Just curious, A core's AL value can be used to determine the inductance of a coil using the formula L=N^2 x AL, but....

What determines the AL value of a core?

I would think it has something to do with the cores permeability and area, but when a gap is introduced the AL value also changes.

What factors determine a core's AL value and what are the relationships between them?

Thanks in advance, this is really got me curious

 

For the case of a single series magnetic material flux path plus air gap and neglecting fringing at the air gap and assuming an unsaturated core, the relationship would be something like ...

\(A_{\tiny{L}}=\frac{\mu_0 \mu_r A}{l+\mu_r g}\)

Where

A = core CSA [m^2]
μ0 = free space permeability [Henry m^-1]
μr = core magnetic material relative permeability [dimensionless]
l = magnetic material path length [m]
g = air gap length [m]

 

T n k

Thanks for the answer. That was just the information I was looking for.

 

I truly hope all of the really good magnetics designers who reads this, forgives me for my over simplification of the topic, and that they refrain from making voodoo dolls in my likeness and sticking pins into them.

AL is a simplification of a complex set of parameters that is the basis of determining what the inductance will be when you wrap turns of wire around a core. AL was developed for smucks like you and me that wanted less math to deal with when designing with magnetics.

Tonight I will sacrifice a chicken to the magnetic gods for my above blasphemies.

Mark