Precise determination of VHF quartz crystal resonator equivalent parameters

A method developed for the accurate determination of VHF quartz crystal resonator equivalent parameters and resonant frequencies is presented. This method uses an electrical equivalent circuit which includes the spurious responses close to the main mode and the resistance from the evaporated electrodes. The equivalent parameters and the resonant frequencies are determined by a non-linear least squares method from the impedance characteristics of the resonators under test. It is shown that an excellent agreement is obtained between the impedance characteristics calculated by the equivalent parameters and the experimental data. Good accordance is obtained between the calculated non-reactive frequency and the experimental value. Although strong spurious responses exist in the vicinity of main resonance, the exact determination of equivalent parameters can be made by this method