Capacitor plate thickness and RF sheet resistance

[JAHAM2BE]

I'm designing a butterfly capacitor for a magnetic loop antenna. I was thinking that for absolute minimum loss the plates would need to be at least 10 skin depths thick - 5 skin depths for current flow on the top and 5 skin depths for current flow on the bottom of the plate.

On the other hand, it might be that with several plates, the multiple parallel current paths could offset any loss through insufficient thickness of the plates. So 2 current paths in parallel (2 rotor blades) would, it seems, require only half of the above-calculated 10-skin-depth thickness; 10 rotor plates would only require 1/10th the thickness. Is this reasoning valid? (Upon closer thought, the relationship between number of parallel current paths and required plate thickness is probably not linear.)

In general, is there an easy way to calculate the loss due to thinner plates?

And while I'm on the subject of RF current flow over a thin sheet of metal - is it correct that the so-called RF sheet resistance (calculated with squares) represents a best-case scenario, and that for long wide sheets that are flat (not tubular), current crowding at conductor edges will increase RF resistance above that calculated with the simple RF sheet resistance calculation method? (This edge crowding loss is in addition to any skin-depth-related loss caused by insufficient thickness.)

[WX7G]

You will be well within the ballpark calculating with squares and not worrying about current crowding. If you get to that level of detail you must then consider the surface roughness (increases resistivity). Ten skin depths in aluminum at 3.5 MHz is about 20 mils. I think that would be rather thin mechanically for capacitor plates.

[JAHAM2BE]

You will be well within the ballpark calculating with squares and not worrying about current crowding.

In this particular context of capacitor plates, with small and short flat surfaces, I can see your point.

More generally though (as in the case of a long strip conductor used as a radiating element), I am still a bit foggy about how exactly to estimate the RF resistance of a strip. The idea of sheet resistance calculated with squares is appealingly simple, but I haven't yet seen an online reference that relates the ideal sheet resistance with things like very thin foils (less than 5 skin depths) or possible edge effects if the topology of the sheet is a flat strip is flat and not tubular (which is I believe the minimum loss condition, ensuring uniform current density and most closely approximating the ideal RF sheet resistance).
 

Ten skin depths in aluminum at 3.5 MHz is about 20 mils. I think that would be rather thin mechanically for capacitor plates.

Well my hardware store has 7 mil (0.2 mm) copper flashing which I was considering using. I wasn't able to try flexing the flashing to see how rigid it was, so it may be that it's too mechanically unstable as you say. But even if it is mechanically stable enough, it's less than 10 skin depths thick (which for 7 MHz is 0.3 mm if I am not mistaken), which is what started to get me concerned about if thickness is sufficient and if insufficient thickness can be counterbalanced with additional parallel current paths through more plates.

[WX7G]

You are correct that the RF current will divide among the plates and the RF resistance will be reduced.

You can explore current crowding using SONNET LITE. NEC can also be used by takes more work. NEC WIN PLUS shows current crowding as temperature plot whereas for EZNEC you will have to look up the current in various segments in a table.

The SONNET LITE program is limited to 16 MB (have to get a number from them to go from 1 MB to 16 MB). 16 MB is enough to model small (and I mean small) structures so you can scale part of your project to UHF. SONNET models metal as infinitely thin and with perfect conductivity.

But for what you are doing I think you can simply use the same method for the capacitor resistance that you are using for the loop resistance. That will tell you which one dominates, capacitor or loop.

[JAHAM2BE]

But for what you are doing I think you can simply use the same method for the capacitor resistance that you are using for the loop resistance. That will tell you which one dominates, capacitor or loop.

That sounds like a good idea to get ballpark figures.

I recently found this RF sheet resistance spreadsheet which is very helpful in these kinds of calculations. You can select the material type (copper, aluminum, etc.) and a range of operating frequencies, and it shows you a table and graph of RF sheet resistivity/square for skin depths from 1 to 5. Very informative!

http://www.microwaves101.com/encyclopedia/RF_sheet_res_examples.cfm#download

As a quick test I calculated the RF sheet resistance of the surface area of a copper torus using the 5-skin-depth copper resistivity values from the table. This yielded identical RF resistance values with the common small loop efficiency calculators (AA5TB and 66pacific, which I believe both use the ARRL handbook formulas). So the table values seem correct, and allow investigation of various types and thicknesses of metals.

I'm starting to explore electromagnetic field simulation software but it's slow going. For now, the sheet resistance method seems good enough to make sure I'm at least not introducing vast losses with my chosen metal type, geometry, and thickness.