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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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