuts [7], [9], [14]- [16].…”

Section: Discussionmentioning

confidence: 91%

Dynamic measurement of amplitude-frequency effect of VHF resonators

Horton¹,

Hague²

2006

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

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Dynamic amplitude-frequency effect measurements made of VHF quartz resonators indicate the presence of two separate mechanisms, the relative contribution of which varies for different cuts. For the SC-cut a stepchange in drive level leads to a frequency shift with very short time constant (1 ms) that is presumably the classic direct nonlinear elastic effect. Others such as AT-, BT-, and LD-cuts show only a much longer time constant (200 ms), presumably a thermally related indirect nonlinear elastic effect. Near the SC-cut, resonators exhibit a combination of both short-and long-time-constant frequency changes. In some cases the two mechanisms produce frequency shifts in opposite directions. This behavior is problematic for some amplitude-frequency-effect measurement approaches because the measured shift depends on the timing of those measurements.It is not surprising that the SC-cut response shows only the direct nonlinear elastic effect, but it is unexpected that the AT-and BT-cuts appear not to show such effect. These results raise a question as to what amplitude-frequency effect criterion is appropriate to use, as well as whether it is proper to determine nonlinear elastic constants from ATcut resonator measurements that assume the effect is not thermally related.

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Section: Discussionmentioning

confidence: 91%

Dynamic measurement of amplitude-frequency effect of VHF resonators

Horton¹,

Hague²

2006

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

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“…It occurred to the author that the possibility existed that oscillator signal AM noise could be converted to FM noise by reason of the crystal resonator frequency-drive sensitivity [2][3][4][5][6][7]. It is undetermined at this point whether the dominant AM noise contributor might be the sustaining stage amplifier or the short-term instability (self noise) of the crystal resonator resistive impedance [8][9].…”

Section: Introductionmentioning

confidence: 91%

“…S a (f) = (δV/V) 2 = (δI/I) 2 (6) where V is the voltage across the crystal resonator at series resonance and I is the current through the motional arm of the resonator (assuming the static capacitance has been anti-resonated). Then:…”

Section: Introductionmentioning

confidence: 99%

Oscillator AM-to-FM noise conversion due to the dynamic frequency-drive sensitivity of the crystal resonator

Driscoll

2008

2008 IEEE International Frequency Control Symposium

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An analysis has been made of the potential effects of AM-to-FM noise conversion in quartz crystal oscillators as a result of the dynamic frequency-drive sensitivity of the crystal resonator. The analysis indicates that it is quite possible for the FM noise resulting from AM-to-FM conversion in the crystal resonator to equal or exceed that due to the conversion of oscillator open loop phase noise to closed loop frequency noise. This is especially true in oscillators designed to exhibit low white phase noise (floor) levels by operating the crystal resonator at relatively high drive level. In addition, the analysis indicates that, for the same drive sensitivity, the relative degradation in FM noise level due to this effect is more severe at lower relative oscillator operating frequencies.

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Amplitude-frequency effects in VHF quartz resonators

Horton¹,

Hague²

Proceedings of the 2005 IEEE International Frequency Control Symposium and Exposition, 2005.

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Evaluation of nonlinear elastic coefficient causing frequency shifts in AT-cut resonators

Cited by 3 publications

References 9 publications

Dynamic measurement of amplitude-frequency effect of VHF resonators

Dynamic measurement of amplitude-frequency effect of VHF resonators

Oscillator AM-to-FM noise conversion due to the dynamic frequency-drive sensitivity of the crystal resonator

Amplitude-frequency effects in VHF quartz resonators

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