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 calculated relatively simply if the following is known:
(1) The maximum amount of current the controllers can produce. This is 0.5 A for our BPC Series. (2) The load capacitance of the piezo is known. The higher the capacitance, the slower the system. (3) The desired signal amplitude (V), which determines the length that the piezo extends.
The physics behind it is quite simple: when we drive the output capacitor, we need some current to charge it and discharge it. The larger the capacitance, the more current we need. The maximum rate of voltage change (called slew-rate) is:

So for example, for a 100 µm stack, having a capacitance of 20 µF:

When you demand an instantaneous voltage change from, say 0 V to 75 V, it will take 3 msec for the output voltage to reach 75 V.
The bandwidth of the system usually refers to the system''s response to a sinusoidal signal of a given amplitude. For a sinusoidal signal of peak amplitude Vpk, and frequency f, the maximum slew-rate is:

The maximum full-range (75 V) bandwidth of the above example would be:

For a 10 µm stack, the results would be 10 times better, or about 530 Hz. Or, if you only wanted a 7.5 V peak to peak signal (10% max amplitude) with the 100 µm stack, again, the result would be about 530 Hz.
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. |