Accurate determination of complex materials coefficients of piezoelectric resonators

This paper presents a method of accurately determining the complex piezoelectric and elastic coefficients of piezoelectric ceramic resonators from the measurement of the normalized electric admittance, Ȳ, which is electric admittance Y of piezoelectric resonator normalized by the angular frequency ω. The coefficients are derived from the measurements near three special frequency points that correspond to the maximum and the minimum normalized susceptance (B̄) and the maximum normalized conductance (Ḡ). The complex elastic coefficient is determined from the frequencies at these points, and the real and imaginary parts of the piezoelectric coefficient are related to the derivative of the susceptance with respect to the frequency and the asymmetry of the conductance, respectively, near the maximum conductance point. The measurements for some lead zirconate titanate (PZT) based ceramics are used as examples to demonstrate the calculation and experimental procedures and the comparisons with the standard methods.