Does low transformer coupling cause increased core flux? - Page 1
Forum section: electronics / projects

author: kubeek
author_rank: Contributor
timestamp: December 21, 2017, 10:04:49 pm
content: I am wondering about how does leakage inductance contribute to total core flux?I think that if I understand correctly, then the flux caused by magnetizing inductance would be the same as in a perfect transformer, but what effect does the reflected current from the secondary cause?It seems to me that the reflected current through Ll1 would add to the core flux and increase it in a hotspot where the leakage lines go through the core.But on the other hand, the leakage loop goes through air around the core, so wouldn´t the vast difference between u0 and u and long length of gap cause the reluctance of the loop to be high and therefore the additional flux to be low (from equations in flux5.png)?(btw how do you write the symbol for micro in this forum?)

author: chris_leyson
author_rank: Super Contributor
timestamp: December 21, 2017, 11:51:48 pm
content: I would say that leakage inductance doesn't contribute to core flux because the leakage inductance is due to stray magnetic flux that is not coupled through the core. Less than perfect coupling results in leakage inductance and the lower the coupling the greater leakage inductance until you reach a point where you have zero coupling, k=0, and you end up with two uncoupled independant inductors.Reflected secondary current will add or subract to total core flux depending on the current direction with respect to the primary.QuoteThat's a good point and I suspect that there are two reasons for that line of thought.Firstly, some diagrams are badly drawn and give the impression of leakage flux passing through the core when in fact the leakage flux doesn't pass through the core. It's the windings that generate or pick up the flux and not the core, the core is just a means of physically steerinfg the flux.Secondly, gapped cores, if the gap is very small then most of the flux will pass across the gap but as you make the gap larger then the field spreads out and so does the flux. With large core gaps some of the flux will couple to the innermost windings adjacent to the core gap and effectively increase their resistance and then they will therefore run hotter.It's two different flux coupling mechanisms, poor winding to core coupling gives rise to leakage inductance but poor coupling across a core gap gives rise to localised heating. Maybe a lumped "gap leakage" model could be formulated to account for gap coupling. Anyway, it's two different flux leakage mechanisms and you have to model that with different models, not easy.

author: kubeek
author_rank: Contributor
timestamp: December 22, 2017, 12:49:48 am
content: I think I mislead you with the gapped core analogy. What I meant was, that when you look at the second picture in flux1.png, the current goes throug that "external" inductor. But what is that core of that inductor and how does it realte to the actual core of the transformer? My idea was to look at it like it is shown in the first picture, where for the leakage loop it is a short piece of core material and a big air gap around that, and for that I wanted to apply the equations for a normal gapped core, hence the last sentence of that post.Something tells me that the leakage would make the flux from primary and secondary unbalanced under load and increse the peak core flux in that spot, but I cannot grasp the mecahnism yet or prove it otherwise. On the other hand the case of zero coupling leads to the simple inductor case, so that seems to disprove that idea, but could there be a sweetspot in the middle where the flux actually increases before going back to just the magnetizing flux?

author: T3sl4co1l
author_rank: Super Contributor
timestamp: December 22, 2017, 02:26:42 am
content: By definition, it doesn't contribute to core flux. That's why it's leaking.More precisely, the flux that leaks between the winding and core, is leakage that constitutes lost core flux.This is different from the leakage between windings, because the geometry is different.If the secondary were wrapped evenly around the core (like a solid foil wrapping, completely covering the core, except for a slit along the inside where the secondary terminals are connected), then the secondary and core fluxes would be identical.If the windings are on opposite sides of the core (as the cartoon suggests), the leakage between windings is about twice the winding-to-core leakage.Tim

author: kubeek
author_rank: Contributor
timestamp: December 22, 2017, 01:35:48 pm
content: Quote from: T3sl4co1l on December 22, 2017, 02:26:42 amI thought that leakage flux is by definiton flux created by one of the coils that doesn´t reach the other coil. That doesn´t mean it doesn´t go through the core, it just exits somewhere along the way and returns around the core, right?

author: T3sl4co1l
author_rank: Super Contributor
timestamp: December 22, 2017, 03:03:37 pm
content: The leakage between windings, yes. Which can involve the core. I'm modifying (generalizing) the definition slightly, so as to talk about winding-to-core and core-to-winding leakage.Another way to think of it, relevant to real devices and materials: when the core saturates, the self-inductance of any given winding is only its leakage inductance.Tim

author: chris_leyson
author_rank: Super Contributor
timestamp: December 22, 2017, 03:43:22 pm
content: I see what you mean now, and to be honest I don't think it's as simple as I made out. You're right, the leakage flux is the flux that doesn't make it to the other winding and I think most of it must go through core, I was thinking of the flux that doesn't make it through the core. If you consider a winding on a core, for example, lets say the magnetizing inductance is 1mH and the leakage inductance is 20uH or 2% of the magnetizing inductance, now if you change the core material for something that has a lower permiability or make the core gap a little larger so you have a magnetizing inductance of 500uH then the leakage inductance will be 10uH so the leakage flux has to go through the core. In other words for a fixed core and coil geometry the magnetizingandleakage inductance will scale with the core permiability so the leakage flux has to pass through the core. Of course some of the flux won't make it through the core but that will only add a tiny amount to the leakage inductance.I think I could also be wrong about flux leaking from the core gap and causing localised heating in the turns near the gap, for some reason I said the resistance increased but I need to look into that one. I have seen a few flyback transformers where the primary turns around the core gap had overheated.Finally to get back to what the OP was asking in the first place, does leakage flux cause localised hot spots in the core ? I would say that in general the leakage flux is only a few percent of the magnetising flux so it wouldn't contribute very much to the total flux and wouldn't give rise to localised heating. There are cases where you actually want more leakage inductance, LLC converters or coupled inductor converters like the zero ripple Cuk converter for example, but as long as you keep the flux density within reasonable limits I don't these topologies cause anymore core heating.

author: T3sl4co1l
author_rank: Super Contributor
timestamp: December 22, 2017, 04:19:34 pm
content: BUT, if you have a k factor that high, you must have the windings on top of each other, and in that case, the only place the windings can leak to, is the space between themselves. And that does not depend upon the core!Indeed, if you take a winding on a bobbin, and measure the leakage while pulling the core on and off, you'll find it changes by less than 10%!Localized heating near the gap is due to the intense H-field there, which induces eddy currents in the metal. H-field is present around all the turns, by nature (because the turns are carrying current!), but it's concentrated by a large factor (say 10x or more) for wires close to the gap.Same goes for proximity effect, where, for a given turn, the H-field from all the turns above and beside it, causes current to bunch up, reducing ampacity / increasing loss.For resonant applications, you're storing a fair amount of energy in the leakage, so it matters how it's obtained. If it's air gap between windings, you're fine -- the loss might not be great because it's basically copper on copper, but the core isn't involved, so you know it won't cause problems there. On the other hand, if it's implemented through magnetic shunts, you have primary and secondary core paths, and the fluxes (linked and leaked) are explicitly in core, and you'd have to run the numbers on core loss.Cores don't generate hot spots, but you can get hot corners because flux density concentrates around inside corners of bends, and outside corners of gaps (because fringing). Well, I suppose there could be hotspots due to inhomogeneous materials, but that'd be some pretty crap material.Tim