| Author |
 Topic  |
|
dave_royle
USA
13 Posts |
 Posted - Sep 02 2011 : 06:09:28
|
shahriar,
Sorry for leaving you hanging, I have been out.
I am not sure you have it yet, let me give you a worked out example:
I have two 0.2m square plates side by side (coplanar) separated by 0.1m. The matrix is:
CAPACITANCE MATRIX, picofarads
1 2
1%GROUP1 1 8.804 -2.285
1%GROUP2 2 -2.285 8.804
The equivalent circuit is:
2.285pf between plates
6.519pf between each plate and infinity/earth (sum of row).
Draw this and you can see that if I measure the capacitance between the plates I will get 5.545pf (all three caps contribute).
Next I add a 10m square plate under the small plates spaced 0.8m under. The matrix is:
CAPACITANCE MATRIX, picofarads
1 2 3
1%GROUP1 1 9.07 -2.043 -6.394
1%GROUP2 2 -2.043 9.07 -6.394
1%GROUP3 3 -6.394 -6.394 419.8
The equivalent circuit is:
2.043pf between small plates.
6.394pf between each small plate and big plate.
0.633pf between each small plate and infinity/earth (sum of group1/group2 rows).
406.212pf between big plate and infinity/earth (sum of group3 row).
Comparing these two examples we can see that:
1 - the capacitance between small plates is very similar.
2 - the relationship between the small plates and infinity/earth in the first example is similar to the relationship between the small plates and the big plate in the second example.
3 - the capacitance between the small plates and infinity/earth is very small in the second example.
The big plate has taken over the role of infinity/earth from the perspective of the small plates. Of course if I make the big plate 1Km square and move it 100m away it will more perfectly replace earth/infinity.
This is why we say that infinity = planet earth. Infinity is somewhat metaphysical, but we can all imagine parasitic capacitance to earth. It is the same as adding a really big plate reasonably far away from our device and considering parasitc capacitance to it.
In other words if a row in a capacitance matrix is non-zero than there is capacitive coupling between that element and the outside world (earth). Consider coplanar traces over ground plane in a PWB (two conductors and ground plane, three elements in matrix). The traces better have zero sum rows in the matrix, the ground plane should be capturing all of their flux, no leakage flux from traces to earth is expected. On the other hand can we expect the ground plane itself to have capactance to earth (this comes up when quantifying EMI problems for example), so that conductor's row will not have a zero sum.
Hope this helps.
Dave |
 |
|
|
rebekasm
USA
2 Posts |
Posted - Jan 16 2022 : 23:31:16
|
Hello Shahriar,
The whole discussion is very good one to understand the capacitance matrix. However, I have some questions regarding to COMSOL capacitance calculation. I have a modelled a system with six electrode and consider a sphere with infinite element as ground node. So, from COMSOL I can get the result for Maxwell/Mutual matrix with ground at infinity. Now, I need to replace the ground node with float at infinity to reduce the matrix, so the potential is constant and I can derive a mutual capacitance matrix with diagonal zero element. In COMSOL AC/DC module it is not possible to do study with ground node. So, do you have any idea how could I approach the problem? |
|
|
|
rebekasm
USA
2 Posts |
Posted - Jan 16 2022 : 23:34:50
|
Hello Shahriar,
The whole discussion is very good one to understand the capacitance matrix. However, I have some questions regarding to COMSOL capacitance calculation. I have a modelled a system with six electrode and consider a sphere with infinite element as ground node. So, from COMSOL I can get the result for Maxwell/Mutual matrix with ground at infinity. Now, I need to replace the ground node with float at infinity to reduce the matrix, so the potential is constant and I can derive a mutual capacitance matrix with diagonal zero element. In COMSOL AC/DC module it is not possible to do study with ground node. So, do you have any idea how could I approach the problem? |
|
|
|
Topic |
|
|
|
Capacitance matrix and impedance measurement?
