I posted this question originally with Electrical Engineering Stack Exchange but nobody seems to know the answer. So I thought a physicist might find the question more approachable.

Formulas for Integral Components:

I am looking for "simple" approximative formulas for integral components. (I.e. devices that are etched into the copper of printed circuit boards.) In particular for:

  • A grounded interdigital capacitor (i.e. above a ground plane and with one set of fingers connected to ground), and
  • a square pad on an infinite ground plane (to estimate SMT pad capacitance). I believe that due to the method of images this is equivalent to a finite parallel plate capacitor with twice the separation but I am not 100% sure.

Alternatively: Is there a free software that can simulate this and can be used to answer the question without investing more than a few hours to learn how to use it?

Sanity-Check Request:

Maybe somebody is also able to sanity-check the following reasoning.

In the absence of a formula for a grounded interdigital capacitor, would the following provide a reasonable estimate:

  1. Calculate the capacitance between the two sets of fingers (with the available formulas)
  2. Add the capacitance of a microstrip of equivalent length to the total length for microstrip contained in one set of fingers

Example using the formula provided here:

  • $\epsilon_r$ = 4.2
  • t = 70 µm (copper thickness)
  • h = 1.6 mm
  • W' = 9.9 mm
  • l = 8.4 mm
  • W=S=l'=s' = 0.3 mm

A1 = 3.63*10^-3 pF/mm, A2 = 8.27*10^-3 pF/mm, N = W'/(W+S)+1 = 17

$$ C_{interdigital} = 2.58 pF $$

Length of microstrip in one set of fingers (the one with 9 fingers):

$$ L_{microstrip} = 9.9 mm + 9\times(8.4+0.3) mm = 88.2 mm $$

$$ C_{microstrip} = 88.2 mm \times 0.0431 pF/mm = 3.80 pF $$

It follows that the interdigital capacitor presents an approximate capacitance to ground of about:

$$ C_{total} = C_{interdigital} + C_{microstrip} = 6 pF $$

Does this calculation make any sense at all?

  • $\begingroup$ I am very happy to see this kind of question here on Physics Stack Exchange. A couple years ago when I first came here this kind of question would have been closed as "engineering" and it makes me proud to see that we've grown beyond that. I am personally interested in this question and might spend a non-trivial amount of time generating an answer, but first let's fix up the post. Please ask one specific question. As it stands, the post asks for formulae for two different capacitor geometries, a software recommendation, and a sanity check. Pick one and put the others in their own posts. $\endgroup$
    – DanielSank
    Commented Jul 12, 2016 at 7:24

1 Answer 1


I'm no expert and only came across this when I was asking a question myself. Working out the capacitance of an IDE form component can be calculated using equation 20 in a paper by a chap called den Otter titled 'Approximate expressions for the capacitance and electrostatic potential of interdigitated electrodes'. I coded the expression into excel/matlab and it gives a very good approximation


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