A planar capacitor analysis by EM simulator 4
Issued on August 21, 2009

Finally I tried to analyze a capacitor of which electrode is meshshape. As well as the previous analysis, only one electrode is meshshape but the other one is still solid metal plane. It is like this.
Fig. 4.0
According to the Analysis 3, we can suppose that the capacitance would be more than the overlapping ratio of the area.
With 10mm*10mm area, necessary memory to analyze exceeds 16MB, which is the limitation of Sonnet Lite. It is because the shape of the upper electrode got complicated. The upper electrode becomes a 5by5 window mesh in the size. Then I reduced the size of the bottom electrode to 4.0mm*4.2mm. A 2by2 window mesh electrode can be placed there.
The cycle of a mesh line is 2.0mm as well as Analysis 3. I changed the width of the line to 0.2mm, 0.4mm, 0.6mm, 0.8mm and 1.0mm. See figures below. The trace line of the upper electrode was placed in the outside of the bottom electrode as well as Analysis 3.
Here I put the summary table.
Even though you make mesh lines thin, overlapping area doesn't rapidly decrease.
Overlapping ratio of electrodes 
100% 
76% 
66% 
53% 
39% 
23% 
Line width and space 
2.0mm0.0mm 
1.0mm1.0mm 
0.8mm1.2mm 
0.6mm1.4mm 
0.4mm1.6mm 
0.2mm1.8mm 
Figure
*Click a figure to enlarge. 






Estimated capacitance 
1.63pF 
1.39pF 
1.26pF 
1.10pF 
0.907pF 
0.686pF 
Ratio of
capacitance 
100% 
85% 
77% 
67% 
56% 
42% 
Fig. 4.3
I got bigger error than Analysis 3, 2 times error in around 20% overlapping ratio.
In
mesh cases the effect in Analysis 3 occurs twodimensionally. In combshape cases it occurs in only single axis. But here it occurs in dual axis. So in low range of the overlapping ratio, the error got about 2 times as big as combshape cases.
Capacitance of a single meshshape electrode capacitor doesn't change in proportion to the overlapping ratio of electrodes. We can not neglect electric lines which pass gap windows of a mesh.
The ratio of capacitance is much more than the overlapping ratio of electrodes in the low range.
Capacitance of a simple and solidmetalplane planar capacitor changes in proportion to the overlapping area of electrodes. But it is different for a capacitor which has gaps inside of an electrode. The capacitance is more than the overlapping ratio of electrodes.
An electromagnetic simulator is useful for this kind of consideration.
End of document.
(C)KANAYA Hidenori
Hide's Radio Shack