I finally understand proximity effect - Page 1
Forum section: electronics / projects

author: cur8xgo
author_rank: Regular Contributor
timestamp: April 25, 2020, 03:48:35 am
content: It took me awhile...for good reason. What follows is a basic intuitive explanation of proximity effect. Correct me if I'm wrong.A few key ideas required to understand whats going on:"Flux does not penetrate a good conductor"-A changing magnetic field will induce an EMF in space. If there is a conductor in that space, a that EMF will induce a current in that conductor (eddy current). That current will oppose the original magnetic field (Lenz law)Therefore:The field in the core window of say an EE transformer will be straight lines, between the layers. Because any other pathway would be intersecting the conductors, and would be cancelled by the induced eddy currents.So now we have established a situation that pretty much (for purposes of this mental model) guarantees that there are eddy currents in the conductors of the transformer.For the moment, lets just agree that those eddy currents must, somehow, consume power. That shouldn't be a stretch for even a beginner to feel comfortable with.Those eddy currents are the "proximity effect".Now, to understand why they get so bad so quickly when layers increase:Yes, we've established how the field is shaped, but what about its magnitude?Before we continue, lets agree, that as the magnitude of the field being cancelled by the eddy currents goes up, the eddy currents go up. (Since they have to cancel a bigger field)Okay lets continue:Lets cut across the windings from the core surface to the outside of the secondary and see how the field changes.A cylinder wrapped around the core will have 0 MMF inside it. No current, no MMF.As we move our measurement into the first layer (primary) and there is current, MMF starts to go up, and keeps going up until we exit the first layer and are now in the space between the first and second layers.At this point we can continue moving through this very tiny space, towards the second layer, and MMF remains where it was until we enter the second layer and it starts to go up again.So, MMF across the windings goes up in a stair-step sort of way with each layer.Another way of thinking of this is probably simpler: per Amperes law, as you draw an imaginary cylinder around each layer, the MMF is proportional to the current in the number of layer(s) you have surrounded. Moving across empty space (although very thin) between the first and second layers, does not change the MMF , since you are still surrounding whatever current you were at the beginning of that space.Each layer adds to the MMF you have, and therefore, to the magnetic field that must be cancelled by the layer next to it. So as we agreed before, the magnitude of the eddy currents will go up as well.And here we are. Yes, the eddy currents go up. But it doesn't yet seem clear why it would be as dramatic as Dowells curves indicate. Lets modify our design to have a 5 layer primary, each layer being 1 turn with 1A in it. So whats our MMF as we expand our imaginary cylinder outward from the core?between layer 1 and 2: MMF = 1A/turn (note: only 1 turn per layer..just putting "turn" here because MMF is so often described as amp turns)between layer 2 and 3: MMF = 2A/turnbetween layer 3 and 4: MMF = 3A/turnbetween layer 4 and 5: MMF = 4A/turnoutside layer 5: MMF = 5A/turnThat first layer has 1A through it. Just imagine that MMF creating a field which cuts across the 2nd layer. It will induce an eddy current which will cancel it (causing the field to be only between the layers, and straight). The eddy current flows in a loop (otherwise it couldnt flow, it has to be in a circuit). The direction of its current is so that it cancels the field that created it nearest the field (space between 1 and 2). The rest of the eddy current loop is in the other direction, and that happens to be in the same direction as the primary 1A current.So lets look at the losses in our second layer:1A primary current1A going in same direction as primary current (part of eddy current circuit)1A going in opposite direction of primary current (part of eddy current circuit)If our first layer loss was just from 1A of current, it would be I^2R = 1W (say R is 1)Our second layer would have the same R, but the loss would be:2A in one direction so I^2R = 4W1A in the other direction so I^2R = 1Wso 5WFive times higher! Care to imagine what you get to in the 3rd, 4th, 5th layers? Its not pretty. And this is before taking skin effect into account which can easily increase the AC resistance of the layers to start with!So, some notes, at least for me:This mental model utility is pretty much over at this point. It explains intuitively whats going on, but does not tell you about the actual distribution of current in the conductors (EDIT: and therefore, critically, what the actual losses are). From what I can tell, you are unlikely to get a meaningful description of that without using a 2D simulator like FEMM or doing some really quite complex math. (FEMM is not that hard to use, I would recommend it)Also, the MMF does not actually go up in a perfectly stepwise fashion, since the current in each conductor is not distributed linearly across it, both because of skin and proximity effects.This model does explain why interleaving works to reduce proximity effect. Any reduction in the MMF between layers will reduce the magnitude of those eddy currents, and therefore the power losses from them. But this reduction in MMF doesn't hurt your transformer turns/volts effect because..hmmmm..actually I haven't thought of that but I'm comfortable it works out. You can probably model it as multiple transformers in series or something like that.Some other notes:It turns out Dowells curves have no theoretical basis. The paper on it was a bit much for me but I think it boils down to Dowells curves being a 1D approximation which requires a 2D set of inputs, and therefore makes no sense. Also, there are several important thing to do when actually trying to design to reduce proximity effect. I dont think theres a very good way to do it (or an excuse to do it) without using a 2D simulator. From the papers I read there are many surprises with how the current actually ends up distributing itself in 2D given the vast possibilities of frequency (skin depth), conductor geometry and window utilization, and design goals, that I think there may not really be a rule of thumb that is useful. Would definitely like to know if thats not the case though!