Overtone Lame-mode quartz crystal resonators fabricated by an etching process

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