Piezo Ceramics Tutorial 14 of 15

Useful Electro-Mechanical Relationships:

Under static or quasi-static (below resonance) conditions, the magnitude of the piezoelectric effect is given by piezoelectric "d" and "g" constants. For the case of the direct piezoelectric effect where the material develops an electric charge from an applied stress, the definitions for "d" for constant field and "g" for constant dielectric displacement should be used. Refer to the table in section 9, Ceramic Property Definitions. For the converse effect where the material develops a strain from an applied electric field, the definitions for "d" and "g" for constant stress should be used. These "d" and "g" coefficients are related by Formula 8 for plates and discs, and Formula 9 for rods.

Formula 8 (Plates & Discs)	d31 = g31T31
Formula 9 (Rods)	d33 = g33T33
whereT33  is the permittivity of the material

The permittivity of the material is related to both the permittivity of free space and the dielectric constant of the material according to Formula 10.

Formula 10	kT33 = T31 / 0
where kT33 is the relative dielectric constant of the material and 0 is the permittivity of free space (8.85x10-12 farad/meter).

At frequencies far below the mechanical resonance frequency, the electro-mechanical coupling factor, K, can be calculated by Formula 11 for plates, Formula 12 for discs, Formula 13 for rods, and Formula 14 for shear plates.

Formula 11 (Plates)
Formula 12 (Discs)
Formula 13 (Rods)
Formula 14 (Shear Plates) where s is the compliance of the material

The coupling factor is a useful expression relating the amount of energy that can be changed from the electrical form to the mechanical form, or visa versa, for the different operational modes. The coupling factor can be expressed as Formula 15.

This value, although related, should not be considered the overall efficiency of the electromechanical transduction, since it does not take into account electrical and mechanical dissipation or losses. When a transducer is not operating at resonance or if it is not properly tuned and matched, the efficiency can be quite low. A properly designed transducer can operate at well over 90% efficiency. The pressure P which a ceramic driver can impart is given approximately by Formula 16.

Indepth technical information can also be found in the Technical Publication Archives as Acrobat® pdf files.