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## 2 Different-size electrodes capacitor

Next I analyzed a planar capacitor of which size of electrodes is not same to the other. It is like this.

Fig. 2.0

The bottom electrode has the same area to the previous analysis, 10mm*10mm. Here I changed the size of the upper electrode.

### 2.1 Expectation of the result

According to the previous analysis, we can easily suppose that the capacitance here would be the same capacitance to a capacitor which has the small electrodes and that the area of the bottom electrodes which is open would be negligible.
Hereafter, let's see whether it is true or not.
The base point in this analysis is the same to the previous one. The capacitance is 9.18pF.

### 2.2 Analysis result

Here I put the summary table.

 Overlapping ratio of electrodes 100% 72.25% 49% 36% 25% 16% 9% Size of the upper electrode 10mm*10mm 8.5mm*8.5mm 7mm*7mm 6mm*6mm 5mm*5mm 4mm*4mm 3mm*3mm Figure Estimated capacitance 9.18pF 6.77pF 4.65pF 3.45pF 2.42pF 1.57pF 0.904pF Ratio of capacitance 100% 74% 51% 38% 26% 17% 10%

The ratio of capacitance is well fit to the overlapping ratio. The error is just less than 2%.
Then we understand that the capacitance of the capacitor here depends on the area of the small electrode. Here we have verified the expectation at the first of this section.
As well as the previous analysis, we have electric field which flows out from the perimeter of electrodes. So we have some error.

### 2.3 Local Conclusion

Capacitance of a planar capacitor depends on the area of the small electrode.

Issued on August 21, 2009