Download Sepic inductor ..Degree of coupling

The following is an article on coupling coefficient in coupled inductor sepic
converters by ti.com that they must be highly congratulated for producing, as no other
semiconductor company (or any other body) has taken upon itself to write upon this
important and yet mystical subject. The following analysis on this article by no means
is criticising the production of this interesting article.
So, the following article states that sepic converters which use coupled inductors can
sometimes benefit from making the coupling between the inductors very loose. This
is because the article states that loose coupling reduces the size of “circulating AC
currents” in the primary and secondary inductors and the sepic capacitor.
http://www.powerpulse.net/techPaper.php?paperID=153
Whilst this is true to an extent, the fact is that even bifilar wound coupled sepic
inductors with a K factor of 0.995, don’t necessarily suffer enormously large
‘circulating AC currents’..With a sepic capacitor of sufficient size, the ‘circulating AC
currents’ will not be a significant problem. A sepic capacitor should be sized such
that the dv of the sepic capacitor’s voltage during a switching period is less than 10%
of the input voltage {-but preferably less than 5% of the V(in)}. If the sepic capacitor
is so sized, then in most cases the “circulating AC currents” will not be a problem in
a sepic with tightly coupled inductors. This is because the L(leak):C(sepic) resonance
frequency is likely to be below the switching frequency. Also, such resonance is
likely to be sufficiently damped out by the combined small ESR’s of the coupled
inductors and the sepic capacitor.
Not only that, but there is more to it, and any engineer planning on using such a
loosely coupled sepic inductor should first consider the full ramifications, which may
well not be favourable for the application..Basically, “a little knowledge is
dangerous” applies, and so the fuller story of sepics with coupled (or uncoupled )
inductors is given here..
Schematic A: Coupled inductor SEPIC with K=0.995 and just 50mR (total) of
resistance between V(in), L(pri), L(sec) & C(sepic):
http://i41.tinypic.com/2gvsk06.jpg
..The above sepic has 2.59Arms in the L(pri). This is comprised partly of the
“circulating AC current” that the ti.com article speaks about. This circulating current
is due to the fact that the resonance frequency of L(leak) & C(sepic) is 97KHz, which
is very close to the sepic’s switching frequency of 104KHz.
-Note that the FET current is 2.03Arms, and if this were a 1:1 flyback, then that
would also be the primary RMS current. So, even though yes, there is a “circulating
current “ overhead, its not massively big, and is not much greater than the L(pri) rms
current that would have been seen in an ‘equivalent’ flyback with 1:1 transformer.
Another point here, is that the above ‘Schematic A’, has unrealistically small
resistance (ESR) in the L(pri), L(sec) & C(sepic)..indeed, its just 50mR total
(including the V(in) source resistance)…obviously if this was greater (as it would be
in reality), then the ”circulating AC currents” that ti.com speak of would have been
well damped down.
-For example, if we make the total ESR of the current path involving V(in), L(pri),
L(sec) & C(sepic) equal to 164mR then the rms current in L(pri) is reduced to
1.97Arms.
[Note that 164mR is equal to SQRT{L(leak)/C(sepic)}]
This L(pri) current of 1.97Arms is less than the “equivalent flyback” current, that
would be seen in a 1:1 flyback primary. –So we can see that even though these
“circulating AC currents”, as termed by ti.com, do exist, they are certainly not
necessarily significant.
Also, worth noting is that the above, worst case “circulating AC current” of
2.59Arms occurs with an unrealistically tight coupling coefficient of 0.995. This
makes the L(leak):C(sepic) resonant frequency come close to the switching frequency
{f(sw)=104Khz, & F(resonance)=97KHz}. In reality, such a tight coupling is
unlikely, and coupling of 0.98 to 0.99 is more likely..
With a coupling coefficient of k=0.99, and reverting to the unrealistically low series
resistance of 50mR , then the L(pri) rms current is 1.81 Arms. The average input
current is 1.75A , so the rms current of 1.81Arms is barely much above that. This
shows that the indicated problem of “circulating AC currents” is not that great a
problem after all. –indeed, the “circulating AC currents”, will almost certainly be
damped out by the small ESR of the L(pri), L(sec), C(sepic) & the source resistance. –
Even if this were not the case, then adding some series damping resistance in series
with L(sec) would give the appropriate damping…{note that such an extra series
resistance should be added in series with L(sec) for a step-up sepic, and in series
with L(pri) for a step down sepic, because that will reduce dissipation in such a
resistor.}
So anyway, we can conclude that these “circulating AC currents” are not really
significant. –Even tiny amounts (as described above) of series resistance will damp
out these “circulating AC currents” significantly.
Also, for such “circulating AC currents” to be a problem, then this would mean that
the resonance frequency of C(sepic) & L(leak) would need to be very close to the
switching frequency. –Even with a tightly coupled sepic inductor with k=0.99, its not
necessarily likely that the aforementioned resonance frequency will be close to the
switching frequency. In the above schematic with K=0.99, then the C(sepic):L(leak)
resonant frequency = 68.7KHz, which is significantly far away from the switching
frequency of 104KHz that “circulating AC currents” are unsignificant.
Also, as mentioned, even if this resonance is near the switching frequency, then the
small amount of stray resistance in the circuit, by way of inductor and capacitor ESR,
will damp these “circulating AC currents” significantly.
So anyway, I am not sure why the above article has avoided mentioning this.
It is worth noting that the “circulating AC currents” that the above article mentions do
not actually cause any hysteresis loss in the coupled inductor’s ferrite..this is because
the path of such “circulating AC currents” goes through the primary in a ‘no-dot to
dot’ direction, and then through the secondary in a ‘dot to no-dot’ direction, thus the
field created by it when traversing the primary is cancelled out by the field created by
it when it traverses the secondary.
The loss mechanism for this “circulating AC current” is in the ESR of the inductor
and and the ESR of the sepic capacitor….however, the very presence of such ‘stray’
resistance will significantly dampen down the “circulating AC current”.
And as has been discussed, adding a small series resistance in series with the L(sec),
for a ‘step-up’ sepic, can significantly reduce the “circulating AC current”.
[obviously, if such a resistance was going to be added, then it would be added in
series with L(pri) for a step-down sepic, and in series with L(sec) for a step-up sepic,
as this would reduce dissipation in such a resistor.]
Custom wound “sectionised” transformer
In fact, in the above article, it is stated that the leakage inductance can be enhanced
by making a custom torroid-based coupled inductor, and deliberately section winding
it such that there is a large leakage term (in the case provided in the above article , the
leakage is 9uH, and the Magnetizing L(pri) is 17uH).
The obvious problem with this is that it requires the custom wound inductor. The
problem with this is that it’s expensive, and adds an element of risk, because one is
relying on the lowly payed winding staff to wind the transformer to the same spec of
magnetising inductance each time. As you know, slightly different spacing of the
sectioned windings can significantly effect the magnetizing inductance produced.
When winding transformers, it is cheapest and most easily repeatable to wind a
typical ETD type transformer (rather than a torroid) in such a way that coupling is
maximised, -in other words, use either bifilar windings, or do interleaved winding of
primary and secondary, in each case, making sure that each winding uses a whole
number of layers (preferably a single layer).
When the winding staff have to custom wind with a specific high leakage term in
mind, then its harder for them to do it repeatably and thus more expensive. I can
appreciate that a wide tolerance on the leakage term is probably acceptable, but it
won’t be too acceptable for the magnetisng inductance to have the wider tolerance.
Realistically, repeatable winding of ‘high leakage’ type transformers is best done
with “sectioned bobbins”. –Unfortunately, sectioned bobbins are expensive.
Another point, is that if a transformer is going to be wound, it may be far simpler to
just opt to do a flyback converter instead.
Another problem with the custom “section wound” transformer offered in the above
article is related to the high leakage term deliberately introduced.
This leakage inductance will ring with the sepic capacitor at a frequency which may
be too close to the feedback loop frequency. This then necessitates using an RC
snubber across the sepic capacitor. The capacitor of such a snubber is unfortunately
sometimes rather large. Indeed the size of this capacitor is:
1 / {2.pi.f(resonance).R(snub)}
where f(resonance) = C(sepic) * L(leak)
R(snub) = SQRT {L(leak)/C(sepic)}
Its worth noting that this ringing problem of the enhanced leakage inductance with
C(sepic) is only common to step-up SEPIC’s , which have a duty cycle greater than
0.5.
Its also worth mentioning that SEPIC’s with tightly coupled transformers don’t
actually require this RC snubber to be placed across the sepic capacitor. –so that is a
reason to avoid using very loosely coupled sepic inductors.
Sepic with uncoupled inductor:
If one is going to commit to doing a sepic with custom wound , loosely coupled
inductors, then it’s worth considering totally uncoupled inductors as an alternative.
This is because of the ubiquitous ‘off-the-shelf’ availability of off-the-shelf inductors.
Admittedly, if doing a step-up sepic with uncoupled inductors, then one will need an
RC snubber across the sepic capacitor..-however, this may well be needed anyway,
even if a loosely coupled sepic converter was being designed. If the
C(sepic):L(leakage) resonant frequency encroaches too near the feedback loop
frequency of the sepic converter, then the RC snubber across the sepic capacitor will
be needed. –So this is a potential disadvantage of doing a loosely coupled sepic
converter, -i.e. that an RC snubber may be needed across the sepic capacitor.
Sepic capacitor values.
As previously discussed, the sepic capacitor should be sized so that within the
switching period, the dv on the sepic capacitor should be no more than 10% of V(in).
{preferably no more than 5% of V(in)}.
In the above sepic of ‘schematic A’, this means a sepic capacitor of 10uF, as shown.
With a typical tight coupling coefficient of 0.98 (as found in eg coilcraft’s MSD1583
coupled inductor), then this gives a leakage of 1070nH. This in turn gives a
C(sepic):L(leakage) resonant frequency of 48,700Hz. This is far enough below the
switching frequency of 104Khz so that it does not give significant problems with the
‘circulating AC currents’ discussed in the article in question. Also, what ringing does
occur, will be sufficiently damped by the ESR’s of the L(pri), L(sec) & C(sepic).
Also, the frequency of 48,700Hz is good because this is generally going to be far
enough above the feedback loop frequency that it won’t require an RC snubber across
the sepic capacitor.
So I am not sure what the article in question means when it talks of the problem of the
‘circulating AC currents’ in tightly coupled sepics.
-Perhaps they are referring to cases when the sepic capacitor has been badly
undersized, and then the C(sepic):L(leakage) resonant frequency is above the
switching frequency and then the C(sepic):L(leakage) resonant frequency is more of
a problem, being less likely to be damped out by the ESR’s of the L(pri), L(sec) &
C(sepic)?
The example sepic given in the article under discussion
The spec for this sepic is vin=12v, vout=12v, iout=4A, f(sw)=228571Hz, CCM,
efficiency=90%, ESR for L(pri) & L(sec) = 12milliohms, ESR for sepic cap = not
stated.
The article clearly shows the ‘circulating AC current’……however, the article fails to
contrast the actual RMS values seen in the loosely and tightly coupled sepic versions.
I put together simulations as per the article (using LTC1871) and found the tightly
coupled L(pri) rms current came out at 4.49A.
The simulation of the article’s loosely coupled sepic gave an L(pri) rms current of
4.4A…so you can see an improvement of just 90mA RMS. –And considering that
the loosely coupled version has a higher peak FET current, its obvious that there’s
likely to be really little or no difference between the tightly coupled and loosely
coupled sepics’ efficiency overall.
In fact, despite the L(pri) current waveforms appearing to be quite different as shown
in the article, the difference in rms current between them is actually extremely slight.
And I was very forgiving in my simulation of the article’s schematic, -using a source
resistance of just 1 milliohm and a sepic capacitor ESR of 1 microohm.
So you can see that the improvement in rms L(pri) current from using the loosely
coupled inductor is very, very slight indeed.
I’d say theres no difference in efficiency (due to the higher peak fet current of the
loosely coupled version) and so taking the trouble to deliberately wind a ‘sectionised
winding’ torroid sepic inductor with loose coupling would be almost certainly a waste
of time.
Incidentally the tightly coupled sepic of the article had a leakage of 250nH which
amounts to a coupling coefficient of 0.9943, -this is extremely tight, and one wonders
if it is possible even with bifilar windings.