Relationship between temperature behavior of resonant and antiresonant frequencies and electromechanical coupling factors of piezoelectric resonators

A relationship between temperature behavior of the resonant frequency FR, the antiresonant frequency FA, and the coupling factor k is given by an equation of the form δFA/FA- δFR/FR= Gδk/k. The factor G as a function of the coupling factor and the order of overtone is calculated for both piezoelectrically unstiffened and stiffened modes. An application of this relationship yields the curve of turnover temperature versus the coupling factor of X-cut lithium tantalate resonators.