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Frequency varies as the current amplitude
squared; f = f0 (1 + aI2), where a
is a constant that is a function of the design, i.e., the appropriate
nonlinear elastic constant for the resonator type used, and I is the current.
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Useful drive levels are limited at the high
end by the nonlinearities of quartz, and at the low end by noise (or defects,
as discussed on the next page).
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J. A. Kusters,
"The SC Cut Crystal - An Overview," Proc. 1981 IEEE Ultrasonics
Symposium, pp. 402-409.
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J.J. Gagnepain and
R. Besson, “Nonlinear Effects in Piezoelectric Quartz Crystals,” in Physical
Acoustics, Vol. XI, pp. 245-288, W.P. Mason & R.N. Thurston, editors,
Academic Press, 1975
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R. L. Filler,
"The Amplitude-Frequency Effect in SC-Cut Resonators," Proc. 39th
Annual Symposium on Frequency Control, pp. 311-316, 1985, IEEE Catalog No.
85CH2186-5.
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D. Hammond, C.
Adams, and L. Cutler, "Precision Crystal Units," Proc. 17th Annual
Symposium on Frequency Control, pp. 215-232, 1963, AD-423381.
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