Magnetic core saturation

SATURATION CURRENT FOR A MAGNETIC CORE, GIVEN INDUCTANCE AND THE PARAMETERS YOU TYPICALLY FIND QUOTED BY CORE SUPPLIERS Isat = ( Bsat . Ae ) / √( L . AL ) Isat = Saturation current Bsat = Saturation flux Ae = Core effective area L = Inductance you require AL = Inductance per turns2 If Bsat isn't quoted, use 0.4T (for ferrite cores) and allow 20% headroom or so.

Now read on... if you're still interested

When designing things like switched mode power supplies, that use inductors that you make yourself by winding them onto a magnetic core, perhaps the most important constraint is saturation of the core. You need to avoid this happening, or all the components apart from the core itself will explode. At the same time, you want to use the smallest core you can get away with, because (a) apart from reservoir capacitors, the core will probably be the physically largest component, and (b) cores are frigging expensive unless you are buying thousands of them at once. (Pause to swear at Chinese manufacturers selling complete power supplies for less than the price you can get the bloody cores for.)

So you need to know the maximum ampere-turns the core can handle, or how much current you can put through a given inductance made using that core (which is the same thing, just differently expressed).

So, obviously, it would be REALLY FUCKING USEFUL if core manufacturers would quote this value in their data sheets. It is equally obvious that the fact that not one of the fuckers actually does this makes them all massive cunts.

They perfectly well could quote it, but they don't. They quote instead various other parameters from which it can be derived, so you have to frig about calculating it. And this in turn creates another problem: how the fuck do you do that?

The obvious answer of "look it up on the internet" is not all that useful, because although there are lots of pages which purport to address the matter, they are all shit. They tend to start right from scratch with magnetic theory as worked out by Faraday. This makes them confusing as fuck, because magnetic theory is brain-bendingly weird and half the things come out back to front compared to how you'd think they ought to come out. (Like, shit that you normally think of in terms of current and can't imagine how it could be described other than by reference to current turns out to be defined by an equation that doesn't even mention current and is all in terms of voltage... voltage??? what the fuck? so you trog through the derivation and yeah, voltage it is; the maths is all fine, and it all makes sense mathematically, but it still doesn't make sense in terms of circuitry.) To have worked it all out starting from nothing shows that Faraday was a fucking genius. But at the same time, when you are designing electronic shit, you don't actually need to know most of it, and its weirdness and all its backwards results are just a distraction and a confusion which make the whole conundrum a lot more difficult than it needs to be. In designing inductors for SMPSes and the like, we are coming at things from pretty much the opposite direction from what Faraday was doing. Yet even those pages which claim to be oriented towards actual design, rather than teaching magnetic physics, still address it in Faraday's terms (which they explain in detail) and then have to turn it all round to make it useful in the context (and this part they explain very badly). And explaining things in terms of sinusoidally-varying voltages, which is not an uncommon approach, is a fucking shite way of doing it when you want to know about stuff for a circuit where all the waveforms are square or triangular. What are you supposed to do, use Fourier series? Fuck that for a game of soldiers.

The situation is: there exists a set of magnetic things, which are described using a particular set of parameters. These are the parameters that you will find on a supplier's website when you are trying to choose a thing. Given the information that people give you - which is not the same as what a theorist would use to talk about them - how do you pick a suitable thing?

On a supplier's website, you typically find:

Now, one of the less rottenly unhelpful equations you can find kicking around the web for calculating saturation current is this:

Isat = ( Bsat . le ) / ( μ0 . μ . N ) N = number of turns μ = relative permeability of core μ0 = (4e-7)π = 1.257e-6 approx.

...which is fairly typical. See the problem? You do NOT as a rule find μ quoted. To find that you usually need to download the datasheet for the core, which is a lot more fucking about than just reading something off the supplier's web page. Sites that go on about core calculations, take note.

You can work it out from what you're given:

μ = ( AL . le ) / ( μ0 . Ae )

(Note: this does still work for gapped cores. You just use the reduced AL value quoted for the gapped version of the core.)

But this doesn't matter anyway. You DO NOT NEED μ. AL will do. Which is excellent, since AL is nearly always quoted and μ more or less never is. Sites that go on about core calculations, TAKE NOTE.

You do of course also need to know Bsat, the saturation flux. This, again, is hardly ever quoted, and not infrequently is even missing from the fucking datasheet, which is utterly shite. But for a ferrite core, you can usually take

Bsat = 0.4 T

as a starting approximation. This value is a rough lower bound taken from the Bsat figures I found poking through a bunch of values for ferrite cores. It varies a bit with different grades of ferrite, but not all that much. It's good enough for going through a supplier's list of ferrite cores to see which ones look like likely possibilities, then once you have made such a preliminary selection you can download the datasheets and look for an accurate value. If there isn't one quoted, just allow yourself 20% or so extra headroom over what you would have allowed anyway. Note that Bsat reduces with increasing temperature; the 0.4T rough figure relates to 100°C.

So after all that, where have we got to?

Well, if you put together the first two equations up above, you can get this, which gives the required result using only parameters which are commonly quoted:


And from that we can get the formulae for saturation current given either the inductance or the number of turns, which are just as straightforward:



Yes, this calculation which so many hundreds of cunt web pages do so much to obscure is actually REALLY FUCKING SIMPLE. You know L, of course. You can take Bsat to be 0.4T to begin with, assuming it's a ferrite core you're after (and it seems to be next to fucking impossible to get a core made of anything else, so you probably are.) You look up a supplier's list of cores, and plug the quoted values for AL and Ae into that formula. And you know straight away whether that core is going to be any good or not.

EASY. So why the FUCK is this apparently the only page on the entire fucking web that actually spells it out? Why does every other fucking page that purports to address this problem make such a fucking meal of it and in the end fail to provide a useful fucking answer? Why is the world so full of dogshit-eating cunt-faced fucking wankers?

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