Abstract
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 their frequency constants, frequency temperature behavior and electrical equivalent circuit parameters. First, torsional rigidity Ct is derived from stress function ψ obtained by solving approximately a partial differential equation by Galerkin's method. Next, from the frequency equation numerous relationships where the first order temperature coefficient a reaches zero exist between thickness-to-width ratio Rzy and cut angle (ψ, 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. Finally, it is shown that torsional quartz crystal resonators of tuning fork-type are successfully obtained with a small R1 of 3.5 to 4.6 kΩ and a large Q value of 241000 to 272000 in a frequency range of about 300 to 600 kHz.
