Fundamentals of Piezoelectricity and Piezo Actuators

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Fundamentals ... (cont.)



Electrical Requirements for Piezo Operation

General
When operated well below the resonant frequency, a PZT behaves as a capacitor: displacement is proportional to charge (first order estimate).

PZT stack actuators are assembled with thin, laminar wafers of electroactive ceramic material electrically connected in parallel.

The (small-signal) capacitance of a stack actuator can be estimated by:

(Equation 14)




Where:

n = number of layers

ε33 T
= dielectric constant [As/Vm]

A = electrode surface area of a single layer [m2
]

ds
= distance between the individual electrodes (layer-thickness) [m]

l0
= actuator length

The equation explains that for a given actuator length l0 = n · dS and a given disk thickness dS, the capacitance is a quadratic function of the ratio dS / d1 where d1 < dS. Therefore, the capacitance of a piezo actuator constructed of 100 m thick layers is 100 times the capacitance of an actuator with 1 mm thick layers if the two actuators are the same length.

Static Operation
When electrically charged, the energy E = (1/2) CU² is stored in a piezo actuator. Every change in the charge (and therefore in the displacement) of the PZT requires a current i:

(Equation 15)




Relationship of current and voltage for the piezo actuator

Where:

i = current [A]

Q = charge [coulomb (As)]

C = capacitance [F]

U = voltage [V]

t = time [s]

For static operation only the leakage current has to be supplied. The high internal resistance reduces leakage currents to the micro-amp or sub-micro-amp range. Even when disconnected from the electrical source, the charged actuator will not make a sudden move but return to its uncharged dimensions very slowly (time constant of several minutes).

For slow position changes, very low current is required. For example, an amplifier with an output current of 20 A fully expands a 20 nF actuator within one second. (Suitable amplifiers can be found using the Control Electronics Selection Guide see link).
Fig. 25. Design of a PZT stack actuator.

Fig. 25. Design of a PZT stack actuator.



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