Gapped ferrite inductor inductance 3x bigger than calculated

[ambrozy]

I have such core:



Origin unknown, probably very old, only Al=125nH is specified. After putting on 20 turns I measure 75uH, with 33 turns 190uH, so Al ~180. the magic happens when I calculate the inductance for such a core by hand or with an online calculator, then it comes out that it should have Al=55nH (I don't know the exact permeability, but the result doesn't change much for a wide range of permeability because of such a large gap).
I suspect that this discrepancy is due to the fact that the actual effective gap area is larger than the Ae of the core, but it would have to be 3x larger for the calculations to agree with the measurements, or am I missing something? And what about flux density per ampturn in this case?

[Kleinstein]

The effective gap area in that configuration is indeed quite a bit larger than just the cross section of the center part.  It is not just more area on top, but also in parts to the sides, even if this misses a few turns. Another part comes from extending the depth, entering / leaving the core to the top and bottom. With a large gap and thus less effective core the air part in the coil can also contribute.

[T3sl4co1l]

As mu_eff goes down (air gap goes up), the ideality of the geometry falls.  That is, fringing and leakage are more and more significant.

So, you'll have higher A_L than predicted from straight (naive?) geometry, A_L will depend on the position and size of the winding, etc.  Losses may also be increased, due to eddy currents induced by the fringing fields (so, especially near the gap, where "near" means within a couple widths; for a gap this wide, this certainly penetrates the bobbin, so will be important to the design).

Likewise, the flux density seems anomalously low, because much of it is bypassing the core and looping around (and within!) your winding instead.

This is one of the advantages of toroids, that the air gap is distributed; you also don't have anything else to calculate, just pick the right part for the job, no air gap to cut (removing a degree of freedom isn't exactly a net positive, it just makes things more straightforward ).  The downside is they're much lossier than ferrite, for the most part; or if you choose the low-mu RF types, losses can be reasonable at low frequencies (the ~MHz used in high performance SMPS), but it'll be bulkier than an optimized ferrite design.  The catch is, because of the fringing fields in the ferrite case, litz wire is probably required.

And you can indeed get quite high Q factors from litz + ferrite; I measured Q ~ 500 on a recent design (RM12 in N49 ferrite, 0.1mm strand litz, ~1mm air gap).  Saturation was also extremely high (about twice expected).

Tim

[Picuino]

Theoretically and disregarding the permeability of the magnetic core versus the air gap:

AL = μ0 · Ae / lg = 1,2566 x 10^-6 · 0.000110m2 / 0.0025m = 55.3 nH

I also use an empirical formula that corrects for the deviation produced when the air gap is larger:

AL = [ 1 + 3 · lg / sqrt(Ae) ] · μ0 · Ae / lg

AL = [1 + 3 · 0.0025m / 0.0105m] · 55.3nH = 95 nH

It gets a little closer, but still does not work. It may be because the air gap is larger than the function can approximate.

Edit:
Does anyone know an empirical formula to approximate Al from the core parameters?

[Picuino]

And what about flux density per ampturn in this case?

Φ = N · I · Al

Φ = Magnetic flux [Weber]
      1Wb = 1Tesla·m^2
N = Turns of wire
I = Current [Amperes]
Al = Inductance per square turns [H]

[ambrozy]

And what about flux density per ampturn in this case?

Φ = N · I · Al

Φ = Magnetic flux [Weber]
      1Wb = 1Tesla·m^2
N = Turns of wire
I = Current [Amperes]
Al = Inductance per square turns [H]

ok so this should be all of it so through core will flow at most that amount, right?

[Picuino]

Yes, but it depends on the core section, which is not always the same. For this formula the maximum magnetic flow will be at the point where the cross section is minimum, the parameter Al_min of the data sheet.

[T3sl4co1l]

Well, flux is flux; density, divide by Ae to get B.

You can also start with Phi = integral voltage dt, which is more convenient if you're using square pulses such as in an SMPS.

Again, actual B inside the core will vary with position because of all the fringing fields.

Does anyone know an empirical formula to approximate Al from the core parameters?

No; it would depend upon, well, all the dimensions of the E-core here, which is a lot of work anyway.  Perhaps one exists somewhere, but it's about as much work to just put on a particular winding, and grind the gap a bit at a time until the desired inductance is reached.

Tim