# What impact does winding tightly versus loosely have on transformer performance?

To make it simple (and actually, directly relevant to what I am working on): what impact does winding tightness have on transformer performance? Lets assume typical laminated EI / EE 60hz transformer, operating at 60hz, within the maximum flux density of the core material.

I suppose this is also a good way to illuminate the oft-mentioned qualitative idea of the "flux capturing" effect of a high permeability core versus air. If most of the flux is in that core, then who cares if there is a little more air, right? But...imagining that holding as "loosely wound" approached infinite diameter seems..shaky.

For instance, so I have a transformer where the primary is wound tight on the core, and another, where the primary is the diameter of the solar system, and because they both encircle the same flux in that core, there is no change in performance? That can't be, right?

So I am imagining leakage inductance probably increases. But, physically, why that is (mental model), doesn't seem to be sinking in. Is it simply because the more air there is inside the turns, the more paths there are for the magnetic circuit? And its as simple as that? I'm imagining actually calculating the flux in the air part of the circuit is probably not trivial, but is that the mental model?

What would be really handy is an engineering type mental model explanation, and then maybe a little mention of why Maxwells equation makes it so.

EDIT: I just realized that the "air part of the circuit" is a little ambiguous. What I mean is, as the additional area inside the turn which is not the core containing the transformer/mutual inductance flux goes up, the ability of that turn to store energy goes up (air core inductor)..i.e. leakage inductance.

Separately is the question of increased mutual inductance, i.e. transformer action through the air, but lets pretend that the secondary winding is always wound tight..for the moment. (or compare/contrast wound tight or also increasing)

• MMF forces can remove insulation on magnet wire with vibration at high currents and also increase leakage inductance or reduce mutual coupling. Dec 21, 2018 at 23:35
• Also note that winding loosely will impact resistance as it increases wire length. Given that resistance is almost never actually desired in inductive devices, this is quite significant. Also note that if you're using loops of wire capable of fitting a larger core, you may as well use a larger core, and if an air/non-ferrous core is desirable, then you should be using one in the first place. The same current will produce the same number of total field lines within the loop of the conductor, but this does not mean the loops will have the same inductance.
– K H
Dec 22, 2018 at 1:09
• Its not proven yet, because I haven't calculated it, but my practical reason for asking this, is that I would like to be able to air cool both the core and the windings by leaving a big enough gap. I am assuming this will offset the very minor increase in resistance (and therefore power dissipation) of the winding, since the wires are so large, and have so few turns, that the change in resistance to add a small gap is very small. Dec 22, 2018 at 3:04
• Specifically, wire diameters are on the order of 0.250", turns are in the neighborhood of 10 to 20, and core areas are in the 24 sq cm territory, and current is in the 100's of amps. So from this perspective, adding a 1/8" gap (for example) will not add a significant amount of resistance to the winding. A couple hundred microohms probably. So power dissipation at say 200 amps would increase by maybe 10 watts, but the winding is dissipating 100 to 200, and the ability to cool that using the gap would greatly outweigh the small increase in dissipation. Dec 22, 2018 at 3:08
• Ahh..but lets say the wires are secured, even though they have a gap, using an insulated former that connects to the wires intermittently but holds them in place so they don't touch each other (gap between them is also desired), or the core. Dec 22, 2018 at 3:09

See my answer here if you want the theory behind the words below: -

Normally, the flux will tend to want to concentrate in the ferrite core because that will have, by far, the lower magnetic reluctance path compared to the air between the coils and the core. The reluctance of the air is in parallel with the reluctance of the core and just like an electrical circuit comprising parallel resistors of vastly unequal values, the current flows in mainly the lower value resistor. That lower value resistor is akin to the core’s reluctance.

So, the flux congregates in the lower reluctance path of the ferrite core.

Now, if we test this out by expanding the radius of the coils, we see that the reluctance of the core remains the same but the reluctance of the now "fatter" air (a parallel component) gets smaller. It gets smaller because there is more air "area" and, of course, reluctance reduces with area.

If you take it to greater extremes, you’ll see a reduction of the percentage of flux congregating in the core and you'll get leakage inductance. This is because the air path is only really useful for generating local lines of flux coupling only a few turns of the primary winding AND importantly, those local lines do not couple to the secondary. Flux not coupled means leakage inductance.

At this point, the unloaded secondary voltage will be noticeably lower due to the overall rate of change of flux being lower. If the secondary were now to be loaded, the situation would become worse because the primary referred load current (due to the secondary load current) is passing through the primary leakage inductance and, effectively lowering the voltage seen on those primary turns that can be said to be 100% coupling the secondary.

The above is the equivalent circuit of a transformer showing how leakage inductances lower the voltage seen at the heart of the circuit (the ideal transformer).

• Thanks again Andy. This helps me make sure my mental model works. From your other answer you linked to, the key practical idea for me, directly related to what I am doing, was " @Andy aka Since R1 || R2 for R1 >> R2 is approximately R2, is the effect of the air gap around the coil minimal until the ratio of the gap/core get close μ of the core? If so, then for a core with a μ of 1000 you could have a significant gap with minimal effect. – crj11 Nov 30 at 19:47" Which you answered as being correct. So from this perspective, looks like adding a gap for cooling is a go. Dec 22, 2018 at 16:16
• What would really hit the spot right now, is an image of an existing design showing such an air cooling gap. If this is a thing, someone has got to have used it, and probably in a 60hz design where the permeability of the core is high. Probably utility I would think. Dec 22, 2018 at 16:17
• It’s not my area but I can imagine that it would work well. Try looking up utility transformers that are oil cooled. The path that the oil takes might easily be equatable to an air cooling technique. Dec 22, 2018 at 16:32