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RF skin current

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MikeMl

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Imagine a hoop, made out of flat copper strip, about 3" wide, tens of feet long. There are tens of Amps of RF current (3-15MHz) flowing along the strip. Do you use 3" or 6" (one side or both sides of the strip) when figuring the cross-section of the surface that the RF flows along?

Suppose you wrap the strip around a plastic pipe formed into a loop (like a hula-hoop) as a mechanical support, such that the strip wraps three-fourths of the way around the pipe, leaving a gap between edges of the strip. Has anything changed? Where does the current flow?

Now, suppose you wrap the strip around a smaller diameter plastic loop, such that the copper strip actually closes over itself, and you solder the seam? You have effectively made a tube over a plastic mandrel. Does the RF current still flow on both the outside of the tube and inside of the tube, or only on the outside?
 

ronsimpson

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Take the last one: a copper water pipe with current in it. I think the current will flow on all surfaces (inside and outside)
Skin effect, is current flowing near the surface but not flowing deep in the copper.
In transformers, the current can flow one way on the outside of the copper and the current seems to flow backwards in the center of the wire. This really increases the heating. With current flowing upward on the outside, the little red circles spin pushing current back down the center.

Wire above, cross section of water pipe below.
upload_2016-7-1_17-48-23.png
 

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dr pepper

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I'm pretty sure Rons correct, so for your first Q 6" would be the answer, maybe a little more if the thickness of the copper is more than twice the skin depth at the freq used.

The second one is tricky, I dont think skin effect would be a major player here, however there may be some odd eddy current effects.

Third the copper would behave as a tube as in rons example, because there is a 'skin' on both sides current will flow both sides.
One difference is as I mentioned if the strip is much thicker than twice the skin depth then you'll reduce performance.

Heres a nifty tool for skin depth.
http://daycounter.com/Calculators/SkinEffect/Skin-Effect-Calculator.phtml
 

Tony Stewart

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Imagine a hoop, made out of flat copper strip, about 3" wide, tens of feet long. There are tens of Amps of RF current (3-15MHz) flowing along the strip. Do you use 3" or 6" (one side or both sides of the strip) when figuring the cross-section of the surface that the RF flows along?

Suppose you wrap the strip around a plastic pipe formed into a loop (like a hula-hoop) as a mechanical support, such that the strip wraps three-fourths of the way around the pipe, leaving a gap between edges of the strip. Has anything changed? Where does the current flow?

Now, suppose you wrap the strip around a smaller diameter plastic loop, such that the copper strip actually closes over itself, and you solder the seam? You have effectively made a tube over a plastic mandrel. Does the RF current still flow on both the outside of the tube and inside of the tube, or only on the outside?
There are many physical effects with these two geometries.
  1. Inductive loss or impedance rise at RF from coil physics depending and on dielectric constant (mandrel),
    1. This is signifcantly reduced if coil gap is reduced to 0 as the path length drops from a coil to an axial cylinder
  2. Conductive Loss
  3. Eddy current/ Skin effect losses
  4. Transmission Line effects of a loop antenna and fractional wavelength
What is your objective?
 
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Tesla23

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Imagine a hoop, made out of flat copper strip, about 3" wide, tens of feet long. There are tens of Amps of RF current (3-15MHz) flowing along the strip. Do you use 3" or 6" (one side or both sides of the strip) when figuring the cross-section of the surface that the RF flows along?

Suppose you wrap the strip around a plastic pipe formed into a loop (like a hula-hoop) as a mechanical support, such that the strip wraps three-fourths of the way around the pipe, leaving a gap between edges of the strip. Has anything changed? Where does the current flow?

Now, suppose you wrap the strip around a smaller diameter plastic loop, such that the copper strip actually closes over itself, and you solder the seam? You have effectively made a tube over a plastic mandrel. Does the RF current still flow on both the outside of the tube and inside of the tube, or only on the outside?
As long as there are no other conductors very close to the strip, current flows on both sides - you use 6". The current will not be uniformly distributed across the surface, you get significant crowding at the edges - this increases the loss. If you are trying to calculate the effective resistance, look here

http://www3.fi.mdp.edu.ar/electroni...cional/microstrip/micorstrip lines comp_2.pdf

see eqn 2 and 3


upload_2016-7-4_23-39-42.png

which give the resistance/l, where K (>1) is the factor that accounts for the current crowding.

A tube as you describe will have negligible current on the inside surface. Even if the ends are open, it is a cutoff waveguide so any fields that enter at the ends are rapidly attenuated. Your 3" wide strip would make a tube about 1" dia, the cutoff frequency of this is about 7GHz, and my attenuation guesstimate is over 30dB/inch. The current on the tube is uniformly distributed, so the resistance is much more straightforward (same doc, eqn 8)

upload_2016-7-4_23-44-43.png
As you wrap the strip to get a part-formed tube you will be somewhere between these, I have no information on this, but my guess would be that as long as the gap was reasonable, the results would be more strip like than tube like. EM simulation software should be able to give you answers to this.
 

MikeMl

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Thanks for the replies, especially Tesla23. I was missing the waveguide idea.

Unfortunately, as a retiree, I no longer have access to EM modelling software I once did at the University (or a grad student to do it for me ;)) ... Are there any freeware EM modelers out there?

I've got the hots to try a Small Transmitting Loop. The price of 2" copper plumbing pipe is quite high, besides being heavy. A local ham came up with a technique of helically wrapping copper flashing strip around a PVC frame, and while that partially solves the weight and cost issues, I believe that adding distributed inductance around the loop with the copper wraps does nothing but increase its loss resistance by skewing the loop to more lossy inductance and less low-loss capacitance to tune it. Wrapping helically does not increase the loop's aperture; only changes the L to C ratio.

I would like to try the PVC frame but just using it to support the copper strip in a linear fashion. I have a choice of making the copper strip wide enough so that it completely encloses the PVC, or leaving the gap, which is what motivated my questions... Maybe one of the reasons that the helical wrapped loop works well despite the flawed LC ratio is because skin current can flow on both surfaces of the copper tape?
 
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Tesla23

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I've got the hots to try a Small Transmitting Loop.
I had a quick look at that, and I'm sceptical. There appears to be no justification for the statement "At the same time the radiation resistance is raised considerably while only raising the IR losses slightly". I can't see any reason why the radiation resistance should rise, I suspect it stays the same and the observed increase in bandwidth is simply due to a decrease in efficiency.

I had a quick google on the topic and I'm not the only one who is sceptical: http://owenduffy.net/blog/?p=5244

I found this interesting: http://www.nonstopsystems.com/radio/pdf-ant/antenna-article-magloop-midnite.pdf
 
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