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Piezoelectricity in formulas

  1. Nov 13, 2015 #1
    Hi all ,

    I am approaching now the piezoelectricity but I am studying economics so i have no knowledge to understand deeply some aspects of it. Anyway i am really interested in understanding it for myself.

    I understood all mechanism behind it but some things are still not clear. Let's start!

    1. If we use a piezoelectric surface to generate energy with a X force (N), am I getting the voltage output once or i'll get voltage output each time i apply the vertical force X?

    2. In formulas terms, I used this formula to calculate the voltage output of a crystal piezoelectric surface pushed with a vertical force is :

    V = [(dmnt) / (εε0A)] ⋅ Fx

    dmn = piezoelectric crystal coefficient | pico-C/N
    t = crystal thickness
    ε = crystal dielectric coefficient
    ε0 = 8.854 x 10-12
    A = area of surface
    Can anyone confirm me this formula? I am not sure i can rely on what i get using this formula. I can say that my force is for sure vertical (approximately).

    Thank you for your help.



    PS. Please, excuse me if i post it in the wrong section but i couldn't classify it in other sections.
  2. jcsd
  3. Nov 13, 2015 #2
    In mechanics, energy is force times distance. In electricity it is voltage times current.

    So each time you push the crystal, you will get the voltage. But since you can't push the crystal very far it will have very little current associated with it. There's no free energy here.

    But the crystals are good as transducers, converting electricity into motion or motion into electricity as signals.
  4. Nov 13, 2015 #3


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    You get the voltage while the force is applied, that is, while the crystal is stressed.

    Seems to agree with the formula here
    http://web.stanford.edu/class/me220/data/lectures/lect10/lect_6.html [Broken]
    Last edited by a moderator: May 7, 2017
  5. Nov 14, 2015 #4
    What if we spoken in terms of delta forces? Image you have a constant force applied on the surface of X1 Newton. Cyclically the force increase at X2. When this happens is what you told me still valid? Each time the force increases crystals generate voltage?

    If yes, what happens with a negative delta (cyclical decrease in vertical force)?

    Image i have 500N constant force applied. Then i got every 10sec an increase to 600N. When i do computations with formulas, do I have to put the delta or the absolute value of the force (100N or 600N as force applied)? It would help me to understand better the functioning of those crystals.

    Thank you


  6. Nov 14, 2015 #5


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    I thought I answered that question. The voltage depends on the applied force. Period.

    Have you read about how the voltages are generated? That would make it obvious.
  7. Nov 14, 2015 #6
    Yes. The crystal deforms slightly producing an imbalance of charge; hence voltage. This deformation is the distance in the E=Fd equation. But since the deformation is slight, the absolute change in charge carriers is also slight, leading to almost no current. The moment you connect wires, all the voltage runs around with almost no energy.

    This can be gotten around by connecting many crystals together. The deformation is thus added, adding the current. The cost is that you need more crystals and a bigger motion for your driving force. Simple pressure is no longer enough. Still, in theory you could recover some vibrational energy and damp the vibration at the same time which could be useful in some applications. You would need much cheaper crystals to make it effective though.
  8. Nov 15, 2015 #7


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    Staff: Mentor

    Energy = voltage times current multiplied by the time elapsed... :smile:
  9. Nov 16, 2015 #8
    If i push the crystals n-times, how do i compute the total output voltage? Is it right to multiply the previous formula for n-times? How can i add in the equation the dispersion?
  10. Nov 16, 2015 #9


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    Wow --- you are just not getting it. Do you understand yet how the voltage is generated?

    If you push the crystal n times with force F releasing it between pushes, you get n pulses of voltage V.
  11. Nov 16, 2015 #10
    Ok, i am sorry for not knowing things.

    Thanks anyway
  12. Nov 16, 2015 #11


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    Sorry for my unnecessary WOW. You need a simple understanding of the basic principles that produce piezoelectric effects.
    I posted a link to a very simple explanation, and it just felt to me (by your question) that you did not read it.

    Did you read this link and watch the video?

    Please feel free to ask questions, but please examine the basic material.
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