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capacitance of a parallel plate capacitor
Posted 2009年11月29日 GMT-5 17:30 Version 4.0, Version 4.1, Version 4.2 29 Replies
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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
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 2014年3月7日 GMT-5 13:19
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Posted:
1 decade ago
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
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
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Posted:
1 decade ago
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.
This kind of parallel-plate capacitor can be done much easier in 2D.
Maarten.
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Posted:
1 decade ago
Thank you Luca
I did it. The differences between the theory and simualtion are to large
Svetlana
I did it. The differences between the theory and simualtion are to large
Svetlana
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Posted:
1 decade ago
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
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
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Posted:
1 decade ago
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.
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Posted:
1 decade ago
Hi
have you checked the capacitor models in the model exchange ?
--
Good luck
Ivar
have you checked the capacitor models in the model exchange ?
--
Good luck
Ivar
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Posted:
1 decade ago
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
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Posted:
1 decade ago
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
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
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Posted:
1 decade ago
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
------
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
------
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Posted:
1 decade ago
Hi
interesting, is it worth to ask support to clarify this in the COMSOL doc too ?
--
Good luck
Ivar
interesting, is it worth to ask support to clarify this in the COMSOL doc too ?
--
Good luck
Ivar
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Posted:
1 decade ago
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?
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Posted:
1 decade ago
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
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
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Posted:
1 decade ago
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
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
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Posted:
1 decade ago
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
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
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Posted:
1 decade ago
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
--
Have fun COMSOLING
Ivar
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Posted:
1 decade ago
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
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
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Posted:
1 decade ago
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
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
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Posted:
1 decade ago
hello
please i want to draw the geometry of parallel plate capacitor.i am new user of comsol please guide me
please i want to draw the geometry of parallel plate capacitor.i am new user of comsol please guide me
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Posted:
1 decade ago
hello
please i want to draw the geometry of parallel plate capacitor.i am new user of comsol please guide me
please help me
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Posted:
1 decade ago
HI.
Am the new user of COMSOL pls help me out in designing the 3d Model of Parallel plate capacitor.
Am the new user of COMSOL pls help me out in designing the 3d Model of Parallel plate capacitor.
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Posted:
1 decade ago
Hi
check the model library and the main web site videos / demos /tutorials that should give you a good start ;)
--
Good luck
Ivar
check the model library and the main web site videos / demos /tutorials that should give you a good start ;)
--
Good luck
Ivar
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Posted:
1 decade ago
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?
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?
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Posted:
1 decade ago
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.
(-)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.
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Posted:
1 decade ago
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
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
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Posted:
1 decade ago
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
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
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Posted:
1 decade ago
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
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
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Posted:
1 decade ago
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
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Posted:
1 decade ago
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
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
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Posted:
1 decade ago
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
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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