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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.