Primary and secondary leakage inductances for LLC transformer?

[treez]

Hello, I have a transformer, its like this:

...Primary inductance with secondary open = 600uH
..Secondary inductance with primary open = 90.1uH

Coupling factor , "K" = 0.91

What are the primary and secondary leakage inductances.

I have the equation L(leakage) = (1-K^2) * [primary inductance with secondary open]

..but i dont know, what this value is, is it some combination of primary and secondary leakage inductance?

 

[FvM]

I have the equation L(leakage) = (1-K^2) * [primary inductance with secondary open]

..but i dont know, what this value is, is it some combination of primary and secondary leakage inductance?

L(leakage) is well-defined, it's the inductance you measure at the primary with secondary shorted.

What are the primary and secondary leakage inductances.

You'll should refer to an equivalent circuit for an unequivocal definition.

 

[mtwieg]

L(leakage) is well-defined, it's the inductance you measure at the primary with secondary shorted.

That's one definition of the leakage inductance. It seems that for power electronics, most people think it's acceptable to use that "lumped" leakage inductance instead of considering primary and secondary leakage inductance separately. I think that's valid for topologies such as flyback, forward, etc, but maybe not for LLC (I don't know, I'm no expert on LLC). But in any case, the single leakage inductance model is not equivalent to a two-leakage model, it's just an approximation. I also believe that even a two-leakage model is not a complete model, since it assumes the leakage inductances are proportional by N^2 (which is not necessarily the case).

 

[szhighstar]

for leakage inductance, we do not calculate according to the formula, should be actual test, when you test leakage inductance of pimary winding , short secondary winding.

 

[treez]

FvM

You'll should refer to an equivalent circuit for an unequivocal definition.

yes i have looked here under "equivalent circuit"

https://en.wikipedia.org/wiki/Transformer

...according to this, the measured laekage is the series combination of the pro leakage (Llkp) in series with Lm and (NP/NS)^*Llks in parallel.

Can this be right?....... do you assume that (NP/NS)^*Llks = Llkp?

 

[FvM]

That's one definition of the leakage inductance. It seems that for power electronics, most people think it's acceptable to use that "lumped" leakage inductance instead of considering primary and secondary leakage inductance separately. I think that's valid for topologies such as flyback, forward, etc, but maybe not for LLC (I don't know, I'm no expert on LLC). But in any case, the single leakage inductance model is not equivalent to a two-leakage model, it's just an approximation. I also believe that even a two-leakage model is not a complete model, since it assumes the leakage inductances are proportional by N^2 (which is not necessarily the case).

Of course it's only one of several possible ieakage inductance definitions. The definition is the basis of the equation in the original post and in so far well defined.

I agree, that a model with separate primary and secondary leakage inductance has more physical plausibility. As long as all elements are linear, it can be transformed into a single Ls model or the SPICE coupled inductor model without changing the circuit behaviour.

The transformation of secondary leakage inductance by N² is just a formal operation involved with the ideal transformer in the model. It doesn't suggest anything else. Leakage inductance may be still asymmetrical, see below.

...according to this, the measured laekage is the series combination of the pro leakage (Llkp) in series with Lm and (NP/NS)^*Llks in parallel.

Yes, that's obviously the required calculation according to the equivalent circuit.

Can this be right?....... do you assume that (NP/NS)^*Llks = Llkp?

I don't assume anything. The equality is only valid for a transformer with leakage inductance symmetrically shared between primary and secondary. This isn't the case for many real transformers. A complete derivation can be found in several papers by Llyod Dixon (formerly Unitrode, see TI Magnetic Design Seminars).