Understanding magnetic core saturation

[ZeroResistance]

If a magnetic core has a saturation limit of 100..
And currently there is 80 amount of magnetism flowing through it.
Now I add another 40 so the total amount of flux is 120...
my questions are

1. From the 120 only 100 can fit into the core so what happens about the remaining 20 will it disperse into air?.

2. At 120 will the whole core seem like an air core or will the existing magnetism still continue to circulate into the core, I mean will the 100 continue to circulate or will the 100 also disperse into air.
The reason I ask this is that I have read at several places that at saturation the core permeability drops to that of air... so just wanted to clarify this..

3. Why does the permeability of the core drop after its limit has reached, I understand that the limit of 100 has been reached but wouldn't the 100 still continue to circulate in the magnetic core? What causes the permeability of the core to drop?

Regards
ZR

[T3sl4co1l]

If you're pushing in the flux (which has units of volt-seconds, aka webers) as EMF (the theoretical voltage applied to the space around the coil), then the extra flux goes entirely into leakage: the space around the winding, of the shape made when there is no core present (which, because the incremental permeability drops towards 1, there isn't a core present for that additional flux, so that's why!).

If you're applying that flux to a real inductor (one with finite winding resistance), then the increase in current flow will cause more voltage drop across the resistance, limiting the amount of flux delivered to the actual field.

The drop in permeability is due to the magnetic spins lining up.  Additional force cannot make them any more lined up, nor is there a way to spontaneously cause more to appear.  There's a fixed population, of limited strength, and that's all you can get.

This is also why ferrimagnetic materials aren't as strong: not all of the spins are in the same direction, in fact some oppose it.  This dilutes the population of spins contributing to the net magnetization.  They are also usually lower density compounds, as opposed to pure elements or alloys (i.e., some atoms in the crystal are inert).  Zinc manganese ferrite ((Zn,Mn)Fe2O4) has a maximum flux density around 0.45T, while (Ni,Zn) ferrite is lower, and YIG is lower still; in contrast, an alloy of iron, nickel and cobalt (100% magnetic atoms) peaks around 2.0T.

You can force the flux density ever higher, but every tesla you add, beyond saturation, is added with the full difficulty of doing it in air alone.  That's not to say the core becomes useless -- its ~1T contribution remains present -- but as you push over 3T or so, it quickly becomes space that you'd rather allocate for more copper (and liquid cooling channels!), and so it becomes a matter of efficiency rather than space savings.

Tim

[ZeroResistance]

which, because the incremental permeability drops towards 1, there isn't a core present for that additional flux, so that's why!).

You use the word "incremental permeability" would that mean that any existing flux flowing through the core still sees a permeability of say 1000 but the extra flux being pushed into the core after it is full sees a permeability of 1...

You can force the flux density ever higher, but every tesla you add, beyond saturation, is added with the full difficulty of doing it in air alone.  That's not to say the core becomes useless -- its ~1T contribution remains present -- but as you push over 3T or so, it quickly becomes space that you'd rather allocate for more copper (and liquid cooling channels!), and so it becomes a matter of efficiency rather than space savings.

So what you mean here is if the 2T limit of iron is reached then the remain 1T will need a humongous amount of current to get the 1T field... right?!

You have put it down very well I hope I understood what you tried to portray, is there a definitive guide that can shed more light on this subject?

[T3sl4co1l]

You use the word "incremental permeability" would that mean that any existing flux flowing through the core still sees a permeability of say 1000 but the extra flux being pushed into the core after it is full sees a permeability of 1...

"Incremental" meaning, for every tiny fraction of a tesla you add, you add a corresponding tiny fraction of amp-turns; the slope, or derivative, dB/dH.

In a linear material, B = mu*H so the derivative is a constant, mu.  In a saturable material, the derivative is decreasing.

You can think of it either way: that the average permeability is decreasing (which is true), or that the incremental permeability is decreasing (which is true), so that each additional bit of flux you add requires an ever-greater amount of magnetization to drive it.

It's equivalent, and the interpretation doesn't matter; use whatever feels right (and is still actually equivalent to the real physics, of course).

So what you mean here is if the 2T limit of iron is reached then the remain 1T will need a humongous amount of current to get the 1T field... right?!

To get that additional 1T, that is (to go from 2 to 3T).

By superposition: you can energize the coil without iron, and you get 2T (say).  With the coil present, you get 3T.  Apparently, the core contributes 1T, saturating in the process.  And the average permeability is 1.5 (i.e., 3/2), though we don't use the average permeability by convention, so don't worry about that.

The incremental permeability is also reflected in the AC impedance measured at the coil terminals.

Tim

[Kleinstein]

Usually approaching saturation is relatively gradual in many materials. Initially it is magnetic domain walls moving (which is easy). Later the magnetic domains need to rotate away from there easy crystal axis, which is not that easy and thus give a lower permeability.

For an low quality iron core there might be a practical limit of something like 1.3-1.5 T, when the (differential) permeability falls below a normally acceptable limit. However quite some range the core is still better than air - up to around 2 T. Only after that the core will be only marginal different from air (could be in the percent range).  With ferrite cores saturation can be more abrupt. Iron cores with oriented crystals (like that used for the higher quality toroid shaped transformers and large transformers) has a larger high permeability range (e.g. 1.8 T) but still fully saturates at the same level as non oriented material.

[ZeroResistance]

I'm still trying to understand this ...
if the core is at 80 and saturation limit is 100 now I add 40 and the core reaches saturation...

After adding 40 and the core has crossed into saturation will the existing core material vanish into thin air... I mean can we consider the core as air at that point of time and will the flux I mean the 100 that is in the core think that it is wading through air rather than iron

OR

the 100 will still think that it is swimming in iron and the remaining 20 will be dispersed in air...

[T3sl4co1l]

the 100 will still think that it is swimming in iron and the remaining 20 will be dispersed in air...

Given that flux is a property of space, not a physical entity surrounded by a medium -- this analogy sounds more appropriate.

The flux in the core doesn't magically squeeze out, it's still there.  It's just that the flux density is not growing any faster than the air around it.

Tim

[Benta]

I'm still trying to understand this ...
if the core is at 80 and saturation limit is 100 now I add 40 and the core reaches saturation...

After adding 40 and the core has crossed into saturation will the existing core material vanish into thin air... I mean can we consider the core as air at that point of time and will the flux I mean the 100 that is in the core think that it is wading through air rather than iron

I think you are picturing this wrong, and have an idea of core saturation as a kind of "brick wall" that you hit at a certain point. This is not the case

The thing is, that when you increase coil current/field, the core permeability (mu) decreases gradually and non-linearily and will at some point reach zero, leaving you with an air inductor, where the core just acts as a bobbin.

The definition of the saturation point is up to you, through selecting how much mu degradation and non-linearity you can accept in your circuit.

[T3sl4co1l]

The thing is, that when you increase coil current/field, the core permeability (mu) decreases gradually and non-linearily and will at some point reach zero, leaving you with an air inductor, where the core just acts as a bobbin.

Susceptibility \$\chi\$ goes to zero, relative permeability goes to 1.

Tim

[Benta]

not zero, 1 of course. It was too late last night.

[MrAl]

I'm still trying to understand this ...
if the core is at 80 and saturation limit is 100 now I add 40 and the core reaches saturation...

After adding 40 and the core has crossed into saturation will the existing core material vanish into thin air... I mean can we consider the core as air at that point of time and will the flux I mean the 100 that is in the core think that it is wading through air rather than iron

OR

the 100 will still think that it is swimming in iron and the remaining 20 will be dispersed in air...

Hi,

As others have been noting, there is no real immediate transition between 'not saturated' to 'completely saturated' as it is a more smooth transition, but from the perspective of a circuit it may appear to be an immediate transition because there may not be (and usually isnt) a mechanism in place that will allow this to happen slowly but will be rather abrupt.  That's because in a circuit that is using a core the external circuit has no way of knowing that the core is saturating, and so it keeps working as if it was not, and that pushes it into further saturation.  So what we know and what we get are a little different and this means that the abrupt transition idea is not a bad one for considering what will happen in many circuits anyway.  We just have to remember that some circuit will require a more careful analysis.

So with that in mind, we can still look at the abrupt transition idea and see maybe what is happening.  For now, let's assume that the limit is an abrupt 100, and what happens when we go over that limit.

First, before we get to that 100, we go through 80, 81, 82, etc., and in the old view that means that more and more domains are flipping to align with the magnetic lines.  These domains are physical and so they are limited in number, and the reason we see a permeability greater than 1 is because they are being flipped and it takes a certain amount of magnetic strength to flip them which is due to the current flow.  As the current increases, more and more domains flip, but then we start to run out of domains because we have a limited chunk of material in the core.  Once we flip all of those domains, we no longer get the back emf that opposes the applied voltage so the current can now rise faster, and given V=L*di/dt which is also di/dt=V/L with constant voltage that must mean that the inductance decreased.  The problem now is in this condition even if we applied just 1v it may lead to a huge current, and we could emulate this with a large magnet instead where the magnet saturates the core and we apply just 1v.

So the simplified view is that the ability of the core to store a magnetic field has gone down a lot and the only thing left is the air around the core which has a permeability of only 1.

As said before, this is a somewhat slower process but because the way many switching regulators are designed (especially the older ones) there is nothing in the circuit to limit the current into the coil so once the current rises beyond a certain point and the permeability goes down, the inductance decreases more and so the current goes up even more and then the perm goes down again and so the inductance goes down again and so the current goes up even more still (so you can see it gets worse and worse even with no change in drive) and so we see a sharp exponential looking rise in current which will blow the pass transistor(s) if there is no current limit.

I would say it is like a bucket being filled up with water with the hose nozzle at the bottom of the bucket so we get some back pressure which limits the flow rate, but once the bucket fills up the hose pops out of the bucket and then there is little back pressure so water flows out of the bucket freely :-)