Various application notes on LLC design consistently assume some maximal deltaB in order to calculate the number of primary turns. They take 200mT, sometimes ~400mT. But then they correct mu of the core by introducing a gap (most often) or a low permeability shunt in the case of the hi-tech planar transformers. This is to adjust Lm to the desired value. Clear. No, not exactly, the sequence of events is pretty mysterious. Gapping the ferrite decreases its Bpeak considerably, so what's the point in limiting oneself to
400mT from the very beginning? I see no post-gapping core losses correction calculation stage. Why is that?
The flux density in the core should be limited to the point where the core material is starting to saturate.
Gapping the core makes it more difficult - you need more ampere turns - to hit that flux density, because it's the ampere-turns divided by the flux path length that determines flux density.
The magnetic path length around an un-gapped core is the actual path length - a few cm - divided by the permeability of the ferrite (upwards of a thousand) which is to say a few tens of microns.
Typical gaps push that up by a factor of ten or more without forcing much of the flux path outside the ferrite core.
You can store more energy in an inductor with a gapped core than you can in he same inductor wound on the ungapped core - the inductance is less but you can put more current through the windings before the core saturates.
The windings might overheat, but that's a design problem.
Since they're used as energy-storage devices in power converters IMO all inductor design should derive from energy-density considerations - how much energy do I need to store, how much can I afford to lose in loss, and what are my size constraints. Same as if you were trying to figure out what rechargeable battery you wanted to buy.
I don't think explaining the air gap as being used to "adjust the Lm" is a good way to explain the purpose of adding an air gap, if that's how they explain it. the goal of it is to store energy, an ungapped ferrite can't store much energy before it saturates and stops behaving like an inductor (being able to store energy!) The average energy that you're storing cycle to cycle is proportional to the square of the RMS current thru it, if you need to store 0.5 joules cycle-to-cycle but your inductor hits saturation at an amount of current that 1/2*L*I^2 to
1/10th that then that won't work at all.
If you add an air gap then the inductor can store more energy because its reluctance goes up, and it won't saturate at some silly low level of current. But all else being equal, for the same peak flux, its reluctance going up means the required magneto-motive force in ampere turns goes up too. MMF = flux*reluctance.
That means all else being equal your design has less "theoretical" energy storage capability (according to the ideal magnetic circuit equation) than before _if_ it had actually been able to store that energy without going into saturation.
Only two thing you can do in reality at that point which is push more current, add more turns, or adjust the core geometry/gap geometry. Pushing more current usually isn't an option, and adjusting the other parameters will alter the value of inductance. But then that also changes the amount of energy your inductor can store...and so forth, it's always an iterative process.
I dp think it's best to start an inductor design from energy density considerations alone don't even think about precise values of Lm until that's squared away. There are equations that will ballpark a core "figure of merit" or "K" or something that give an idea of what kind of geometry and material/gap size might be required for a particular application and energy density requirement. then pick a family of cores and play around with their particular figures to limit your search space, and see if they get you close to what you need.
Designing the One True Inductor that's best for a given application is a hard task because of the iteration and how every parameter of importance tends to interact (sometimes non-linearly) with every other.
I will only add that 200mT is quite extreme flux density, even for low loss materials at modest frequencies. 20mT at, say, 1MHz, is much more typical.
(Failure to observe Bmax limits, results in excessive core heating, until Tc is reached, around which Bsat drops exponentially. Then heating shifts from core to copper, and your house of cards kind of, uh, falls apart and catches fire.)
How is that possible? B=mu*H, H is determined by the number of turns and thus constant, mu is decreased by a large factor due to the effective length extension. Do you mean that the current goes up as the inductance goes low and N*I remains constant, hence B too?
This is a valid general reasoning, but an LLC transformer is still a transformer and you don't want it to store any energy. The gapping there is just a crude form of tuning Lm to get the desired resonant value.
But since you have some gap and the resulting storage capacity, you can pump some energy into leakage inductance without saturating your ferrite. Hence, you can integrate the entire resonant inductor Lr into the same core (if you are good) or a large part of it (typically) and use a smaller external inductor for the remaining part of Lr. But this is just a useful side effect.
Shunting the main ferrite with some other material is a third option, but probably applicable only to high-volume designs.
I also think that legg has got his formulation wrong. There's no guarantee that I'm right - ferrite core transformer theory is a mess, and the traditi onal reference written by E.C.Snelling for Mullard (which got taken over by Philips and turned in Ferroxcube) made it even more difficult to understan d.
Siemens wrote much better applications note on designing ferrite cored tran sformers, which I first came across around 1978.
Since then Siemens has spun of its ferrite core business as EPCOS which the n merged with TDK.
At one point in the 1990's the late great Tony William e-mailed a large bun ch of .pdf files to me and Win Hill and a bunch of other lucky people.
When I went looking for them, what I found was a 33MB .pdf file of the EPCO S 2107 ferrite data book, with useful stuff on the theory from page 124 to
141.
Finding it on the web proved tedious. What I did find
is rather more specific, and talks about multi-gapped cores, which look int eresting.
seems to be the 2013 data book, which isn't as good as the 2017 version.
But you still use an increasing flux in the core to generate the volts that transfer the energy.
That's storing energy in the inductance of the transformer, even if that is n't what you are interested in doing. When you run the flux down again - to generate the revers voltage, you take the energy out, only to put it back in again as you ramp the flux though zero up to an equal and opposite level before repeating the cycle.
It can be.
The flux that represents your leakage inductance is just a fraction of the total flux you are generating. The fact that the leakage flux doesn't go ar ound the whole core isn't of any practical significance.
Obviously, but I miss your point. Leakage inductance/flux is typically small, but so what? You are going to build a tiny Lr and here is your tiny Lr. The problem is how to make it big enough in order to fully integrate the transformer with the resonant inductor. Crazy ideas apply here.
Why? This is how an LLC resonant tank works and looking at it from the basic principles point of view is making the picture intentionally unclear, IMHO. You can have a zero leakage inductance transformer, by coincidence with the correct value of Lm, connect an inductor in series with the primary, add a capacitor or two and an LLC resonant tank appears.
Nothing is bizzare enough in the case of planar magnetics.
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page 86. There are entire papers on that, but to cover the NRE expenses the design must be high volume. In smaller scale it is just easier to grind a gap.
You've always got some got capacitance between the windings.
Treating leakage inductance as separable parameter strikes me as the wrong way to think about what's going on. All transformers have some leakage indu ctance.
I found transformers a lot more comprehensible when I concentrated on the t ransformer equation
V1 = L1.dI1/dt + M.dI2/dt
V2 = M.DI1/dt + L2.dI2/dt
where the mutual inductance M = k.(L1.L2)^0.5
and k is a slightly less than one for a closely coupled winding on the same core. Closest to one for bifilar windings, lower for windings in separate layers.
It doesn't say why anybody would do it.
After all, an air gap would have exactly the same effect. If you substitute something with some permeability (intermediate between air and the core ma terial), you wouldn't have to have such a tight tolerance on the size of th e gap, which might be attractive in high volume production.
Also, you can get away with that on smaller and less spherical cores, but it's harder to do on a pot core (low surface area, large v_e) or toroid (no surface area -- surrounded by windings).
I've always admired Snelling's work, as being both methodical constructive. It's the first instance that I'm aware of the appearance of the equation Pc = k . f^a . B^b
If more manufacturers had standardized their material evaluation methods and carried on with this work, it would have been to the general benefit of the industry. Many still have not even converted their data to SI units.
ee that I'm right - ferrite core transformer theory is a mess, and the trad itional reference written by E.C.Snelling for Mullard (which got taken over by Philips and turned in Ferroxcube) made it even more difficult to unders tand.
ransformers, which I first came across around 1978.
then merged with TDK.
bunch of .pdf files to me and Win Hill and a bunch of other lucky people.
PCOS 2107 ferrite data book, with useful stuff on the theory from page 124 to 141.
interesting.
Snelling may have been methodical and constructive, but his presentation wa s very difficult to follow, and certainly didn't set my thinking on the rig ht track.
I doubt if he ever taught students - though I have run into teachers who di d leave me more confused than I had been when I started.
I came across the Siemens application notes after I'd been exposed to Snell ing, and found them much clearer, and they greatly improved the way I thoug ht about transformers.
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