Transformer coupling coefficients

[Don Foreman]

I'd like to know what realistic or reasonable values for coupling
coefficients (k) might be in ferrite switchmode transformers. I'm
interested in forward converter power range of 50 to several hundred
watts.

I'd be interested in typical values for suitably-sized toroids, pot
cores, E-E cores and U-U cores. Bifilar and/or surrounded windings
(e.g. parallel windings above and below another winding) may be used.

Anybody have any experience with this?

 

[Tim Wescott]

I'd like to know what realistic or reasonable values for coupling
coefficients (k) might be in ferrite switchmode transformers. I'm
interested in forward converter power range of 50 to several hundred
watts.

I'd be interested in typical values for suitably-sized toroids, pot
cores, E-E cores and U-U cores. Bifilar and/or surrounded windings
(e.g. parallel windings above and below another winding) may be used.

Anybody have any experience with this?

Really close to one, in my experience -- which has a lot more to do with
RF than power supplies.

I often see the leakage inductance of a ferrite quoted as being equal to
one turn of wire around the outside of the core. I _don't_ know if this
is really some fundamental constant due to the geometry of the thing, or
if it just works out that way, or if it's all BS. But if it's true you
can back out from leakage inductance to coupling coefficients.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Posting from Google? See http://cfaj.freeshell.org/google/

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html

 

[Don Foreman]

Really close to one, in my experience -- which has a lot more to do with
RF than power supplies.

I often see the leakage inductance of a ferrite quoted as being equal to
one turn of wire around the outside of the core. I _don't_ know if this
is really some fundamental constant due to the geometry of the thing, or
if it just works out that way, or if it's all BS. But if it's true you
can back out from leakage inductance to coupling coefficients.

Yes. Leakage inductance is really what I'm after in the first place.
It really is determined by geometry and the relative permeability of
the core material. Windings that occupy exactly the same space would
have perfect coupling. Leakage happens to the extent that this
impossibility is not realized.

I suppose I could use FEMM before winding up some test samples, but
for k > 0.99 I'm probably in the simulation error and noise.

 

[legg]

Really close to one, in my experience -- which has a lot more to do with
RF than power supplies.

I often see the leakage inductance of a ferrite quoted as being equal to
one turn of wire around the outside of the core. I _don't_ know if this
is really some fundamental constant due to the geometry of the thing, or
if it just works out that way, or if it's all BS. But if it's true you
can back out from leakage inductance to coupling coefficients.

Because leakage inductance can vary with the winding structure and
turns ratio, a fixed value based on core structure alone is wishfull
thinking.

RL

 

[Don Foreman]

Because leakage inductance can vary with the winding structure and
turns ratio, a fixed value based on core structure alone is wishfull
thinking.

RL

Understood. I'm not looking for a silver bullet or a "simple answer
to a complex issue". I'd just like to know some typical values
that people who use such things routinely may have seen in practice.
That's also why I asked about k rather than leakage inductance. k
does not depend on turns count, just on geometry and relative
permeabilities.

I was surprised to find k's on the order of .998 in a couple of quick
FEMM simulations. Maybe the question is moot.

 

[John Woodgate]

I was surprised to find k's on the order of .998 in a couple of quick
FEMM simulations. Maybe the question is moot.

I'm not sure what you mean by 'moot'. It can mean 'debatable', but I
suspect you mean 'pointless'.

It's true that for normal constructions, k is so close to 1 that it can
be assumed to be 1. It is more helpful to consider leakage inductance,
which is easy to measure, at least if there are only two windings. You
measure the inductance of one winding with the other winding
short-circuited. You can also include leakage inductance as a discrete
component in simulations.

 

[J.A. Legris]

I'm not sure what you mean by 'moot'. It can mean 'debatable', but I
suspect you mean 'pointless'.

It looks like an Anglo/Americano distinction. Merriam-Webster shows a
second sense: deprived of practical significance - made abstract or
purely academic. I've never heard it used in the original sense. Maybe
the distinction on the west side of the pond is moot.

 

[John Woodgate]

It looks like an Anglo/Americano distinction. Merriam-Webster shows a
second sense: deprived of practical significance - made abstract or
purely academic. I've never heard it used in the original sense. Maybe
the distinction on the west side of the pond is moot.

Yes, I've noticed this difference before, and decided to follow it up in
this case, because it seemed simple enough to get a result without too
much confusion. The transition in meaning is rather easy, but it doesn't
seem to have made it into English dictionaries (no, I haven't looked at
ALL of them!).

debatable -> purely academic -> pointless

 

[Tim Wescott]

Understood. I'm not looking for a silver bullet or a "simple answer
to a complex issue". I'd just like to know some typical values
that people who use such things routinely may have seen in practice.
That's also why I asked about k rather than leakage inductance. k
does not depend on turns count, just on geometry and relative
permeabilities.

I was surprised to find k's on the order of .998 in a couple of quick
FEMM simulations. Maybe the question is moot.

You'll still need snubbers on the primary, though.

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

Posting from Google? See http://cfaj.freeshell.org/google/

"Applied Control Theory for Embedded Systems" came out in April.
See details at http://www.wescottdesign.com/actfes/actfes.html

 

[Don Foreman]

I'm not sure what you mean by 'moot'. It can mean 'debatable', but I
suspect you mean 'pointless'.

How about "don't amount to a hill of beans", or "hit don't make no
nevermind, ol' Son!"

It's true that for normal constructions, k is so close to 1 that it can
be assumed to be 1. It is more helpful to consider leakage inductance,
which is easy to measure, at least if there are only two windings. You
measure the inductance of one winding with the other winding
short-circuited. You can also include leakage inductance as a discrete
component in simulations.

Right. k is generic to a geometry, leakage inductance is specific
to a particular set of windings and the k that exists between them.
For given geometry and k, leakage inductance will increase as
self-inductance increases. Things are clearer for me if I separate
the variables of geometry and numbers of turns because they are
somewhat separate parameters.

 

[Don Foreman]

You'll still need snubbers on the primary, though.

Usually so, except for H-bridge or half-bridge configurations.
Question is how much snubbing. Snubbing is dissipative
so less is better -- as long as it's enough!

 

[John Woodgate]

For given geometry and k, leakage inductance will increase as
self-inductance increases.

But it's reasonably nearly proportional to self-inductance, provided the
windings are not very different in 'window-fill'.

Things are clearer for me if I separate the variables of geometry and
numbers of turns because they are somewhat separate parameters.

See above.

 

[Don Foreman]

But it's reasonably nearly proportional to self-inductance, provided the
windings are not very different in 'window-fill'.

Yes, and the proportionality constant is k -- which is what I'm
asking about. I guess I'll have to do some experiments.

An overnight soak of an inductor and a transformer in some lacquer
thinner did a very nice job of freeing up the little ferrite cores.
Man, the one out of a fluorescent ballast has a 2.61mm gap!

 

[John Woodgate]

Yes, and the proportionality constant is k --

k is very nearly 1. The leakage inductance is very much smaller than the
winding inductance, not k (or 1/k !) times it. You may say it's (1-k)
times, if you define k to make it true.

 

[Harry Dellamano]

k is very nearly 1. The leakage inductance is very much smaller than the
winding inductance, not k (or 1/k !) times it. You may say it's (1-k)
times, if you define k to make it true.

--
OOO - Own Opinions Only. Try www.jmwa.demon.co.uk and www.isce.org.uk
2006 is YMMVI- Your mileage may vary immensely.

John Woodgate, J M Woodgate and Associates, Rayleigh, Essex UK

You guys are just killing me! Please read;
http://www.onsemi.com/pub/Collateral/AN1679-D.PDF
regards,
harry

 

[legg]

Understood. I'm not looking for a silver bullet or a "simple answer
to a complex issue". I'd just like to know some typical values
that people who use such things routinely may have seen in practice.
That's also why I asked about k rather than leakage inductance. k
does not depend on turns count, just on geometry and relative
permeabilities.

I was surprised to find k's on the order of .998 in a couple of quick
FEMM simulations. Maybe the question is moot.

I believe that the coefficient k is an abstraction introduced to
remind the simulator user that something is missing in the model.

It has no physical derivation.

RL

 

[Don Foreman]

I believe that the coefficient k is an abstraction introduced to
remind the simulator user that something is missing in the model.

It has no physical derivation.

RL

It is defined in fundamental physical terms: It is a ratio of
flux linkages. Transformer theory was well-developed long before
simulators or even computers existed. Many or most texts
express k as lambda sub ij / lambda sub jj where lambda ij is flux
linking winding i resulting from excitation of winding j.

 

[Don Foreman]

k is defined as a ratio of flux linkages, not something I define.
Leakage inductance will depend on turns ratio as well as k, but you're
right in that it is a 1-nk sort of relationship.

 

[Don Foreman]

You guys are just killing me! Please read;
http://www.onsemi.com/pub/Collateral/AN1679-D.PDF
regards,
harry

I saw nothing in that appnote dealing with values of k found in common
practice.

So far all I'm hearing is "close to 1", which isn't very helpful. The
difference between .990 and .995 can be significant, and .999 works
even better. Are these realistic values? I guess nobody here knows
either, oh well! Thanks anyway and nevermind.

 

[John Woodgate]

You guys are just killing me! Please read;
http://www.onsemi.com/pub/Collateral/AN1679-D.PDF

What astonishing insight does this give? To try to introduce all that in
a news article to someone more or less beginning to understand
transformers is simply counter-productive.