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Magnetic Permeability

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ramonest:
I am trying to understand the concept of magnetic permeability. Right now I'm stuck with understanding if the proper definition is:

mu = B/H
(With mu-> magnetic permeability, B->Magnetic flux density and H->Magnetic field strength)

or:

mu = dB/dH

For the simplification that magnetic permeability is constant and the BH curve crosses the (0,0) both definitions are equal (in a sense).

But if you take into account a real BH curve with the saturation it is no longer the same. If you want to calculate the inductance of an inductor working with a DC bias and some AC ripple it will have different value depending on the definition used, specially if the DC bias moves the operating point close to the "elbow" of the BH curve.

I'm using the basic formula for inductance:
L = ((N^2)*Ac*mu)/(lc)

Where N->Number of turns, Ac->Effective area of the core and lc-> effective length of the core.

No air-gap is used (which is why I was interested in the saturation or close to it case).

I would really appreciate it if someone can clarify that! Or point to some sources that properly define it.
Thanks in advance!

(I'm not sure if this should go to beginners section or is more suited for another section)

cur8xgo:

--- Quote from: ramonest on June 21, 2019, 05:03:10 pm ---I am trying to understand the concept of magnetic permeability. Right now I'm stuck with understanding if the proper definition is:

mu = B/H
(With mu-> magnetic permeability, B->Magnetic flux density and H->Magnetic field strength)

or:

mu = dB/dH

For the simplification that magnetic permeability is constant and the BH curve crosses the (0,0) both definitions are equal (in a sense).

But if you take into account a real BH curve with the saturation it is no longer the same. If you want to calculate the inductance of an inductor working with a DC bias and some AC ripple it will have different value depending on the definition used, specially if the DC bias moves the operating point close to the "elbow" of the BH curve.

I'm using the basic formula for inductance:
L = ((N^2)*Ac*mu)/(lc)

Where N->Number of turns, Ac->Effective area of the core and lc-> effective length of the core.

No air-gap is used (which is why I was interested in the saturation or close to it case).

I would really appreciate it if someone can clarify that! Or point to some sources that properly define it.
Thanks in advance!

(I'm not sure if this should go to beginners section or is more suited for another section)

--- End quote ---

Clarify what? You answered your own question. Permeability changes with flux in some materials. Not so much in air/vacuum/non magnetics.

Achu:
Actually in practice the permeability is a function of H.And variation is non linear which explains the saturation of the B/H curve.
Also in the case of inductors when designing the I believe one has to consider the current being carried and the core properties.(Pardon me if I am wrong)

Berni:
Yep you found out on your own why inductors you can buy at DigiKey or Mouser or Farnell have a rated saturation current.

Once you put enough current trough it to get you up to the top of that chart the inductance starts to rapidly change. Obviously you are not supposed to operate an inductor in that area.(Unless you need the effect of saturation as part of your circuits functionality)

schmitt trigger:
Welcome to the exciting world of hysteresis curves and flux saturation.

Magnetic materials have permeabilities hundreds or even thousand larger than air. Which means that for a given geometry and number of turns you will have inductance values which would be impossible to achieve with an air core inductor.

But on this life nothing is free.  You have to pay a couple of penalties when using magnetic materials.

The first is that at H=0, the initial permeability is very high, but it will gradually decrease as the flux increases, until you reach saturation and the permeability drops to very low values.
The second is that those materials have remanence. In plain words it means that the magnetic flux follows two distinct paths, the hysteresis curve. And with AC-excitation, where the curve is transversed back and forth with each cycle, the area inside the curve represents wasted energy, the core loss.

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