Evaluation of the lower limit of crystal oscillator noise through the resonator's design parameters

This article discusses the method of determining the lower limit of the noise level of precision crystal oscillators based on the calculation of the crystal's maximum excitation power. Power limit is determined by the limiting values of the mechanical stresses arising from the excitation of the thickness-shear waves, and takes into account the design parameters of the resonator, such as natural frequency, the number of mechanical harmonic, curvature radius of the lens surface of the piezoelectric element, and the radius of the electrodes. In this paper we derive formulas for practical calculation of the lower noise level resonators of AT - cut.