Methodology for characterizing loss factors of piezoelectric ceramics

The methodology to obtain the loss factors in piezoelectric ceramics is proposed in this paper. There are three hysteresis loss components for piezoelectric vibrators, i.e., dielectric, elastic and piezoelectric losses. The equations were derived about the relations between mechanical quality factors and all contributing loss factors by the complex analysis of the admittance/impedance expressions for specific piezoelectric vibrators. By characterizing mechanical quality factors and coupling coefficients in k₃₁, k_t, k₃₃, k_p, and k₁₅ modes, 20 loss factors can be obtained for the piezoelectric ceramic with ∞mm or 6 mm crystal symmetry.