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Transformer proximity effect: Pri and Sec interaction? (aka Interleaving?)

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cur8xgo:
Okay I think I've had a bit of progress here.

I've been reading a dozen or so sources on magnetism, eddy currents, and skin and proximity effect.

My current favorite is this one:

https://flylib.com/books/en/1.389.1/proximity_effect.html

Specifically this part, which I think (or imagine) put together a critical concept in a single sentence that I did not see in the others, although several of them hinted at this indirectly:

"The skin effect and the proximity effect are two manifestations of the same principle: that magnetic lines of flux cannot penetrate a good conductor."

After contemplating this and reading about how a superconductor is essentially immune _permanently_ to even DC magnetic fields, I had an ah-ha moment (or a couple).

Suddenly all the mentions of "surface currents" and flux lines needing to end on currents made sense.

Any conductor experiencing a changing magnetic flux, will experience an emf according to Faraday's law, and therefore a current (since its a conductor).

This current will generate a field that opposes the field that created the eddy current, because Lenz's law.

Ah-ha moment #1: In a superconductor, this eddy current magnetic field will COMPLETELY cancel the originating field. Thus the eddy current truly exists on the "surface" of the superconductor (getting a little wierd here...whats the current density? but I think thats further than I need to go..). Also in a superconductor, that eddy current will go on forever and ever as long as the superconductor is superconductive. So it can essentially shield a static magnetic field.

Ah-ha moment #2: In a normal conductor, there are losses. So you can't have an eddy current circulating forever and canceling out the originating field for free. Heat will be generated and any canceling will be partial and decay.

Ah-ha moment #3: As frequency goes up, flux rate of change goes up, so the induced emf and therefore the eddy current magnitude goes up, increasing the skin and proximity effects. For skin effect this means fields which create eddy currents that reinforce current more towards the surface and oppose it more towards the center. For proximity effect this means eddy currents which reinforce current near the conductor which generated the field, and oppose it away from that conductor.

Next on the list, hopefully:

#4 - The whole thing where the field lines in a transformer core window exist only between the layers. I think I'm almost there. But with skin depth doesn't the field penetrate conductors at least a little?

#5 - So, proximity effect literally has currents going two directions in the same wire?

#6 - Finally completely understanding the diagram/concept that EVERY proximity effect document has..that thing where the currents are all adding up exponentially layer by layer. I get the idea its just not feeling totally sunk in yet. I think one thing that bothers me is where does one layer precisely begin and the previous one end, and what do things look like right there?




ejeffrey:

--- Quote from: cur8xgo on June 25, 2019, 02:41:07 am ---Specifically this part, which I think (or imagine) put together a critical concept in a single sentence that I did not see in the others, although several of them hinted at this indirectly:

"The skin effect and the proximity effect are two manifestations of the same principle: that magnetic lines of flux cannot penetrate a good conductor."

--- End quote ---

Yes, that is it.


--- Quote ---After contemplating this and reading about how a superconductor is essentially immune _permanently_ to even DC magnetic fields, I had an ah-ha moment (or a couple).

--- End quote ---

It isn't important for understanding proximity effect. but superconductivity is a bit different.


--- Quote ---Ah-ha moment #1: In a superconductor, this eddy current magnetic field will COMPLETELY cancel the originating field. Thus the eddy current truly exists on the "surface" of the superconductor (getting a little wierd here...whats the current density? but I think thats further than I need to go..). Also in a superconductor, that eddy current will go on forever and ever as long as the superconductor is superconductive. So it can essentially shield a static magnetic field.

--- End quote ---

Superconductors don't work the same way as conductors taken to the limit R=0.  A "perfect conductor" would just freeze in whatever magnetic field was present when the resistance became zero.  It would provide perfect reaction to any attempt to change the magnetic field.  When superconductors go through the superconducting phase transition, they either expel magnetic fields completely (the Meisner effect), or they form what is called a "vortex phase" where the magnetic field is concentrated into vortexes with diameter ~nanometers.  The vortexes themselves are in the normal state, and the rest of the metal is in the superconducting state and has zero field.

Also, superconductors have a skin depth called the london penetration depth that applies for even DC fields.  It on the order of 100 nm.  So even though the resistivity is zero, the current is distributed over some finite cross section which basically has to do with the carrier density.


--- Quote ---#4 - The whole thing where the field lines in a transformer core window exist only between the layers. I think I'm almost there. But with skin depth doesn't the field penetrate conductors at least a little?

--- End quote ---

OK, enough about superconductors, back to regular metals: yes, but it falls of exponentially.  Tim's example above was assuming that the winding thickness was much greater than the skin depth so that you could assume the current density drops to zero in the middle.


--- Quote ---#5 - So, proximity effect literally has currents going two directions in the same wire?

--- End quote ---

Yes, exactly.


--- Quote ---#6 - Finally completely understanding the diagram/concept that EVERY proximity effect document has..that thing where the currents are all adding up exponentially layer by layer. I get the idea its just not feeling totally sunk in yet. I think one thing that bothers me is where does one layer precisely begin and the previous one end, and what do things look like right there?

--- End quote ---

At the boundary between layers (some of) the induced current jumps from the inside to the outside and begins circulating on the other side.  If you have a spiral conductor with 1 amp, there will be one amp flowing from beginning to end, and a bunch of current loops superimposed on that.

T3sl4co1l:
Note that superconducting magnets can of course be charged,including freezing in an ambient field (as mentioned).

Interesting side effect: what does a "lossy" superconductor look like?  For it to be "super", it has to have zero DC resistance, so, that's out; but maybe it could have AC resistance?  And indeed, this seems to be the case; if nothing else, consider that YCBO remains a black ceramic (i.e., very lossy at visible frequencies) at all temperatures.  Somewhere between -- quite literally, "DC to light"! -- it goes from a perfect conductor (at small signals) to a good absorber.

As it happens, the crossover happens at frequencies on the order of the electron coupling energy (~meV, so, far IR or thereabouts), and in fact, exposure to light above this energy level does locally destroy superconduction.

For larger signals, it happens that vortices can be popped open just by applying enough field.  Like magnetic domains popping in ferromagnets.  You get the same* Barkhausen noise, for essentially the same reason. :)  The bulk effect overall is called flux pinning, and is how that superconducting levitating magnet track demo is possible.

*Don't think I've seen this discussed in a paper properly, but that should be right!?

Anyway, the supercurrent does indeed flow on the surface, about a Debye scattering length deep.  (This length describes the distance a charge's field carries through the material; in effect, the shielding ability of the material, or in a sense, the quantum equivalent of skin depth.  Optical penetration depth in metals is related.)  So, 10s-100s nm.

The current density is indeed quite high, which makes the local magnetic field extremely high -- if the critical field is exceeded, superconduction is lost.  So a lot of surface area is desirable -- in fact, cables are made of a great many strands, embedded in a metal matrix (which also serves as an eddy current brake if quenching occurs, getting merely incredibly hot instead of explosive arcing breakdown?), drawn down to stretch the superconductor into very thin (micron) wires, and this is stacked up to get thousands of strands together.

It's Litz for DC. ;D

(Mind, superconducting cable for AC, can't be metal matrix -- that'd be lossy -- this works just for DC cables and static magnets.)

Anyway, back to sort-of reality --


--- Quote from: ejeffrey on June 25, 2019, 03:52:07 am ---At the boundary between layers (some of) the induced current jumps from the inside to the outside and begins circulating on the other side.  If you have a spiral conductor with 1 amp, there will be one amp flowing from beginning to end, and a bunch of current loops superimposed on that.

--- End quote ---

Yeah, note where the arrows first double up on each layer of the diagram I marked up. :-+

Effectively, the proximity current wrapping around the conductor, where the above turn enters, is the image current of that winding entry.

Tim

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