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 Significant error in a simple case

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Ashutosh98 Posted - Oct 21 2022 : 18:16:36
My progress with the project I am working on has led me to a stage where I must compare 2 solution methods and decide which is giving a better approximation. For doing that, i resorted to calculating the capacitance of a parallel plate capacitor.
I made a 2D system using 2 straight edge panels to model the plate geometry. I assumed a hypothetical simplistic case; the medium between the 2 plates having a relative permitivitty of 4, the distance between the 2 plates being 2 meters, the length and depth of the plates being equal to 1 meter each.

For reference, i used the traditional formula for capacticance (epsilon*eeMedium*Area/d), and got a value of 17.708 pF.

The .lst file was developed as follows:
* 2D Capacitor
* This capacitor is made by a dielectric material with relative permittivity
* equal to 4.0, sandwiched between two square metal contacts
* with negligible thickness

* First Plate -> Offset by 1 meters in the verticle direction
* Second Plate -> Offset by 1 meters in the negative verticle direction
C Plate.txt 4.0 0.0 -1.0
C Plate.txt 4.0 0.0 1.0

The Plate.txt geometry file is developed as follows:
0 Plate goemtry for parallel plate capacitor
* Plate made with stright edge 2D elements

S Plate -0.5 0.0 0.0 0.0
S Plate 0.0 0.0 0.5 0.0

Fastercap gives the result as 39.29 pF, which means there is an error of over 120%. Additionally, the result varies significantly with changing the number of straight edge panels.
Is there any basic mistake I am comitting, since for such a simple case, I think there shouldn't be such a high error (also some of the 2D examples in the Fastercap documentation seemed to have reasonably accurate predictions).

Thank you in advance

Ashutosh Mukherjee
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Ashutosh98 Posted - Oct 25 2022 : 10:21:50
Thanks for the reply Enrico!

Thanks a lot for the tip. I did try with small distances:

The plates being 10mmx20mm and being seperated by a distance of 5 micrometers. The analytical solution gives a capacitance of 141.664 pF whereas FasterCap gives a solution of 213.69 pF, which is an error of about 50%.

I also tried out the 3D case given in the Fastercap documentation (Capacitor.lst) according to which the capacitor plates are 1x1 meters each, with a gap of 0.6 meters filled with dielectric medium of relative permitivitty 0.6. In that case, Fastercap gives a result of 65.428 pF whereas the expected analytical result is 44.27 pF, which again is an error of about 47%.

I would like to ask if these errors are genuine, and this kind of error I should be expecting for all cases, or whether I am making a mistake in interpreting?

Ashutosh Mukherjee
Enrico Posted - Oct 24 2022 : 23:58:54
Hi Ashutosh,

if the plates are 1m x 1m an their distance is 2m, then this is very far from being a ideal parallel plate capacitor, as you have very important fringing fields effect.

You should compare with a capacitor with small plate-to-plate distance, so that the field is almost uniform between the plates and the fringing field is relatively negligible.

You can find such examples in the Samples directory; in the file comments you can also find the theoretical formula and value against which you should compare (akin to what you did here).

Surely you also need a fine enough discretizaiton of the plates for the problem at hand - again see the comments in the sample files.

Best Regards,

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