Toroidal core winding limitations

Question

For traditional laminated EI mains frequency power transformer cores, the core dimensions and core material determine, for a given primary voltage and frequency, a minimum number of primary turns required to prevent core saturation. There is of course some wiggle room in deciding what level of flux defines "saturation", but as a first approximation, the original claim is true.

Once the number of primary turns is determined, the VA capability of the transformer is limited by (among other things) the winding ampacity (current carrying capability). Therefore, classically, transformer designers would use as much copper as would fit through the core's window to minimize copper losses, and heating, and consequently maximize VA rating. Typically, half the window space would be filled with copper for the primary winding, and the other half would be for the secondary winding(s).

However, I have noticed that this design principal does not seem to be applied to toroidal mains frequency power transformers. That is, the core window tends to contain significant area that is not filled with copper. For example: taken from here.

Obviously, there are physical interference problems with adding more copper. There is a given wire thickness such that number of primary turns will completely cover the surface of the interior hole of the toroid. But there should be another (larger) thickness such that two layers, (each with a different number of turns) would have, in total, the required number of primary turns. Or alternatively, there could be two layers with different diameter wires, each with the required number of primary turns, which are wired in parallel. Yet a third possibility, is to have one layer with the required number of primary turns, a second layer with almost that number with the remainder forming a sparse third layer.

It seems to me that the mechanical problems are increasing the copper through the window of a toroidal transformer are not insurmountable.

My question is, given that a higher price may be charged for a transformer with a higher VA rating, other things being equal, why do manufacturers of mains frequency toroidal power transformers leave such a large area in the window of the core empty of copper? Is there some other limitation on the VA rating of a toroidal core transformer such that adding more copper would not increase the VA rating? Is there some other factor, such as flux leakage, that would sufficiently offset economic advantage of higher VA rating? Or is it simply that the technical challenge of adding more copper would offset the price advantage?

---

Edit: I just watched a video by Sam Ben-Yaakov entitled "Skin and proximity effects: an intuitive explanation of Dowell’s loss model". In this video, Sam Ben-Yaakov explains that a counter-intuitive effect is sometimes observed in multi-layer magnetic windings. In some cases, using larger wire and multiple layers can have greater AC resistance than using smaller diameter wires with fewer layers. This counter-intuitive effect is the result of the proximity effect.

The skin depth of copper at 60 Hz is about 8.5 mm. So, except for high current transformers, the skin effect will not be significant. However, I am wondering if the proximity effect may be sufficient to explain why mains frequency toroidal power transformers (of say less than 1000 VA) do not use larger wires with more layers for increased power rating. So far, this is only a guess on my part, but if someone with greater knowledge of magnetics can confirm or dispel this notion, it would be appreciated.

Answer 1

I presume it's got to do with manufacturing aswell. For rectangular cores you can assemble two wound rods and then stick them together almost without gap in the center between the windings.

Toroids are wound when they are already closed. The winding wheel machine has to travel through the hole and needs space for this.

Answer 2

It's when you hit the knee of diminishing returns.

The hole left looks big, but it's only a small fraction of the total winding window within the core.

If you put a few more turns on, they would be longer turns than those already on there which would

• use more copper than the previous turns (cost)
• create more winding resistance than the previous turns (performance)

There's always a tradeoff with transformers between the cost of the iron core, and the copper windings. When copper is relatively more expensive, transformer design tends to shift to more iron and less copper.

There are only a limited number of stock sizes of toroidal core made, so if you want to design a transformer of a particular VA, you might be left with a choice between ordering a small run of a custom sized core (expensive unless you're buying very large numbers), or using a cheaper but over-sized stock core.

Ultimately it comes down to cost, but we'd need a peep at the manufacturer's costing spreadsheet to see how that design stacks up against one with different material ratios.

Answer 3

Product cost.

In general: if it doesn't have an obvious electrical explanation, and it's a standard commodity part: it's money. Always money.

Copper is simply a more expensive base metal than iron is; granted this isn't bog standard A36 but a more specialized alloy, prepared in thin sheets, but the copper is still several times more expensive.

There may be concerns with cooling as well, though this is a scale-dependent effect -- the larger a transformer, and the more "overstuffed" the winding, the most distance heat has to travel from the center outward. Basic toroids, I believe, are mostly just dry wound materials; varnish impregnation seems optional. So it seems it's not a big priority most of the time. Even with varnish, I would guess toroids over some 10s of kVA would start to have thermal management concerns; in which case, open-winding (dry type) transformers might be more attractive. (Most(?) transformers in the 10s of kVA up, will be three-phase as well, which is, shall we say, a bit harder to pull off in strip-wound toroidal form!)

As noted, skin effect is irrelevant until quite large conductor diameters. Which is indeed another scale-dependent effect.

Proximity effect depends on the number of layers, in a block, which carry the same direction of current flow. In a toroid, say you laid down 4 layers of primary and 2-3 layers of secondary: the primary layers (particularly those furthest from the secondary i.e. closest to the core / at the start end of the winding) count extra, while the secondary being fewer layers has less loss per length. Such a transformer might still have balanced losses, because the secondary is longer (outer-diameter length per turn).

An excellent explanation of proximity effect can be found here:

https://www.e-magnetica.pl/doku.php/proximity_effect

Given the dimensions of wire at typical currents (10s, 100s A) and number of layers, this would probably start to apply in the 10s, maybe 50kVA range and up, for toroids. For typical shell type windings, rectangular wire is a common sight; I believe aluminum sheet is used in pole transformers.

Answer 4

the core window tends to contain significant area that is not filled with copper

There are two big factors:

1. Manufacturability
2. Volumetric inefficiency

Look up how toroidal transformer winding machines work. There must always be a significant opening in the core to allow the shuttle winder mechanism to pass through. As the wire diameter increases, the shuttle's size also grows - the shuttle has to, after all, contain all the wire that will fit onto the winding, and any insulation tape material(s) used, copper tape for electrostatic shields, etc. A shuttle takes one material kind at any given time, of course, but still - the larger the transformer, the wider the tapes you'll be using, the more space is needed for the shuttle.

So, even before any other design concerns come into play, the cost-effectiveness of manufacturing machinery is a constraint. It is possible to do some minor miracles in terms of filling up the window, but that takes custom winders and is a pain. Most transformer shops reject production jobs that their standard machinery can't handle, and the few that can wind toroids up to a full window charge extra, since if you really need it, you can afford to pay extra :)

A small toroidal window is a volumetrically inefficient due to overhead from overlapping tape layers. A 30-40% overlap on insulation tape on the outside of the toroid translates to 100-300% overlap on the inside. Whatever tape overlap ratio you have on the outside of the core becomes multiplied by OD/ID ratio.

That means that a "single layer" of tape insulation grows to several layers in the small window - and it gets worse the larger the OD of the core compared to the ID. Same goes with windings: a small window requires stacking of windings that otherwise don't even fill up a single layer on the outside of the core.

In other words, small toroidal windows are unusable. Usually if you need a toroidal transformer, there's a specific requirement for it, and it's worth the extra cost in spite of perhaps "inefficient" use of the core. Otherwise, you'd be using the cheaper EI or similar cores.