Talk:Skin effect

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[edit] Litz Translation

Presently the German Litzendraht is translated as "braided wire", but I'm not sure that's correct, as litz is typically twisted rather than braided. Ccrrccrr 03:36, 17 January 2007 (UTC)

[edit] Skin effect and Faraday cages

While reading for this article, I discovered that some of the effects that are attributed in Wikipedia to Faraday shielding (see Faraday cage article) are in fact due to the skin effect. To put it briefly, Faraday shielding is due to the behaviour of electrostatic charges trying to maximize their distances from each other, while the skin effect is due to a magnetic field, created by a changing current, acting on that current. On the other hand, perhaps someone really smart will tell me that both effects are just different aspects of some deeper principle. I'll wait for comments before wading in to the Faraday cage article. -- Heron

The only area I can see where there may be confusion is in the Faraday cage article where it says that the cage has a dual purpose - the additional one being RF screening. However, I dont think this screening effect arises from skin effect but by the conducting walls efficiently reflecting the EM radiation (ie keeping out or keeping it in.--Light current 19:34, 11 September 2005 (UTC)

There are other areas of confusion in that article. Under "Real-world Faraday cages", the TEMPEST shield, cordless phone and microwave oven paragraphs all describe an RF-reflecting shield, not a Faraday cage in the electrostatic sense. I'm just not sure whether this means that they are not Faraday cages, or that they are Faraday cages but are used in a way that Faraday could not have envisaged. --Heron 20:03, 11 September 2005 (UTC)

Well, I think if they have 6 conducting walls, they are Faraday cages, but they are also RF screened rooms. THere is, IMHO, no practical difference. So I would go with your latter statement ;-) --Light current 20:09, 11 September 2005 (UTC)

[edit] Lamb and 1883

According to Paul Nahin's biography of Oliver Heaviside, Horace Lamb published a paper on the skin effect in January 1883 in spherical conductors, and Oliver Heaviside generalized that in 1885. --Wtshymanski 23:23, 7 Jun 2005 (UTC)

What is a spherical conductor please? I think you would need a whole load of balls to make any useful conductor.--Light current 05:43, 9 September 2005 (UTC)

The spherical conductor that Lamb was interested in was the Earth's core. [1] --Heron 11:46, 9 September 2005 (UTC)

Ah ha! Or just one big ball! --Light current 13:39, 9 September 2005 (UTC)

Think of a magnetically-"induced" current and you'll see how one might use a sphere as a simple model to understand the effect.
Atlant 13:10, 9 September 2005 (UTC)

[edit] Skin Effect at Power Frequencies

Anyone know why we have to look out for skin effect in power transmission at 50/60 Hz? I have not heard of this one before!.--Light current 05:32, 9 September 2005 (UTC)

See the "Examples" section of this article. The skin depth in copper at 60 Hz is 8.57 mm, and many power busbars are more than twice that thickness. --Heron 11:35, 9 September 2005 (UTC)

Yes, but what practical consequences does it have in the design of power transmission networks apart from the extremely minor one of making the busbars a bit thicker for strength? This is such a minor point and is misleading (tending to indicate something mysterious at power frequencies)--Light current 13:45, 9 September 2005 (UTC)

AIUI it is of consequence in power distribution but is not usually a factor for DIYers or normal electricians because the currents involved in domestic and small commercial installations do not normally require conductors which are thick enough for the skin effect to have any significant effect. At mains frequency it is only when dealing with currents in the thousands of amps that the skin effect is likely to have to be considered. Even then, standard tables of conductor sizes will take the skin effect into account where necessary so it is only where doing something unusually complicated not covered by a standard conductor design that the skin effect will have to be considered.--Ali@gwc.org.uk 16:34, 9 September 2005 (UTC)

It is of NO consequence in power systems so I propose that the reference to power frequency problems is deleted.

The only area where skin effect is of any consequence at all in power distribution systems is in lightning and surge protection because the high frequencies travel down the outside of the conductor. This is why lightning conductors have large suface area/volume ratio.--Light current 16:43, 9 September 2005 (UTC)

I wish to modify my earlier, rather rash statement of skin effect being of NO consequence, to it being of little or minor consequence at power frequencies. Apologies to all concerned --Light current 21:54, 10 September 2005 (UTC)

I don't think it's fair to say that skin effect is of NO consequence; standard engineering tables for power busbars routinely take into account skin effect and specifically cite it as a reason that busbars may carry less current at power frequencies than at DC.[2][3][4], etc.
It also turns out that designers of squirrel-cage induction motors must consider the skin effect. [5] (hope that link works!) When the induction motor is first energized, the rotor experiences a magnetic field that changes at the mains frequency (and a proportionally-large skin effect in its "windings"). But as the rotor accelerates, the magnetic field acting on the rotor appears to be just one or two Hertz and the skin effect disappears. This increased impedance at starting apparently aids the starting of induction motors.
I don't see anything wrong with keeping the discussion in the article, and your coment about impedance to lightning-induced surges would also be a valuable addition.

Atlant 17:19, 9 September 2005 (UTC)

Well theoretically busbars will have slightly less capacity at 60Hz than dc (they will get a bit warmer). but can you quote a reference that shows power engineers actually taking this into account in their system designs. I'll be surprised if you can!--Light current 17:25, 9 September 2005 (UTC)

[6] which contains an article from Electrical Apparatus magazine which contains:

The effective thickness of the "skin" carrying most of the current is about 3/8" for copper conductors at 60 Hz. When a circular cable exceeds about 3/4" in diameter, then, the material at the center carries little current. Large tubular busbars are therefore hollow. That saves considerable material as well as improving heat dissipation.
In transmission line conductors, an outer-layer of relatively low resistance material (usually aluminum because of its light weight) carries the current, wrapped around a steel (for strength) inner core, where electrical resistance isn't important.
Skin effect is useful in squirrel cage rotors. At lockedrotor, when frequency in the cage is high, the top or outer portion of each rotor bar carries most of the current. As the motor accelerates, and cage frequency drops, the effective depth of current penetration drops with it (see "How rotor slot design can influence electric motor performance," EA February 1984). That permits many useful variations in accelerating torque characteristics.
Googling also seems to indicate that most purchased large copper busbar is hollow and most HT power conductors are aluminum-over-steel, so the engineers don't need to think much about the skin effect 'cause the thinking was already done for them. :-)
Atlant 17:54, 9 September 2005 (UTC)

I rather think here that the primary pupose of Al over steel for overhead lines is more about cable strength than skin effect considerations. But I could be wrong (often am). The artice was IMHO giving slightly too much weight to skin effect at power frequencies. ;-)--Light current 18:31, 9 September 2005 (UTC)

Skin effect is necessary to consider even at commercial power frequencies, where the conductors are large enough. Since skin depth is a few millimetres, usually this means only circuits with currents in the thousdands of amperes range are affected...but they are indeed affected. I've seen the isolated phase bus for a 120 MVA generator and it's a hollow tube, because a solid cross-section would be inefficient. --Wtshymanski 20:05, 9 September 2005 (UTC)

In fact, large AC generators often use a flowing hydrogen atmosphere to improve cooling and reduce windage losses. The flowing hydrogen also removes heat (created by Joule heating) of the busbars that connect the generator to the power station's step-up transformers. Because of skin effect, the inner portion of these large busbars is not needed, thereby allowing engineers to utilize the interior for gas cooling. Bert 21:59, 10 October 2005 (UTC)

CAn anyone calculate the percentage rise in resistance of copper from DC to 60 Hz. Ie how much of a difference does skin effect make at 60Hz?--Light current 19:39, 10 September 2005 (UTC)

You forgot to mention the diameter of your conductor. According to the Terman formula (which I just added to the article), the resistance of a roughly 26-mm diameter wire (if you can get wire that thick) would increase by 10% at 60 Hz. --Heron 21:15, 10 September 2005 (UTC)
I'm pretty sure that "200 mm" in the Terman formula only applies to one kind of metal (iron?). I added iron and copper and aluminum to the article, using the data from their wikipedia articles and Permeability (electromagnetism). I would *like* to add steel. What is the conductivity of steel? What metal does the Terman formula apply to? --70.189.77.59 18:06, 25 October 2006 (UTC)

[edit] multiple frequencies

Has anyone seen any information about how multiple frequencies in a wire effect the resistance? (i.e. 60kHz noise plus 60Hz power transmission, plus transmission signals from VFD's, etc.) I understand the basic equations, but I'm having trouble figuring out how all the frequencies combine in a single wire. I'm thinking that the ammount of current in each frequency will definitely effect which one has more influence on the overall resistance of the wire, but I'm not quite sure how to mathematically approach this. Has anyone seen anything talking about this, or am I going to have to form my own theories? Beijota2 15:21, 16 March 2006 (UTC)

I generally assume that multiple frequencies do *not* effect the resistance. (In particular, I assume that the temperature-dependent resistance of the wire does not significantly change, which is certainly an approximation).
I generally assume that my wires are linear enough that the superposition theorem applies. I never calculate an "overall resistance". Instead, I calculate things like V=I*R, P=R*I^2, etc. at each frequency independently, pretending that one frequency is the only one on the wire. To find the total power spent heating the wire, I find the power at each frequency independently (using the frequency-dependent resistance), then add them all up.
If the superposition theorem did *not* apply to wires, we would see all kinds of non-linear effects that we currently only see in things like diodes and nonlinear optics.
Does that answer your question? --70.189.77.59 16:51, 25 October 2006 (UTC)
Surely the short answer to this question is that skin effects make the resistance of a conductor slightly frequency dependent. Higher frequencies will be very gradually filtered out as they propagate along a transmission line. If a nicely balanced "white" spectrum of voltages is input, a "pink" spectrum will be received (ie biased towards lower frequencies). StuFifeScotland 19:05, 28 October 2006 (UTC)

[edit] Large power transformers

Litz wire will be used in large power transformers. If this means in 50/60 Hz distribution transformers, this is the first I've heard of it!! Are any pictures available? --Light current 05:40, 9 September 2005 (UTC)

Just been looking in my copy of Higher Electrical Engineering (Shappard, Moreton, and Spence) pub Pitman 1970 ISBN 0 273 40063 0 (a standard work for first/second year undergrads in Britain). In the section on power transformer construction I would like to quote a short extract from the section on windings. The coils are made of varnished cotton or paper covered wire or strip and are circular in shape to prevent high mechanical stress.... If ever there was a place to mention Litz wire this was it. But they dont. Thats because its not used. So can we please delete this erroneous statement. --Light current 17:55, 9 September 2005 (UTC)

THanks Atlant for pointing me to those pictures. I was trying to see if there was any indication of special windig wire (Litz) being used. But there is not enough detail in the photos to see.--Light current 19:04, 9 September 2005 (UTC)

I think of "Litz wire" in terms of RF transformers, but having seen large power trnaformers being built I can assure you that the heavy current windings are in multiple parallel strands, rather like Litz wire but much larger in cross-sectional area. --Wtshymanski 20:05, 9 September 2005 (UTC)
In that case, I'll revert my deletion of that line from the article. It would be nice if you could find a reference, though, that proves that these multiple strands are there to mitigate the skin effect, and not for some mechanical reason (e.g. to reduce bending stresses). --Heron 21:57, 9 September 2005 (UTC)

The term used is "transposed" conductors. The transformers are wound with stips of copper, bundled two stips wide and some number tall. The thickness of the strip is chosen to give less than 1/2 skin depth at power line frequency to manage skin / proximity losses. The width is chosen to be 1/2 of the width of the disired bundle width. The stips are stacked up as tall as needed to give the total cross section needed to handle the current. One space for conductor is left open so that the stips can be "rolled" and maintain the overal retangular bundle shape. The change of position is called a "transposition". The tranpositions are spaced such that each strip will be in each possible position in the bundle some intiger number of times. Like litz, the individual strips are insulated with a lesser amount of insulation and more insulation is applied around the bundle. Same idea as litz wire but the use of retangular wire and retangular bundles results in less wasted space in the winding.

Look at the first picture on this page: http://www.copper.org/innovations/1999/09/transformer_innovations.html

They also mention copper foil windings, also a method of mitigating skin loss.

[edit] Lightning teaser

Since we know that current travels down the outside of conductors at high frequency, why is it that lightning conductors are solid of rectangular X-section and not just made from hollow copper pipe? (much cheaper) --Light current 19:09, 9 September 2005 (UTC)

Serious lightning conductors usually aren't made of solid copper; instead, they are braided from a number of strands of relatively fine-gauge (17 gauge'ish?) copper to form an overall conductor that's maybe 3/4 inch in diameter with a lot of included air-space.[7]
It's just the copper grounding wire we buy at Radio Shack that is solid. I think it's function would probably be better-described as "electrostatic discharge" where it helps to keep the antenna or what-have-you at ground potential and not allow the build-up of a charge that might attract a lightning strike. I'm sure that this solid style wire would demonstrate a pretty high impedance in the face of real lightning strikes.
Atlant 00:17, 10 September 2005 (UTC)

Well, over here, al lightning conductors are made of solid copper sometimes in an insulating sheath of pvc or something, pinned to the walls of tall municipal buildings and churches etc. --Light current 07:04, 10 September 2005 (UTC)

Any way, the question remains, why are lightning conductors not made from hollow copper piping. (apart from the fact it may be more difficult to bend.)--Light current 18:40, 10 September 2005 (UTC)

You can make a down conductor from a hollow copper tube, e.g. a water pipe, but do not try to make it the few tenths of a mmm, which is the area where a lightning current flows, as this will make it evaporate immediately if a lightning strikes. The massive conductor is much more robust both thermally and mechanically and even if a waterpipe can easily do the job, it is more tricky to bend. NSV 10-10-2005, 1250UTC

Solid or stranded conductors are used primarily for mechanical strength and thermal mass. When conducting very large peak currents, a hollow conductor may actually collapse due to "magnetic pinch" effects. The higher the di/dt, the greater the effect - robust lightning conductors designed to withstand high current positive lightning strikes must be physically strong. Bert 20:03, 10 October 2005 (UTC)

Think Fourier analysis: lightning has high frequency radio components because of the sharp edges (ie rapid rise and fall times) of the pulses. The pulses themselves are typically 5 coulombs at 40 kA, meaning about 0.13 ms wide and therefore 8 kHz fundamental frequency. Skin depth can be calculated from this. StuFifeScotland 19:05, 28 October 2006 (UTC)

[edit] Silver plating

What happens to the skin resistance when the silver tarnishes?--Light current 22:00, 10 September 2005 (UTC)

I did some simple experiments on this some years ago. I took lengths of copper waveguide and measured the microwave attenuation (using a vector network analyser) before and after they were internally weathered or chromate conversion coated. Remarkably, neither had any significant effect! I concluded that either: 1) the surface 'corrosion' layer had the same high conductivity as the clean metal (very unlikely!); 2) the layer was such a good insulator that the current effectively moved deeper into the clean metal; or 3) the corrosion layer is so much thinner than the skin depth (which was less than a micron, ie < 0.001 mm) that only a small percentage of the current is flowing in it. StuFifeScotland 19:05, 28 October 2006 (UTC)

[edit] Change of Phase With Depth

A little known fact is that the phase of the current changes with depth, as well as the amplitude. This is touched on at the skin depth page, though in very mathematically language. It is quite intriguing to realise that, in the middle of the conductor, the current may actually be flowing the opposite way to that on the surface! StuFifeScotland 19:05, 28 October 2006 (UTC)

[edit] Table removed from article

rough draft -- please double-check these numbers, then remove this notice


material skin depth at 60 Hz skin depth at frequency f
(general) d = \sqrt{\rho} / \sqrt {\pi f\mu }
Copper 8 mm d = {65~\mathrm{mm}}/\sqrt { f/\mathrm{Hz} }
Transformer iron 0.1 mm d = {0.80~\mathrm{mm}}/\sqrt { f/\mathrm{Hz} }
Aluminum 10 mm d = {82~\mathrm{mm}}/\sqrt { f/\mathrm{Hz} }
Nickel 3 mm d = {23.5~\mathrm{mm}}/\sqrt { f/\mathrm{Hz} }
Steel  ???  ???
Water  ???  ???

[edit] Small note about minor edit summary

In my edit summary, I mentioned a person the nearest google to 'opoku kofi'. Having done a little research - as I should have done in the first place - it now appears that 80.87.70.4 has recently been adding little bits of text to (amongst other things) engineering-related articles. My edit summary thus contained irrelevant information.
Just clarifying. --Shirt58 10:27, 6 February 2007 (UTC)

[edit] Please put some "Whys" instead of "Whats"

I'm trying to understand various things to do with EM waves, yet all I can see on wikipedia is a bunch of "Whats", decribing what it is in words, then what it is formulae. But I want to know why!!!! Everything on this page is useful if you wanted to calculate the effect, or if you never heard of it and wanted to know what it is, but I've read all that, I know WHAT it is, I want to know why it is. Please, it's driving me nuts!!! -OOPSIE- 10:56, 27 February 2007 (UTC)

Agreed! From what (little) I understand, it's due to electromagnetic inductance and / or eddy currents or some such, but I'd love for there to be a nice explanation in the article. Nickwithers 03:44, 2 March 2007 (UTC)
I'll do my best. Meanwhile, take a look at the latest Eddy Currents article and the Discussion page of Skin Depth. I'll work on the Skin Effect and Skin Depth articles when time allows. At the moment, I agree that they are good engineers' articles, but the physics is rather cloudy. StuFifeScotland 15:08, 27 March 2007 (UTC)
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