Demonstration of doubly rotated X-cut quartz plate oscillators with a slot vibrating in length extensional mode

This paper describes the finite element method analysis of (XYlt) -35°/-1° rotated X-cut quartz oscillators vibrating in the length-extensional mode and the experimental data of the sample processed monolithically by the wet etching. The oscillator consists of the resonator with a slot and an integral mounting system and has the first order temperature frequency coefficient α = -0.6 ×10^-6 /°C, the second order temperature frequency coefficient β = -3.5 ×10^-8 /°C², and the parameters of the electrical equivalent circuit in the air: the series inductance L₁ = 2.70 H, the capacitance ratio r = 192, the series resistance R₁ = 1080 Ω, and Q = 19000.