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Ashutosh98
India
7 Posts 
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 

Enrico
503 Posts 
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 platetoplate 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, Enrico



Ashutosh98
India
7 Posts 
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 



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