Derivation of piezoelectric losses from admittance spectra

High power density piezoelectrics are required to miniaturize devices such as ultrasonic motors, transformers, and sound projectors. The power density is limited by the heat generation in piezoelectrics, therefore, clarification of the loss mechanisms is necessary. This paper provides a methodology to determine the electromechanical losses, i.e., dielectric, elastic and piezoelectric loss factors in piezoelectrics by means of a detailed analysis of the admittance/impedance spectra. This method was applied to determine the piezoelectric losses for lead zirconate titanate ceramics and lead magnesium niobate-lead titanate single crystals. The analytical solution provides a new method for obtaining the piezoelectric loss factor, which is usually neglected in practice by transducer designers. Finite element simulation demonstrated the importance of piezoelectric losses to yield a more accurate fitting to the experimental data. A phenomenological model based on two phase-shifts and the Devonshire theory of a polarizable-deformable insulator is developed to interpret the experimentally observed magnitudes of the mechanical quality factor at resonance and anti-resonance.