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- Piotr Wyderski

September 30, 2018, 10:06 pm

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

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

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

Seven Transistor Labs, LLC

Electrical Engineering Consultation and Design

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Re: Flux density in an LLC core

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

important.

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

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

Seven Transistor Labs, LLC

Electrical Engineering Consultation and Design

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Re: Flux density in an LLC core

legg wrote:

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

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

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

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:

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

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:

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.

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.

*776922b6e0d52/ferrites-air-gaps-pb.pdf>*interesting.

*9ff22c2ba503/ferrites-and-accessories-db-130501.pdf>*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

Bill Sloman, Sydney

Re: Flux density in an LLC core

On Monday, October 1, 2018 at 8:06:18 AM UTC+10, Piotr Wyderski wrote:

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.

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

Bill Sloman, Sydney

Re: Flux density in an LLC core

On 09/30/2018 06:06 PM, Piotr Wyderski wrote:

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

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

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.

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 to1/10th 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 thatenergy 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:

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.

Best regards, Piotr

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.

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:

s

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.

An odd way of looking at it.

Sounds bizarre.

s

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.

An odd way of looking at it.

Sounds bizarre.

--

Bill Sloman, Sydney

Bill Sloman, Sydney

Re: Flux density in an LLC core

snipped-for-privacy@ieee.org wrote:

> 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.

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.

http://orbit.dtu.dk/files/131741663/APEC

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

> 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.

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.

http://orbit.dtu.dk/files/131741663/APEC

___2017___Presentation.pdfpage 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:

the total flux you are generating.

A physical impossibility -

s

.

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.

the total flux you are generating.

A physical impossibility -

s

.

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.

--

Bill Sloman, Sydney

Bill Sloman, Sydney

Re: Flux density in an LLC core

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

Seven Transistor Labs, LLC

Electrical Engineering Consultation and Design

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