Naser,

If the interpretation of ideal iron core is that it is a core of zero reluctance, then yes - leakage flux will automatically become zero !

The reason is that a zero reluctance path acts as a magnetic short across any other path of finite non-zero reluctance that occurs in parallel to the ideal core (such as any leakage path), so the core (like any short) will "pull all magnetic lines of flux" within itself, leaving none for leakage !

But of course as you rightly say, this is a very, very ideal condition, that never occurs in practice.

(I still haven't found time to go through your earlier motors document, though I still have it with me ! Tomorrow I have my end-semester examination, followed by evaluation hours until about 9-10 May, after which I will get down to your document, and see if I can make sense of it.

Sorry for the very prolonged wait !!)

With best wishes.

-Sanjay

L= do/di inductance of any core could be defined as variation of flux to variation of current.

Inductive Reactance offers to the circuit,

X = 2( pai)(f)(L), with f= zero for DC, X would be zero, yet the leaks flux would appear, as the core and coil are having resistance the inherent property of material( R= (raw)(l)/A) which would be responsible for leakage of flux also, or could say with zero reactance (f=zero) the leak flux of gold coup’s be less than silver for same setup….

Dear Professor Sanjoy Roy ,

Thanks a lot for your kind and prompt response.

Would you please see the attached file for my justification?

In case there is just one MMF source (that is only one winding wound on the core) I agree with you. But what about a two-winding structure when two MMFs are applied to the magnetic circuit of the core? As I have proven in the attached file, ideal core just leads to the two MMFs being equal, thus yielding the current transformation ratio for an ideal transformer. There may still be leakage fluxes in both the primary and the secondary circuits. Agree?

Not entirely !

If the core is truly zero reluctance, it will pull all magnetic flux lines within itself, thereby leaving nothing to leakage !!

Across the core, the usual KVL will apply, that is mmf of primary and secondary added will set up the required flux. Since reluctance is zero, the mmf required to set up any finite flux is zero - which is nothing but the ideal transformer concept.

-Sanjay

Dear Professor Sanjoy Roy

Thanks a lot for your response.

Please take into account that total mmf will be zero in this ideal core case; Nevertheless, we have current in both primary and secondary windings, acting as sources of mmf across primary and secondary leakage reluctances, respectively.

Please check what I had attached. There, the Magnetic Equivalent Circuit (MEC) has been drawn; under ideal core conditions, what we can deduce is just equality of primary and secondary MMFs, yielding the current transformation ratio for an ideal transformer. We can still have leakage fluxes and this is not strange at all.

This is the reason why the books list the zero leakage flux condition for the ideal transformer as a separate prerequisite for the ideal transformer, rather than the core reluctance being zero.

I mean none of them necessarily leads to the other: The core can be ideal but we can still have leakage fluxes in the primary and secondary windings (Of course in case there was only one winding, the flux would choose the least reluctance path, as you correctly mentioned). Also, the leakage flux can be negligible (the windings are wound on each other), but the core can still be non-ideal, having a non-zero reluctance.

Total mmf across the core is indeed zero for the ideal case.

If you go a little deep into this, you will realise that the well known ideal transformer relation (and similar relations for ideal multi-circuit transformer configurations):

Np.Ip = Ns.Is

is nothing but a manifestation of this feature !

Dear Professor Sanjoy Roy

Yes. This is the exact statement I also mentioned.

But what about the leakage paths, along which just one mmf component (primary or secondary) act? When there are these two mmf components, we will have leakage fluxes which are obtained by division of the corresponding mmf by the corresponding reluctance.

So there can be a situation where the core is ideal; there is zero reluctance. But, at the same time, you have primary leakage and secondary leakage.

This is the exact point I mentioned.

Agree?

در بسامد ثابت این تلفات با مجذور شار هسته نسبت مستقیم دارند واز آنجایی که شار هسته نیز تقریبا با ولتاژ ورودی نسبت مستقیم دارد

Naser,

The zero-reluctance core will confine all flux lines within itself, leaving none for leakage.

It effectively "shorts" the high reluctance leakage path (much like a short circuit current path that drags all current away from a path of relatively high resistance, in a current-voltage Thevenin circuit).

To summarise:

• There will be no flux to leak, though the finite reluctance leakage path does exist physically.
• All the flux is confined within the zero reluctance core.

Hope that sorts out the confusion ?

-Sanjay

Dear Sanjoy Roy

Thanks a lot for collaborating in the discussion. It is my honor to be in contact with a Professor like you.

Please let me to confront your point. Please check the Magnetic Equivalent Circuit (MEC) I have drawn and attached. There is no reason to think zero reluctance path will make leakage flux zero. Of course, I have assumed a single phase transformer of core-type. Of course, for a shell-type transformer when both windings are wound on the middle limb, the MEC will be different and in that case, your deduction applies well.

I hope we can conclude this discussion.

With reference to the figure included in your last message, here is my summary response:

If the two leakage paths do carry some flux, then your core+coils arrangement is simply non-ideal !

(I don't know how I can explain this any better over RG messages, so I conclude; hoping that I could convey what I intended to !!)

With best wishes.

-Sanjay

While zero core reluctance can significantly reduce leakage flux by directing more magnetic flux through the intended path, it does not guarantee zero leakage flux on its own. The elimination of leakage flux requires both high permeability materials (low core reluctance) and optimal design of the magnetic circuit to ensure tight magnetic coupling and minimize stray paths for the flux

Ahmad,

What you say is certainly the design perspective of the leakage reduction problem - it is what will happen in a real system.

What Naser and me were talking about is more the ideality of the problem.

-Sanjay

Dear Dr Ahmad Razmdideh

Thanks for your kind response.

As Prof Sanjoy Roy mentioned, we are assuming an ideal core with no reluctance. I claim it does not automatically yield zero leakage flux, while others (like Prof Sanjoy Roy) believe it does!

I have detailed the problem by drawing a magnetic equivalent circuit, and have justified my claim.