Quartz crystal unit modeling at cryogenic temperatures

The aim of this paper was to develop the new quartz crystal electrical model including its temperature properties in the temperature range from 83.15 K (−190 °C) to 303.15 K (+30 °C) through experimental set-up and simulation analysis. Both the methodology of the quartz resonator measurements, the instrument setup, and the measurement methods needed to collect the necessary data as well as polynomial approximation of temperature dependence were described. The electrical model of AT-cut type quartz crystal for cryogenic temperatures was developed, in which its elements were expressed as functions of temperature. Using these polynomials, the behavioral model for PSPICE computer program has been worked out.