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Piezo Engineering Tutorial
C.3.6 Heating and Power Dissipation
An ideal capacitor does not dissipate any power in terms of heat. However, in practice a piezo actuator does
not act as an ideal capacitor and does have some internal resistance that generates heat when current is
flowing through the actuator. The dielectric loss factor, or loss tangent, is defined as:
Equation 9
where ESR is the equivalent series resistance of the capacitor and X
tangent can also be written as the ratio of active (resistive) power (P) to reactive power (Q):
Equation 10
The higher the loss tangent, the more energy is converted to heat (energy lost) as an alternating electric field
is introduced to the material. For soft PZT materials, which are typically used for nanopositioning
applications, the loss tangent generally is between .01 to .03 for lower amplitude signals (~1-10 volts) and
can be as high as 0.1 to 0.25 for higher amplitude signals (~50-100 volts).
The reactive power (Q) is defined as:
Equation 11
For a single frequency (f) the capacitive reactance is:
Equation 12
Using
Equation
10 ,
Equation 11
actuator for a sinusoidal voltage with an amplitude of V
Equation 13
Equation
13 is a very useful approximation and shows the effects of power loss in piezoelectric devices.
This power loss is linearly proportional to the frequency of operation and the capacitance of the piezo
actuator, and proportional to the applied time-varying voltage squared. Since voltage is proportional to
position, the power loss is proportional to the square of the commanded time-varying position signal applied
to the piezo stage.
Figure C-6
shows an illustration of how the power loss changes as a function of frequency and applied
voltage for a typical piezo actuator with a capacitance of 4 μF.
50
and
Equation
12 , it can be shown that the power dissipated in a piezo
/2 and frequency f is:
pp
Appendix C
QNP3 Hardware Manual
is the capacitive reactance. The loss
c
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