Measurement of quartz crystal unit parameters based on the precise derivation of zero phase frequency

Measurement of quartz crystal unit parameters based on the precise derivation of zero phase frequency

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It is usually considered that the resonance frequency of quartz crystal resonator is only related to dynamic inductance L 1 and dynamic capacitance C 1, and load resonance frequency has connection with L 1, C 1 and static capacitance C 0. Hence, the dynamic resistance cannot be measured by frequency. The deduction show that all the frequencies relates to L 1, C 1, C 0 and dynamic resistance R 1. Then, a method for measuring the total equivalent parameters of quartz crystal resonator based on zero phase frequency is proposed in this Letter. The simulation results of advanced design system (ADS) verify the validity of this proposal in theory. After that, the phase-frequency-curves of a quartz crystal resonator with 10 and 5 MHz are measured, which can obtain equivalent parameters of through data processing. The results show that this method has calculated parameters essentially in agreement with nominal parameters. This method does not have reciprocating debugging process, and the test process is simple as well. In addition, the approximate calculation is not used in this method, and it could be widely extent to the field of sensors, such as quartz crystal microbalance sensors, temperature sensors and so on.


    1. 1)
      • 1. Bottom, V.E.: ‘Introduce to crystal unite design’ (Van Nostrand Reinhold Company, New York, NY, USA, 1982).
    2. 2)
      • 2. IEC: ‘IEC60444-2: Measurement of quartz crystal unit parameters by zero phase technique in a pi-network. Part 2: Phase offset method for measurement of motional capacitance of quartz crystal units’, 1980. Available at
    3. 3)
      • 3. Huang, X.H., Liu, D., Wang, Y., Chen, Y.: ‘Precise derivation for the equivalent circuit parameters of a crystal resonator with series capacitor’, IEEE Trans. Ultrason. Ferroelectr. Freq. Control, 2012, 59, (6), pp. 13161317, doi: 10.1109/tuffc.2012.2323.

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