It drops off slowly. The exponential equations (what almost everybody touts as "skin effect") actually does not describe what happens within a cylindrical conductor. It describes penetration depth for E/M waves that are normal to a flat surface. As the conductor morphs from flat to cylindrical, the fields within fail to fall off as the planar model describes.
If you wish to know the exact skin depth, you need to use
Bessels. And they do not describe skin depth as shallow as the exponential.
Well, write the equations... Show the exact solution, but use Bessels, as the exponential is wrong.
I will say, all your discussion of heating, surface area are are spot on. But you are not positioned to even worry about the regime I speak of. So glibly discounting the science... That is not an accurate position. However, the regime discussed is beyond the experience of most so is not a worry..
As a point of interest, my warm to cold feedthroughs traverse the room temp to 4.5 Kelvin domain, and as the copper gets colder the conductivity rises. As that happens the skin depth decreases. At 60 hz the conductivity at 20 to 50 Kelvin increases so much that the skin depth decreases to the .050 inch range, and the current density related dissipation begins to compromise the connections between the copper and superconductor, not a good thing. While we start with a 2 inch diameter copper conductor, by the time it gets to liquid helium temps it's just a 2 inch diameter shell of .050 thickness, resistive wise.
The navy with their superconducting motor drive r and d...the superconducting windmill turbines..all have to worry about these details..me, I just worry about lunch...
Jn
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As an added interest....
One of the reasons for load PFC is skinning and proximity effect caused conductor dissipation because of the harmonics. A load panel and it's bus bars will have a specific ampacity at 60 Hz, but 120 and 180 Hz currents from non corrected loads can exceed the panel ratings heat wise even though the base load draw is within the ratings.
If your load draws large 2nd and 3rd (or 12th as in some of our large scr based 3 phase supplies), you have to consider additional derating of the load panel.
Most consider only the harmonic impact on transformers, and neglect the poor load panel..
Jn
One of the reasons for load PFC is skinning and proximity effect caused conductor dissipation because of the harmonics. A load panel and it's bus bars will have a specific ampacity at 60 Hz, but 120 and 180 Hz currents from non corrected loads can exceed the panel ratings heat wise even though the base load draw is within the ratings.
If your load draws large 2nd and 3rd (or 12th as in some of our large scr based 3 phase supplies), you have to consider additional derating of the load panel.
Most consider only the harmonic impact on transformers, and neglect the poor load panel..
Jn
I found this on internet... quite easy to read ....
What Is the Skin Effect? | Reactance and Impedance -- Inductive | Electronics Textbook
What Is the Skin Effect? | Reactance and Impedance -- Inductive | Electronics Textbook
A quick google search for skin and proximity effect heating provided this article...pardon my not knowing how to properly cite it..it is excellent, a must read for anybody working multiconductor, tray, conduit in high current distribution systems.
Proximity Heating Effects in Power Cables
Jonathan Blackledge, Eugene Coyle and Kevin O’Connell
Engineering Letters, 21:3, EL_21_3_01
(Advance online publication: 19 August 2013)
I copy verbatim the discussion as it pretty much reinforces what I've been stating..they do some really neat analysis..
X. DISCUSSION
The phenomenon of both the skin and proximity effect,
although recognised as reducing the ampacity of cables, has
not yet evolved into a set of de-rating tables that can be easily
applied on a day to day basis in engineering design. The
problem in quantifying harmonic heating effects is that they
are a function of frequency. The greater the harmonic distortion present, the larger the number of harmonics present.
Each harmonic current generates its own individual heating
effect and thus, a harmonic rating factor has to be taken into
account for a large number of individual elements. Further, in
general, proximity effects tend to be understated because the
effect on extraneous metalwork including metal enclosures
such as cable trays and metal cladding on cables, has, to
date, not been fully considered either experimentally or in the
Standard International Electrotechnical Commission 60287-
1-1. It is for this reason that, the model considered in the
paper has been developed
jn
ps...the only caveat to this discussion as well as that paper, is that it is being assumed that that stranded copper wire is isotropic. IT IS NOT!! A solid conductor will have isotropic conductivity, but a stranded one has higher conductivity axially and less radially. As a result, several things additionally happen. First, as the strands twist along the cable, for the current to remain crowded at one edge of the conductor, the current has to jump from strand to strand. That introduces a resistive proximity effect loss component that a solid conductor will not have. Second, a stranded conductor will not have as much skin and proximity effect as a solid one. Third, a very aged stranded conductor will be even worse w/r to radial conduction, showing more anisotropy.
This is a very common concern in the superconductor rutherford cable used for magnets.
Proximity Heating Effects in Power Cables
Jonathan Blackledge, Eugene Coyle and Kevin O’Connell
Engineering Letters, 21:3, EL_21_3_01
(Advance online publication: 19 August 2013)
I copy verbatim the discussion as it pretty much reinforces what I've been stating..they do some really neat analysis..
X. DISCUSSION
The phenomenon of both the skin and proximity effect,
although recognised as reducing the ampacity of cables, has
not yet evolved into a set of de-rating tables that can be easily
applied on a day to day basis in engineering design. The
problem in quantifying harmonic heating effects is that they
are a function of frequency. The greater the harmonic distortion present, the larger the number of harmonics present.
Each harmonic current generates its own individual heating
effect and thus, a harmonic rating factor has to be taken into
account for a large number of individual elements. Further, in
general, proximity effects tend to be understated because the
effect on extraneous metalwork including metal enclosures
such as cable trays and metal cladding on cables, has, to
date, not been fully considered either experimentally or in the
Standard International Electrotechnical Commission 60287-
1-1. It is for this reason that, the model considered in the
paper has been developed
jn
ps...the only caveat to this discussion as well as that paper, is that it is being assumed that that stranded copper wire is isotropic. IT IS NOT!! A solid conductor will have isotropic conductivity, but a stranded one has higher conductivity axially and less radially. As a result, several things additionally happen. First, as the strands twist along the cable, for the current to remain crowded at one edge of the conductor, the current has to jump from strand to strand. That introduces a resistive proximity effect loss component that a solid conductor will not have. Second, a stranded conductor will not have as much skin and proximity effect as a solid one. Third, a very aged stranded conductor will be even worse w/r to radial conduction, showing more anisotropy.
This is a very common concern in the superconductor rutherford cable used for magnets.
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Somebody translated my anti-skin-effect method article from 199x into english:
Self-made high-quality audio without skin effect
They called it "Self-made high-quality audio without skin effect".
Self-made high-quality audio without skin effect
They called it "Self-made high-quality audio without skin effect".
Who said that?
Wikipedia?
You read these letters on a monitor screen now - because skin-effect causes inductivity (electromagnetic induction) in coils in power supply of your monitor.
Skin-effect is a fundamental feature of ANY TWO+ FLYING ELECTRONS, regardless of their AC frequency.
Polyphonic musical signal has time-to-time very high gradients, equal to very high frequency (Ageyev's theorem).
Thats it. Very simple.
Very simple to anyone, who graduated from university or colledge.
Wrong even at 50 Hz power transmission it is common to use 3 or 4 conductors spaced to make maximum use of the metal
Avoiding "skin effect" in high power voltage transmission | Huggins Photography
Unlikely to be a problem with HiFi though.
Well it's much more important at radio frequencies.
At audio and power line frequencies, you have to consider:
a] conductor diameter
b] circuit impedance
c] frequency
d] circuit/cable, loop/series inductance.
* * * * * * * * * *
while it's a factor in huge AC power lines, it's overwhelmed by other factors in speaker cables.
What have switched mode power supplies running way above audio frequencies got to do with audio cables?
That is grade A USDA approved BS. Show us these gradients from your music collection. You will find none.
Riiight. So you saying you are superior or something?
Gentlemen, permit me to demonstrate the sound of my anki-skin-effect cables - by the sampled record of Ben Webster (saxophone), Jazz, 1977.
Ben Webster (1977) "Wrap Your Troubles In Dreams" (LP) vinyl - YouTube
I have made this sampling a year ago, in winter 2019.
Other details here, in other thread:
2N2222A phono preamp
Ben Webster (1977) "Wrap Your Troubles In Dreams" (LP) vinyl - YouTube
I have made this sampling a year ago, in winter 2019.
Other details here, in other thread:
2N2222A phono preamp
Pink Floyd DSOM
Hm-m-m-m....
Maybe music from England will satisfy Your taste?
How about english group called "Pink Floyd"?
Little known song called "Time"?
No?
Yes?
Here my another sampling from vinyl:
"Time" Pink Floyd (1973) "The Dark Side of the Moon". Vinyl (LP). - YouTube
I apologize for quality: vinyl disk is 47 years old, the MM head is 15+ years old, photo stage/receiver is 50 years old,
BUT the anti-skin cables are NEW!
See comparison with CD/vinyl:
The Dark Side of the Moon: analog & digital comparison (CD, SACD, Vinyl, Tape) - YouTube
I see you don't like Jazz?
Hm-m-m-m....
Maybe music from England will satisfy Your taste?
How about english group called "Pink Floyd"?
Little known song called "Time"?
No?
Yes?
Here my another sampling from vinyl:
"Time" Pink Floyd (1973) "The Dark Side of the Moon". Vinyl (LP). - YouTube
I apologize for quality: vinyl disk is 47 years old, the MM head is 15+ years old, photo stage/receiver is 50 years old,
BUT the anti-skin cables are NEW!
See comparison with CD/vinyl:
The Dark Side of the Moon: analog & digital comparison (CD, SACD, Vinyl, Tape) - YouTube
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