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The effective frequency-temperature curve of a crystal resonator operated with series load capacitance differs from that of the crystal alone. Since the principal method of compensating for the crystal frequency-temperature behavior in a crystal oscillator employs series varactors and a temperature sensitive compensation network, it is of major importance to be able to understand and deal with this effect in the design of crystal oscillators and crystal resonators assigned in the manufacture of these parts. The necessary formulas and discussions are given in this paper. Mass-loading effects are included and sample charts are provided.
Adrian Anghelescu
"Load capacitance effect on frequency-temperature characteristics of AT-cut quartz crystals", Proc. SPIE 7297, Advanced Topics in Optoelectronics, Microelectronics, and Nanotechnologies IV, 72970N (7 January 2009); https://doi.org/10.1117/12.823633
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Adrian Anghelescu, "Load capacitance effect on frequency-temperature characteristics of AT-cut quartz crystals," Proc. SPIE 7297, Advanced Topics in Optoelectronics, Microelectronics, and Nanotechnologies IV, 72970N (7 January 2009); https://doi.org/10.1117/12.823633