Somehow I have a suspicion that big pot cores are difficult to make. They have to be baked at high temperatures and the material is brittle and may crack easily during cooling. I suspect that additives that reduce the brittleness also influence magnetic properties.
Meh, sintering is a well developed science. More just a matter of, taking the time to tune the shape exactly, in case compensation for differential shrinkage is necessary; and actually making and running the tooling.
There aren't many customers for big ones (over a few cm), and there are better shapes for thermal performance (windings have more cooling in an E or ETD), and high power rarely needs the shielding afforded by something like that. Large toroids are also moderately available, have seen 6" ones in stock from time to time. Have used 4" (102mm) ones myself.
Additives of any sort, are forbidden; any (nonmagnetic) impurity would collect at the grain boundaries, effectively increasing airgap, reducing mu_r. Or dissolve into the ferrite, causing whatever effect it would (probably more hysteresis?). I'm not aware of anything that has useful impact on brittleness of the fired body, though if you mean for the green (pressed powder) part, there are organic binders to help with that (which burn out, at modest expense to shrinkage).
Neat aside: ferrite is among the ceramics that exhibit ductile deformation, albeit to a very limited extent. Evidence is found the scratches left by grinding: smooth tracks suggest material being peeled away, while jagged tracks suggest brittle fracture. You see a bit of both in micrographs, IIRC.
But it's also a rather soft compound (Mohs hardness about uh, 5 is it?), nor very strong (say, comparable to above-average concrete), not at all like a porcelain (mostly silica glass, quite strong, even a bit flexible -- in the elastic range that is). So, probably any flexibility it might have is balanced by the poor strength, so it's still pretty brittle overall.
I've always been confused about the relative high prices of ferrites in general. Baked clay is as cheap as dirt, and plain steel is a few euro's per kg, but ferrites can easily cost a few orders of magnitude more and I never really understood why. Even if you look at websites like Aliexpress, big ferrites are never cheap.
Yeah well, baked clay doesn't have technical let alone analytical chemical purity.
I don't know exactly how tight the formulations are, but every new grade that pushes losses say 10% lower than the previous generation, must be worth a fair amount of development to achieve. It's not like they're doing that every single year. On top of that, they have to match the exact composition in production, using good purity feedstocks with careful process control.
As a highly refined, technical material, I'd say it's one of the cheaper things, and indeed the generally cheap elements involved, I would say, are probably partly why.
Consider, for example, an equal volume of epoxy or other fancy plastic resin -- the costs are probably ballpark similar, of course the cheapest (say ABS, etc.) will be less, but the fancy stuff like epoxy, uh UV-cure 3D printing goo, etc., those are highly refined and modified substances, ultimately produced from dirt-cheap (literally) feedstocks (i.e., petroleum for the most part).
Air gaps in magnetics are common, which I also find somewhat contradictory. First you concentrate the field, and then you wreck it with an air gap. Main Idea as I understand is to make the saturation characteristics a lot more gentle. The distance of the airgap has a huge influence on the magnetic properties, so good bearings are essential and the electronics should be able to cope with changing magnetic coupling.
Indeed, it's all about having the right amount.
Note that energy storage goes as B^2 / (2 mu). High mu means less energy.
But low mu also hurts, ultimately because copper has some resistance. If it had zero resistance, we could just let the current circulate forever, whatever the flux density. But with resistance, energy stored in the inductor has a clock that ticks down very quickly, and we need to compromise between resistance and reactance.
Ideally, we'd have a metal with about 1/20th the resistivity of copper, or less. This gives slow enough time constants (~ms), in air-cored inductors, that are useful for typical power conversion purposes (if the cutoff frequency is ~1kHz, then a Q of ~100 might be expected at 100kHz, i.e., efficiency ~99%).
Alas, we can't have that outside of cryostats, so we settle for permeable cores. We need to concentrate the field to make copper more effective, but not so concentrated that our maximum energy storage is hindered.
There are some places where a low-mu (distributed airgap) ferrite would be helpful, but mostly it's better to have the regular stuff in stock, and cut it as needed -- since we can make our own airgap of almost any arbitrary size by cutting.
And again, optimizing production quantity is a big part of the cost of anything. Big parts aren't so much expensive by sheer volume, as they are by the much smaller scale on which they're produced. Or, if they run batches of them less often, there's more warehousing cost to store the extra, or more opportunity cost effectively paid by the customers waiting for them when stock runs out, etc...
So also, it's probably better to modify standard cores, which will also then fit in standard bobbins, don't have to do anything custom at all, it's real nice.
And we do suffer some from that, like the intense fringing field around the gap, increasing losses or necessitating a more expensive winding (fine stranding?). It's all a compromise.
In contrast, when we don't want energy storage, we do indeed want mu as high as possible, and as little air gap as possible. Transformers should simply be an instantaneous ratio between windings, without storing energy themselves: maximum magnetizing inductance and minimum leakage inductance. This is the case where we especially work at concentrating that magnetic field.
Tim
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