Relation Between Transformer Leakage-Inductance and Mutual Coupling Needed
Klaus Vestergaard Kragelund
I'm currently involved in evaluating different transformer strategies for a
discontinous flyback converter. Our main concern is the cross-regulation
between the tree outputs. I have read somewhere that the leakage-inductance
which is the inductance not coupled to the other windings also effects the
mutual coupling between windings. We need good coupling to avoid secondary
linear regulators to keep the outputs within spec.
I have made a transformer that has interleaved primary winding (first one
section of the primary is wound - then the secondaries - and on top of
those the last primary section). This interleaved design gave us a 5 fold
reduction in leakage inductance as opposed to that of a single primary
winding.
My question is how do you relate the coupling coefficient with the leakage
inductance of the windings. Or is it nessesary to measure the coupling ?
Furtheremore anyone got experience in measuring the cross-regulation of the
transformer? We currently just insert the thing into the converter and do
some trancient load steps and work it out from that. But this test could
have other factors in the equation (- I would like to have a setup with the
transformer only and test it seperately.
Thanks
Klaus
P.S The leakage inductance of the interleaved winding fell to 0.5% versus
the leakage of the standard design which was 2.5%. Does anyone know what is
practically possible - is these numbers low og high?
Reg Edwards
Then measure primary primary with the secondary short circuit.
There's enough info there to give you equivalent leakeage inductance of the
whole transformer lumped in series with the primary.
As a check interchange primary and secondary and do same again.
--
****************************
Regards, Reg G4FGQ
Free Radio Modelling Software
Http://www.g4fgq.com
****************************
Klaus Vestergaard Kragelund <Klau...@hotmail.com> wrote in message
news:3c680c13$0$22260$edfa...@dspool01.news.tele.dk...
Klaus Vestergaard Kragelund
news:a497oa$1d02vb$2...@ID-124126.news.dfncis.de...
> Measure inductance of primary winding with the secondary open circuit.
>
> Then measure primary primary with the secondary short circuit.
>
This is actually what we are doing. Isn't the measurent of the primary with
the secondary's open just the primary inductance? And the primary with the
secondary shorted just the leakage?
The measurements we made was (with the above method):
Primary inductance = 2mH, Leakage 10uH
Secondary 1 inductance = 240uH, Leakage 2.5uH
Secondary 2 inductance = 170uH, Leakage 1.9uH
.
...
How would you transfer this to a single primary leakage inductance ? And
more importantly how do you get the mutual coupling from these measurements?
Thanks
Klaus
R.Legg
What you are actually trying to do, is to reduce cross-regulation
between secondaries.
In order to do this, it's not so important to worry about leakage
inductance between primary and secondary, as it is to ensure good
coupling between the secondaries and, if possible, ensure that
auxiliary loads also load the main regulated output.
Wind secondaries bifilar / multifilar /twisted bundles.
If you need +12 and +5, try +5 and +8 in series instead, so that
stacked voltages ensure 5V winding and rectifier conduction as the 12V
is loaded.
(A forward converter with coupled inductor will have better
cross-regulation, at the added expense of the output inductor.)
RL
John Woodgate
<Klau...@hotmail.com> wrote (in <3c685279$0$89083$edfa...@dspool01.ne
ws.tele.dk>) about 'Relation Between Transformer Leakage-Inductance and
Mutual Coupling Needed', on Tue, 12 Feb 2002:
>This is actually what we are doing. Isn't the measurent of the primary with
>the secondary's open just the primary inductance? And the primary with the
>secondary shorted just the leakage?
Yes, in both cases.
>
>The measurements we made was (with the above method):
>
>Primary inductance = 2mH, Leakage 10uH
>Secondary 1 inductance = 240uH, Leakage 2.5uH
>Secondary 2 inductance = 170uH, Leakage 1.9uH
>.
>...
>
>How would you transfer this to a single primary leakage inductance ?
The primary leakage inductance is what you measure, 10 uH. Since the
secondary leakage inductances are due to flux (generated by the current
during the measurement) that *doesn't link with the primary*, they have
no effect on the primary.
>And
>more importantly how do you get the mutual coupling from these measurements?
It's unusual, AFAIK, to use the 'mutual coupling' concept for this sort
of transformer. You can draw the equivalent circuit as an ideal
transformer, with coupling factor k = 1, each winding having inductance
L - Lleak, with separate inductors Lleak in series with each winding.
This model gives you all the information you need, without introducing a
k<1.
--
Regards, John Woodgate, OOO - Own Opinions Only. http://www.jmwa.demon.co.uk
After swimming across the Hellespont, I felt like a Hero.
PLEASE do NOT copy news posts to me by E-MAIL!
Gerhard van Eerden
For good cross regulation it is necessary to have low leakage inductance
between the secondary windings.
The leakage inductance between primary and secondary has no significant
effect on cross regulation but determines the amount of power that will be
dissipated in a primary clip or snubber.
There a more factors that determine cross regulation:
-rectifier voltage drop variations
-PCB trace resistance and inductance
-smoothing capacitance and its ESR and ESL.
Stacking outputs does improve cross regulation.Best is to stack after the
rectifier, at the expense of some additional loss.
Best regards,
Gerhard
"Klaus Vestergaard Kragelund" <Klau...@hotmail.com> schreef in bericht
news:3c680c13$0$22260$edfa...@dspool01.news.tele.dk...
Reg Edwards
circuit incorporating a perfect transformer and include the leakage
inductance referred to either the the primary or secondary circuit taking
into account the turns ratio. The turns ratio of the perfect transformer is
obtained from the primary and secondary inductance measurements.
It was all sorted out in European elementary electrical engineering books at
least 130 years back.
The abysmal standard of education of so-called Western electrical engineers
is astounding. Laziness? Complacency? Arrogance? No wonder the Chinese,
Russian, Japanese, Korean, Indian, etc., are taking over.
Street kids existing in the sewers of South American cities are better
educated in arihmetic than 17 year-old students in Western schools. Their
next meal depends on the accuracy of a mental calculation of what to charge
for the sale of a sniff of heroin.
---
qrk
Lp = inductance of primary winding with all other windings open
Lps = inductance of primary winding with the secondary shorted, or
leakage inductance
You can also find information on winding geometry and the effects on
leakage inductance in "Soft Ferrites", by E. C. Snelling, chapter
11.7. You technical university library might have this book.
-
Mark Chun
Santa Barbara, CA
John Woodgate
wrote (in <3c6bc5ac...@news.west.net>) about 'Relation Between
Transformer Leakage-Inductance and Mutual Coupling Needed', on Wed, 13
Feb 2002:
>Coupling coefficient = K = sqrt[(Lp-Lps)/L1)]
>
>Lp = inductance of primary winding with all other windings open
>Lps = inductance of primary winding with the secondary shorted, or
>leakage inductance
What is L1?
Tony Williams
Klaus Vestergaard Kragelund <Klau...@hotmail.com> wrote:
> P.S The leakage inductance of the interleaved winding fell
> to 0.5% versus the leakage of the standard design which was
> 2.5%. Does anyone know what is practically possible - is
> these numbers low og high?
I have a table of leakage factors (m) for various
winding schemes. (m) is related to the coupling
factor (k) by the following definitions.
lp = (1-k^2)*Lp and (1-k^2) = 2m, so lp/Lp = 2m.
For a simple scheme, Pri/Sec superimposed, they
predict lp/Lp = 0.36%.
For an interleaved scheme, Pri/Sec/Pri, they
predict an improvement to lp/Lp = 0.1%.
That's an improvement ratio of 3.6:1.
Warning: They do remark that the sums should not
be used to predict the absolute values for leakage
inductance, only to *compare* winding schemes.
Note that this table is for 50Hz mains transformers,
where the large number of turns makes it easier to
wind clearly defined sectionalised layers. This
may not be the case for ferrite transformers.
--------------------------------------------------
Other posters have already remarked that the Pri
is not relevant during a flyback, and you should
be looking at the Sec-Sec coupling. Perhaps you
could take the highest-power Sec and regard that
as the notional "Pri" for the other Secs during
the flyback.
If Sec-Sec capacitance is not important, then
very good coupling can be obtained with multi-
-filar winding.... many strands wound at the same
time, 1 strand each for each low power Sec and the
remaining strands paralleled-up to form the high
power Main Sec.
--
Tony Williams.
R.Legg
It's always 'obvious' after you've been shown how.
But, quite frankly, the model always follows the prototype, with
varying degrees of useful accuracy or practical simplification.
I notice you don't cite useful references (never mind any dating from
1872) for the inquirer to look up the specific relation in question.
Most useful articles dealing with this question simply illustrate the
electromechanical phenomena, and illustrate practical physical methods
of reducing the effect.
If the 'obvious' solution were so obvious, I'd expect to see a neat
equation. Gotta go, I'm due for my 8.46am fix.
Regards
RL
"Reg Edwards" <g4fgq...@btinternet.com> wrote in message news:<a4canv$1df9gm$4...@ID-124126.news.dfncis.de>...
Harry Dellamano
"Tony Williams" <to...@ledelec.demon.co.uk> wrote in message
news:4b08132...@ledelec.demon.co.uk...
> In article <3c680c13$0$22260$edfa...@dspool01.news.tele.dk>,
> I have a table of leakage factors (m) for various
> winding schemes. (m) is related to the coupling
> factor (k) by the following definitions.
>
> lp = (1-k^2)*Lp and (1-k^2) = 2m, so lp/Lp = 2m.
>
Hey Tony, good stuff there. Tell us more about this "table of leakage
factors". Sounds very interesting. Can we get our hands on that
documentation?
regards
harry
Tony Williams
Harry Dellamano <har...@tdsystems.org> wrote:
> "Tony Williams" <to...@ledelec.demon.co.uk> wrote
> > lp = (1-k^2)*Lp and (1-k^2) = 2m, so lp/Lp = 2m.
> Hey Tony, good stuff there. Tell us more about this
> "table of leakage factors". Sounds very interesting.
> Can we get our hands on that documentation?
It's an old book on small transformer design that I've
mentioned here before Harry (repeatedly, say some).
Printed in 1953, author named K.A MacFadyen, and I
obtained it (by accident really) as a cancelled
junk book, from a place I once worked at.
Since this book contains old (and sometimes forgotten)
design knowlege, I do try and post sections from it,
as and when the occasions arises.
I posted the leakage inductance versus winding scheme
calcs from it a few years ago (in sed). I believe that
WH has an archive of that post.
I should note an error in my previous post. That
ratio of 3.6:1 between simple and interleaved schemes
was not a theoretical prediction, the table is of
actual measurements. The approximate theoretical
prediction is given elsewhere, as about 4:1.
Note also; Terms such as k, m, or lp/Lp should not
be used (indeed are dangerous) if comparing different
transformers, or even different stimulus levels on
the same transformer. This is because lp is never
concerned with the permeability of the core material,
whereas Lp is always determined by that permeability.
--
Tony Williams.
Harry Dellamano
> In article <u6l19v5...@corp.supernews.com>,
> Harry Dellamano <har...@tdsystems.org> wrote:
>
> > "Tony Williams" <to...@ledelec.demon.co.uk> wrote
> > > lp = (1-k^2)*Lp and (1-k^2) = 2m, so lp/Lp = 2m.
>
> > Hey Tony, good stuff there. Tell us more about this
> > "table of leakage factors". Sounds very interesting.
> > Can we get our hands on that documentation?
>
> It's an old book on small transformer design that I've
> mentioned here before Harry (repeatedly, say some).
> Printed in 1953, author named K.A MacFadyen, and I
> obtained it (by accident really) as a cancelled
> junk book, from a place I once worked at.
>
his 1978 edition of "Transformer and Inductor Design Handbook". Nobody told
me I was supposed to read it! He does have six pages on leakage inductance
in there. No charts or tables thou.
regards
harry
John Woodgate
<to...@ledelec.demon.co.uk> wrote (in <4b083bc...@ledelec.demon.co.
uk>) about 'Relation Between Transformer Leakage-Inductance and Mutual
Coupling Needed', on Wed, 13 Feb 2002:
>> "table of leakage factors". Sounds very interesting.
>> Can we get our hands on that documentation?
>
> It's an old book on small transformer design that I've
> mentioned here before Harry (repeatedly, say some).
> Printed in 1953, author named K.A MacFadyen, and I
> obtained it (by accident really) as a cancelled
> junk book, from a place I once worked at.
>
There is a lot of similar lore in the 'Radio(tron) Designers Handbook',
republished about 4 years go. ISBN 0 7506 3638 1.
Gerhard van Eerden
Leakage inductance between two windings, same winding breadth, wound with
little or no spacing between turns can be calculated!
Consider one winding shorted and determine the area that is available for
field lines from the other winding: Area (A) is the distance between the two
windings times the length of one turn.
Lleakage = Uo*N^2*A/l
N is number of turns, l is winding breadth.
The above formulae can be applied with sufficient accuracy if frequency and
wire type is considered:
For massive winding wire at low frequencies (freqs at which skin depth is
greater than wire diameter) and for Litz wire (single wire diam < skin
depth) take the distance between conductor centers.
At frequencies for which skin depth < 0.5* wire diameter ( massive wire) the
distance between the two windings reduces to the skin depth + insulation.
The conclusion is that the leakage inductance of transformers wound with
massive wire reduces at high frequencies (confirmed by measurements).
This does not apply to Litz wire since each individual wire has a varying
distance (0 to Litz diam.) to the interface between the two windings.
Skin depth for copper at 100KHz is 0.21mm and is inverse proportional to
sqrt of frequency (2.1mm at1KHz and 0.021mm at 10MHz)
From the above formulae it can be concluded that sandwiching (W1-W2-W2-W1)
instead of standard (W1-W2) in the same winding volume, reduces the leakage
inductance by a factor of four (two paralleled leakage inductances that are
each half the original value due to halving of the distance (neglecting
insulation thickness).
Expressing the leakage inductance as a percentage (n) of the magnetizing
inductance is useful for determining the ratio between the power dissipation
in the primary clip and the transferred power:
Pclip/Ptrans = n*Vclip/(Vclip-Vfb).
Vclip is the (zener) clip voltage and Vfb is th flyback voltage seen at the
primary winding when the secondary is conducting and the leakage has
demagnetized.
Best regards,
Gerhard
"Tony Williams" <to...@ledelec.demon.co.uk> schreef in bericht
news:4b08132...@ledelec.demon.co.uk...
Klaus Vestergaard Kragelund
Before asking this question I looked through 4-5 different books on power
electronics and found nothing specific such as a formula. Tonight after
reading your posts I took out an old book from 1963 my farther left me that
had some pages on transformers (and a lot of pages on tube-amplifiers). I
found more there than in all the other references. I would think the issue
of leakage inductance and inter-winding coupling would be one of the most
important issues of flyback transformer design but the litterature is very
scarse. I will have to get a hold of the books you guys has recommended :-)
Thanks again
Klaus
"Gerhard van Eerden" <gvee...@tref.nl> wrote in message
news:a4ehri$503$1...@reader09.wxs.nl...
ber...@ami.com.au
You are unfortuantely QUITE RIGHT. Western Countries are full up with
paper shuffling parasites in control of the EDUCATION purse strings
and the quality of education is the victim. I know a professor who was
a trainee engineer under me before he graduated. He was hopeless then
and from all accounts he is still hopeless, despite his Ph.D degree.
aeolus
qrk
<j...@jmwa.demon.co.uk> wrote:
>I read in sci.electronics.design that qrk <ma...@reson.DELETE.ME.com>
>wrote (in <3c6bc5ac...@news.west.net>) about 'Relation Between
>Transformer Leakage-Inductance and Mutual Coupling Needed', on Wed, 13
>Feb 2002:
>>Coupling coefficient = K = sqrt[(Lp-Lps)/L1)]
>>
>>Lp = inductance of primary winding with all other windings open
>>Lps = inductance of primary winding with the secondary shorted, or
>>leakage inductance
>
>What is L1?
Oops, L1 is supposed to be Lp and there's too many ")". Need more
sleep.
Thus, K = sqrt[(Lp-Lps)/Lp]
rodg...@siteconnect.com
Go read the papers here:
http://ece-www.colorado.edu/~pwrelect/publications.html
and the references therein and I think you will find a good deal of
what you need to know.
Rodger
Malcolm Reeves
<Klau...@hotmail.com> wrote:
>Thankyou very much indeed for your very helpfull responses.
>
>Before asking this question I looked through 4-5 different books on power
>electronics and found nothing specific such as a formula.
The bible on ferrites in Snelling's Soft Ferrites. This covers
leakage inductance, the effects of litz wire, or bunches, Dowell's
work on skin/proximity effects and layers, etc.
Amazon has it as out of print but all *good* electronics libraries
should have a copy :-).
...malcolm
--
Malcolm Reeves BSc CEng MIEE MIRSE, Full Circuit Ltd, Chippenham, UK
(mre...@fullcircuit.com, mre...@fullcircuit.co.uk or mre...@iee.org).
Design Service for Analogue/Digital H/W & S/W Railway Signalling and Power
electronics. More details plus freeware, Win95/98 DUN and Pspice tips, see:
http://www.fullcircuit.com or http://www.fullcircuit.co.uk
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