I have an aversion to open magnetic loops so prefer to avoid air-cored inductors if at all possible. Yes I know they're the most linear but they're also susceptible to noise pick-up and given the choice of lowest noise or lowest distortion, I'll go for the former. I hear from one or two sources that Barkhausen noise is a thing in ferrites but so far I haven't noticed it myself.
I did a brief search and also asked Perplexity AI about manufacturers which are using gapped ferrite-core XO inductors. It only mentioned Bose (but didn't mention 'gapped') and conflated iron-cored and ferrite-cored inductors so didn't bring any clarity. I searched images and saw none of closed-circuit ferrite-cored crossover inductors. However for low values in power supply applications, such inductors are now very much a thing. Here's an example : https://standexelectronics.com/products/pq32-series-planar-inductors/. This example is using flat wire, I'll be sticking with normal round wire for now.
How to design and implement closed-circuit ferrite cored XO inductors in practice ? I'll take an example - replacing the 1.2mH bass/mid series inductor in my Paiyon speakers. I don't have a pic of the original - I dismantled it years ago in a bid to upgrade it and substituted a Sendust toroidal for it. (At that time I hadn't realized that such a substitution wasn't too bright as Sendust has a 'progressive soft saturation' characteristic which makes its inductance vary with bias. Meaning that the LPF cutoff frequency varies with signal strength). Anyway, here is a slightly more complex XO from the same manufacturer as a guide :
The bass/mid series inductor was (I think) similar to these 'bar' shaped inductors which are laminated iron-cored. Its kinda fortunate that the value 1.2mH is printed on the silkscreen of the PCB. As a first pass I selected a PQ core that I had to hand, PQ2020.
The first thing to note is - when you buy PQ cores (try here : https://vi.aliexpress.com/item/1005003707051594.html) they aren't gapped. Gapping is absolutely essential for a couple of reasons - firstly to get a close tolerance inductance value and second to get a useful current handling capability before saturation. Ungapped cores are only really useful for making transformers, not precise valued inductors. Seeing as ferrite is a tricky material to grind down I have gone the route of creating a gap using a few layers of yellow transformer (mylar) tape around the core outer legs to space the two halves apart slightly. My trusty micrometer tells me that one thickness of this tape is about 0.055mm. But how to determine how big a gap to make? This is where we need a modicum of math....
Here's a snippet from a table in FerroxCube's catalog, for PQ2020 cores :
Of note from comparison of 3C81 with 3C90 materials is the core material's characteristic permeability doesn't matter that much, what determines the AL number (and hence, inductance) is the gap length. A bigger gap gives a lower AL value. We use AL to calculate the inductance - multiply it by the number of turns squared to get the inductance value. The bigger the gap, the higher the saturation current but along with a bigger gap you'll also need more turns of wire to achieve your target inductance. So there's a trade - if you have a target DCR for your L that'll determine the gap size you need. If that doesn't allow enough current then you'll need to step up the core size.
As I initially didn't have a feel for the math I kicked off with as large a gap size I thought I could achieve fairly easily with layers of 55um tape and that looked like 620um to me, giving AL of 160. Seeing as to keep the core halves parallel to one another we need to make a gap in both outer legs, the total gap is actually twice the thickness of all the layers of the trafo tape. By observation, the spacing of the outer legs apart creates a same-sized airgap in the centre leg too. Meaning six layers of tape (which gives 330um) results in a total gap of double that, 660um. I'd expect the AL to be slightly lower than 160 as 660um is a bigger gap than 620um. But in fact it turned out to be surprisingly close - the first two inductors measured 1.21mH and 1.22mH on my LCR meter.
With this gap size, where will saturation occur? Here's the equation to help with that : B = (AL * N * I)/Ae.
Here B is the flux in mT, N is the number of turns, I is the current (Amps) and Ae is the effective cross-section of the core which is gotten from the manufacturer's table, for PQ2020 its 62mm^2
With ferrite the maximum B is around 400-500mT. Rearranging to find I we get B * Ae / (AL * N).
Back to the 1.2mH - to calculate N take SQRT (L/AL) where L needs to be in nH as that's the units of AL. With AL = 160 we get N = 86.6 say 87T. Plugging this back into the I equation (taking Bmax = 400mT) the saturation current is 1.8A which might be a bit limiting in practice. I've decided to let it ride and listen to see if I can hear it saturate - a cracking sound apparently - as I raise the volume.
The first pass PQ2020s are inside the speakers now and I forgot to take pics, but I'll try again another day with larger cores.
I did a brief search and also asked Perplexity AI about manufacturers which are using gapped ferrite-core XO inductors. It only mentioned Bose (but didn't mention 'gapped') and conflated iron-cored and ferrite-cored inductors so didn't bring any clarity. I searched images and saw none of closed-circuit ferrite-cored crossover inductors. However for low values in power supply applications, such inductors are now very much a thing. Here's an example : https://standexelectronics.com/products/pq32-series-planar-inductors/. This example is using flat wire, I'll be sticking with normal round wire for now.
How to design and implement closed-circuit ferrite cored XO inductors in practice ? I'll take an example - replacing the 1.2mH bass/mid series inductor in my Paiyon speakers. I don't have a pic of the original - I dismantled it years ago in a bid to upgrade it and substituted a Sendust toroidal for it. (At that time I hadn't realized that such a substitution wasn't too bright as Sendust has a 'progressive soft saturation' characteristic which makes its inductance vary with bias. Meaning that the LPF cutoff frequency varies with signal strength). Anyway, here is a slightly more complex XO from the same manufacturer as a guide :
The bass/mid series inductor was (I think) similar to these 'bar' shaped inductors which are laminated iron-cored. Its kinda fortunate that the value 1.2mH is printed on the silkscreen of the PCB. As a first pass I selected a PQ core that I had to hand, PQ2020.
The first thing to note is - when you buy PQ cores (try here : https://vi.aliexpress.com/item/1005003707051594.html) they aren't gapped. Gapping is absolutely essential for a couple of reasons - firstly to get a close tolerance inductance value and second to get a useful current handling capability before saturation. Ungapped cores are only really useful for making transformers, not precise valued inductors. Seeing as ferrite is a tricky material to grind down I have gone the route of creating a gap using a few layers of yellow transformer (mylar) tape around the core outer legs to space the two halves apart slightly. My trusty micrometer tells me that one thickness of this tape is about 0.055mm. But how to determine how big a gap to make? This is where we need a modicum of math....
Here's a snippet from a table in FerroxCube's catalog, for PQ2020 cores :
Of note from comparison of 3C81 with 3C90 materials is the core material's characteristic permeability doesn't matter that much, what determines the AL number (and hence, inductance) is the gap length. A bigger gap gives a lower AL value. We use AL to calculate the inductance - multiply it by the number of turns squared to get the inductance value. The bigger the gap, the higher the saturation current but along with a bigger gap you'll also need more turns of wire to achieve your target inductance. So there's a trade - if you have a target DCR for your L that'll determine the gap size you need. If that doesn't allow enough current then you'll need to step up the core size.
As I initially didn't have a feel for the math I kicked off with as large a gap size I thought I could achieve fairly easily with layers of 55um tape and that looked like 620um to me, giving AL of 160. Seeing as to keep the core halves parallel to one another we need to make a gap in both outer legs, the total gap is actually twice the thickness of all the layers of the trafo tape. By observation, the spacing of the outer legs apart creates a same-sized airgap in the centre leg too. Meaning six layers of tape (which gives 330um) results in a total gap of double that, 660um. I'd expect the AL to be slightly lower than 160 as 660um is a bigger gap than 620um. But in fact it turned out to be surprisingly close - the first two inductors measured 1.21mH and 1.22mH on my LCR meter.
With this gap size, where will saturation occur? Here's the equation to help with that : B = (AL * N * I)/Ae.
Here B is the flux in mT, N is the number of turns, I is the current (Amps) and Ae is the effective cross-section of the core which is gotten from the manufacturer's table, for PQ2020 its 62mm^2
With ferrite the maximum B is around 400-500mT. Rearranging to find I we get B * Ae / (AL * N).
Back to the 1.2mH - to calculate N take SQRT (L/AL) where L needs to be in nH as that's the units of AL. With AL = 160 we get N = 86.6 say 87T. Plugging this back into the I equation (taking Bmax = 400mT) the saturation current is 1.8A which might be a bit limiting in practice. I've decided to let it ride and listen to see if I can hear it saturate - a cracking sound apparently - as I raise the volume.
The first pass PQ2020s are inside the speakers now and I forgot to take pics, but I'll try again another day with larger cores.
