FREQUENCY-TEMPERATURE CHARACTERISTIC ANALYSIS OF PIEZOELECTRIC RESONATORS USING FINITE ELEMENT MODELING

The resonators made of piezoelectric crystals such as a quartz crystal are widely used. Their frequency-temperature characteristics are of primary importance for their applications to the frequency control devices. The characteristics estimation is useful for determining their design parameters. In the present paper, several types of resonators are numerically analyzed. The numerical solutions are made using 3-D Finite Element Modeling, and the results are compared with the theoretical values whenever they are available. To demonstrate the validity of the present numerical approach, the application is made to the analysis of the plates with some well-established cutting angles. For the resonator stable with temperature change, the cutting angle is important in which the temperature coefficient of the first order is chosen to be zero. The rotated Y-cut plates in thickness-shear mode are considered. The equivalent circuit representation is often used for describing the characteristics at the electrical terminals which enables the circuit analysis including the effect of temperature change by using the circuit simulators. The equivalent circuit parameters are obtained by fitting the admittance-frequency curve from the finite element analysis.