Constancy on quality factor of dual-T quartz crystal resonator circuit

In this paper, we have studied the quality factor of a dual-T quartz crystal resonator circuit of which its resonance frequency can be changed a several thousand ppm exceeding the limit of the piezoelectric coupling factor of a crystal resonator. We derived the relation between the quality factor of the dual-T circuit and the equivalent circuit parameters of the component crystal resonators. We have made the measurement and have shown that the frequency change about 1000 ppm can be obtained with constant quality factor comparable to its component crystal resonator. We made an oscillator using this dual-T circuit and also showed about 1000 ppm frequency tunability.