Talk:Skin effect

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.[1][2][3], etc.

It also turns out that designers of squirrel-cage induction motors must consider the skin effect. [4] (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)

[5] 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)

Steel is not a standarized thing; it should depend on the composition. the first ext link has a calculator and table which simplies things when sd is close to the radius.66.217.164.195 03:38, 14 August 2007 (UTC)

Power busbars are mentioned in every electromagnetics text. i think it's even mentioned in some freshman physics books, and it's certainly not extraneous.66.217.164.195 03:40, 14 August 2007 (UTC)

Seems to me a 10 metre diameter solid wire would carry a lot more current than a 8mm wire, even at a skin depth of 8mm. The cross-sectional area (carrying current) down to the skin depth is much higher for the 10 metre wire. Agreed anything thicker than 8mm might be wasteful. —Preceding unsigned comment added by 202.150.120.146 (talk) 10:18, 22 January 2008 (UTC)

A possible example of practical application of the skin effect on 60 Hz power is cross country power lines. They are often composed of three smaller conductors arranged in a triangular configuration instead of a single, larger diameter conductor. I have always believed this was to avoid wasting copper due to the skin effect. It also saves steel in the support towers. A picture of such power lines might be appropriate. --EPA3 (talk) 20:47, 20 August 2009 (UTC)

"I have always believed" is not on the approved list of reliable sources. A picture of this might be appropriate iff we find a reliable source.Ccrrccrr (talk) 22:13, 21 August 2009 (UTC)

Concerning the photograph of the high voltage transmission line and its caption, the reason for multiple wires grouped together is, (as I recall from university lectures many years ago), to reduce the electric field strength at the conductor surface. This reduces corona around the wire and hence losses and RFI. The bundled group simulates a very much larger wire. As regards to skin effect being a problem in transmission lines at 50 or 60Hz, whilst the line may have a large diameter, it is composed of a number of aluminium [or aluminum in North America!] wires spiral wrapped around a steel rope. Hence it is divided into a large number of individual strands which would reduce the resistance increase due to skin effect. I've not heard of skin effect concerns for HV transmission lines before, but I'm not a power distribution engineer, and it may be a "thing" - I'd be interested to hear if this is so. Jympton Spriggs (talk) 06:28, 25 November 2016 (UTC)

I believe the caption is correct, even if the main reason for the three wire bundle is to reduce field strength.Constant314 (talk) 10:20, 25 November 2016 (UTC)

Immaterial. The stranding of the cables would do all the work in this regard. Jympton Spriggs (talk) 02:35, 26 November 2016 (UTC)

Splitting transmission lines in bundles is often and intuitively attributed to the skin effect. Indeed the skin effect is not really a relevant factor here [1]. At low frequencies as in 50/60Hz the skin depth of aluminum would be around 11mm. This is considerably more than the usual thickness of the aluminium layer, which consists of separated wires, whereas the skin depth is based on the model of solid conductors. At a 3 layer conductor the contribution of the skin effect to the resistance of the line is less than 0.1% [2]. In contrast to the very small effect of the skin effect, there are many other good reasons for using bundle conductors, such as reduced corona discharge losses [3], reduced audible noise [4] and reduced EM interference. Therefore the picture of the transmission line in an article about the skin effect is misleading.

[1] [Morgan, V. T., & Findlay, R. D. (1991). The effect of frequency on the resistance and internal inductance of bare ACSR conductors. IEEE transactions on power delivery, 6(3), 1319-1326.] [2] [Conseil international des grands réseaux électriques. (2008). Alternating current (AC) resistance of helically stranded conductors. Paris] (21 rue d'Artois, 75008: CIGRÉ.] [3] [Clarke, E. (September 01, 1932). Three-Phase Multiple-Conductor Circuits. Transactions of the American Institute of Electrical Engineers, 51, 3, 809-821.] [4] [Sforzini, M., Cortina, R., Sacerdote, G., & Piazza, R. (March 01, 1975). Acoustic noise caused by a.c. corona on conductors: Results of an experimental investigation in the anechoic chamber. Ieee Transactions on Power Apparatus and Systems, 94, 2, 591-601.]

Grrrvn (talk) 18:08, 17 August 2020 (UTC)

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)

There are cases like a light bulb, where the resistance goes down when the element heats up (nonlinear resistance). this is used as a "trick" in amateur radio for LF antennas. i honestly don't know how to do the calculations for what you are describing; it's probably best done numerically on a computer.66.217.164.195 03:35, 14 August 2007 (UTC)

Whether a lamp's resistance goes up or down with temperature depends on the filament material. Early lamps, like Edison's, used carbonized bamboo, which had a negative temperature coefficient. Modern lamps use tungsten, and their resistance increases with temperature. In any case, at any particular filament temperature the lamp is resistive, even though its resistance parameter varies with temperature. — Preceding unsigned comment added by 2605:6000:E88B:F900:E4DD:DB44:1235:4672 (talk) 16:26, 9 April 2020 (UTC)

Lower bound for skin depth in silicon

There is a statement about the skin depth in silicon not being less than about 11m. This statement does not have a reliable source and I believe that it is incorrect, so I will remove it. There does not need to be any justification other than there is no reliable source cited, but I will give a more elaborate justification. The formula, as given, is correct if you can neglect dielectric loss. Any type of loss will decrease skin depth. Using these equations from wavenumber:

$\delta ={\frac {1}{k''}}$

$k=k'-jk''={\sqrt {-j\omega \mu (\sigma +j\omega \epsilon )}}={\sqrt {-(\omega \mu ''+j\omega \mu ')(\sigma +\omega \epsilon ''+j\omega \epsilon ')}}\;$ ,

In the equation for wavenumber, you see $\sigma +\omega \epsilon ''$. The dielectric loss term ands to the conductivity term. This effectively reduces resistivity as frequency increases. It is straight forward, but tedious, to carry out all the multiplications, gather terms, and apply the formula for the square root of a complex numbers. The result shows that if there is any dielectric (or magnetic) loss, then there is no non-zero lower bound. If someone would like to check the math, I would be grateful.

I plugged numbers in, assuming a dielectric loss tangent of 0.3% at 10GHz I got 0.9m at 10GHz. The conclusion that skin depth in silicon is deep enough to ignore is still correct. Of course, I could have made a mistake. If anyone would like to run the numbers, I used ${\epsilon ''}/{\epsilon '}=0.003,\epsilon _{r}=12,\sigma =435\mu \;\mathrm {S/m}$ Constant314 (talk) 23:52, 21 February 2021 (UTC)

I assume that is $\epsilon _{r}'=12$. I got $k''\approx 175$ nepers/meter, i.e. a skin depth of around 6mm. I agree that with dielectric loss, $k''$ increases to infinity. Without it, I got ${\frac {\sigma {\sqrt {\epsilon }}}{2\epsilon }}$ as the asymptotic value of $k''$ (in this case, around 21 nepers/meter, or a skin depth of around 5cm). Unsure why our answers differ. XabqEfdg (talk) 06:16, 9 June 2024 (UTC)

Rather than clutter up other people's watch list, lets continue the discussion at User:Constant314/Derivation of skin depth. Constant314 (talk) 17:56, 9 June 2024 (UTC)

Current density graph

Hi, first contribution here I think the graph labeled as "Current_Density_in_Round_Wire_for_Variuos_Skin_Depths" is wrong, or maybe I don't understand the scale. If the number labeled on each curve is skin_depth/wire_radius, let's consider a 1.0 ratio (which is not showed here), then, at the center of the wire, current density shhould be 1/e (~0.37) of Js (current density at surface). And so, at <1 ratio, value at should then be <1/e. However, curves seem to show a value way higher (~0.95 just for 0.9 ratio curve), considering a linear Y scale. WaldenoffFR (talk) 21:14, 11 March 2023 (UTC)

I drew the graph. It is correct; it is simply the evaluation of the equation given in that section. The relation that you are thinking about only holds when skin depth is small with respect to the radius of the wire. Constant314 (talk) 22:34, 11 March 2023 (UTC)

Derivation of skin depth

The new material seems to be only a derivation of the wave equation. You need several more steps to derive skin depth. But it is not necessary, since the equation δ = 1/k" appears in many reliable sources. The derivation should probably be removed under WP:NOTTEXTBOOK. Constant314 (talk) 17:51, 9 June 2024 (UTC)

Agreed, the detail is not necessary. I think there should be a section on electromagnetic waves though, or the mention in the lead should be removed. XabqEfdg (talk) 20:34, 9 June 2024 (UTC)