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The frequency of a doubly rotated
resonator, such as the SC-cut, varies linearly with a voltage applied to the
resonator’s electrodes. (The frequency
of a singly rotated, i.e., = 0, resonator, such as the AT-cut, does not vary with
voltage.) For example, the voltage
sensitivity of a 5 MHz fundamental mode SC-cut resonator is 7 x 10-9
per volt, as shown in the upper middle above.
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Therefore, when an AC voltage of frequency
fv is applied to the electrodes, sidebands (i.e., spectral lines)
at fv
from the carrier frequency fo are generated, as shown above, in
the middle. By adjusting the magnitude
of the AC voltage, the sidebands can be made identical to the sidebands
produced by sinusoidal vibration at frequency fv. When the vibration and AC voltage are
applied simultaneously, the amplitude and phase of the AC voltage can be
adjusted so as to cancel the vibration induced sidebands.
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A 60 dB suppression of the sidebands, at a
single frequency, has been demonstrated.
An accelerometer sensed the vibration, and the output signal from the
accelerometer was applied to the resonator’s electrodes after calibration of
the output’s phase and amplitude. Away
from the frequency of optimum suppression, the suppression degraded due to
frequency dependent phase shifts in the (simple) circuitry used, and
mechanical resonances in the setup.
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V. J. Rosati and R.
L. Filler, "Reduction of the Effects of Vibration on SC-Cut Quartz
Crystal Oscillators," Proc. 35th Annual Symposium on Frequency Control,
pp. 117-121, 1981, AD-A110870
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