Derivation of losses from impedance spectrum for contour modes of ceramic resonator

Method of loss coefficients calculation from mechanical quality factors of transversal vibration modes is presented. Theoretical formulae are derived for the contour mode of thin square plate and width extensional mode of a thin rectangular plate. Mechanical quality factors are expressed as a function of loss coefficients for ceramic with known Poisson's ratio. Measured impedance spectra are compared with calculations and used for the characterization of losses on lead-free BCZT and lead-based PZT piezoelectric ceramics. Full set of loss coefficients active for planar vibration modes is characterized on a single sample. Mechanical quality factor at resonance is the same for the contour extensional mode of a thin square plate and for the width extensional mode of a thin rectangular plate. Loss coefficients reach the biggest values for the piezoelectric losses, followed by the dielectric and elastic losses. Our results show that the BCZT ceramics have losses of the same magnitude as soft PZT ceramic.