What Causes the Skin Effect in High Frequency Currents?

[chitrageetam]

Can anybody explain the skin effect more clearly-
why does the current tries to concentrate more closely to the surface of
the conductor at high frequencies?
what is happpening inside the conductor?
thanks

 

[Phrak]

I'd like to know too.

 

[pallidin]

Here's a brief description from this site: http://www.mos.org/sln/toe/skineffect.html


All electric currents generate magnetic fields that in turn can affect the current (this is the principle behind electric guitar pickups). In a direct current case everything is constant and so nothing seems to happen. With an alternating current, however, there is a delay in the magnetic field's response to the change in current and the 'old' magnetic field tends to push the current towards the outside of the conductor. As the frequency increases, so does the effect until at very high frequencies the entire current flows in a very narrow skin on the conductor--hence the name.
The earliest work on explaining the skin effect was done by Lord Kelvin (of temperature fame) in 1887. Tesla also investigated the effect.

 

[pallidin]

Also, a more detailed decription can be found here:

http://www.nationmaster.com/encyclopedia/Skin-effect

 

[Phrak]

I looked-over your last link, pallidin. It's a copy of the Wikipedia article, which I read, until it hit Bessel functions. Unfortunately, the article doesn't answer 'why'? The best explanation Wikipedia comes up with is 'eddy currents'; a non-answer. So...

Chitra, I don't have the full answer yet. Maybe someone else will come up with it

The changing current produces annular magnetic fields within the conductor changing in phase with the current. The change in the magnetic field induces an electric field. From the schematical picture in the Wikipedia article, I assume, preliminarily, but without too much skepticism that the induced electric field in the center of the wire is opposite the instantaneous and externally applied electromotive force.

The larger answer is, of course the Bessel function that could say that the magnetic and electric fields alternate in direction any number of times over the radial coordinate depending on the frequency in question. Thus, those little loops of eddy currents could change direction any number of times depending on frequency. It all depends on what the solution to the differential equation specifically says when the eddy currents, as well as the electric and magnetic fields, are all included. I didn't include the additional effects of eddy currents in my simple, and partial explanation.

 

[chitrageetam]

Thanks for your replies Palladin and Phrak, the explanation seems more fit for
eddy current losses than for skin effect losses..
Another thing is I am not able to believe..the line..
"there is a delay in the magnetic field's response to the change in current"..
I have been in an impression that "Current and magnetic field are two forms of
same entity..they do not have a cause and effect relation but they two sides
of the same coin." I mean they are not one after the other, they are simultaneous."
Isnt it? In that case, why will there be any delay between them at all?

 

[Phrak]

A little additional thought on this, and it's apparent that the 'eddy current' paradigm is misleading. The simplest constraints are of a wire having circular cross-section, but the following argument equally applies to other sections.

For a round wire, the solution is cylindrically symmetric and periodic in the wavelength. Any currents that may flow radially should be periodic at half-wavelength intervals. But skin effect is noticable with frequencies as little as 60 Hz; a half wavelength of about 1.5 million kilometers. I don't know of any power lines that long, so the popular 'eddy current' loops seem misleading. Even at 300 KHz it's shouldn't be often descriptive. The only apparent excuse for perpetuating this phraseology would require a hypothetical inclusion of chaotic behavior of the currents, but this is not included in the quoted formulae for skin effect.

In either case, the cause of increased resistance is the result of induced back-emf.

 

[cabraham]

A little additional thought on this, and it's apparent that the 'eddy current' paradigm is misleading. The simplest constraints are of a wire having circular cross-section, but the following argument equally applies to other sections.

The solution is cylindrically symmetric, and periodic in the wavelength. Any currents that may flow radially should occur at half-wavelength intervals. But skin effect is noticable with frequencies as little as 60 Hz; a half wavelength of about 1.5 million kilometers. I don't know of any power lines that long, so the popular 'eddy current' loops seem misleading. Even at 300 KHz it's shouldn't be often descriptive. The only possible support for this would be chaotic behavior.

The cause of increased resistance is the result of induced back-emf.

Are you sure about the half wavelength being 1.5 million kilometers? I get 2,499 km instead. It is easy to compute. Using t-lines with no insulation, just air, and no ferromagnetic material , the speed is 3e8 m/sec, or 3e05 km/sec = 300,000 km/sec. At 60 Hz, one wavelength is (300,000 km/sec) / (60 cyc/sec) = 5,000 km/cyc. Thus half a wavelength is 2,500 km. Just wondering.

As far as increased resistance goes, it happens because the current is not uniformly distributed in the cross section of the wire, but bunched or crowded into a fraction of the area. A smaller area incurs larger resistance. Of course the inductance, or what some people refer to as "back emf" is responsible for the current distribution being non-uniform. BR.

Claude

 

[Phrak]

Are you sure about the half wavelength being 1.5 million kilometers? I get 2,499 km instead. It is easy to compute. Using t-lines with no insulation, just air, and no ferromagnetic material , the speed is 3e8 m/sec, or 3e05 km/sec = 300,000 km/sec. At 60 Hz, one wavelength is (300,000 km/sec) / (60 cyc/sec) = 5,000 km/cyc. Thus half a wavelength is 2,500 km. Just wondering.

Did I screw up that badly? Oh well.

I meant to say 1.5 million meters, where the velocity of propagation is a rough 60% that of light.

As far as increased resistance goes, it happens because the current is not uniformly distributed in the cross section of the wire, but bunched or crowded into a fraction of the area. A smaller area incurs larger resistance. Of course the inductance, or what some people refer to as "back emf" is responsible for the current distribution being non-uniform. BR.

Claude

The changing magnetic field induces an electric field that opposes the applied electric field. So I thought back-emf would be more appropriate. The induced electric field is stronger toward the center of the wire, therefore the skin effect thing.

But, I'd like to know if the summed electric field, and therefore currents, ever reverses within the wire's center.

 

[djsourabh]

But actually the inductance L increases hence current decreases,
then why the ac 'resistance' is calculated as
Rac =1.6*Rdc ?
& not the inductance?
&
what happens to the power factor?