Flux density in an LLC core

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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?

    Best regards, Piotr



Re: Flux density in an LLC core
On Mon, 1 Oct 2018 00:06:11 +0200, Piotr Wyderski

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The gap has no effect on the flux peak, if voltage, frequency, turns
and xsectional area remain constant.

Peak flux, frequency and core volume determine flux-induced core loss.


RL

Re: Flux density in an LLC core
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Exactly right.

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.)

Tim

--  
Seven Transistor Labs, LLC
Electrical Engineering Consultation and Design
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Re: Flux density in an LLC core
Tim Williams wrote:

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But how? It seems it would be fair to say I mistunderstand something  
important.

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3C95 is specified at 200mT/100kHz. Want something extreme?


https://www.youtube.com/watch?v=YdqnVp1bUQg


and its associated app note:

https://www.infineon.com/dgdl/Infineon-ApplicationNote_EVAL_600W_12V_LLC_C7_with_600V_C7_XMC-AN-v01_00-EN.pdf?fileId55%46d46253f6505701544cc1d15c20d7

These guys take the poor 3C95 to 370mT.



Modest frequency you say? :->

    Best regards, Piotr

Re: Flux density in an LLC core
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Pfft, 100kHz is child's play. ;-)

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).

Tim

--  
Seven Transistor Labs, LLC
Electrical Engineering Consultation and Design
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Re: Flux density in an LLC core
legg wrote:

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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?

    Best regards, Piotr

Re: Flux density in an LLC core
On Monday, October 1, 2018 at 4:30:51 PM UTC+10, Piotr Wyderski wrote:
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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

<https://en.tdk-electronics.tdk.com/download/2113430/7dc6417a70e37082863776
922b6e0d52/ferrites-air-gaps-pb.pdf>

is rather more specific, and talks about multi-gapped cores, which look int
eresting.

<https://en.tdk-electronics.tdk.com/download/519704/069c210d0363d7b4682d9ff
22c2ba503/ferrites-and-accessories-db-130501.pdf>

seems to be the 2013 data book, which isn't as good as the 2017 version.

--  
Bill Sloman, Sydney

Re: Flux density in an LLC core
On Mon, 1 Oct 2018 00:55:29 -0700 (PDT), snipped-for-privacy@ieee.org wrote:

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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.

RL

Re: Flux density in an LLC core
On Tuesday, October 2, 2018 at 6:06:35 AM UTC+10, legg wrote:
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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.
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ransformers, which I first came across around 1978.
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then merged with TDK.  
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bunch of .pdf files to me and Win Hill and a bunch of other lucky people.
Quoted text here. Click to load it
PCOS 2107 ferrite data book, with useful stuff on the theory from page 124  
to 141.
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776922b6e0d52/ferrites-air-gaps-pb.pdf>
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interesting.
9ff22c2ba503/ferrites-and-accessories-db-130501.pdf>
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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.

--  
Bill Sloman, Sydney


Re: Flux density in an LLC core
On 02/10/2018 02:46, snipped-for-privacy@ieee.org wrote:
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I spoke to Snelling on the phone in about 1978. I phoned for  
applications advice and got put through to him. He was very superior,  
unfriendly and unhelpful.

piglet


Re: Flux density in an LLC core
legg wrote:

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OK, I did the math. Shocking, how I could have believed otherwise for years.

Many thanks again!

    Best regards, Piotr

Re: Flux density in an LLC core
On 10/01/2018 03:23 AM, Piotr Wyderski wrote:
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I don't think it can be otherwise, or you could violate conservation of  
energy vis a vis Lenz's law.

Re: Flux density in an LLC core
On Monday, October 1, 2018 at 8:06:18 AM UTC+10, Piotr Wyderski wrote:
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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.

--  
Bill Sloman, Sydney


Re: Flux density in an LLC core
On 09/30/2018 06:06 PM, Piotr Wyderski wrote:
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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.





Re: Flux density in an LLC core
bitrex wrote:

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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.

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Shunting the main ferrite with some other material is a third option,
but probably applicable only to high-volume designs.

    Best regards, Piotr

Re: Flux density in an LLC core
On Monday, October 1, 2018 at 4:57:51 PM UTC+10, Piotr Wyderski wrote:
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s  
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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.

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It can be.
  
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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.

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An odd way of looking at it.

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Sounds bizarre.

--  
Bill Sloman, Sydney


Re: Flux density in an LLC core
snipped-for-privacy@ieee.org wrote:

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 > The fact that the leakage flux doesn't go around 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.

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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.

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Nothing is bizzare enough in the case of planar magnetics.

http://orbit.dtu.dk/files/131741663/APEC_2017_Presentation.pdf

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.

    Best regards, Piotr




Re: Flux density in an LLC core
On Monday, October 1, 2018 at 7:09:26 PM UTC+10, Piotr Wyderski wrote:
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the total flux you are generating.
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A physical impossibility -

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s  
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.

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.

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It doesn't say why anybody would do it.  

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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.

--  
Bill Sloman, Sydney


Re: Flux density in an LLC core
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Sure, but then you need to place an inductor in parallel with it, as well as  
in series.

From your 600W PS app note:
"An important transformer parameter in an LLC design is the primary or  
magnetizing inductance L_m." (p.25)

Note the ratio of inductances is discussed, which gives the ratio of  
resonant frequencies and therefore the loop gain.

Would just be an LC resonant converter if it were otherwise :-)

Tim

--  
Seven Transistor Labs, LLC
Electrical Engineering Consultation and Design
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Re: Flux density in an LLC core
Piotr Wyderski wrote:
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   The Baby Bird (Goo-Gull) is not accommodating; what is a  LLC design?
   Thanks.


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