This paper describes new cuts for torsional mode quartz crystal resonators, which are designated "TT-Cut" classified into "TT(X_1)-Cut" and "TT(X_2)-Cut". The objective of this paper is propose a new cut for torsional quartz crystal resonators and to clarify its frequency characteristics, frequency temperature behavior and electrical equivalent circuit parameters. First, a frequency equation of a resonator vibrating in torsion is shown. Since a torsion problem is equivalent to solving a torsional rigidity C_t, the derivative procedure of C_t is described in detail. The calculated results are then compared with the measured data of tuning fork-type, so that the present resonators are found to be successfully obtained with a frequency of about 400kHz and the second order temperature coefficient β of approximately one third of the flexural quartz crystal resonators.
View full abstract