4 Single mesh-shape electrode capacitor

Finally I tried to analyze a capacitor of which electrode is mesh-shape. As well as the previous analysis, only one electrode is mesh-shape but the other one is still solid metal plane. It is like this.

Fig. 4.0

4.1 Expectation of the result

According to the Analysis 3, we can suppose that the capacitance would be more than the overlapping ratio of the area.

4.2 Analysis configuration

With 10mm10mm 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 5-by-5 window mesh in the size. Then I reduced the size of the bottom electrode to 4.0mm4.2mm. A 2-by-2 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.

4.3 Analysis result

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	2.0mm-0.0mm	1.0mm-1.0mm	0.8mm-1.2mm	0.6mm-1.4mm	0.4mm-1.6mm	0.2mm-1.8mm
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.

4.4 Supposition of the reason for error

In mesh cases the effect in Analysis 3 occurs two-dimensionally. In comb-shape 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 comb-shape cases.

4.5 Local Conclusion

Capacitance of a single mesh-shape 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.

5 Conclusion

Capacitance of a simple and solid-metal-plane 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.