A planar capacitor analysis by EM simulator 3
Issued on August 21, 2009

Next I tried a complicated case. I analyzed a capacitor of which electrode is combshape. Both of electrodes are not combshape. One electrode is combshape but the other one is still solid metal plane. It is like this.
Fig. 3.0
The bottom electrode has the same area to the previous analysis, 10mm*10mm. Here I changed the width of the comb teeth so as to reduce the area facing the bottom plane from 90% to 0%.
According to the analysis before, we can suppose that the capacitance would be in proportion to the area of the electrodes facing each other.
Hereafter, let's see whether it is true or not.
To evaluate the effect of the width of comb teeth I changed the place of the trace line of the upper electrode. It was placed in the outside of the bottom electrode.
Fig. 3.1
The cycle of the comb teeth was 2.0mm. I reduced the width of the comb teeth from 2.0mm to 0mm by 0.2mm.
Here I put the summary table.
Table 3.1
Overlapping ratio of electrodes 
100% 
90% 
80% 
70% 
60% 
50% 
Comb teeth width and space 
2.0mm0.0mm 
1.8mm0.2mm 
1.6mm0.4mm 
1.4mm0.6mm 
1.2mm0.8mm 
1.0mm1.0mm 
Figure 






Estimated capacitance 
9.24pF 
8.81pF 
8.10pF 
7.30pF 
6.46pF 
5.59pF 
Ratio of
capacitance 
100% 
95% 
88% 
79% 
70% 
60% 
Overlapping ratio of electrodes 
40% 
30% 
20% 
10% 
0% 
Comb teeth width and space 
0.8mm1.2mm 
0.6mm1.4mm 
0.4mm1.6mm 
0.2mm1.8mm 
0.0mm2.0mm 
Figure 





Estimated capacitance 
4.70pF 
3.80pF 
2.85pF 
1.92pF 
0.239pF 
Ratio of capacitance 
51% 
41% 
31% 
21% 
3% 
Fig. 3.2
The expectation was wrong. Seeing Fig. 3.2 the line of Ratio of capacitance (Blue line) is far from the expectation line (Dark green line). In 10% overlapping ratio the ratio of capacitance exceeds more than 10%.
Then I subtracted the capacitance in 0% case so as to know how much the trace line of the upper electrode affected. But the Magenta line is still far from the expected line. This difference is not a simple error.
I know that a capacitor which has this type of electrode is quite different from simple cases before.
Probably, electric lines from the bottom electrode through gaps between comb tooth come back to the upper side of comb tooth. Those electric lines must increase the capacitance.
In simple cases before, we can neglect electric lines which flow out from the edge of electrodes. But in this case we can not neglect them because of many electric lines through many gaps between comb tooth.
Capacitance of a single combshape electrode capacitor doesn't change in proportion to the overlapping ratio of electrodes. We can not neglect electric lines which pass gaps of comb tooth. The ratio of capacitance is more than the overlapping ratio of electrodes.
(C)KANAYA Hidenori
Hide's Radio Shack