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

It is usually considered that the resonance frequency of quartz crystal resonator is only related to dynamic inductance L1 and dynamic capacitance C1, and load resonance frequency has connection with L1, C1 and static capacitance C0. Hence, the dynamic resistance cannot be measured by frequency. The deduction show that all the frequencies relates to L1, C1, C0 and dynamic resistance R1. 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.