Sensor Relevant Physical Quantities

Piezoelectric Charge and Voltage Coefflcient/-Constant. For a piezoelectric material interactions between the electrical field and mechanical quantities have to be considered. In a good approximation this can be described via the linear context 

Here D is the vector of the dielectric displacement (size 3x1, unit C/m ), S is the strain (size 6x1, dimension 1), E is a vector of the electric field strength (size 3x1, unit V/m) and T is a vector of the mechanical tension (size 6x1, unit N/m ). As the piezoelectric constants depend on the direction in space they are described as tensors e- is the permittivity constant also called dielectric permittivity at constant mechanical tension T (size 3x3, unit F/m) and 5 , is the elastic compliance matrix (size 6x6, unit m /N). The piezoelectric charge coefficient df (size 6x3, unit C/N) defines the dielectric displacement per mechanical tension at constant electrical field and (size 3x6, unit m/V) defines the strain per eiectric fieid at constant mechanical tension [84], The first equation describes the direct piezo effect (sensor equation) and the second the inverse piezo effect (actuator equation). 

For short-circuited electrodes E is held constant at zero (upper index E), for open electrodes the dielectric displacement D remains constant. 

The (7.3), (7.4), (7.5) and (7.6) show that the piezoelectric coefficients g and d can be defined in two ways. In the hydrostatic mode the piezoelectric coefficients are represented by the effective quantities dj, = 33 + 2dsi and 9h = 933 + 2 31. For hydrophone materials the product dhffh is often reported as a measure of quality [85]. 

Sensitivity. The sensitivity of a piezoelectric material is taken to be equal to the generated open-circuit voltage that drop s across to the contact with the distance t (= thickness) divided by the applied stress or the product g t, where g is the relevant piezoelectric voltage coefficient. The voltage coefficient g is connected with the charge coefficient d via the dielectric permittivity = CrCo according to 

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