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Need capacitance formulae!

  1. Jul 10, 2012 #1

    Hopefully this is going to be pretty basic stuff for someone. I have a mechanically variable capacitor and to prevent electrode shorting, I have deposited a small amount of oxide on the side walls. For my Matlab model I need the equation for capacitance which takes this oxide into account. I can't seem to find a generic formula for capacitance of a parallel plate or comb capacitor with oxide on the side walls (not filling entire gap between electrodes). I need formulas for both geometries.

    Thanks in advance!

  2. jcsd
  3. Jul 10, 2012 #2
    Closed form expressions for capacitance only exist for specific geometries, parallel plate being the simplest. The parallel plate formula assumes that plates separation is much less than plate area, and that the plates are the same shape and not offset from each other. It would be easy to incorporate various layers of DK stacked between the plates into this formula. Sounds like your difficulty is your geometry, not your DK. Maybe you need to describe your geometry more. If it is like the variable capacitor found in old tube radios, you will only have a closed form expression if the geometry was specifically designed to provide it.
  4. Jul 10, 2012 #3
    Sorry if I was unclear. Perhaps it would be best to ignore the variable capacitor part as the geometry is exactly that of a standard parallel plate capacitor and comb capacitor. Typically the capacitance would be C = eA/d and C = 2NeA/d The only issue is I have deposited a thin layer of dielectric material onto the electrodes and need a modified equation for the capacitance now.
  5. Jul 10, 2012 #4

    jim hardy

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    Gold Member

    Hmmm interesting

    so you need to figure an effective Dielectric Constant for the space between the plates?

    dielectric constant for Al2O3 is 9 to 11 per wikipedia

    so it seems to me this would be analogous to conductances in series, sum of (DC-1 X thickness) ? for first approximation anyway?

    and if the film is very thin in comparison to air gap it effectively disappears ?

    is my thinking straight ? More energy per cc is stored in the film, but it's very thin.

    old jim
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