Total internal confinement of magnetic field

[tim9000]

Adding a return winding very slightly reduces the inductance because the one circumferential current loop with an air core is cancelled, it slightly increases the resistance but greatly reduces the external coupling.

Right, so if I have a return wire running back along the circumference of the toroid, it's only going to reduce the inductance by one turn (the turn that was coupling to air) and thus the inductance will be L = (N-1)*Flux / i
instead of L = N*Flux / i
?
Because when you said:

nductance rises as the area of the loops increase, so would you not expect total confinement to reduce the inductance to a minimum?

I thought you were implying there would hardly be any inductance of a totally confined toroid.

 

[Baluncore]

There are two ways to wind a coil onto a toroid. A turn can pass through the hole or it can run externally along the toroid without entering the hole. Those are two quite different magnetic situations.

A winding that passes through the hole has a closed path for the magnetic field that remains within the magnetic material of the toroid, with high inductance. An external winding has half it's magnetic field through air and so has much lower inductance per turn.

You cannot equate those two quite different perpendicular paths to combine them into the one inductance equation.
The number of turns on a toroidal core is a directional count of the number of times the same wire passes through the hole.

 

[tim9000]

A winding that passes through the hole has a closed path for the magnetic field that remains within the magnetic material of the toroid, with high inductance. An external winding has half it's magnetic field through air and so has much lower inductance per turn.

Agreed and understood, I'm just not sure why if it was totally confined then why would:

you not expect total confinement to reduce the inductance to a minimum? Less confinement, more inductance?

" as I said, I'd have thought better confinement in the core, more inductance.

Ok, say that N is the amount of loops the wire does around the core, through the hole, so a return path does nothing to that inductance equation?

 

[Baluncore]

Ok, say that N is the amount of loops the wire does around the core, through the hole, so a return path does nothing to that inductance equation?

The one turn circumferential loop that can be canceled by a return winding is perpendicular to the wanted toroidal current and field, so the total inductance is the simple sum of those two inductances in series. When you introduce a return winding, you cancel the smaller external inductance and so only the toroidal inductor remains.

That is why a return loop compensated toroidal winding will have a significantly lower external field, but at the cost of a slightly lower total inductance.

 

[tim9000]

Meaning total inductance = L from loops through hole of toroid + L from the one resulting which is perpendicular to the loops through the hole (which can be canceled and sacrificed for the sake of no EMI)?

If you wouldn't mind, do you think you could please comment on this:
https://www.physicsforums.com/threads/induction-and-flux-linkage-clarification.792734/

 

[Baluncore]

If you wouldn't mind, do you think you could please comment on this:

In what respect? The coupling of coils is "mutual inductance". http://en.wikipedia.org/wiki/Inductance#Coupled_inductors_and_mutual_inductance

Being orthogonal, internal toroid flux and the internal part of the external flux are independent. On the other hand, a bifilar wound toroidal transformer would have very tight coupling between windings. They are used for RF impedance matching and coupling transformers.

The coupling coefficient between two coils can be adjusted from -1 through zero to +1 by using a variometer. A variometer can also be used as a variabe inductor by connecting the two coils in series. http://www.g3ynh.info/comps/Vari_L.html

 

[tim9000]

On the other hand, a bifilar wound toroidal transformer would have very tight coupling between windings.

I assume you mean you wind the transformer with the primary and secondary wires together at once.

The coupling coefficient between two coils can be adjusted from -1 through zero to +1 by using a variometer. A variometer can also be used as a variabe inductor by connecting the two coils in series. http://www.g3ynh.info/comps/Vari_L.html

Very interesting page, but I still don't quite understand the coupling coefficient completely yet.

In what respect?

Well the formula L = N/reluctance, where N is the amount of turns on inductor 1, is that the inductance for just L11, or for 'L11 + L12'?
And also it's getting the K in the first place I'm unsure about, how do you calculate or measure flux12 or flux 21?
Thanks

 

[Baluncore]

And also it's getting the K in the first place I'm unsure about, how do you calculate or measure flux12 or flux 21?

If you are a beginner to EM then I really think you should avoid calculating mutual inductance. There are a few analytic solutions, but they require simple geometry and assume a surrounding environment of free space. Numerical solutions are available using finite element methods.

L = N/reluctance, where N is the amount of turns on inductor 1, is that the inductance for just L11, or for 'L11 + L12'?

Further discussion of mutual inductance should be in that other thread. Keep this thread for toroids.

 

[tim9000]

If you are a beginner to EM then I really think you should avoid calculating mutual inductance. There are a few analytic solutions, but they require simple geometry and assume a surrounding environment of free space. Numerical solutions are available using finite element methods.

I'm not so much a beginner as someone who needs to rapidly refresh what I learned years ago and build on it. FEA?? Really...Are you saying that there is no simple way to calculate the L12 and L21 (specifically the flux of Fi12 and Fi21)? Could you please comment as to this and about whether the inductance formula is for mutual and self inductance, or just self inductance, on the other thread?
Greatly appreciated.

 

[Baluncore]

Mutual inductance has little to do with “total internal confinement of magnetic field” but; Each and every dw of the winding on L1 generates a dipole vector field that interacts with each and every other dw of L1 itself, of L2 somewhere else with some orientation and every other patch of the environment. So you have a huge scattering matrix that describes the cross coupling of the entire system. It can get very complex when there are phase shifts due to propagation delays.

There are a few algebraic solutions for mutual inductance of basic geometrical situations. I would suggest you find a copy of “Inductance Calculations” by G.W.Grover. Use http://www.bookfinder.com/ to locate a low cost copy, or maybe a new Dover Publications reprint.

 

[tim9000]

Mutual inductance has little to do with “total internal confinement of magnetic field” but; Each and every dw of the winding on L1 generates a dipole vector field that interacts with each and every other dw of L1 itself, of L2 somewhere else with some orientation and every other patch of the environment. So you have a huge scattering matrix that describes the cross coupling of the entire system. It can get very complex when there are phase shifts due to propagation delays.

when you say 'dw' I assume you mean infinetesimally small part of the winding.
Right, so you can't really measure mutual flux Fi12 or Fi21, you need to work it out algebraically from the specific geometry?
And the standard inductance formula is just for L11 = N/Reluc and mutual inductance is much more complex to determine?
I surtainly will hunt for the book, cheers for the recomendation?