Modular Piezoelectric Actuators

Piezo Driver Bandwidth Tutorial

Knowing the rate at which a piezo is capable of changing lengths is essential in many high-speed applications. The bandwidth of a piezo controller and stack can be estimated if the following is known:

1. The maximum amount of current the controllers can produce. This is 0.5 A for our BPC Series Piezo Controllers, which is the driver used in the examples below.
2. The load capacitance of the piezo. The higher the capacitance, the slower the system.
3. The desired signal amplitude (V), which determines the length that the piezo extends.
4. The absolute maximum bandwidth of the driver, which is independent of the load being driven.

To drive the output capacitor, current is needed to charge it and to discharge it. The change in charge, dV/dt, is called the slew rate. The larger the capacitance, the more current needed:

For example, if a 100 µm stack with a capacitance of 20 µF is being driven by a BPC Series piezo controller with a maximum current of 0.5 A, the slew rate is given by

Hence, for an instantaneous voltage change from 0 V to 75 V, it would take 3 ms for the output voltage to reach 75 V.

Note: For these calculations, it is assumed that the absolute maximum bandwidth of the driver is much higher than the bandwidths calculated, and thus, driver bandwidth is not a limiting factor. Also please note that these calculations only apply for open-loop systems. In closed-loop mode, the slow response of the feedback loop puts another limit on the bandwidth.

Sinusoidal Signal

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The bandwidth of the system usually refers to the system's response to a sinusoidal signal of a given amplitude. For a piezo element driven by a sinusoidal signal of peak amplitude A, peak-to-peak voltage V_pp, and frequency f, we have:

A diagram of voltage as a function of time is shown to the right. The maximum slew rate, or voltage change, is reached at t = 2nπ, (n=0, 1, 2,...) at point a in the diagram to the right:

From the first equation, above:

Thus,

For the example above, the maximum full-range (75 V) bandwidth would be

.

For a smaller piezo stack with 10 times lower capacitance, the results would be 10 times better, or about 1060 Hz. Or, if the peak-to-peak signal is reduced to 7.5 V (10% max amplitude) with the 100 µm stack, again, the result would be 10 times better at about 1060 Hz.

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Triangle Wave Signal

For a piezo actuator driven by a triangle wave of max voltage V_peak and minimum voltage of 0, the slew rate is equal to the slope:

.

Or, since f = 1/T:

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Square Wave Signal

For a piezo actuator driven by a square wave of maximum voltage V_peak and minimum voltage 0, the slew rate limits the minimum rise and fall times. In this case, the slew rate is equal to the slope while the signal is rising or falling. If t_r is the minimum rise time, then

or

.

For additional information about piezo theory and operation, see the Piezoelectric Tutorials page.