AT-cut resonator
SC-cut resonator
4-15
5gf
fo = 10Mz
fo = 10Mz
5gf
Text Box: Frequency Change (Hz)
Frequency Change (Hz)
Text Box: Frequency Change (Hz)
Frequency Change (Hz)
30
20
10
0
240
120
180
60
300
360
240
120
180
60
300
360
+10
-10
Azimuth angle y (degrees)
Azimuth angle y (degrees)
Frequency change for symmetrical bending, SC-cut crystal.
Frequency change for symmetrical bending, AT-cut crystal.
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Bending Force vs. Frequency Change
   The above shows experimental results of the frequency change vs. the azimuthal angle for symmetrical bending about a diameter.  The resonators were 12 mm diameter, AT-cut and SC-cut, plano-plano.  A constant force of 5 grams was applied, the measurements were repeated as the resonator was rotated, and the frequency changes were plotted as a function of azimuthal angle .
   At all azimuthal angles, the SC-cut is less sensitive to bending than the AT-cut when the force is applied normal to the plane of the resonator, as it was in these experiments.  For the AT-cut, the frequency change vs. angle has no zero crossing.  The integral of frequency changes from 0o to 360o is much smaller for the SC-cut than for the AT-cut (even though there was a significant measurement uncertainty in the SC-cut results).  In addition, when the force was varied from zero to ~15 grams, the frequency change vs. applied force was much more linear for the SC-cut than the AT-cut.


E. D. Fletcher and A. J. Douglas, “A Comparison Of The Effects Of Bending Moments On The Vibrations Of AT And SC (or TTC) Cuts Of Quartz,” Proc. 33rd  Annual Symposium on Frequency Control, pp. 346-350, 1979.