Frequency variations in quartz crystal resonators due to internal dissipation
作者:
G. Theobald,
J. J. Gagnepain,
期刊:
Journal of Applied Physics
(AIP Available online 1979)
卷期:
Volume 50,
issue 10
页码: 6309-6315
ISSN:0021-8979
年代: 1979
DOI:10.1063/1.325771
出版商: AIP
数据来源: AIP
摘要:
The amplitude‐frequency effect in quartz crystal resonators is a consequence of the nonlinear elastic behavior of the crystal. However, dissipation due to internal losses can also induce frequency changes caused by amplitude variations, but in this case with a large time constant. Nonuniform heating introduces thermal stresses and density changes which act on a propagating wave by nonlinear coupling through the third‐order elastic constants. Both the heat and wave equations are solved for the quartz crystal, and thermal exchanges with the surrounding medium are considered for several types of mounting. The resonator frequency change due to variation of the driving level, which appears as the indirect amplitude‐frequency effect, is calculated. It is shown that the large time constants experimentally observed can be mainly attributed to thermal diffusion through the connection wires.
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