A method for the measurement of the k factor in lossy piezoelectric materials

In general the coupling factor k is a dimensionless parameter, defined as a particular combination of the dielectric, elastic and piezoelectric constants, and which may be useful for the internal energy conversion description in piezoelectric materials. In this paper, a method for k factor measurement in lossy materials is described: by using the 1D model of a piezoelectric element vibrating in the length extensional mode, it is shown that this parameter can be evaluated by measuring the velocity on the element external surfaces orthogonal to the wave propagation direction, and the voltage across the element, at the antiresonance frequency. The proposed measurement method was tested by using the same analytical 1D model to compute the coupling factor as a function of mechanical and dielectric losses; the obtained data show that the method gives good results for materials with any dielectric losses, while for very high mechanical losses the choice of the frequency at which the measurement is done is crucial.