# Transformer Design I do not understand how to adjust AL when adding an air gap

I am trying to follow: http://ludens.cl/Electron/Magnet.html

Specifically this section and how AL is adapted when an air gap is added (Initial AL is 6µH):

Let's see what happens if we add an air gap of just 1 mm total, which is done by separating the >core halves by 0.5mm: The magnetic flux will now travel through 120mm of ferrite having a permeability of 2000, and 1mm >of air having a permeability of unity. 2000mm of ferrite would have as much magnetic reluctance >as our single mm of air! So the air gap has added 16.667 times as much reluctance as the ferrite >core originally had. Plus the original reluctance, we have now 17.667 times as much reluctance as >before. Which means that our core now has an effective permeability of only 120, instead of the >former 2000! Which in turn means that the new AL value is about 0.36µH per turns squared, and >that our 45-turn primary winding now has only 0.00072H inductance. This in turn means that it >will charge up to 1.25A, and store 0.00056J per cycle, resulting in an output power of 56W for >our switching power supply, which looks very much better than the meager 3.4W obtained without an >air gap! All this is while maintaining exactly the same magnetic flux in the core!

It looks like the factor is calculated as (current effective permeability)/MPL where the MPL does not include the air gap. Am I interpreting that correctly? It also seems that in the example they divide the initial AL of 6µH by 16.667 to get the 0.36µH as opposed to 17.667 - is that a mistake? Otherwise I do not understand how a larger gap than 1mm would be calculated here to adjust the AL appropriately - How would I adjust the calculation for say 2mm?

While I can also blindly follow what's stated here for 1mm, I do not understand the connection on why it can scale like this, why can it scale like this?

Also I understand that AL is inductance per turns squared.... does it have a name though, a word I can use for searching as opposed to just trying to search AL as that is not helpful in google.

What am I missing in the understanding?

Thanks.

• Yes. Permeability is defined that way. Imagine that you use a ruler to measure the physical path length. Then you divide by the permeability to get the actual magnetic path length. That's the better way to see it. In short, the only thing that matters when storing energy is the in-vacuum path length that is left over after permeability is accounted for. Permeability is just a measure of how much matter is in there that forms a magnetic short circuit. 1000 means that for each meter of matter there is only 1 mm of left-over vacuum to store energy. The rest is a magnetic short circuit.
– jonk
Sep 4, 2021 at 5:07
• I'm an energy storage indive circuit, most of the energy is stored in the air gap. In many magnetic circuits the gap predominates and you can ignore the core in path length calculations with minimal error. Sep 4, 2021 at 6:24
• For a single turn coil permeance equals inductance factor = inverse of reluctance. Sep 4, 2021 at 8:45
• I've seen Al called "specific inductance".
– user16324
Sep 4, 2021 at 11:22

And finally: $$L=N^2 A_L$$