抄録
This paper describes new cuts.for torsional mode quartz crystal resonators, which are called “TT (Y)-cut.” The object of this paper is to propose new cuts for torsional quartz crystal resonators with a zero temperature coefficient and to clarify frequency constant, frequency temperature behavior and electrical equivalent circuit parameters for the typical cuts. First, we show a frequency equation that is given as a function of torsional rigidity Ct. Namely, the problem of a vibration for torsional mode is substantially equivalent to that of torsional rigidity Ct, and it is obtained from stress function Ψ which satisfies the boundary conditions. Next, from the frequency equation numerous relationships where α reaches zero are found to exist between thickness-to-width ratio Rzy and cut angle (φ, θ), especially, the second order temperature coefficient β has a small value of -1.25×10-8/°C2 whose absolute value is approximately one third of the flexural mode quartz crystal resonators. The value of β is then compared with the measured data of -1.00×10-8/°C2. Finally, it is shown that torsional quartz crystal resonators of tuning fork-type are successfully obtained with a small R1 of 3.0 to 6.5 kΩ and a large Q value of 175, 000 to 347, 000 in a frequency range of about 300 to 600 kHz.
