Analysis of Q-Value of Quartz Crystal Tuning Fork Using Thermoelastic Coupling Equations

We analytically investigated the Q-value of a quartz crystal tuning fork by applying the thermoelastic equations given by Sieh to one arm of the tuning fork approximated as a cantilever beam and obtained a new formula for the Q-value of a quartz crystal tuning fork. According to our calculations under both adiabatic and isothermal boundary conditions, the calculated Q-value of an etching-processed quartz crystal tuning fork under the adiabatic boundary condition was closer to the measured value than that under the isothermal boundary condition. We also discussed why the crystal impedance (CI) value increases with increasing temperature over 25 degrees C and decreases with increasing temperature under 25 degrees C in CI value-temperature characteristics. (C) 2009 The Japan Society of Applied Physics