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Leakage inductance modeling

 

If we take simple 1: 1 transformer, with equal winding inductances L and mutual inductance M,  and with equal leakage inductances LL for each winding. Then we define K = M/L = (L - LL)/L, from which we can get LL = L(1-K).  This can be extended to any turns ratio, provided LL1/L1 = LL2/L2. Some special constructions do not meet this.

Best wishes John Woodgate OOO-Own Opinions Only www.woodjohn.uk Rayleigh, Essex UK MAY THE VIRUS NOT BE WITH YOU dum nisi ex silvis sumus
On 2020-07-10 22:32, hyu hyu via groups.io wrote:

Hello and thanks to everyone for your replies.

Bordodynov, based on your first .asc schematic I will use L(1-k), it seems is the same this equation or explicitly connecting the leakage inductance.

Hyu

On Friday, July 10, 2020, 03:18:34 PM GMT-3, John Woodgate <jmw@...> wrote:


Yes. This is often interpreted as two different definitions of K, with terms like 'coupling coefficient', coupling constant', 'coupling ratio' being used. Some textbooks evade the issue by defining K as mutual inductance M divided by sqrt(L1*L2) and not mentioning K when discussing leakage inductance.

Best wishes John Woodgate OOO-Own Opinions Only www.woodjohn.uk Rayleigh, Essex UK MAY THE VIRUS NOT BE WITH YOU dum nisi ex silvis sumus
On 2020-07-10 18:26, Andy I wrote:
hyu hyu wrote, " I was reading the LTspice help and realize the Leakage inductance is calculated with coupling coefficient squared."

Jerry Lee Marcel asked, "Where do you see that?"

It's here:

    Lleak = sqrt(L1*L2)*(1-K*K)

See it here: LTspice Help > F.A.Q. > Simulating Transformers

One danger with transformers, is that there are multiple terms and definitions and one needs to be extra careful about using them consistently.

Andy

Virus-free. www.avg.com

 

Hello and thanks to everyone for your replies.

Bordodynov, based on your first .asc schematic I will use L(1-k), it seems is the same this equation or explicitly connecting the leakage inductance.

Hyu

On Friday, July 10, 2020, 03:18:34 PM GMT-3, John Woodgate <jmw@...> wrote:


Yes. This is often interpreted as two different definitions of K, with terms like 'coupling coefficient', coupling constant', 'coupling ratio' being used. Some textbooks evade the issue by defining K as mutual inductance M divided by sqrt(L1*L2) and not mentioning K when discussing leakage inductance.

Best wishes John Woodgate OOO-Own Opinions Only www.woodjohn.uk Rayleigh, Essex UK MAY THE VIRUS NOT BE WITH YOU dum nisi ex silvis sumus
On 2020-07-10 18:26, Andy I wrote:
hyu hyu wrote, " I was reading the LTspice help and realize the Leakage inductance is calculated with coupling coefficient squared."

Jerry Lee Marcel asked, "Where do you see that?"

It's here:

    Lleak = sqrt(L1*L2)*(1-K*K)

See it here: LTspice Help > F.A.Q. > Simulating Transformers

One danger with transformers, is that there are multiple terms and definitions and one needs to be extra careful about using them consistently.

Andy

Virus-free. www.avg.com

 

Yes. This is often interpreted as two different definitions of K, with terms like 'coupling coefficient', coupling constant', 'coupling ratio' being used. Some textbooks evade the issue by defining K as mutual inductance M divided by sqrt(L1*L2) and not mentioning K when discussing leakage inductance.

Best wishes John Woodgate OOO-Own Opinions Only www.woodjohn.uk Rayleigh, Essex UK MAY THE VIRUS NOT BE WITH YOU dum nisi ex silvis sumus
On 2020-07-10 18:26, Andy I wrote:
hyu hyu wrote, " I was reading the LTspice help and realize the Leakage inductance is calculated with coupling coefficient squared."

Jerry Lee Marcel asked, "Where do you see that?"

It's here:

    Lleak = sqrt(L1*L2)*(1-K*K)

See it here: LTspice Help > F.A.Q. > Simulating Transformers

One danger with transformers, is that there are multiple terms and definitions and one needs to be extra careful about using them consistently.

Andy

Virus-free. www.avg.com

 

hyu hyu wrote, " I was reading the LTspice help and realize the Leakage inductance is calculated with coupling coefficient squared."

Jerry Lee Marcel asked, "Where do you see that?"

It's here:

    Lleak = sqrt(L1*L2)*(1-K*K)

See it here: LTspice Help > F.A.Q. > Simulating Transformers

One danger with transformers, is that there are multiple terms and definitions and one needs to be extra careful about using them consistently.

Andy
 

 Hi.
You might wonder why.
Or you could just check what I did.
Take a look at my Mutual_Ind.zip file in the TEMP folder.

Bordodynov.
 

On Fri, Jul 10, 2020 at 06:11 AM, hyu hyu wrote:
Hello everyone, I was reading the LTspice help and realize the Leakage inductance is calculated with coupling coefficient squared.
Where do you see that?
 
 
But in LTwiki and other sources its calculated as Leakage = L (1 - k)   , no square
Of course, and that's how LTspice behaves. You can compare schematics done with a K statement with another done with explicit leakage inductances and you will see the results are identical. At least that's how it works for me.
 
 
Edited

On Thu, Jul 9, 2020 at 09:11 PM, hyu hyu wrote:
I was reading the LTspice help and realize the Leakage inductance is calculated with coupling coefficient squared.
 
But in LTwiki and other sources its calculated as Leakage = L (1 - k) , no square
 
What am I missing?
 
Which formula do you recommend to use to model the transformer? or use an explicit leakage inductance?
To model leakage inductance in LTspice use the LTwiki definition.  That is exactly how LTspice does it.

In the lab since one measures a series connection of windings (input winding measured, output winding shorted), it is not possible to directly measure the leakage inductance associated with an individual winding.
 

Hello everyone, I was reading the LTspice help and realize the Leakage inductance is calculated with coupling coefficient squared.

But in LTwiki and other sources its calculated as Leakage = L (1 - k)   , no square

What am I missing?

Which formula do you recommend to use to model the transformer? or use an explicit leakage inductance?

Thanks in advance

One source:  

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