Equivalent circuit of an AT-cut quartz resonator and its application

The equivalent circuit of a AT-cut quartz resonator can be modified as a series circuit consisting of an inductance, a capacitance, a resistance in parallel with a capacitor, which are related to the dimensions, density, and elastic, dielectric, piezoelectric constants and electrode area of the quartz. In the other hand, a contacting fluid will cause an extra resistance and an inductance appeared, and an inductance appeared due to electrode mass loading effect. In this paper, two derivation methods of equivalent circuit models are used and compared to explain an AT-cut quartz resonator. Also a method to distinguish and calculate each components in equivalent circuit from gain-phase measurement is provided. Finally, the relation between air pressure and equivalent inductance and resistance are measured. The results shown that the lower air pressure the smaller equivalent inductance and resistance, when air pressure change from 1 atm to 1 g/cm2, the equivalent resistance and the resonant frequency of resonator will change 5 Ω and 90 Hz, respectively.