Lame-mode quartz crystal resonators

A quartz crystal resonator of Lame-mode is available for realization of a frequency over approximately 3 MHz because its frequency constant has a value of 360 kHz/spl middot/cm at a cut angle /spl phi/=36/spl deg/ and its frequency is dependent upon contour dimensions of the resonator. In this paper relationships of frequency constant (f/spl middot/2z/sub 0/), frequency temperature coefficients /spl alpha/, /spl beta/ and a capacitance ratio r versus cut angle /spl phi/, and also frequency temperature behavior are shown theoretically and experimentally. The calculated values agree well with the measured ones, and a quartz crystal resonator of Lame-mode is successfully obtained with a zero temperature coefficient at room temperature, a small series resistance R/sub 1/ and a small capacitance ratio r.