Exploring the Factors Affecting Leakage Flux in Transformers

[jaumzaum]

Hi! I was wondering why even a real transformer has a very low leakage flux, what makes it be this way way?
Is it the ferromagnetic material? If so, why? If the core was made of completely vacuum would the leakage be 100%?

 

[anorlunda]

The ideal transformer is not a representation of a real transformer in a circuit. It is one of the components in this equivalent circuit for a real transformer.

Why is the leakage so low? That's a terrible way to phrase a question. Someone else might ask why the same leakage is so high.

To analyze leakage, you need to look at the 3D construction techniques, and the materials. The primary factor determining leakage is the distance between primary and secondary coils.

Perhaps the ultimate low leakage is in the autotransformer design, where the primary and secondary share the same coil.

 

[Motocross9]

I have had this same question as well. I believe it has to do with boundary conditions for the magnetic field. If you use the boundary conditions on $\vec H$ and $\vec B$ at an interface of two linear materials, you get the relation $\tan\theta_{2}/\tan\theta_{1}=\mu_{2}/\mu_{1}$
Note that this is only true for linear materials and doesn't apply to ferromagnetic materials; however, I've seen textbooks consider ferromagnetic materials as linear materials with a very high permeability. Even so, if you try to determine the incident angle in which total internal reflection occurs, you run into problems. I am not sure how you would prove it, but intuition suggests that for ferromagnetic materials, total internal reflection probably occurs at very small incident angles, so very little field escapes that material. Note that I do not know if this is what actually happens; I've not found a satisfactory answer anywhere, so this is just thought.

 

[berkeman]

Hi! I was wondering why even a real transformer has a very low leakage flux, what makes it be this way way?
Is it the ferromagnetic material? If so, why?

As @anorlunda says, the ratio of $L_k$ to $L_m$ (leakage inductance to magnetizing inductance) varies with the transformer type and size and application.

I work mostly with small communication transformers (think "Ethernet") and with middle-size switching power supply transformers. For the comm transformers, low leakage inductance can be very important. And for switching power supply transformers, low leakage inductance can help to lower noise coupling from the transformer to other magnetic circuits nearby.

But usually when you are trying to minimize $L_k$ there are tradeoffs in the design and the cost of the transformer. There are special winding techniques that can be used, but those are generally more expensive and you have to justify the cost on a performance basis.

If the core was made of completely vacuum would the leakage be 100%?

Not 100%, but pretty high. Air-core transformers are used for some applications, but only when high $L_k$ values can be tolerated.

 

[anorlunda]

Hi! I was wondering why even a real transformer has a very low leakage flux, what makes it be this way way?
Is it the ferromagnetic material? If so, why? If the core was made of completely vacuum would the leakage be 100%?

You should read the Wikipedia page about transformers. The session discussing leakage tells about cases where people want high leakage.

 

[rude man]

Basic reason is that magnetic flux cannot be contained as well as electric current.

Outside a wire there is paracically zero current. But a magnetic field leaks easily. Even a toroid transformer which contains magnetic flux very well, some of the flux generated near the excitation winding will not make it to a secondary winding. In other words, a coupling coefficient of 1.00 is unrealizable to a significant extent.

 

[DaveE]

A rule of thumb (i.e. not exactly right!) I learned in my transformer design days, was that the leakage flux in a given winding is the flux that would be present if there was no core, or other strong coupling to the other windings. Leakage flux is the magnetic flux that isn't well coupled. Like an air core inductor wound just like the winding in question. Each different winding in a transformer will add it's own bit to the total leakage.

You can (sort of) think of the EM fields as a superposition of the with and without core cases. Adding a core both creates lots of additional flux as well as coupling it to the other windings, this will not eliminate the flux that would be created by the "air core" winding that would exist without a core present.

Of course it's not all about the core, although that is a common approximation. It's about possible flux paths that don't couple to the other windings. Transformer designers that care about leakage flux (good or bad) will pay a lot of attention to the geometry of the windings to control the area that is (or isn't) common to the other windings.

Finally, practical transformer designs are often very dependent on requirements in addition to the basic physics; like safety standards, cost of materials, reliability, or manufacturing issues. This is an area that is either dominated by practical experience (the stuff that you only learn in industry), or by computer simulations of very specific field configurations.

 

[shjacks45]

Transformer cores route flux efficiently depending on the the core permeability. Iron/metal transformer cores usually have a gap to prevent saturation of the core. An Iron powder core does not have a continuous flux path (metal particles insulated from each other) so some flux doesn't travel through core. Some high quality audiophile transformers are in a permalloy (high permeability) can which shields. Some IF transformers had a coil inside a ferrite shell, also shielding.