Calculation of Capacitance in 3D plate capacitor model

Numerical methods and mathematical models of Elmer
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Matt8709
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Joined: 24 Jun 2016, 16:50
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Calculation of Capacitance in 3D plate capacitor model

Post by Matt8709 »

Hi everybody,

I have the following situation:
1) I build 2 Plates for the capacitor in freecad and saved them in .step format.
2) I merged them in gmesh (see attached .geo file) and built a airbox aroud.
3) I simulated the Electric Potential of this setup
--> Until here, everything seems to be OK.

But now, I want to calculate the capacitance of this plate capacitor.
Therefore I activated the calculate capacitance matrix in the solver settings and added the capacitance body-nr. in the boundary conditions of GND and VDD.
But the calculated capacitance is wrong, because it gives me 1.6e-9F and the theoretical value with this 10mmx10mm plates in 1mm distance should be 8.854e-13F.

Code: Select all

StatElecSolve: Capacitance matrix computation performed (i,j,C_ij)
StatElecSolve:   1  1    1.64744E-09
StatElecSolve: Capacitance matrix was saved to file capatest.dat
ComputeChange: SS (ITER=1) (NRM,RELC): ( 0.65536916      2.0000000     ) :: electrostatics
WritePostFile: Saving results in ElmerPost format to file ./case.ep
ElmerSolver: *** Elmer Solver: ALL DONE ***
ElmerSolver: The end
SOLVER TOTAL TIME(CPU,REAL):         0.23        0.23
ELMER SOLVER FINISHED AT: 2016/06/24 15:48:50
Can someone explain me what is wrong in my simulation script???

See the attached files for inspection :)

Regards,
Matthias
Attachments
Elmer Potential filled
Elmer Potential filled
Elmer_Potential_filled.PNG (105.72 KiB) Viewed 5931 times
Elmer Potential
Elmer Potential
Elmer_Potential.PNG (92.06 KiB) Viewed 5931 times
plate_capacitor.zip
Project
(129.94 KiB) Downloaded 443 times
mzenker
Posts: 1999
Joined: 07 Dec 2009, 11:49
Location: Germany

Re: Calculation of Capacitance in 3D plate capacitor model

Post by mzenker »

Hi Matthias,

I think you have drawn your geometry in mm, but Elmer assumes m (see Bounding Box in Model->Summary in ElmerGUI). To correct this, write

Code: Select all

Coordinate Scaling = 0.001
into the free text field in Model->Setup, section "Simulation".

HTH and have a nice weekend,

Matthias
Matt8709
Posts: 2
Joined: 24 Jun 2016, 16:50
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Re: Calculation of Capacitance in 3D plate capacitor model

Post by Matt8709 »

Hi Matthias,

thank you very much for your answer!
With the right scaling, the result is 1.65pF thats in the right range but it is still not what I expect.

In theory C=epsilon0*epsilonR*A/d
-> C=8.854e-12*1*10e-3*10e-3/1e-3 = 8.854e-13.

The result in Elmer is nearly the double.. :?:

Code: Select all

StatElecSolve:  Solve (s)             :   1.8000000000000016E-002
StatElecSolve: Capacitance matrix computation performed (i,j,C_ij)
StatElecSolve:   1  1    1.64744E-12
StatElecSolve: Capacitance matrix was saved to file capatest.dat
ComputeChange: SS (ITER=1) (NRM,RELC): ( 0.65536916      2.0000000     ) :: electrostatics
WritePostFile: Saving results in ElmerPost format to file ./case.ep
ElmerSolver: *** Elmer Solver: ALL DONE ***
What could be wrong?

regards,
Matthias
mzenker
Posts: 1999
Joined: 07 Dec 2009, 11:49
Location: Germany

Re: Calculation of Capacitance in 3D plate capacitor model

Post by mzenker »

Hi Matthias,

I have never used the capacitance matrix myself, but from the documentation (models manual, chapter "electostatics") it seems to me that you need to define only one capacitance body, the other one being grounded.

HTH,

Matthias
RaJa
Posts: 77
Joined: 22 Oct 2014, 09:48
Antispam: Yes

Re: Calculation of Capacitance in 3D plate capacitor model

Post by RaJa »

Matthias, have you solved your problem? I'd like to do similar simulations, but with a more complex structure. So it would be nice to set it up correctly.

Thanks,
Rainer
Wil
Posts: 72
Joined: 10 Jan 2014, 13:26
Antispam: Yes
Location: Austria

Re: Calculation of Capacitance in 3D plate capacitor model

Post by Wil »

Matt8709 wrote:Hi Matthias,

thank you very much for your answer!
With the right scaling, the result is 1.65pF thats in the right range but it is still not what I expect.

In theory C=epsilon0*epsilonR*A/d
-> C=8.854e-12*1*10e-3*10e-3/1e-3 = 8.854e-13.

The result in Elmer is nearly the double.. :?:

Code: Select all

StatElecSolve:  Solve (s)             :   1.8000000000000016E-002
StatElecSolve: Capacitance matrix computation performed (i,j,C_ij)
StatElecSolve:   1  1    1.64744E-12
StatElecSolve: Capacitance matrix was saved to file capatest.dat
ComputeChange: SS (ITER=1) (NRM,RELC): ( 0.65536916      2.0000000     ) :: electrostatics
WritePostFile: Saving results in ElmerPost format to file ./case.ep
ElmerSolver: *** Elmer Solver: ALL DONE ***
What could be wrong?

regards,
Matthias
I think the FEM results are right.. you get a larger value than in theory because you also simulate a larger capacitor. You also have to consider the outer faces of your 3D model. The analytics is only valid for the inner part of your model ... only in the gap! You should change your model to simulate only the inner part or maybe introduce a new domain in-between the two plates.
You should also consider a finer mesh on the surface of the two plates.
BR,
Wil
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