# Piezoelectric Equations

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1. Jun 14, 2017

What are the governing equations to determine the output energy of a ceramic rectangular multi-layer piezoelectric component after one actuation? I am familiar with most of the properties and looking to characterize a piezo component from the direct piezo effect.

Last edited by a moderator: Jun 14, 2017
2. Jun 14, 2017

### Dr.D

While I don't know them off the top of my head, I know that I have seen the governing equations posted on the 'net. I suggest a search there to get what you want.

3. Jun 14, 2017

### dlgoff

Here you go. http://www.piezo.com/tech2intropiezotrans.html

4. Jun 14, 2017

Thank you but I am looking for more specific information on the power output. The max deflection and voltage equation is useful but not applicable to what I am looking for

5. Jun 14, 2017

Many of the searches use numerous different variables to characterize the output power. I am looking for more of a concise equation relative to my specific component of a ceramic multi-layer rectangular generator. I essentially am looking to find the error of the theoretical and calculated values. I have a piezo component that I hooked leads up to and measured the output power for one actuation by actuating at 10Hz and then dividing by 10 to get a per actuation value. I now am looking for the theoretical value, any help is appreciated.

6. Jun 15, 2017

### Staff: Mentor

The output power depends on the load connected to the cell. So you need two simultaneous equations, one for the cell and one for the load.

7. Jun 15, 2017

What about for storage purposes like a small cap bank or battery?

8. Jun 15, 2017

### Staff: Mentor

The purpose doesn't matter.

9. Jun 15, 2017

So wouldn't you characterize this by just taking the input energy to the cap bank? The electrical contribution equation that I have seen in terms of material properties is; We = V/2 * k332*s33D*P2

What other equation would be needed?

K33 = Mechanical coupling factor
s33=elastic compliance
P=Pressure piezo is exposed to
V = volume

10. Jun 15, 2017

### Staff: Mentor

Think of it this way, power is voltage times current. V*I
If the load is an open circuit, no current, I=0 P=0
If the load is a short circuit, no voltage, V=0 P=0
If your circuit looks like this, the important second equation, is $I=C\frac{dV}{dt}$

P is the piezoelectric device. The diode is there to prevent current flow backwards when you're not pushing.

The really hard part is to determine the voltage versus time curve of each activation of the piezoelectric device. I fear that it is more complicated than you're ready for.

This article may help. Look especially at the references linked. Some of those devices may be similar to what you want to do.
https://en.wikipedia.org/wiki/Energy_harvesting#Piezoelectric

You haven't said how much power you need to be successful. Most piezoelectric devices can make s few milliwatts in the proper circuit.

11. Jun 16, 2017

I am looking to achieve about 10mW per actuation with about 20Hz. Obviously the force is going to impact the overall power as a larger force yields a larger output. Most achieve the most power at resonance which is the problem I am currently dealing with.

12. Jun 16, 2017

### Staff: Mentor

I would use an oscilloscope. I would also consider a literature search for the results of experiments and for tips on how to improve performance.

13. Jun 16, 2017

So if I set up the piezo in a circuit to determine the power and at lets say 15Hz the output is 50mW. Does that mean per actuation (every 66ms [1/15Hz]), the output would be 3.33 mW (50mW/15Hz). Does this make sense on how you would characterize output power based on a single actuation?

14. Jun 16, 2017

### Staff: Mentor

No. Power has the wrong units. A single activation might result in a defined amount of energy. Power is in watts, energy is in watt*seconds. An actuation might give 10 watts for 0.01 seconds resulting in 0.01 watt*seconds. If you get 10 such activation per second, the average power over the second would be 0.0001 watts.

But even the amount of energy per activation is not constant. As the capacitor charges, it approaches full charge and the energy added for each activation gradually goes to zero.

The short answer is that you're not going to find a simple number or a simple formula to give you an answer. It will take either a very complicated analysis or some experimentation. If complicated analysis is not your thing, some benchtop experiments might be your best choice.