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Varying capacitance due to thickness reduction

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Hello,

I am simulating a capacitor with a compliant dielectric and compliant electrodes in COMSOL 3.5a, using the Structural mechanics and electrostatics modes. I am using 2D axial symmetry
I wanted to know whether it is possible to plot the change in capacitance which occurs due to structural deformation of the capacitor, e.g. increase in surface area and consequent reduction in thickness.

Any suggestions would be helpful.

Thank you,
Aseem

12 Replies Last Post Apr 20, 2012, 12:02 p.m. EDT
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago Apr 19, 2011, 8:32 a.m. EDT
Hi

check the lumped port/terminal entries, and check the doc, there is an example I beleive in the Model library

--
Good luck
Ivar
Hi check the lumped port/terminal entries, and check the doc, there is an example I beleive in the Model library -- Good luck Ivar

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Posted: 1 decade ago Apr 19, 2011, 8:46 a.m. EDT
Hi Ivar,

C11_emes variable plots the capacitance only when the voltage is being applied.

I was wondering if I could also plot capacitance which occurs because of structural deformation as well.

Because, capacitance can also be calculated as C = (epsilon)*(Area_dielectric / Thickness_dielectric).

Thanks
-Aseem
Hi Ivar, C11_emes variable plots the capacitance only when the voltage is being applied. I was wondering if I could also plot capacitance which occurs because of structural deformation as well. Because, capacitance can also be calculated as C = (epsilon)*(Area_dielectric / Thickness_dielectric). Thanks -Aseem

Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago Apr 19, 2011, 11:00 a.m. EDT
Hi

try it out you have the integration operator there, you can also calculate via the energy

--
Good luck
Ivar
Hi try it out you have the integration operator there, you can also calculate via the energy -- Good luck Ivar

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Posted: 1 decade ago Apr 20, 2011, 9:23 a.m. EDT
Hi,

No. The energy method does not work either.

Is it possible to track the change in distance between two points or nodes in COMSOL as the geometry gets deformed? Then I might be able to use the above mentioned formula and calculate change in capacitance as a function of the thickness.

Any ideas?

Thanks
Aseem
Hi, No. The energy method does not work either. Is it possible to track the change in distance between two points or nodes in COMSOL as the geometry gets deformed? Then I might be able to use the above mentioned formula and calculate change in capacitance as a function of the thickness. Any ideas? Thanks Aseem

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Posted: 1 decade ago Apr 20, 2011, 11:14 a.m. EDT
hi

i think this can be done with parametric sweep in 4.0 and 4.0a but i dont know weather the provision is available in 3.5a. you can declare any quantity as a parameter and under study you can mention the range of values this parameter can take. this variation can be discrete or continuous. if it is discrete u should have those values in a text file and you should load them. to view results you should define boundary probe or domain probe depending on weather you want results on a boundary or in a domain.

regards
deepak
hi i think this can be done with parametric sweep in 4.0 and 4.0a but i dont know weather the provision is available in 3.5a. you can declare any quantity as a parameter and under study you can mention the range of values this parameter can take. this variation can be discrete or continuous. if it is discrete u should have those values in a text file and you should load them. to view results you should define boundary probe or domain probe depending on weather you want results on a boundary or in a domain. regards deepak

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Posted: 1 decade ago Apr 20, 2011, 1:36 p.m. EDT
Hey,

I too have the same issue of deriving the varying capacitance in capacitive pressure sensor. Thing is i am not sure as to how to enter the formulae. Where can i get the syntax of such expressions.please help.if i get that i can work out something.

Thanks a lot
Hey, I too have the same issue of deriving the varying capacitance in capacitive pressure sensor. Thing is i am not sure as to how to enter the formulae. Where can i get the syntax of such expressions.please help.if i get that i can work out something. Thanks a lot

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Posted: 1 decade ago Apr 20, 2011, 6:01 p.m. EDT
I am working on the similar model. The purpose is obtaining the capacitance using an interface (thanks to live link to matlab). My problem is from matlab, with the deformation of the dielectric, I can easily access using
mpheval(model,’w’) %for gradient of deformation in zZ direction for example
But with the capacitance, let say es.C11 the mpheval(model,’es.C11’) doesn’t work.
Is there any other way to obtain this value?
Any hint or discuss will be very useful for me. Thank you so much

LOAN
I am working on the similar model. The purpose is obtaining the capacitance using an interface (thanks to live link to matlab). My problem is from matlab, with the deformation of the dielectric, I can easily access using mpheval(model,’w’) %for gradient of deformation in zZ direction for example But with the capacitance, let say es.C11 the mpheval(model,’es.C11’) doesn’t work. Is there any other way to obtain this value? Any hint or discuss will be very useful for me. Thank you so much LOAN

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Posted: 1 decade ago Apr 21, 2011, 4:29 a.m. EDT
Hello RV Coll,

Try by applying a small potential difference across the electrodes and then plotting the C11_emes component.

Worked for me.
I hope this helps.
Hello RV Coll, Try by applying a small potential difference across the electrodes and then plotting the C11_emes component. Worked for me. I hope this helps.

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Posted: 1 decade ago Apr 27, 2011, 12:17 p.m. EDT
Hello everyone,

My problem is similar to RV Coll's. However, what i'm looking for is deriving capacitance by the variation in the gap of the dielectric b/w the plates.
I'm applying pressure on the top plate>plate deforms by displacing into the gap>gap spacing reduces>capacitance changes because of the formula on paper

C=epsilon*A/g

However, to integrate capacitance with the mechanics part i'm facing difficulties.

I'm attaching my model. In the 'variables' field under 'Definitions' is the formula

epsilon0/(2[um]+w)

Now, 2[um] is the gap between the plates and epsilon0 is defined in 'parameters'. What i'm not sure is the 'w'. w must be the deflection of the top plate. I do not know if it is being derived from the results 'solid.disp'. Nor am i getting proper results when i change the gap (like 10[um] instead of 2[um])

If some one could help me figure that out....i shall,forever, be grateful.

Cheers!

Abhi
Hello everyone, My problem is similar to RV Coll's. However, what i'm looking for is deriving capacitance by the variation in the gap of the dielectric b/w the plates. I'm applying pressure on the top plate>plate deforms by displacing into the gap>gap spacing reduces>capacitance changes because of the formula on paper C=epsilon*A/g However, to integrate capacitance with the mechanics part i'm facing difficulties. I'm attaching my model. In the 'variables' field under 'Definitions' is the formula epsilon0/(2[um]+w) Now, 2[um] is the gap between the plates and epsilon0 is defined in 'parameters'. What i'm not sure is the 'w'. w must be the deflection of the top plate. I do not know if it is being derived from the results 'solid.disp'. Nor am i getting proper results when i change the gap (like 10[um] instead of 2[um]) If some one could help me figure that out....i shall,forever, be grateful. Cheers! Abhi


Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago Apr 27, 2011, 3:50 p.m. EDT
Hi

a few comments:

In V4 there are many physical constants aready defined, epsilon0 among others, but you should not forget to add the suffix "_const" to the name, this tag tells COMSOL to use its internal values, hence use "epsilon0_const"

u,v,w are the 3D dependent variables solved for in "structural", so indeed w is the displacement along "z".

solid.disp = sqrt(u^2+v^2+w^2) the total displacement vector norm (check it in the equations view, turn on via preferences)

So for me the formula is correct, and too get to C = epsilonr*epsilon0*Area/Distance = 1.854E-15 F from my estimation for a 1.5[um] separation epsilonr=1and 10[um] radius disc capacitor with "0" deformation or pressure applied.

So what is so wrong ?
Do not forget that the displacements/deformations are scaled to be "visible" as the membrane is only deflecting at most 42 nm for 5 bars pressure difference

--
Good luck
Ivar
Hi a few comments: In V4 there are many physical constants aready defined, epsilon0 among others, but you should not forget to add the suffix "_const" to the name, this tag tells COMSOL to use its internal values, hence use "epsilon0_const" u,v,w are the 3D dependent variables solved for in "structural", so indeed w is the displacement along "z". solid.disp = sqrt(u^2+v^2+w^2) the total displacement vector norm (check it in the equations view, turn on via preferences) So for me the formula is correct, and too get to C = epsilonr*epsilon0*Area/Distance = 1.854E-15 F from my estimation for a 1.5[um] separation epsilonr=1and 10[um] radius disc capacitor with "0" deformation or pressure applied. So what is so wrong ? Do not forget that the displacements/deformations are scaled to be "visible" as the membrane is only deflecting at most 42 nm for 5 bars pressure difference -- Good luck Ivar

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Posted: 1 decade ago Apr 20, 2012, 7:41 a.m. EDT
in this model i want to plot vlotage vs pressure. is it possible sir.
in this model i want to plot vlotage vs pressure. is it possible sir.

Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago Apr 20, 2012, 12:02 p.m. EDT
Hi

V and p are they dependent variables or one defined with a parameter ?

many cases are possible, if you define V as a parameter (or a parametric or "continuation" solver sequence) and caclulate the resulting p than you can plot p versus v in the Derived values section which creates a table and plot out the table in a line graph

--
Good luck
Ivar
Hi V and p are they dependent variables or one defined with a parameter ? many cases are possible, if you define V as a parameter (or a parametric or "continuation" solver sequence) and caclulate the resulting p than you can plot p versus v in the Derived values section which creates a table and plot out the table in a line graph -- Good luck Ivar

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