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

[cur8xgo]

I am trying to grasp whats going on with proximity effect in the case of multiple windings interacting.

For instance as described here: http://ridleyengineering.com/images/phocadownload/13%20proximity%20loss.pdf

I think I get it when we are talking about one winding by itself. Conductor thickness / skin effect ratio, use Dowell equation for total layers, voila Rac/Rdc ratio.

However, I don't really have a mental model for how multiple windings are interacting, for instance primary and secondary in a two winding transformer.

I see all the ingredients are there for interaction and optimization..currents going in opposite directions, gains from reducing layers, interleaving windings, etc...

And that document describes interleaving.

However its not sinking in. I am missing something.

In my dream world they do not interact at all and I can just calculate the Rac/Rdc ratio of the secondary as if the primary isn't there.

And in this way optimize the design for proximity effect for both primary and secondary.

Or I suppose, my dream world could exist if the windings are just not overlapped and are on different parts of the core. (true I think?)

T3sl4co1l: I know you recommended an interleaved design and I wish I understood how it works but I don't yet.

[MagicSmoker]

Oversimplifying somewhat, proximity loss is the same as skin effect (which itself is the product of eddy currents), except the source of the alternating magnetic fields is adjacent winding layers in which current direction/polarity is the same. As each new layer is added to a winding, the magnetic fields from all of the layers in it sum together in stepwise fashion. Hence you want to minimize the number of layers.

If a winding layer has current flowing in the opposing direction, as happens when you go from primary to secondary in a forward converter, then the magnetic fields cancel each other out, also in stepwise fashion from the point of meeting. Thus, you can also minimize proximity loss by alternating between primary and secondary each layer if you must have more than one layer for each winding. Alternating layers, or interleaving, also reduces leakage inductance, so would seem to be a win-win all around, except that each time you change from primary to secondary (or vice versa) you might need to wind 1-3 layers of insulating tape to meet safety agency requirements, and you will also need to bring these layers out to a pair of pins on the bobbin, so there are practical limits to the number of alternating layers which can be accommodated. Also, interleaving increases the stray capacitance between the primary and secondary which makes common mode noise worse. Lots of nuances involved here...

...quite a few of which I am leaving out, but if all you remember is that you can minimize proximity effect first by minimizing the layer count (even if that means reducing the wire diameter, which might seem counterintuitive at first blush) and second by interleaving the primary and secondary, where space, bobbin pin count, stray capacitance and labor cost to wind the transformer permit (them being some of the nuances involved here).

[cur8xgo]

Oversimplifying somewhat, proximity loss is the same as skin effect (which itself is the product of eddy currents), except the source of the alternating magnetic fields is adjacent winding layers in which current direction/polarity is the same. As each new layer is added to a winding, the magnetic fields from all of the layers in it sum together in stepwise fashion. Hence you want to minimize the number of layers.

Okay to try and make sure my thinking is consistent: it should not surprise me that the field from each turn add like this. After all, thats exactly what one designed the winding to do in the first place, although the goal was to have that field confined to the core. The field outside the core is the leakage field of the transformer, correct?

To validate that idea, if you designed a transformer with the same turns for pri and sec, and wound both windings simultaneously in a single plane (multiple layers though), with, lets say foil so its easier to imagine, would you end up with a zero leakage inductance transformer? And, simultaneously, zero proximity effect transformer? I would think skin effect would still be present though.

If a winding layer has current flowing in the opposing direction, as happens when you go from primary to secondary in a forward converter, then the magnetic fields cancel each other out, also in stepwise fashion from the point of meeting. Thus, you can also minimize proximity loss by alternating between primary and secondary each layer if you must have more than one layer for each winding. Alternating layers, or interleaving, also reduces leakage inductance, so would seem to be a win-win all around, except that each time you change from primary to secondary (or vice versa) you might need to wind 1-3 layers of insulating tape to meet safety agency requirements, and you will also need to bring these layers out to a pair of pins on the bobbin, so there are practical limits to the number of alternating layers which can be accommodated. Also, interleaving increases the stray capacitance between the primary and secondary which makes common mode noise worse. Lots of nuances involved here...

...quite a few of which I am leaving out, but if all you remember is that you can minimize proximity effect first by minimizing the layer count (even if that means reducing the wire diameter, which might seem counterintuitive at first blush) and second by interleaving the primary and secondary, where space, bobbin pin count, stray capacitance and labor cost to wind the transformer permit (them being some of the nuances involved here).

The thing I don't get here, is why do you have to alternate? Why can't you just wind them simultaneously the whole way (or until one winding has all its turns)?

Also my model is breaking down when I try to figure out why the current density (proximity effect) increases step wise for each layer.

I see the winding as creating one big summed field. The only reason I can see current decreasing in each layer is that somehow the field from each layer can only affect the conductor immediately next to it. Why would that be true though?  Cant the field from layer 1 reach out and influence field 15?

So trying to imagine this..I realize the system has to be analyzed at an "operating point" and can't be looked at as cause and effect for each layer.

So if we say the winding has a certain current through it, obviously, the same for all layers, the outer layer is going to have the worst current density because.....why?

BTW Colonel McLymans Transformer and Inductor Design Handbook has a section on proximity effect and my instinct tells me the answers are there..I just can't seem to make it all fit in my head.

[cur8xgo]

This picture is probably explaining everything I just dont get it though

"Flux does not penetrate conductors"?? Aren't the currents going in the same direction?

[cur8xgo]

Here too..I have been just reading and re-reading this. I have to figure out why this isn't sinking in.

[MagicSmoker]

Oversimplifying somewhat, proximity loss is the same as skin effect (which itself is the product of eddy currents), except the source of the alternating magnetic fields is adjacent winding layers in which current direction/polarity is the same. As each new layer is added to a winding, the magnetic fields from all of the layers in it sum together in stepwise fashion. Hence you want to minimize the number of layers.

Okay to try and make sure my thinking is consistent: it should not surprise me that the field from each turn add like this. After all, thats exactly what one designed the winding to do in the first place, although the goal was to have that field confined to the core. The field outside the core is the leakage field of the transformer, correct?

Let's leave leakage inductance out of this for now. It is hard enough to explain proximity effect and I have bungled doing it before!

The first thing to keep in mind is that in a true transformer (as compared to a flyback transformer or choke/inductor) the primary and secondary fields resulting from actual power transfer are supposed to completely cancel out (they don't, and that gives rise to leakage inductance, but I digress on something I expressly said I wouldn't). As a result, the only field left in the core of a true transformer is the result of "magnetization" - basically, a small amount of current that flows in the primary when the secondary is open circuit (as a result of the magnetizing inductance). This implies that the core of a true transformer can transfer almost limitless power regardless of its cross-sectional area, and that is theoretically true.. so long as the windings are superconductors, anyway. But I digress AGAIN.

The next thing to keep in mind is that Dowell treats each layer of a winding as a sheet or foil producing a magnetic field of x amp-turns, where x is the number of turns times the current through any one of them. Thus, when a second layer is wound on top of the first its field adds to the first's, so that the field strength at the top of the second layer is twice that at the top of the first layer, and so on. If a layer for a winding conducting current in the opposite direction is placed next then its field will cancel out that of the layer beneath it. Just as eddy currents force current out of the center of a conductor towards its periphery, proximity effect forces current away from the high field strength side of a layer to its low field strength. Minimizing the effective number of layers makes the most use of the wire diameter (or foil thickness) in each winding, then.

To validate that idea, if you designed a transformer with the same turns for pri and sec, and wound both windings simultaneously in a single plane (multiple layers though), with, lets say foil so its easier to imagine, would you end up with a zero leakage inductance transformer? And, simultaneously, zero proximity effect transformer? I would think skin effect would still be present though.

That's called bifilar winding and it does, indeed, reduce both leakage inductance and proximity effect. It drastically increases stray capacitance between primary and secondary, however, and no safety agency in the world will approve it even if quad-build magnet wire is used.

Also my model is breaking down when I try to figure out why the current density (proximity effect) increases step wise for each layer.

Note sure how to help you visualize this. There are likely some good illustrations on the google (or duckduckgo) machine if you do an image search for "proximity effect" in transformers or the like.

I see the winding as creating one big summed field. The only reason I can see current decreasing in each layer is that somehow the field from each layer can only affect the conductor immediately next to it. Why would that be true though?  Cant the field from layer 1 reach out and influence field 15?

Same comment as above, except I'll add that you should think of the field as amp*turns, but use Dowell's transformation which treats a layer with, say, 10 turns, each carrying 10A, as equivalent to a foil of the same width carrying 100A. It might be easier to visualize the vector summation of fields from stacked layers that way. Or maybe not. I learned this - in much the same painstaking and difficult way you seem to be experiencing - about 20+ years ago.

[T3sl4co1l]

A toy situation may help.  Consider a transformer made from multiple turns of full-width solid sheet.  The sheet is much thicker than the skin depth, therefore any current appearing on one side, is isolated from any current on the other side.  It's an effective shield.

If we have one turn of this sheet, around a core, then magnetizing current flows on the inside surface.  (The image current is simply that of the field.  If you like, the core itself acts as an inductive load.)

If we have two turns, the current of the outer turn (which flows on its inside surface) sees the adjacent turn -- it doesn't see the core, it's shielded by the sheet under it.  So it induces an equal current in the inner turn, around its outside surface.  But now the inner turn is carrying two currents, equal and opposite.  But not actually opposite, because the total is still one current, so the current curls around the edge of the sheet and flows on the inside surface doubly.  Which increases the losses by, what, 5 times?  (1 for the extra outer current, plus 2^2 = 4 for the inner current, total 5.)

If we have a single turn primary and secondary, the same thing happens, but with the magnetizing current being small (assuming a high inductance core here, for a transformer as such) and the load current appearing on the facing sides of the primary and secondary (so, if primary is on top, then its inner surface, and the secondary's outer surface).  And if we stack up turns for each section, the above effect happens, towards the facing sides rather than towards just the inside.

If we interleave primary and secondary, then we always have complementary induced currents, and for that matter, for example if we have a pair of sheets rolled up as a 1:1 transformer, then in the middle of the roll, we have complementary currents on the inside and outside facing surfaces of each conductor -- we've actually halved the current density compared to the single layer case!

As for wire windings -- they are more permeable to magnetic fields (they aren't solid shields) -- but a similar thing happens within the cross section of a single wire.  There is also a proximity effect between adjacent turns within a layer, and so there can be some value in increasing the winding pitch from closest spacing (this is most apparent in single layer air-core inductors, where the Q goes down by almost half at closest spacing, from a maximum Q at pitch = 2 * conductor dia.).

Incidentally, this may perhaps give some insight into why thick sheets don't make good windings either -- the current is forced out to the edge, especially when multiple turns are stacked without interleave (the induced current curling around the edge to reach the other side).

Tim

[MagicSmoker]

Here's a decent video on proximity effect:

[cur8xgo]

Thanks MagicSmoker and T3sl4co1l. I have not seen that video and I'm going to watch it. I'm also going to study what you both wrote.

I'm using several different sources on this topic to try and triangulate what I'm missing:

Dowells original 1966 paper
Colonel McLyman's Transformer and Inductor Design Handbook (has proximity effect section)
Ridley engineering PDF as linked before
Intro to power electronics powerpoint from Univ. Colorado http://ecee.colorado.edu/~ecen5797/course_material/Lecture35slides.pdf

I'm noticing a common theme between all these sources: the stepwise mmf, the representing "net" current.

There are some things which bother me though and I need to resolve. But I'm going to put it all into one post here after I look at the video and get my thoughts together.

[cur8xgo]

I think I need to step back a bit. I'm noticing that I am having trouble with even the most basic proximity effect descriptions.

For instance, heres an image from the U of Colorado slideshow:

http://ecee.colorado.edu/~ecen5797/course_material/Lecture35slides.pdf



There are several things I don't get about this simple diagram. Heres my thinking:

-We are looking at two rectangular conductors, each much thicker than skin depth.

-Presumably they are wrapped to the left..so they come out of the page and turn left, making conductor 1 the inner conductor.

-Current density for conductor 1 is pressed up to its outer edge.

-Its not clear to me what is causing this, from this diagram. I'll take a stab at it:

-We have "i" in conductor 1 (C1). Presumably this is the actual winding current (not an eddy current).

-i in C1 creates an mmf INSIDE of it, which is not shown on the diagram.

-i in C2 creates an mmf (and therefore flux) which IS shown on the diagram, between C1 and C2. This mmf should be twice the mmf that C1 generated. Therefore C1 is experiencing "two mmf".

-The mmf C1 experiences, according to the right hand rule, should generate a current that is flowing out of the page, in the same direction as the winding current.

-But here Im losing the track..."i" is already on the diagram, and I have lost the cause and effect trail.

-the "-i" in C2 doesn't really make sense to me.

BTW the video was a bit paint-by-numbers, he didn't seem to be interested in explaining the underlying mechanism, more like how to just plug the numbers in to the equation.

[jmelson]

Why can't you just wind them simultaneously the whole way (or until one winding has all its turns)?

This would make the BEST transformer, in terms of coupling between windings.  BUT, on the other hand, it would be worst for interwinding capacitance.
Also, hard to maintain isolation between windings where that may be required (line voltage vs. low voltage).  This would be called a bifilar (or trifilar, etc.) winding, and there are places where it is used.  But, the interwinding capacitance can be a real issue.

Jon

[cur8xgo]

This is my idea of how the proximity effect eddy current flows...but I know something is wrong here.

This is a view I don't see in the texts. Showing the winding as a spiral with the top of the core removed.

Does the eddy current  take this long circuitous path around the entire conductor length? If not..why would it "cross" at any particular point?

Also this doesn't explain why the current density gets distorted...

EDIT: Yes this shows current going two opposite directions inside a conductor. So what I think ends up happening here is..the eddy "current" superimposes on the other current in the wire and thats what distorts the current density.  However I don't see how the magnitude of the eddy current is near the same as the main current. And does the eddy "current" (or effect) increase stepwise each layer?

[T3sl4co1l]

-i in C1 creates an mmf INSIDE of it, which is not shown on the diagram.

-i in C2 creates an mmf (and therefore flux) which IS shown on the diagram, between C1 and C2. This mmf should be twice the mmf that C1 generated. Therefore C1 is experiencing "two mmf".

-The mmf C1 experiences, according to the right hand rule, should generate a current that is flowing out of the page, in the same direction as the winding current.

The concentric circle and dot are showing current out of the page, and the crossed circle, into.

The winding direction (curling to the right or left) doesn't matter, if there are conductors to the right of these which are carrying the load current i.

If there are no other conductors and this is a lone inductor, then the right side is where the currents are piling up, so the right side is towards the center of the core.

Tim

[T3sl4co1l]

Corrected diagram:



The trick is, we can only add up currents in the cross section, as long as the cross section is a true representation of the circuit.  Sooner or later the turns need to actually get into the cross section, though, and that is where we must break away from the 2D model and consider the 3D fields.  Namely, the eddy currents wrap around the affected conductor, where the outer conductor enters.

I also drew eddies on the "start" lead just because.

Ed: oh, the 2nd layer turnaround arrows should be a single one. That doesn't add up as shown.

Tim

[cur8xgo]

Corrected diagram:



The trick is, we can only add up currents in the cross section, as long as the cross section is a true representation of the circuit.  Sooner or later the turns need to actually get into the cross section, though, and that is where we must break away from the 2D model and consider the 3D fields.  Namely, the eddy currents wrap around the affected conductor, where the outer conductor enters.

I also drew eddies on the "start" lead just because.

Ed: oh, the 2nd layer turnaround arrows should be a single one. That doesn't add up as shown.

Tim

Thanks! That took some work and I appreciate it. I'm going to go through a day or two of study and see if I can get to the next stage of understanding, your drawing will be very useful.

[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]

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."

Yes, that is it.

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).

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

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.

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.

#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?

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.

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

Yes, exactly.

#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?

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.

(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 --

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.

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