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Electrical Requirements for Piezo Operation

General
When operated far below the resonant frequency a Piezo behaves as a capacitor where displacement is proportional to charge (first order estimation).

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

Design of a Piezo stack actuator.

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

C » n*e₀*e₃₃*A/d_s       (4-14)

Where
n = number of layers

e₀ = dielectric constant in vacuum [As/Vm]

e₃₃ = relative dielectric constant [without Dimensions]

A = electrode surface area [m²]

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

The above equation shows that for a given actuator length l₀ and a given disk thickness d₀ capacitance is a quadratic function of the ratio d₀ / d₁ where d₁ < d₀. Therefore, the capacitance of a piezo actuator constructed of 100 µm 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 Piezo requires a current i:

i= dQ/dt = C * (dU/dt)       (4-15)

Relationship of current and voltage for the piezo actuator

Where

i = current [A]

Q = charge [Coulomb; As]

C = capacitance [Farad; As/V]

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 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 Dimensionss very slowly (> 1 hour).

For slow position changes, very low current is required. For example an amplifier with an output current of 20 µA fully expands a 20 nF actuator within one second. (See section "Piezo Control Electronics" section for variety of Piezo amplifiers).

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