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capacitance of a parallel plate capacitor

Posted Nov 29, 2009, 5:30 p.m. EST Version 4.0, Version 4.1, Version 4.2 29 Replies

Svetlana Avramov-Zamurovic
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These are the steps for my capacitor simulation
1. set two solid blocks (dimensions (25x1x20) ) 1 distance away from each other.
2. set a solid box (65x43x60) to surround the plates of the capacitor.
3. subtracted plates from the surrounding box.
4. set the plates to be copper and surrounding box to be air.
5. set one plate to be port 1 ( defined as input) ; set the other plate to be port 2; used energy method
6. set the surrounding box to be ground
7.meshed and got the solution
I calculated theoretically what the capacitance for a parallel plate capacitor should be 0.004425 pF
My COMSOL result is 30% off ( 0.005736977 pF). I do not believe this is realistic.
Can somebody help me find an error in my process?
Svetlana
29 Replies Last Post Mar 7, 2014, 1:19 p.m. EST
Luca Ferrario
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Posted: 1 decade ago Nov 30, 2009, 5:04 a.m. EST
Hello Svetlana
I think that you should try to use forced voltage method, you should set 1 plate like input(check the voice Use port as input) with any kind of voltage and the second plate with another port number without input.
I used this method to validate sperimental values and i found the same solutions.

Bye
Luca
Hello Svetlana I think that you should try to use forced voltage method, you should set 1 plate like input(check the voice Use port as input) with any kind of voltage and the second plate with another port number without input. I used this method to validate sperimental values and i found the same solutions. Bye Luca
Maarten Cauwe
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Posted: 1 decade ago Dec 1, 2009, 8:33 a.m. EST
Just set the second plate as ground in stead of port 2 and leave the box floating.

This kind of parallel-plate capacitor can be done much easier in 2D.

Maarten.
Just set the second plate as ground in stead of port 2 and leave the box floating. This kind of parallel-plate capacitor can be done much easier in 2D. Maarten.
Svetlana Avramov-Zamurovic
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Posted: 1 decade ago Dec 1, 2009, 7:25 p.m. EST
Thank you Luca
I did it. The differences between the theory and simualtion are to large
Svetlana
Thank you Luca I did it. The differences between the theory and simualtion are to large Svetlana
Svetlana Avramov-Zamurovic
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Posted: 1 decade ago Dec 1, 2009, 7:29 p.m. EST
Thank you Maarten
but I need 3d model since I plan to design a capacitive sensor to measure a distance from a platform. I also need grounded space since the sensor will be enclosed. This simple problem is just a common sense check.
Svetlana
Thank you Maarten but I need 3d model since I plan to design a capacitive sensor to measure a distance from a platform. I also need grounded space since the sensor will be enclosed. This simple problem is just a common sense check. Svetlana
Sunil Patil
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Posted: 1 decade ago Feb 15, 2011, 1:48 a.m. EST

Thank you Maarten
but I need 3d model since I plan to design a capacitive sensor to measure a distance from a platform. I also need grounded space since the sensor will be enclosed. This simple problem is just a common sense check.
Svetlana


Can you please explain how to compute capacitance in above mentioned problem?
I can get value of C11_emes from sub domain integration in F-m^3 for subdomain 1 and same value for subdomain 2. If i compute same for subdomain 1 and 2 it simply adds up. Is the parallel plate capacitor is C11 or C12?

pls explain.

[QUOTE] Thank you Maarten but I need 3d model since I plan to design a capacitive sensor to measure a distance from a platform. I also need grounded space since the sensor will be enclosed. This simple problem is just a common sense check. Svetlana [/QUOTE] Can you please explain how to compute capacitance in above mentioned problem? I can get value of C11_emes from sub domain integration in F-m^3 for subdomain 1 and same value for subdomain 2. If i compute same for subdomain 1 and 2 it simply adds up. Is the parallel plate capacitor is C11 or C12? pls explain.
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Feb 15, 2011, 2:31 a.m. EST
Hi

have you checked the capacitor models in the model exchange ?

--
Good luck
Ivar
Hi have you checked the capacitor models in the model exchange ? -- Good luck Ivar
Sunil Patil
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Posted: 1 decade ago Feb 15, 2011, 4:44 a.m. EST

Hi

have you checked the capacitor models in the model exchange ?

--
Good luck
Ivar


Thank you Ivar,
I have checked, www.comsol.eu/support/knowledgebase/951/.
Even that has C31 -negative.
I am repeating my problem,

I am computing capacitance between the two metallic plates (1m X 1m X 1m) with surrounding box grounded. One of the plate boundaries are set as port 1 with forced voltage input=10 V and other as port 2. Once solved, I go to Postprocessing>Point Evaluation to determine C11 and C12. I get,
Value: 6.476987e-11 [F], Expression: C11_emes, Point: 17
Value: -1.775192e-11 [F], Expression: C21_emes, Point: 17.

Could you please tell me what might be the problem?


Thank you very much.
sunil


[QUOTE] Hi have you checked the capacitor models in the model exchange ? -- Good luck Ivar [/QUOTE] Thank you Ivar, I have checked, http://www.comsol.eu/support/knowledgebase/951/. Even that has C31 -negative. I am repeating my problem, I am computing capacitance between the two metallic plates (1m X 1m X 1m) with surrounding box grounded. One of the plate boundaries are set as port 1 with forced voltage input=10 V and other as port 2. Once solved, I go to Postprocessing>Point Evaluation to determine C11 and C12. I get, Value: 6.476987e-11 [F], Expression: C11_emes, Point: 17 Value: -1.775192e-11 [F], Expression: C21_emes, Point: 17. Could you please tell me what might be the problem? Thank you very much. sunil
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Feb 15, 2011, 9:44 a.m. EST
Hi

is'nt the port capacitance measurement done between GND and the port ?

I would try GND one plate and use port1 (only) on the other plate

--
Good luck
Ivar
Hi is'nt the port capacitance measurement done between GND and the port ? I would try GND one plate and use port1 (only) on the other plate -- Good luck Ivar
Lothar Schultheis
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Posted: 1 decade ago Feb 15, 2011, 11:16 a.m. EST
Hi
there is an issue of conventions within capacitance matrix notation used in FEM and in electronics. You should google "non-negative off diagonal capacitive matrix elements"

I copied this from a forum in 2001
------
" The short explanation is that in the SPICE capacitance matrix, all
elements are always positive. The diagonal elements are the
capacitance to ground and the off diagonals represent the coupling
between conductors.

The other matrix is the Maxwell capacitance matrix. The definition of
the Maxwell C matrix elements is different from the SPICE C matrix. In
the Maxwell C matrix, all off diagonal elements are always negative
and the diagonal elements represent the "loaded capacitance" or "total
capacitance". The off diagonal elements of each matrix are numerically
equal. If you take one row of the Maxwell C matrix and add up all the
elements, it will be equal to the diagonal element in the
corresponding row of the SPICE C matrix.

The quick way to tell if you've got a C matrix from a field solver
result is to look at the off diagonal elements. If they are negative,
it came from a field solver. I have tried in vane, to get field solver
companies to label their capacitance matrices as Maxwell Capacitance
matrices, to help avoid the confusion and emphasize the fact that
there really are two different matrices, each with a slightly
different definition. So far, only Ansoft has done this."


Hope this helps

Lothar

------
Hi there is an issue of conventions within capacitance matrix notation used in FEM and in electronics. You should google "non-negative off diagonal capacitive matrix elements" I copied this from a forum in 2001 ------ " The short explanation is that in the SPICE capacitance matrix, all elements are always positive. The diagonal elements are the capacitance to ground and the off diagonals represent the coupling between conductors. The other matrix is the Maxwell capacitance matrix. The definition of the Maxwell C matrix elements is different from the SPICE C matrix. In the Maxwell C matrix, all off diagonal elements are always negative and the diagonal elements represent the "loaded capacitance" or "total capacitance". The off diagonal elements of each matrix are numerically equal. If you take one row of the Maxwell C matrix and add up all the elements, it will be equal to the diagonal element in the corresponding row of the SPICE C matrix. The quick way to tell if you've got a C matrix from a field solver result is to look at the off diagonal elements. If they are negative, it came from a field solver. I have tried in vane, to get field solver companies to label their capacitance matrices as Maxwell Capacitance matrices, to help avoid the confusion and emphasize the fact that there really are two different matrices, each with a slightly different definition. So far, only Ansoft has done this." Hope this helps Lothar ------
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Feb 16, 2011, 1:20 a.m. EST
Hi

interesting, is it worth to ask support to clarify this in the COMSOL doc too ?

--
Good luck
Ivar
Hi interesting, is it worth to ask support to clarify this in the COMSOL doc too ? -- Good luck Ivar
Sunil Patil
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Posted: 1 decade ago Feb 16, 2011, 5:40 a.m. EST
Thank you for your response. Well I am not the core Mathematician or physicist. For time being, may I know which numbers here make sense for parallel plate capacitor? I mean C11 or C12? if not then how to get it?
Thank you for your response. Well I am not the core Mathematician or physicist. For time being, may I know which numbers here make sense for parallel plate capacitor? I mean C11 or C12? if not then how to get it?
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Feb 16, 2011, 6:18 a.m. EST
Hi

knowing that

C[F] = epsilon[F/m]*epsilonr[1]*A[m^2]/d[m]

and if I understand you well you have an plate area of A=1[m^2] and a plate distance of d=1[m], and knowing that epsilon=8.85E-12[F/m] and epsilonr=1 for air you should select the one getting closest. I assume the C11 is the one

But again, check carefully the COMSOL doc if the port value is not evaluated between GND and the port entry (and not between two ports)

Some "fringe field" effects could give some differences, a few % I would expect


--
Good luck
Ivar
Hi knowing that C[F] = epsilon[F/m]*epsilonr[1]*A[m^2]/d[m] and if I understand you well you have an plate area of A=1[m^2] and a plate distance of d=1[m], and knowing that epsilon=8.85E-12[F/m] and epsilonr=1 for air you should select the one getting closest. I assume the C11 is the one But again, check carefully the COMSOL doc if the port value is not evaluated between GND and the port entry (and not between two ports) Some "fringe field" effects could give some differences, a few % I would expect -- Good luck Ivar
Sunil Patil
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Posted: 1 decade ago Feb 16, 2011, 6:24 a.m. EST
Thank you Ivar,
I am getting C11 with one plate along with outer box grounded and another as port 1.
Value: 6.476987e-11 [F], Expression: C11_emes, Point: 17

whereas, if outer box kept floating, then C11 comes,

Value: 4.878925e-11 [F], Expression: C11_emes, Point: 17

Sunil
Thank you Ivar, I am getting C11 with one plate along with outer box grounded and another as port 1. Value: 6.476987e-11 [F], Expression: C11_emes, Point: 17 whereas, if outer box kept floating, then C11 comes, Value: 4.878925e-11 [F], Expression: C11_emes, Point: 17 Sunil
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Feb 16, 2011, 10:01 a.m. EST
Hi

In 4.1 if I make a single centered 1m^3 box, surrounded by a 10m radial sphere, all epsilonr=1, gnd on one side of the box, of 1m^2 area, a port 1 (1V) on the other. I get es.C11 4.45E-11[F] with a normal mesh, and stationary solver

However, I have also tried to make the electrodes rather thick (not just an interior boundary, then I get easily 30% fringe effects, so the original thread (apart that the units in um where not mentioned) results differences are for me realistic.

If I ground my sphere external surface (instad of "0" charge) I get 6.56E11 I'm not astonished the interacting area is higher even if the distance is larger

By increasing the mesh density to "finer" I get to 5.6E-11F for external area grounded, and it's hardly changing with the external area radius being changed between 2.5 to 10m. While with the external shell floating and "finer" mesh I get 3.76E-11[F],

Obviously the mesh density is too poor at "normal" values. Furthermore, I have a square electrode, with corners = singularities in ACDC.

==========

If I try a cylinder of radius sqrt(1/pi) and length 1m hence the same area of 1[m^2] and inter-electrode distance of 1[m] I get only 3e-11F with the 10m spherical shell floating, and 4.6E-11F with the shell at GND for finer mesh AS well for the normal mesh (to within 2%)

adding an external infinite shell does neither not change any calculated values

CONCLUSIONS for me:
- Always check the mesh dependence (nothing new)
- Always consider "smoothing" sharp corner (singularities) in ACDC (neither not new)
- some 30-50% changes on capacitive values are easily obtained due to fringe effects

In fact I see many similarities with the Maxwell stress tensor calculations for solving forces in ACDC


--
Good luck
Ivar
Hi In 4.1 if I make a single centered 1m^3 box, surrounded by a 10m radial sphere, all epsilonr=1, gnd on one side of the box, of 1m^2 area, a port 1 (1V) on the other. I get es.C11 4.45E-11[F] with a normal mesh, and stationary solver However, I have also tried to make the electrodes rather thick (not just an interior boundary, then I get easily 30% fringe effects, so the original thread (apart that the units in um where not mentioned) results differences are for me realistic. If I ground my sphere external surface (instad of "0" charge) I get 6.56E11 I'm not astonished the interacting area is higher even if the distance is larger By increasing the mesh density to "finer" I get to 5.6E-11F for external area grounded, and it's hardly changing with the external area radius being changed between 2.5 to 10m. While with the external shell floating and "finer" mesh I get 3.76E-11[F], Obviously the mesh density is too poor at "normal" values. Furthermore, I have a square electrode, with corners = singularities in ACDC. ========== If I try a cylinder of radius sqrt(1/pi) and length 1m hence the same area of 1[m^2] and inter-electrode distance of 1[m] I get only 3e-11F with the 10m spherical shell floating, and 4.6E-11F with the shell at GND for finer mesh AS well for the normal mesh (to within 2%) adding an external infinite shell does neither not change any calculated values CONCLUSIONS for me: - Always check the mesh dependence (nothing new) - Always consider "smoothing" sharp corner (singularities) in ACDC (neither not new) - some 30-50% changes on capacitive values are easily obtained due to fringe effects In fact I see many similarities with the Maxwell stress tensor calculations for solving forces in ACDC -- Good luck Ivar
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Feb 16, 2011, 10:02 a.m. EST
Sorry, I forgot to attach the other file, and once posted one seem to not to be able to "reattach a file ?
--
Have fun COMSOLING
Ivar
Sorry, I forgot to attach the other file, and once posted one seem to not to be able to "reattach a file ? -- Have fun COMSOLING Ivar
Lothar Schultheis
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Posted: 1 decade ago Feb 16, 2011, 1:08 p.m. EST
Hi

I think if the capacitor consists of port 1 and 2 with surrounding grounded then:
C11 measures (but is not equal to!) capacitance of port 1 to gnd
C22 measures (but is not equal to!) capacitance of port 2 to gnd
-C12 (=-C21) is the capacitance of port 1 to port 2

Good luck

Lothar
Hi I think if the capacitor consists of port 1 and 2 with surrounding grounded then: C11 measures (but is not equal to!) capacitance of port 1 to gnd C22 measures (but is not equal to!) capacitance of port 2 to gnd -C12 (=-C21) is the capacitance of port 1 to port 2 Good luck Lothar
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Feb 17, 2011, 5:57 a.m. EST
Hi

well in V4 there is only C11 or C22 no cross values, and anyhow if I create two ports I get the double of the capacity than for 1 port, sounds logic no ?

--
Good luck
Ivar
Hi well in V4 there is only C11 or C22 no cross values, and anyhow if I create two ports I get the double of the capacity than for 1 port, sounds logic no ? -- Good luck Ivar
ABDUL
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Posted: 1 decade ago Jun 8, 2011, 1:26 p.m. EDT
hello
please i want to draw the geometry of parallel plate capacitor.i am new user of comsol please guide me
hello please i want to draw the geometry of parallel plate capacitor.i am new user of comsol please guide me
ABDUL
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Posted: 1 decade ago Jun 11, 2011, 3:01 a.m. EDT

hello
please i want to draw the geometry of parallel plate capacitor.i am new user of comsol please guide me


please help me
[QUOTE] hello please i want to draw the geometry of parallel plate capacitor.i am new user of comsol please guide me [/QUOTE] please help me
Neethu Kori
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Posted: 1 decade ago Feb 16, 2012, 12:10 a.m. EST
HI.

Am the new user of COMSOL pls help me out in designing the 3d Model of Parallel plate capacitor.
HI. Am the new user of COMSOL pls help me out in designing the 3d Model of Parallel plate capacitor.
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Feb 16, 2012, 2:24 a.m. EST
Hi

check the model library and the main web site videos / demos /tutorials that should give you a good start ;)

--
Good luck
Ivar
Hi check the model library and the main web site videos / demos /tutorials that should give you a good start ;) -- Good luck Ivar
Hesham Omran
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Posted: 1 decade ago Aug 15, 2012, 7:26 a.m. EDT
Hi

I am using 4.2
I have two electrodes on top of ground plane
How to measure the cross cap between the electrodes, and the cap of each to ground?
Hi I am using 4.2 I have two electrodes on top of ground plane How to measure the cross cap between the electrodes, and the cap of each to ground?
Manuel Aeschbacher
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Posted: 1 decade ago Oct 18, 2012, 6:14 a.m. EDT
If anyone is interested in that: I have a parallel plate capacitor connected with two terminals one to 10V the other to 0V. Further I have grounded Walls. I this case:
(-)C12 = Capacitance between Port 1 and Port 2
C22 = Capacitance between Port 1 and Port 2 but the Ground is treaten as floating, so if you insert a grounded plate between both plates the capacitance will increase.
Thats not what is mostly wanted. The capacitance should only be measured between Port 1 and 2.
If anyone is interested in that: I have a parallel plate capacitor connected with two terminals one to 10V the other to 0V. Further I have grounded Walls. I this case: (-)C12 = Capacitance between Port 1 and Port 2 C22 = Capacitance between Port 1 and Port 2 but the Ground is treaten as floating, so if you insert a grounded plate between both plates the capacitance will increase. Thats not what is mostly wanted. The capacitance should only be measured between Port 1 and 2.
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Oct 18, 2012, 9:22 a.m. EDT
Hi

I believe that the capacitance is defined between GND and one port/terminal, not between two terminals. And in 4.3a the capacitance variable does not show up if you have more than one terminal. Check your doc

--
Good luck
Ivar
Hi I believe that the capacitance is defined between GND and one port/terminal, not between two terminals. And in 4.3a the capacitance variable does not show up if you have more than one terminal. Check your doc -- Good luck Ivar
Abid Iqbal
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Posted: 1 decade ago Nov 5, 2012, 11:19 p.m. EST
Dear Ivar
I want to apply the ac voltage on two parallel plate capacitor, how can i apply on it? I have tried the electrostatic module with wave function and applied it to the capacitor plate and with negative side on the other plate. i dont know whether it is correct or not. the second thing is that i want to change the electric field arrow with its magnitude but it remain same.
Please help me in this regards.
Abid
Dear Ivar I want to apply the ac voltage on two parallel plate capacitor, how can i apply on it? I have tried the electrostatic module with wave function and applied it to the capacitor plate and with negative side on the other plate. i dont know whether it is correct or not. the second thing is that i want to change the electric field arrow with its magnitude but it remain same. Please help me in this regards. Abid
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Nov 6, 2012, 12:44 a.m. EST
Hi

the easiest is t apply GND on one and set an amplitude on a terminal on the other plate, then solve with a frequency domain solver and add the AC frequency(or full frequency range) in the solver node

--
Good luck
Ivar
Hi the easiest is t apply GND on one and set an amplitude on a terminal on the other plate, then solve with a frequency domain solver and add the AC frequency(or full frequency range) in the solver node -- Good luck Ivar
Jeffrey Fong
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Posted: 1 decade ago Mar 24, 2013, 2:35 a.m. EDT

Hi

I believe that the capacitance is defined between GND and one port/terminal, not between two terminals. And in 4.3a the capacitance variable does not show up if you have more than one terminal. Check your doc

--
Good luck
Ivar


What if you wanted to model alternating plates with negative and positive voltages across from two different sets of alternating grounds?

ie.

GND1 GND2 GND1 GND2
--------- --------- --------- ---------

--------- --------- --------- ---------
+100V -100V +100V -100V
[QUOTE] Hi I believe that the capacitance is defined between GND and one port/terminal, not between two terminals. And in 4.3a the capacitance variable does not show up if you have more than one terminal. Check your doc -- Good luck Ivar [/QUOTE] What if you wanted to model alternating plates with negative and positive voltages across from two different sets of alternating grounds? ie. GND1 GND2 GND1 GND2 --------- --------- --------- --------- --------- --------- --------- --------- +100V -100V +100V -100V
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)
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Posted: 1 decade ago Mar 24, 2013, 2:47 p.m. EDT
Hi

here you have capcitive couplings between the different "gnd" and the different electrodes. As the capacity is indepenent of absolute voltage you can model two by two, or use the full equations as C is linking dI/dt and U and when you solve you get both U and I in EC

--
Good luck
Ivar
Hi here you have capcitive couplings between the different "gnd" and the different electrodes. As the capacity is indepenent of absolute voltage you can model two by two, or use the full equations as C is linking dI/dt and U and when you solve you get both U and I in EC -- Good luck Ivar
Primož Cuznar
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Posted: 1 decade ago Mar 7, 2014, 1:19 p.m. EST
Hi!
I am analysing capacitance over few layers and I wonder why those spikes appear in attached file? Is this some kind of numerical/computing problem? I think it should be flatline ... problem could be when voltage passes 0V point, yes?

applied voltage: 0.5*sin(2*pi*400*t [1/s])
time: range(10^(-6), 2.5*10^(-4), 0.125)

Could anyone answer? Thanks
Hi! I am analysing capacitance over few layers and I wonder why those spikes appear in attached file? Is this some kind of numerical/computing problem? I think it should be flatline ... problem could be when voltage passes 0V point, yes? applied voltage: 0.5*sin(2*pi*400*t [1/s]) time: range(10^(-6), 2.5*10^(-4), 0.125) Could anyone answer? Thanks

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