Eigen-frequency and frequency response calculation of piezoelectric resonator parameters

Equations for the calculation of the equivalent circuit parameters of the piezoelectric resonator are presented. The results from both eigen-frequency and frequency response analyses could be used for calculating the electrical parameters of the Butterworth Van Dyke model of the piezoelectric resonator. The values of the electrical parameters C₁, and L₁ obtained from both types of analyses were found to be similar, and were found to compare reasonably well with the measured values of two 12 MHz AT-cut quartz resonators. The values of R₁, and Q were less well predicted when the resonator has a lower Q. The static capacitance C₀ could be calculated accurately by its frequency response at 1 Hz. The eigen-frequency analysis is better suited than the frequency response analysis for the study of electrode and plate geometry designs, hence the eigen-frequency equations for calculating the equivalent circuit parameters are more useful for parametric designs.