The calculation of electrical circuit parameters of quartz crystal resonators with consideration of equivalent viscosity

Electrical circuit parameters such as resistance and quality factor of a quartz crystal resonator cannot be determined through vibration analysis without considering the presence of dissipation. We know that electrical parameters are strongly affected by viscosity from material damping, manufacturing, and packaging processes. The results show that the motional resistance from theoretical calculation with material viscosity which is from earlier measurements is much smaller than actual measurements, and it is suspected that the viscosity from substructures, bonding, air, packaging and so on are not considered but are significant. Thus, this paper we calculate electrical parameters of AT-cut quartz crystal resonators through the consideration of equivalent viscosity with complex elastic constants.