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·cm at a cut angle φ=36° and its frequency is dependent upon contour dimensions of the resonator. In this paper relationships of frequency constant (f·2z₀), frequency temperature coefficients α, β and a capacitance ratio r versus cut angle φ, 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 R₁ and a small capacitance ratio r