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Subject: Re: Core gapping techniques and general SMPS magnetics stuff
NNTP-Posting-Date: Tue, 17 Dec 2002 17:30:36 GMT
Organization: AT&T Broadband
Date: Tue, 17 Dec 2002 17:30:36 GMT
John Woodgate, Christopher R. Carlen wrote:
>> Uh-oh. Now I see the problem. There is no way to know how the
>> permeability has changed so as to know what H to shoot for, even
>> though I may be able to empirically determine the Al change.
Er, but only if the gap is so small that it doesn't dominate the core
>> Wait, the catalog shows a formula for calculating the effective
>> permeability for a given gap size, provided the gap isn't too large.
>> No criteria are provided for evaluating that, however. One can also
>> back out ue from the inductance formula L=N^2 ue u0 A/Le.
> I don't know what you mean by 'back out'. The point is that ue isn't
> any where near constant, at least for silicon iron. Ferrites may be
> more linear.
Core linearity doesn't really matter. All that matters is that the
reluctance of the air gap (which is linear) is very much larger than
the core's reluctance. The core is a magnetic short circuit to flux.
Virtually all of the energy is stored in the air gap. Just think of
the core as a way to stuff a ten pound winding into a one pound gap.
>> So one could at least do an interative exercise to converge upon a
>> suitable gap size to get the flux within bounds.
>> Finally, I am interested in these Hanna curves. Where might I find
> We went through all this here in 1998. Obviously, you weren't paying
> attention! (;-)
> Actually, Hanna is really applicable when the AC component of the
> induction is small compared with the DC component, and I'm not sure
> that applies to your coil.
Yes, although the Hanna curves could be adjusted for *peak* flux, a
high ac component can lead to subsequent core and winding losses being
more of a limitation than either saturation or dc losses.
> I once had Hanna's original paper, but I can't find it at present.
> I don't know where you will find published Hanna curves for ferrites.
> But the paper tells you how to generate your own. IIRC, it's a
> tedious process and you need an Owen Bridge or equivalent. No doubt
> you can do it with a PIC. (;-) You plot curves of LI^2/V against NI/l
> for a succession of gap lengths and then draw a tangent curve (IIRC)
> to the original curves. This is your Hanna curve. L = inductance,
> I = direct current, V = volume of core, N = number of turns,
> l = length of magnetic circuit. To generalize it, you replace the
> gap length applicable to each section of the tangent curve by alpha
> = (gap length/l).
> Then you enter the chart with LI^2/V and read off the corresponding
> NI/l and the gap length ratio alpha.
That is probably overkill for most applications of an inductor with
dc bias. I think all Chris wants is a formula which chews on maximum
peak flux density, core cross sectional area, desired inductance and
peak current, and spits out optimum gap length and number of turns.
He will then calculate a workable wire size and check various losses
and perhaps adjust operating frequency and inductance and try again.
Chris, if this is your desired methodology, then I would suggest the
following: first calculate the number of turns as (Imax*L)/(Bmax*Ae)
and then get your gap length from (Ae*n^2)/L. For greater accuracy
you might factor in a fringing adjustment to the cross sectional area.
I dimly recall that, to a first order, the linear dimensions of the
cross sectional gap area (which starts out the same as core area, Ae)
should be increased by one half the gap length.
It's been a while since I've used this method so watch out for
forgotten factors or other errors. -- analog