Subject: Re: Core gapping techniques and general SMPS magnetics stuff
Date: 18 Dec 2002 12:11:11 -0600
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On Tue, 17 Dec 2002 12:36:42 +0000 (GMT), Tony Williams
>In article ,
> Christopher R. Carlen wrote:
>> This brings up an interesting question. I have determined that H=NI/Le
>> for a closed magnetic path, where N is number of turns, I is current,
>> and Le is the effective path length in meters. Thus, B may be
>> determined from the permeability (which is of course non-linear, but a
>> reasonable approximation of peak flux density may be made from the
>> effective permeability, ue, of the core.)
>> Of course that leads to way to much flux without a gap in my case. I
>> will tell you how I dealt with this in my example calculations, and you
>> can tell me if this is neglecting some coupling between the relations
>> that I have overlooked:
>> Take the E19/8/5 core in 3C90, with ue=1650 ungapped and Al=1170
>> (nH/turn^2). I want to make for example a 100uH inductor, to carry a
>> peak current of 1.2A without exceeding 160 mT.
>> To make 100uH, I need 9.245 turns. The effective path length Le=0.04m,
>> so H=9.245*(1.2A)/(0.04m)=277 A/m. That gives a B=ue*u0*H=574 mT.
>> Egad! That's well past the saturation point.
>> A gap of 0.35mm is shown to reduce Al and ue so that Al=100 and ue=140.
>> Now I'd need N=31.6 turns to get 100uH.
> My quick doodles (in oersteds and gauss, so probably wrong)
> suggest that, with a 0.35mm gap, ue drops to about 107.
> But that is theory, disregarding the effect of fringing,
> which will be large with such a small gap.
Isn't the effect of fringing small with a small gap?
>> With the new number of turns I get H=948 A/m.
> H = 4.pi.n.I/10.le for an ungapped core.
> H = 4.pi.n.I/10(le + u.d) for a core with gap= d.
> (le and d are in cm in this old system.)
> Which I think brings your H down to about 71 A/m.
> Which is more consistent with the fact that the resultant
> flux density, B, has come down from 540mT to 167mT.