The Modified Analysis Of Quartz Crystal Tuning Fork Resonators And Finite Element Calculation Of Their Electrical Circuit Parameters

Quartz crystal tuning fork resonators are irreplaceable electronic components today. Theyhave high-precision and high-stability frequency control devices in various circuit applications. Forthese reasons, quartz crystal tuning fork resonators play an irreplaceable role in the informationtransmission, frequency generation, and time standards. Therefore, we must improve the analysisof the quartz crystal tuning fork resonators through the vibration modes and circuit parameters.The vibration modes can be solved by the beam theory with modifications and circuit parameterscan be solved by considering the piezoelectric and viscous properties of quartz crystals.Starting from the Euler beam theory, we have seen various methods on the calculation of thevibration frequency of a quartz crystal tuning fork resonator. We improved Sezawa’s theory byadopting the Timoshenko beam theory to modify the results and method. Through the comparisonof two sets of results from beam theories, we found that the Sezawa’s method with Timoshenkobeam equations can improve the vibration analysis. Quartz crystal tuning fork circuit parametercalculation cannot be done without considering the damping of materials and structures undercurrent resonator model. In order to achieve better calculation of circuit parameters, we use finiteelement software like ANSYS with the consideration of material viscosity through complex elasticconstants. The results show that the static capacitance model presented in this study and thespecific parameters of the dynamic circuit model agreed well, thus proving that the finite elementmethod with complex material constants will be a reliable tool in the prediction of electricalproperties of quartz crystal tuning fork resonators.