Is it possible, knowing the air gap and the selected core, to calculate its coupling coefficient?

[Glebiys]

Hello.
I'm studying the principle of transformer calculation for Dual Active Bridge converter.

Primary/Secondary turns 36:23
Selected core ETD 54/28/19 N87 (I haven't decided on the size of the air gap yet)

Question: Is it possible to pre-calculate the values of leakage inductance and magnetization?

Knowing Al (from the datasheet) and the number of turns, I can get the total inductance of the primary winding.

It turns out, knowing k (coupling coefficient) I can get the value of leakage inductance. Next, we can find the magnetization inductance.
As far as I understand, k depends on the size of the air gap.

I have seen the following method for calculating k:

As far as I understand, this is achievable by measurements on a working model.
It is not possible to assemble a test model now.

I found an example calculation for LLC transformer, there was k = 0.9. I have DAB and a different core.

Summary:
Is it possible, knowing the type of core and the number of turns in the winding, to determine what leakage inductance will be in total?
Is there any way to find out k for my core? Or is it determined by experimenting with a working model?
I need to know the leakage inductance in the transformer in order to determine the inductance of the external leakage inductance to obtain the required total leakage inductance.
I had an idea to take k = 0.9, choose some air gap. After that, I will get certain values of inductances. After winding the transformer, I can actually measure the inductance and wind the missing inductance on an external inductance.

 

[FvM]

Leakage inductance respectively coupling coefficient strongly depends on the coil geometry which wasn't yet shown.

 

[Easy peasy]

The way the windings are placed is of paramount importance to losses, and coupling - not the core

there is a natural conflict between safety isolation systems - use of insulating materials - and the need to have the windings in close proximity to reduce leakage flux ( increased coupling )

This is where degree qualified and experienced engineers apply their know how to produce a desired result that is also reasonable to manufacture.

 

[Glebiys]

@FvM, @Easy peasy, Thank you for the answer!

I chose a core with a total air gap of 0.5mm.

 

[FvM]

In the first order, leakage inductance between transformer windings is the leakage of an air core transformer and not affected by the core. Respectively changing the gap keeps leakage constant. Coupling coefficient will vary according to variation of magnetizing inductance Lh.

 

[Easy peasy]

I cannot agree with this:

" Coupling coefficient will vary according to variation of magnetizing inductance "

--- Updated Jul 24, 2023 ---

there is no effect on coupling by way of gap in the core, coupling purely relates to the winding geometries.

 

[FvM]

I cannot agree with this

Aggree it's counter-intuitive but it's just math.

According to Llk = Lp*(1-k^2) quoted above, if you vary Lp by gap variation and keep Llk, k varies too.

 

[Easy peasy]

I see your point re the math, the energy stored in the leakage, is due to the flux in the gaps between the windings, this is not really affected by the core or its gap - this fact is borne out in testing too - the absolute value of Llk varies < 7% typically for core or no core . . . (?)