Discussion Forum

Posted: 1 decade ago 2011年8月12日 GMT-4 12:22

The reason why you dont see the fringe is because you have made it a one domain problem. If you put an air boundary outside the block that you made the capacitor you will see the fringe. And C11 would then not give 8.85pF because at that size your capacitance is affected by the fringe. Hope this helps Shahriar [QUOTE] Hi, All I have some questions related to modeling of capacitor in COMSOL. Using a very basic parallel plate example, if I have 1m width and 1m distance between the two plates, then the theoretical value is just 8.85pF (equal to the vacumm permittivity constant). The result from COMSOL also matches this well. However, in Comsol, when I tried to plot the field lines for this capacitor, all the field line appears as straight lines between these two plates, there is no fringe field outside. Any suggestion on how to modify the simple model to allow fringe lines to show up on the edge and outside as in reality? My target is to put another conductor near the two plates so that the capacitance between the two plates will change when the distance from that third conductor to them changes. However, without fringe lines escaping from the two plates, the capacitance between the two plates will always stay the same as theoretical value no matter how I move the third conductor. Thanks, HJ [/QUOTE]

Posted: 1 decade ago 2011年8月12日 GMT-4 12:36

Shahriar, Thanks a lot for your reply. I have actually tried to add another much larger rectangular box to enclose these two plates. As you said, the fringe field will show up. However, the capacitance is then almost doubled if I set zero boundary condition on the enclosing box. If I set the enclosing box to ground condition to absorb some of the fringe lines, then the capacitance calculated is smaller, but still much larger than the theoretical two plate values. So two ensuing questions: - How do set the enclosing boundary so that the calculated capacitance is close to theoretical value? - If the enclosing box boundary is needed, then its size would need to be much larger than the capacitor to be studied, for capacitor with more complex shape, the "out of memory" errors quickly occur as much more areas outside the capacitor also needs to be calculated even though only the fringe field near the capacitor matters in many cases, any suggestions on how to optimize the setup. HJ

Posted: 1 decade ago 2011年8月12日 GMT-4 16:10

HJ, Your capacitor is not an ideal capacitor (1mx1mx1m) so the formula epsilon0xA/d does not hold here. That formula holds when the plate dimensions are significantly larger than the separation distance so that the electric field lines are perfectly going from one plate to the other. In this case, the fringe is significant and so your capacitance expectation is not correct. - You can do a volume integration of the energy density of the capacitor block and that equals 1/2CV^2 so then you can calculate C - and that will give you the theoretical capacitance. But realize that this is only in the volume where the field terminates on the other plate - ideal case - Dealing with the other box boundary is complicated - you could use infinite elements, or you could put a large ground plane (and match that with experiment) somewhere in your geometry so then the effect of the box boundary far away is small. I hope this help Shahriar [QUOTE] Shahriar, Thanks a lot for your reply. I have actually tried to add another much larger rectangular box to enclose these two plates. As you said, the fringe field will show up. However, the capacitance is then almost doubled if I set zero boundary condition on the enclosing box. If I set the enclosing box to ground condition to absorb some of the fringe lines, then the capacitance calculated is smaller, but still much larger than the theoretical two plate values. So two ensuing questions: - How do set the enclosing boundary so that the calculated capacitance is close to theoretical value? - If the enclosing box boundary is needed, then its size would need to be much larger than the capacitor to be studied, for capacitor with more complex shape, the "out of memory" errors quickly occur as much more areas outside the capacitor also needs to be calculated even though only the fringe field near the capacitor matters in many cases, any suggestions on how to optimize the setup. HJ [/QUOTE]