Transformer Design I do not understand how to adjust AL when adding an air gap - Page 1
Forum section: electronics / beginners

author: axawire
author_rank: Contributor
timestamp: September 04, 2021, 04:09:42 am
content: I am trying to follow:http://ludens.cl/Electron/Magnet.htmlSpecifically 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.

author: iMo
author_rank: Super Contributor
timestamp: September 04, 2021, 10:55:25 am
content: Magnetic reluctanceR = Len / (mu * A), where Len is length of the mag circuit, A is its cross-section (let A=1), mu is the permeability of the material (mu_air = 1).R_core = 120mm / (2000 * A)R_gap = 1mm / (1 * A)R_gap/R_core = 16.667R_tot = 1 + 16.667 = 17.667 here "1" is always 1Effective permeability of the core with added air gapmu_eff = mu_core / R_totmu_eff = 2000 / 17.6667 = 113.2PS:Without an air gapL_core = 6uHWith 1mm air gapL_core_with_gap = L_core * mu_eff / mu_core = 6uH * 113.2 / 2000 = 0.3396uH (aprox)With 2mm air gapL_core_with_gap = 0.1748uH (aprox)

author: axawire
author_rank: Contributor
timestamp: September 04, 2021, 04:45:13 pm
content: Thank you so much!

author: iMo
author_rank: Super Contributor
timestamp: September 05, 2021, 06:32:34 am
content: Mind those equations work formu_core >> mu_airLen_core >> Len_airAL scales the same way as the L (with the constant amount of turns)..