Measurement of Small Values of Electromechanical Coupling Coefficient in Piezoelectric Transducers

Abstract

The electromechanical coupling coefficient k is usually derived from the difference between resonance and antiresonance frequencies fR and fA of a particular mode obtained from observations of the maximum and minimum values of electrical impedance. A simple relationship between fR, fA, and k exists only when the mechanical Q is infinite and the electrical losses negligible. This relationship breaks down when k2Q<2, a region which is important since the minor modes of barium-titanate transducers may have Q values of several hundreds and k<10%. For example, it has been found that, with 4<k Q<1/2 k, the apparent value kapp of k, derived directly from observations of fR and fA, is locked to Q rather than k by the relationship kapp≃(2/Q)12. The region k<20% and 100<Q<1000 has been analyzed and the resulting formulas processed by computer. The final data are presented in graphical form, making it possible to derive accurate values of k and Q from observations of the magnitudes and frequencies of the impedance maximum and minimum.