Aspect ratio dependence of electromechanical coupling coefficient of piezoelectric resonators

Abstract

The most important parameter characterizing a piezoelectric material is the electromechanical coupling coefficient, which specifies the conversion efficiency between electrical and mechanical energies for a given vibration mode. For the resonance along the poling direction, there are two coupling coefficients defined, i.e., kt and k33, which are for resonators of the same mode but two extreme aspect ratios and they differ substantially. We have derived a unified formula for this coupling coefficient as a function of the vibrator aspect ratio. The unified formula can provide more accurate description to the effective coupling coefficient of resonators not satisfying the extreme aspect ratio requirements.

Unified model for the electromechanical coupling factor of orthorhombic piezoelectric rectangular bar with arbitrary aspect ratio

“…They are very similar to the set of equations from the work of Kim et al, 9,14 except that they are written for a mm2 symmetry class material. They can be simplified considering a 6mm or a 4mm symmetry class material reducing the number of independent constants.…”

“…One can notice a difference between the coupling coefficients from the FEM calculation and the analytical formula when G is decreasing from large value to 1. This can be explained by the choice of the g (G) function because, in spite of a reasonable justification in its determination, 14 FEM calculation shows that the variation around the value G = 1 is more pronounced.…”

“…15 is also valid for a 6mm or a 4mm symmetry class material and gives the same results as in Kim's work. 14 Fig . 5 presents the variations of the electromechanical coupling factor for the PIN-PMN-PT single crystal 4 using Eq.…”

Pb(In1/2Nb1/2)O3–Pb(Mg1/3Nb2/3)O3–PbTiO3 Piezoelectric Single-Crystal Rectangular Beams: Mode-Coupling Effect and Its Application to Ultrasonic Array Transducers

“…In fact, the dimensions (i.e., L and H) of the rectangular cross-section and hence the value of G of the PIN-PMN-PT rectangular beams have the significant effects on their mode coupling and resonance characteristics, which have been discussed in Section 2.1. The electromechanical coupling coefficients of PZT piezoelectric resonators have been reported to depend heavily on the aspect ratio [22].…”

Electromechanical coupling coefficient k31eff for arbitrary aspect ratio resonators made of [001] and [011] poled (1−x)Pb(Mg1/3Nb2/3)O3–xPbTiO3 single crystals

“…However, in related textbooks on piezoelectricity and in the IEEE piezoelectric standard, the electromechanical coupling coefficients are defined using one-dimensional ͑1D͒ equivalent circuit models as fixed constants, 4,5 which cannot accurately reflect the true electromechanical energy conversion efficiency when the geometry of the resonators do not satisfy the assumed boundary conditions. Focused on this issue, Kim et al [6][7][8] studied the effect of aspect ratio dependence of the electromechanical coupling coefficients by solving two-dimensional coupled vibration equations and derived explicit analytical expressions for the aspect ratio dependence of the electromechanical coupling coefficient k 33 and k 31 for PZT vibrators, which has ϱm ͑same as 6mm͒ symmetry.…”