The standard formula for the capacitance of a parallel plate capacitor, having two plates separated by a distance t and the space in between the plates filled with a substance of permittivity epsilon, is

Capacitance = (epsilon)*(Area of plates)/tThe units of capacitance are Farads if the area is expressed in square metres and the thickness of the dielectric is expressed in metres. (The permittivity epsilon is equal to the relative dielectric constant times 8.85E-12)

At microwave frequencies we can make a good electromagnetic screen with a perforated metal plate, if the perforation hole size is very much less than a wavelength at the frequency of interest.

As the wavelength increases as the frequency is lowered (because frequency * wavelength = 3E8 metres/sec in vacuum) the hole sizes can be made larger as we reduce the frequency.

The question we pose is, at medium frequencies where the hole size is much smaller than a wavelength, what is the capacitance of a parallel plate capacitor with perforated plates each of area A, having a packing fraction P (let us suppose P = 0.01) such that the actual area of metal is PA square metres?

Let us also suppose the total width of the perforated plates is much greater than their spacing (or else they are surrounded by guard rings) to avoid fringing effects, and let us also suppose that the holes have maximum linear aperture sizes much less than the spacing of the plates.

Has anyone done this experiment? What do you think?

If you have any ideas or empirical measurements, please email me at d.jefferies@surrey.ac.uk

10 March 2000.

We have now done preliminary experiments. For the conditions stated above, the capacitance is largely independent of the amount of metal missing, and only depends on the area and separation of the perforated plates. Our separation was 5.5mm and the hole sizes 2mm and 3mm, with about 2/3 of the metal removed (the hole area was 2/3 and the metal area 1/3 of the total). The measured capacitance did not change noticeably or significantly when measured with perforated plates or with solid plates.

However, when the spacing was reduced to 0.2mm the capacitance changed in proportion to the amount of metal missing, that is, it fell to about 1/3 the value of the capacitance measured with solid plates.

Copyright © D.Jefferies 1999, 2000.

D.Jefferies email 10th March 2000