capacitance at infinity

Hello,

So i was trying to calculate the capacitance between two parallel plates as an exercise. I noticed that it gave me an answer in negative farads. One plate was at 1V, and the other was at 0V (it didn't want to simulate unless I had sources assigned). Both plates are PEC.

Also, how far should my electric boundaries be from these plates?

Thanks

EMC Studio Static3D solver gives 0.441 pF capacitance for such model.

So what on earth could i be doing wrong with the simulation set up.

Welcome to the wonderful world of CST.

I've been pulling my hair out trying to figure out what's what with CST EMStudio for quite some time now...to no avail.

In any case, not only does your simple problem give a negative value for capacitance, but I find that the tet mesh gives a much different result than the hex mesh. (The tet mesh result is close to what e_m_c reported).

I've seen these same kind of disparate results with magnetostatic problems as well.

Moreover CST EMS and PS seem to give lousy field plots as well, IMO (at least with default mesh and "plot quality" settings).

I now have very little faith in using CST EMS...so I'm teaching myself to use Ansoft Maxwell...I'm thinking maybe I can create the problem geometry using CST, and then export and solve the problem using Ansoft Maxwell (And btw this software is not without its "issues" either, IMO).

Ok, I've been looking into this some more, and I may have to eat some of my words here.

When I was putzing around with this problem the other day, I was also in the middle of trying to simulate two coupled coils on a double-U ferrite core with an air gap...I think I got the various sets of result matricies in front of me mixed up.

Anyway, I should say that CST, in keeping with tradition, doesn't do a very good job of explaining things, IMO, and when I first looked at their very brief explanation of their "capacitance matrix", it seemed to imply that I should expect positive values. (Which is what I mistakenly thought I got in one instance).

I think what they are doing with their capacitance matrix (with two conductors, 1 and 2, at potentials 1 and 2, referenced to the boundary) is the following:

Q1 = C10*V1 + C12*(V1-V2)
Q2 = C20*V2 + C12*(V2-V1)

Which in matrix form I think is:

|Q1| |C10 + C12, -C12 | |V1|
|Q2| | -C12, C20 + C12| |V2|

So if this is what they're doing, then I suppose the negative sign is understandable and C12 is the capacitance between the conductors, C10 is the capacitance between the first conductor and the boundary and C20 is the capacitance between
the second conductor and the boundary.

I ran this same problem in Maxwell and it gives C12 = 0.438 pf, so it is in disagreement with CST.

Later if I get some time I'm going to try to run some problems for which there's an exact analytical solution such as an isolated sphere and see what result CST gives me.

Thank you for keeping us also informed about your progress! I've noted that Maxwell and EMC Studio results are matched well (0.438 pF, 0.441 pF). Probaby in CST the model is defined in different way?

P.S. In EMC Studio I've used potential 0 for one of the plates as I remember. The same was present in the intial attached model.

Well CST EMS did pretty good with the isolated sphere capacitance problem. A one cm diameter sphere, infinitely far away from anything, has a calculated capacitance of 0.556 pF.

Using a large air box around the sphere (I think I added 15 cm space all around), using adaptive tet meshing with an "electric" boundary, I got a result of 0.553 pF; using adaptive hex meshing, with 15 cm air space and an "open" boundary, the result was 0.5557 pF.

If I get a chance later, I'll try two spheres and see what happens.

With EMC Studio Static 3D 1 cm diameter sphere provides following capacitances for different surface mesh (there is not required to mesh volume, only surface is meshed, no bounding volume as well):

Number of Triangles = 152 -- Capacitance 0.54051 pF
Number of Triangles = 822 -- Capacitance 0.55288 pF
Number of Triangles = 3504 -- Capacitance 0.55523 pF
Number of Triangles = 14518 -- Capacitance 0.55576 pF


If you are going to do something with 2 spheres, here are some possible results to compare:
===============================================

2 1cm-diameter spheres:
Sphere 1 : potential 0 (reference structure) : center X = 0 cm
Sphere 2 : potential 1 : center X = 2 cm
face-to-face distance is 1 cm

Capacitance of Sphere 2 referenced to Sphere 1 is 0.372 pF
===============================================

2 1cm-diameter spheres:
Sphere 1 : potential 1 : center X = 0 cm
Sphere 2 : potential 2 : center X = 2 cm
face-to-face distance is 1 cm
Reference = Infinity

Capacitance matrix :

C11 = C22 = 0.446 pF
C12 = C21 = 0.149 pF
================================================

2 1cm-diameter spheres over Infinite Ground Plane:
Sphere 1 : potential 1 : center X = 0 cm : center Z = 1.5 cm
Sphere 2 : potential 2 : center X = 2 cm : center Z = 1.5 cm
face-to-face distance is 1 cm
face-to-ground distance is 1 cm
Reference = Ground Plane

Capacitance matrix :

C11 = C22 = 0.591 pF
C12 = C21 = 0.090 pF
================================================

You can also use a test case with an isolated metal cube - a cube with a side of 1 cm has a capacitance (to infinity) equal to 0.735109 pF. This is a very high acccuracy (~0.01% or so) numerical result, there is no analytical solution for the cube.

There are a plenty of test cases (geometries) for which either analytical result is known, or an approximate analytical or numerical results are known - you can use them as a sanity check for your capacitance simulations.

What would be interesting is to compare the simulation times (vs accuracy) for different software tools (though software vendors normally prohibit a direct comparison/benchmarking of the tools).

I don't like the disparate results I'm seeing with two 1 cm spheres.

But before I say anything else, I should say that I really don't understand the boundary conditions available in CST EMStudio...a situation I blame jointly on apparent bugs in the software in combination with their lousy documentation and lack of examples.

For example, in the help file, they say this:

"A boundary potential can be assigned only if the corresponding boundary condition in the "Boundaries" tab is set to "normal" or "electric".

Xmin, Ymin, Zmin, Xmax, Ymax, Zmax

Defines the boundary potential at the specific boundary. Three different settings are possible:

Default: Zero potential is assigned to the boundary.

Fixed: A defined constant potential will be assigned to the boundary.

Floating: Similar to Fixed the boundary will also have a constant potential. However its initial value is unknown and will be calculated during the simulation."

Now, I wonder what they mean by the statement "[z]ero potential is assigned to the boundary"?

Do they mean to say a potential of zero volts?

In any case, whenever I use "electric" (perfect conductor) boundary conditions, and I try to set the boundary potential to a "fixed" zero volts, using the hex mesh solver, I get an error message:

"All PEC regions are linked to source definitions. This problem is overdetermined and leads to a singular capacitance matrix."

When I use the tet mesh solver, first it says: "Fixed or floating boundary potentials have been defined, but are not available in combination with tetrahedral meshing. Using *electric* boundary conditions with zero potential."

Then it says: "No active excitation has been defined. All fields will be zero. Electrostatic Solver stops".

So, let's see, first, it said it didn't like my electric boundary conditions with a fixed potential of zero volts, so it changed things to "electric boundary conditions with zero potential"...now if that isn't the same thing I had, isn't it at least the so-called "default" condition, with it's mysterious "zero potential" whatever that means?

But then it stopped, saying that "no active excitation has been defined" (yet the spheres had assigned potentials of 1 and -1 volts).

And when I use the "default" boundary potential, I get no error message with either solver, and neither solver stops.

How is that possible? When "it" uses the "default" boundary potential with the tet mesh solver, the solver stops due to lack of "active excitation", but when I use it, it works, everything else being the same?

Apparently CST EM Studio has some bugs.

In any case, the result with "electric" boundary, "default" boundary potential and hex mesh solver is:

Capacitance Matrix:
----------------------------------------------------

potential1 potential2

potential1 5.985172e-013 F -1.367237e-013 F
potential2 -1.367241e-013 F 5.985172e-013 F

----------------------------------------------------

With the tet mesh solver, I get:

Capacitance Matrix:

----------------------------------------------------

potential1 potential2

potential1 5.750449e-013 F -1.257179e-013 F
potential2 -1.257179e-013 F 5.746637e-013 F

----------------------------------------------------

Note the difference between the two solvers for the same conditions.

Using the tet mesh with adaptive meshing, I get this:

Capacitance Matrix:

----------------------------------------------------

potential1 potential2

potential1 5.994367e-013 F -1.365508e-013 F
potential2 -1.365508e-013 F 6.001875e-013 F

----------------------------------------------------

With hex adaptive meshing I get this:


Capacitance Matrix:

----------------------------------------------------

potential1 potential2

potential1 5.946815e-013 F -1.346052e-013 F
potential2 -1.346055e-013 F 5.946815e-013 F

----------------------------------------------------


And with tet adaptive meshing I get this:


Capacitance Matrix:

----------------------------------------------------

potential1 potential2

potential1 5.994367e-013 F -1.365508e-013 F
potential2 -1.365508e-013 F 6.001875e-013 F

----------------------------------------------------

With "tangential" boundary conditions, the hex mesh solver gives me the warning that:

"All PEC regions are linked to source definitions. This problem is
overdetermined and leads to a singular capacitance matrix."

It gives this result:

Capacitance Matrix:

----------------------------------------------------

potential1 potential2

potential1 3.644430e-013 F -3.644392e-013 F
potential2 -3.644385e-013 F 3.644431e-013 F

----------------------------------------------------

Unlike the hex mesh solver, the tet mesh solver, with the same "tangential" boundary conditions, gives no warnings and gives a result:


Capacitance Matrix:

----------------------------------------------------

potential1 potential2

potential1 3.500884e-013 F -3.500884e-013 F
potential2 -3.500884e-013 F 3.500884e-013 F

----------------------------------------------------

And here's the result with the tet mesh solver using adaptive meshing:

Capacitance Matrix:

----------------------------------------------------

potential1 potential2

potential1 3.679652e-013 F -3.679650e-013 F
potential2 -3.679650e-013 F 3.679652e-013 F

----------------------------------------------------

And the hex mesh solver using adaptive meshing:


Capacitance Matrix:

----------------------------------------------------

potential1 potential2

potential1 3.633909e-013 F -3.633708e-013 F
potential2 -3.633783e-013 F 3.633908e-013 F

----------------------------------------------------

Here is the hex mesh solver with "open" boundaries (the tet mesh solver does not work with open boundaries).

Capacitance Matrix:

----------------------------------------------------

potential1 potential2

potential1 5.805210e-013 F -1.465024e-013 F
potential2 -1.465005e-013 F 5.805210e-013 F

----------------------------------------------------

And here is the hex mesh solver with adaptive meshing.


Capacitance Matrix:

----------------------------------------------------

potential1 potential2

potential1 5.792628e-013 F -1.459477e-013 F
potential2 -1.459462e-013 F 5.792628e-013 F

----------------------------------------------------

It seems that with CST EM Studio, you can have any result you want. You don't like the present result? Try a different solver...