PdP133. Accuracy of the formulas used for the characterization of piezoelectric thickness mode resonators with impedance analyzers

Abstract

Abstract The resonance method allows the determination of different elastic, dielectric, and piezoelectric constants of the material using an adequately shaped sample. The accuracy of the relationships between the measured electrical input impedance quantities and the material constants is of capital importance. In the International Standards1–2 these relations, and consequently the derived formulas, are based either on the exact one-dimensional expression of the input impedance of an ideal lossless resonator, or on the simplified (Butterworth-Van Dyke) equivalent circuit. In this paper, the accuracy of equations frequently used for the measurement of the longitudinal acoustic velocity, vD t, the thickness electromechanical coupling coefficient, kt, and the mechanical quality factor, Qm are analyzed. The exact one-dimensional model of a thickness expander piezoelectric resonator, with a rigorous account of the internal mechanical losses, is taken as a reference.