In this lecture, we will first discuss about four important constants used for quantification of Piezoelectric sensing and actuation. These are:

• Piezoelectric Charge Constant ( d ),
• Piezoelectric Voltage Constant ( g ),
• Electro-mechanical Coupling Factor ( k ) and
• Frequency Constant ( N_p ).

Piezoelectric Charge Constant

The piezoelectric charge constant d , expressed in ‘m/V' or ‘pC/N' (1 Pico-Coulomb (pC) = 10^-12 Coulomb), is defined by the following simple relationship:

(31.1)

where the geometric parameters are explained in Fig. 30.2. Here, ‘ q ' denotes the charge collected in the electrode surfaces, F_i , i = 1..3, denote the forces along the respective directions and V₃ denotes the voltage applied along the z direction. The first expression of coupling coefficients signify d as the mechanical strain experienced by a piezoelectric element for an applied voltage V; while the second relationship defines d as the induced polarization generated by a force F.  The piezoelectric constants  d₃₁,d₃₂ are usually negative signifying the generation of positive strain upon the application of positive voltage.

Piezoelectric Voltage Constant

The piezoelectric voltage constant, g expressed in V-m/N, is similarly defined as:

(31.2)

where, V₃ is the voltage sensed along the z -direction due to the application of pressure. Like d₃₁ , g₃₁ is also usually negative signifying the generation of positive voltage upon the application of tensile force to the system. In general, a relatively large value of d indicates the superiority of the piezoelectric material as an actuator and similarly, a higher value of g indicates better suitability of the material as a sensor. However, neither of these coefficients describe the quality of a piezoelectric material as an efficient energy converter. For example, hard PZT has higher d₃₁ than soft PZT; whereas, the soft PZT has higher efficiency in energy conversion.