屈曲捩りモード音又型水晶振動子の周波数温度特性 Frequency Temperature Characteristics of Flexural-Torsional Mode Tuning Fork Type Quartz Crystal Resonator
It is well known that a flexural-torsional quartz crystal resonator which couples a torsional mode vibration to a flexural one has a cubic curve in frequency temperature characteristics as well as an AT-cut quartz crystal resonator. This paper describes the frequency temperature characteristics of a tuning fork type quartz crystal resonator which couples the torsional mode vibration to the flexural one and the estimated results of the various constants for the resonator manufactured for trial experiments. First, a secular equation coupled the torsional mode vibration to the flexural one, is calculated. From the secular equation, frequency temperature characteristics for the flexural-torsional mode tuning fork type resonator have been theoretically analized, namely, concerning a relationship of the resonant frequency, the frequency temperature coefficients versus thickness, a normalized frequncy, and a cut angle. Next, the calculated values are compared with the experimental ones by manufacturing tuning fork type flexural-torsional quartz crystal resonators. At the same time, the various constants of the resonators manufactured for trial experiments are estimated. As a result, it is confirmed that tuning fork type flexural-torsional quartz crystal resonators with excellent frequency temperature characteristics, low crystal impedance, and a high quarity factor are realized.
日本時計学会誌 120(0), 49-63, 1987