# Calculating the mutual coupling coefficient of E cores

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1. Jul 15, 2017

### tim9000

Hi,
I can't find my inductance calculations book. Say that you were considering magnetic flux linkage more from a geometric perspective:
-Does the mutual coupling coefficient for a series of coils all on the same steel core add up to a maximum total of ~1?
Because I tried simulating a three phase 'E' core TX on LTSpice, and I had issues making the coefficients between coils near 1 (it tells me I've made an impossible relation or something).

-For example, if you were looking at a three phase Isolation transformer, ignoring self-couplings, what would the coupling coefficient between one primary coil to another primary coil be, approximately?

Intuitively, I thought it'd be about M = 1/2 between each adjacent primary pair of coils, and the same mutual coupling coefficient between adjacent primary-secondary pairs, with each of the primary-secondary pair which are sitting on the same limb at about M: ~1.

However, given the LTSpice, maybe it's more like M = 1/3 between adjacent limb coils?

Similarly, I'm wondering how much of a difference (improvement) would a bifilar winding make to [reducing] the amount of leakage flux, and how much is going to couple through the core to another coil anyway (because the steel permeability is so high).

Thank you!

2. Jul 15, 2017

### Staff: Mentor

3. Jul 16, 2017

### jim hardy

Why would it ?
What's definition of mutual coupling?

4. Jul 16, 2017

### tim9000

With regards to the coupling:

Yes, it is exactly a comparison of this core with the various winding typologies that I would like to discuss. How would the coil windings of the above picture compare to that of a bifilar wound "HV/LV" TX (in keeping with the labels of the picture). I presume there is the least leakage flux (self-inductance) with bifilar winding. Similarly, if you had (for instance) a single phase core-type core, where the primary and secondary are on opposite sides of the magnetic path, how much poorer is the coupling coefficient between the coils (very generally speaking)? I presume the leakage flux would be worst here, comparatively.

As I recall M = k√(L1*L2), but I'm not sure how to evaluate this for a three phase core...

I don't necessarily think it should, I'm my query was spurred on by LTSpice not permitting it.

Thanks guys

5. Jul 16, 2017

### jim hardy

Good, i don't either. Draw a picture. Any flux that only links one coil can't be mutual.

6. Jul 16, 2017

### Staff: Mentor

I don't think I've ever seen a high voltage / low voltage bifilar wound transformer. The whole point of bifilar winding is to lower the leakage inductance (while sacrificing higher Cww). How could you achieve high voltage isolation in a bifilar wound transformer?

7. Jul 17, 2017

### tim9000

Not one coil, core.

Cheers

8. Jul 17, 2017

### tim9000

I'm sure there aren't HV/LV bifilar, that's why I put quotation marks around the label.

Cheers

9. Jul 18, 2017

### jim hardy

???

10. Jul 18, 2017

### tim9000

You said any flux that only links one coil; I'm not talking about any flux only linking one coil.

I brought up Bifilar because I wanted to in a way use it as a comparison standard between coil magnetic couplings, as it is the best possible.

As I said, I wanted a bit of a general sense of how effective various winding arrangements are. Something I should have done in the first instance, here is an illustration for your comparison:

Keeping in mind that each coil is linked to each other coil because they're all on the same core.

A) -> Comparison of coils on adjacent limbs: Imagine that each colour has HV and LV windings. What would the mutual coupling between, say, red and green primaries, or red and blue primaries, be?
A) -> Comparison of coils on same core: say that there are HV and LV coils comprising each red, green and blue. What would the mutual coupling the HV and LV red coils be?

B) Comparison of coils on the same core: Say red is the primary, and orange is the secondary winding, green is the primary winding, grey is the secondary winding etc. What would the coupling of the Red to orange coils be? Similarly, what would the coupling of the Red to grey, red to green, be?

C) Red is wound bifilar with orange, etc: what is the coupling of red to orange, what is the coupling of red to green?

I hope this clarifies my original line of inquiry.

Thanks

11. Jul 18, 2017

### jim hardy

You worked that years ago in your magamp thread.
The magnetic circuit apportions flux according to the mmf(amp-turns) in each leg. It's a circuit that you solve with mmf's and reluctances.

12. Jul 19, 2017

### tim9000

There must be differences in leakeage fluxes between the three winding types. Also:
If I were to treat this like a simple NI -- reluctance circuit, then would not: each of the A), B) and C) all have the same coil coupling relationships, comparatively? Because certainly bifilar winding, is has far superior coupling to that of B) where the primary and secondary are on the same limb, but occupying different parts of it.

Note: there are primary and secondary coils in A) but you can't see them because the outer RED coil obscures the ORANGE secondary coil underneath.

As per my last post, I have my own personal expectations of what the coupling order of best to worst would be. [For example, I expect bifilar coils wound on the same section of core like red to orange as in C), would have better coupling to that of the HV/LV (primary/secondary) coils in A), which itself would have better coupling of red to orange than in C), which would have the poorest coupling]. But there are a couple of things I don't understand, for instance:
When you have a better coupling of primary to secondary on the same limb (like in the case of bifilar) is there also an impact on the other coils on the other limbs, like coupling between adjacent limb primary-primary coils gets worse? This is to say, would the coupling of the red to green primaries, be the same for B) as they would for C)? After all, the magnetic path hasn't changed, just the winding geometry. Or has improving the coupling of red to orange between those coils also decreased the coupling of red to green? etc.

[That flux generated by red passes through orange, then it passes through grey/green and purple/blue, but if you've improved the way it couples through orange, does this also effect how well it passes through grey/green and purple/blue, or can you have your cake and eat it too. If so, as long as the insulation was high enough, bifilar would be win-win]

Thank you

13. Jul 19, 2017

### jim hardy

You posited single phase.
In that case
Flux generated by red passes through orange then divides between the other two legs according to MMF's from current in their respective windings and of course reluctance.

14. Jul 19, 2017

### tim9000

Regarding the A), B), C) illustration, single or three phase doesn't matter, at this point I'm just trying to step-wise discuss if there are any differences in leakage flux and mutual coupling between windings on the same limb or adjacent limbs.

Thanks

15. Jul 19, 2017

### jim hardy

Why look for word crutch rules to memorize and mis-apply? Just go back to basics. It saves a lot of trouble.

http://www.electronics-tutorials.ws/inductor/mutual-inductance.html

Calculate Φ12 for all the coil pairs on your E-core.
Does it change with amp-turns in L2?

Last edited: Jul 19, 2017
16. Jul 25, 2017

### tim9000

Sorry for the delayed reply.
I understand that Φ12 will vary ever so slightly than Φ13 due to a slight proximity difference b/w ends of the core (if 2 is the limb in the middle of the 'E') but will basically be the same. (I.e. the small extra reluctance will divide the flux not quite 50/50 between coils 2 and 3)
But my point at this very moment is that the flux (example from coil 1 primary) Φ12 travels through the core on it's way to coil 3 primary, via coil 1's secondary in slightly different ways. The secondary could be tightly coupled as in C) or over the top of it as in A) or in series with it as in B). So does this make no difference to the coupling of coil 1 to coil 3?

Thanks

17. Jul 25, 2017

### jim hardy

I'd think not. What happens in leftmost leg stays in leftmost leg.

18. Jul 26, 2017

### tim9000

Can you elaborate on that? :p

19. Jul 26, 2017

### jim hardy

Back to the basics ?

https://www.princeton.edu/ssp/josep...ide-to-maxwells-equations-D.-FleischLEISC.pdf

which my undergrad course instructor simplified to

Ienclosed is of course amp-turns..

Applying that,

so MMF is not changed by rearranging the coils.

Last edited: Jul 26, 2017
20. Aug 3, 2017

### tim9000

Ah geez, I did know how to derive all of Maxwell's laws once. I don't have my formula exercise book on me at present.
It's the right hand side I'm hazy on: was it something like all the electric charge that moves due to the magnetic field on the surface cancels out due to symmetry or something, so it's zero?

As per your previous post, if I'm not mistaken lenclosed is zero, because no H is enclosed, because H is parallel to the plane of the loop. However, if the lenclosed was on the same plane as the coil turns Ienclosed would be the integral of the flux.

I think this is too crude a method of analysis to use Ampere's law precisely due to one of the factors I'm trying to examine, namely leakage flux.

Based on your last reply I'll hazard some guesses. Now, the amount of flux that flows through the core might not change,(I'm leaning towards this being the case). However, for example I'm highly skeptical that the amount of flux that flow from red to orange will be the same in B) as it is in C). (Due to a poorer coupling than when bifilar).

This may have other consequences beyond these immediate primary-secondary coils as I previously queried, or it may not. I.e. conceivably the coupling to adjacent limb coils is the same throughout A) B) & C) are the same because the respective leakage flux doesn't change throughout the three arrangements(?) But that's what I'm seeking clarity for.

Thanks as always

21. Aug 3, 2017

### jim hardy

Now you've changed the question.

You asked about coupling between windings on different limbs.
Now you're talking about windings on the same limb.

22. Aug 14, 2017

### tim9000

Sorry, ten day late reply.
Actually, I attempted to communicate that the question was always how the flux would vary between coils on the same limb and on adjacent limbs.

So, I think thus far we clarified that the flux between adjacent limbs would be the same relative in either A), B) or C).
But that there would be differing leakage flux between coils on the same limb relative to the A), B) or C) winding arrangement. Thus, I would conclude that this amount of leakage flux doesn't impact the coupling between limbs, just merely coils on the same limb, which is where the advantage lies.

Did anyone know roughly how much of an impact these A, B and C variations would have to the mutual coupling coefficients in this regard?

Cheers

23. Aug 14, 2017

### jim hardy

I took this
to mean primary coils on different limbs.
I didn't think about multiple voltage primary windings which might be tapped or might be separate coils..

24. Aug 15, 2017

### tim9000

No worries mate. I struggle to communicate at the best of times. I have near limitless patience with PF because I'm asking people to help me out with understanding these scientific things, and when they reply it's nice of them, because they have no obligation to me to read my long posts. So if I need to repeat the odd thing, or try explaining something another way, then it's a price I'm happy to pay for people taking time out of their lives to help me.

That's my view anyway.

Have a think about it and get back to me if you can.

Cheers

25. Aug 15, 2017

### jim hardy

I believe that would be so.

I too would expect some small difference . .

It is difficult to communicate with precision, isn't it ?
my old friend Lavoisier