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Coupling factor "k" in LTspice..meaning?

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treez

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Hello,
For a transformer in LTspice, can you confirm that the k factor (coupling factor) gives the leakage inductance by this formula….(1-k^2)*L(pri)?

Also, that this leakage inductance value is that inductance value that you would measure if you shorted the secondary and measured the inductance at the primary terminals?

That is (1-k^2)*L(pri) = Llkp + Llkp//L(pri)

Where:
Llkp = Leakage term in the primary of the transformer
 

 
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thanks, I am quivering at the potential inaccuracy as per your valid explanation

A previous thread here, shows that the k factor is…..

SQRT [(Lp/(Lp + Lr)] ....................(A)

Where
Lp = Inductance measured at primary with secondary open
Lr = Leakage measured at primary with secondary shorted

Which is the best expression for what k factor is?, the above(A), or the previous one (B)…

{Leakage = (1-k^2)*L(pri)} ........................(B)

In (B), does L(pri) mean the primary magnetising inductance, or the inductance measured at the primary with the secondary open?
 
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The question can't be answered without referring to an equivalent circuit clarifying what Llkl or Lpri mean. For a 1:1 transformer with leakage, a symmetrical equivalent circuit is shown below. You can easily verify it by measuring the short and open circuit inductance of coupled inductors in SPICE.

Equivalent Circuit.png

It shows that L(pri) in your formula for the observable leakage inductance is not identical with the shunt element in the equivalent circuit (or the magnetizing inductance) L*k. Instead it's the open circuit inductance L.

You can supplement the equivalent circuit with an ideal transformer to apply it to coupled inductors with arbitrary windings ratio.
 

Thankyou, as I thought, the "L(pri)" in equation (B) of post #3, and the "Lp" in the equation (A) of post#3, both refer to the inductance measurement at the primary with the secondary open, and not the primary magnetising inductance.

By the leakage measured at the primary with the secondary shorted, as you know, this measures both the leakage in the primary , and the secondary........the measuring tool will see the secondary leakage inductance as if it were in parallel with the primary magnetising inductance, and it will "see" this term in series with the primary leakage inductance component.
 

I was seeing your previous post before you added everything after the first line.

I believe that Equation (A) is referring to an asymmetrical equivalent circuit (usually annotated with the terms Lσ and Lh), Lp (or Lh) is not the observed open circuit inductance, Lr + Lp (or Lσ + Lh) is it.

My suggestion is to start with the simple and straightforward relations shown in post #4 (possibly after verifying it's validity in a SPICE test circuit) and set up your own equations.
 

Figure 8, page 4 of the following, plus the text on the LHS of page 4 actually states that measuring the inductance at the primary with the secondary short circuited, does NOT give us the leakage inductance. Instead it gives us “Llkp + Lm//Llks”

Where…
Llkp = leakage inductance in primary side
Lm = magnetising inductance of primary
Llks = secondary side leakage inductance. (= Llkp/n^2)
n = np/ns

https://www.fairchildsemi.com/application-notes/AN/AN-4151.pdf

This is quite surprising, because I had always thought that measuring the inductance at the primary with the secondary shorted gives the leakage inductance.
Clearly it does not...because "Llkp + Lm//Llks” is not the leakage inductance
 
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I don't know what's your specific point here.

There are different equivalent circuits in use, also the Fairchildsemi AN is referring to asymmetrical and symmetrical circuits which are linked to different equations and involve different methods to derive the parameters from measurements.
 

thanks,
I don't know what's your specific point here.
Click to expand...
we are investigating the transformer parameters in LLC converters.

its related to this post
https://www.edaboard.com/threads/347424/

And the fact that the consideration for internal and external leakage and magnetising elements is not given in the Fairchild AN, so we have to investigate it ourselves....for example, when you find the lower resonant frequency in the schem of this link (below) you have to have a magnetising inductance term for the "w = 1/sqrt(LC)" equation.......
https://www.edaboard.com/threads/347424/
.....is it the primary side leakage in series with the primary magnetising inductor...all in parallel with the external magnetising inductor?
 

Bottom centre of page 24 (of link below) states that the leakage is L* (1-k^2)

There is no mention of what “L” stands for in the article.
Click to expand...

You get the same expression if you calculate the short circuit input inductance of the equivalent circuit derived in post #4. Consequently, L is the measured open circuit inductance.

I must confess that I'm not motivated to go through the various application notes and decode their arbitrary equations. I already gave my suggestion how to proceed in post #6.
 
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I recall k = M / √(Lp*Ls)
LTI indicate
L LEAK = L • (1 – K • K)
or k= √(1-Lleak/L)
yet from Maxwell's Equations and Neumann formula results in
777870063d0bf48353d0949354195032.png
Ref Wiki.

which is what I recall..

my leap of faith leads to ...
L= √(L1L2) and k=M/L

you can explore from there and confirm or deny.
 
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I'm positive we've had this exact topic before here, but the forums search is failing me.

I believe the bottom line is that from a black box perspective, there are multiple accurate equivalent circuits for coupled inductors (assuming they are lossless and linear). You can see it as equivalent to a T circuit with separate leakages on the primary and secondary, or with just one leakage on either the primary or secondary. In the latter case, this is sometimes called the "industrial leakage," and it is what you measure when you short out one winding. Its quantity is different from the leakages in the T model. But the two models are equally valid.
 
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thanks, we are only interested here in that leakage which is relevant to the calculations for the LLC resonant converter.
Also, for the pdf in the link of post #10 above, what value of inductance would you use to calculate the lower resonant frequency of the LLC converter pictured there. This LLC converter does not conform to the AN-4151 application note by Fairchild, because it has both intrinsic and external leakage and magnetising inductance terms.
 

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