An analysis of frequency temperature characteristics and electrical equivalent circuit parameters of a new shape GT cut quartz crystal resonator formed by an etching method

The author presents a theoretical and experimental study of the frequency-temperature behavior and electrical characteristics of a GT-cut quartz crystal resonator with the two supporting portions at both ends of the vibrational portion which couples width-extensional vibration and length-extensional vibration. It is clarified why the GT cut quartz crystal resonator has better frequency-temperature characteristics than the conventional GT plate. An electrical equivalent circuit of a GT-cut quartz crystal resonator with electrical coupling and elastic internal coupling, which is a coupling quartz crystal resonator, is proposed. The electrical equivalent-circuit parameters of the present GT-cut quartz crystal resonator are discussed. Because the present GT-cut quartz crystal resonator has a very small coupling factor of about 3%, the principal vibration and the subvibration can be treated independently. Based on this result, the equivalent-circuit parameters of the resonator have been analyzed theoretically and the results are compared with the measured data. The calculated results agree well with the measured values