I want a 2.2mH toroid inductor working at 200kHz switching frequency able to keep 2A saturated current. I found a ferrite core provider with these possibilities : - Core FT50-61 (12.7x7.15x4.9) with AL=69 needs 178.6 turns - Core FT50-75 (12.7x7.15x4.9) with AL=4200 needs 22.9 turns
So which core should I choose to make a 2.2mH toroidal inductor 2A saturated current? I suppose that the AL parameter is the key. Can you explain me why?
As Tim said, everything matters! There are even a few points that the other two answers have missed.
Permeability is not a constant. Switching frequency, DC bias, and even temperature affect the permeability of a core. If you're using a company such as Mag Inc, Ferrox, TDK EPCOS or the like, they will have plenty of graphs showing you these property curves.
Not all materials are created equally. Some materials have an excellent DC bias and you can put tons of amps through them and only lose ~20% of your initial perm. Others will fall off like a rock! You may have 2.2mH with 23 turns at first, but when you lose 20-30% of that perm (look at the graphs, some cores can lose over 50-60%!) you will not have enough inductance. In this instance, you may do 50 turns for 4.4mH so that when you get to full DC bias you are still above the 2.2mH goal.
At a maximum of 2A, DC Bias probably won't affect you much, but it is something to look out for. I think your primary concern is going to be switching frequency, so just make sure the Permeability Vs. Frequency graph from the core datasheet is fairly flat.
You always want to calculate your required inductance at the worst case scenario (full 2A, switching frequency, a little margin).
Do yourself a favor and check out Magnectics Inc. I use their cores all the time and they have step by step guides for designing inductors and such.
With an \$A_L\$ of 69 nH/turn\$^2\$, to get 2200 \$\mu H\$ requires 178.6 turns i.e. turns squared x 69 nH = 2201 \$\mu H\$.
With an \$A_L\$ of 4200 nH/turn\$^2\$, to get 2200 \$\mu H\$ requires 22.9 turns i.e. turns squared x 4200 nH = 2203 \$\mu H\$.
Both achieve the same inductance but the scenario with the fewest turns will saturate the core to a much greater extent. This is because of the relationship between B (flux density) and H (magnetic field strength). The higher the ratio between B and H the higher is the core permeability.
When \$A_L\$ is a low value the permeability is naturally lower so, for a given H field, B is smaller and hence core saturation problems are not as big.
Notice that 178.6 turns is 7.8x as many turns as 22.9 BUT, notice that 4200 nH/turn\$^2\$ is nearly 61 times higher than 69 nH/turn\$^2\$. This makes all the difference.
Cores with the same dimensions but having lower permeability (either due to material differences or gapping) will naturally saturate to a lesser extent for the same winding inductance. On the other hand, more turns means more \$I^2R\$ loss so you need to make choices and optimize what you want/need.
Actually, everything matters. It's why I just buy coils...
The two biggest things that matter for the specifications you've given are \$A_L\$, which determines the inductance per turns\$^2\$, and the point at which the core saturates.
If I'm remembering all this stuff correctly, the core will saturate at a certain magnetic field strength, depending on the material. The field strength depends on the coil current times turns, divided by the average magnetic path through the core. So lots of turns on an itty-bitty core will get you the inductance you want, but the core may saturate. You need to choose a core large enough to get you the inductance you want without saturating the core.
While you're stressing out over that, you also need to consider that the core is also lossy, both because it's (possibly) conductive and because reversals in the magnetic field dissipate energy in the core (if you look at the B-H curve of a material, the area inside that curve is proportional to the energy lost each cycle).
And, finally, the wire you use is also lossy, and you can only go so big (and in high-frequency applications, it works better to use individually insulated multiple strands, to get a sorta-litz wire effect).
If you check out the Fair-rite website, they have a ton of instructional videos. Your cores are probably Fair-rite, or Fair-rite knockoffs, so the videos should be helpful even down to the material designations.
