From: "Christopher R. Carlen"
Subject: Re: Core gapping techniques and general SMPS magnetics stuff
Date: Mon, 16 Dec 2002 10:12:00 -0800
Organization: Sandia National Laboratories, Albuquerque, NM USA
NNTP-Posting-Date: Mon, 16 Dec 2002 17:10:42 +0000 (UTC)
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John Woodgate wrote:
> I read in sci.electronics.design that Chris Carlen
> wrote (in rod.itd.earthlink.net>) about 'Core gapping techniques and general SMPS
> magnetics stuff', on Mon, 16 Dec 2002:
>>But it doesn't seem that difficult. I can
>>do it a bit by trial and error. Just stick some space in their until I
>>get the L I want, for the number of turns I want.
> It's not that simple. You have TWO variables, gap thickness AND number
> of turns. Only a Hanna curve or some substitute will give you the
> optimum combination, AFAIK.
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.
The question is, does putting in a gap change the H formula from that
which is appropriate for a path of uniform permeability? It does at the
boundary, as has already been discussed in my other post, but if we
abstract the real physical gapped core to a virtual core with a
continuous and uniform permeability around the path, (is this the right
way to think about this?), then we can go with the original H formula,
using the effective permeability associated with the gap, which
accounts for the abstraction that I am talking about. Another question
here would be, does the gap change the effective path length substantially?
With the new number of turns I get H=948 A/m. So B=167 mT using the new
ue. That's right where I want to be, without accounting for temperature
The point is, is this the right way to go about peak flux estimation?
If it is reasonable (basically I'm assuming that the gap doesn't
significantly alter the approach to finding H), then it seems that
one could simply put on the number of turns they want to get the H they
want and gap until the inductance is right.
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.
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. 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 some?
There are quite a few apparent errors in the formulas given in the
Ferroxcube catalog. I will be posting a discussion of those and what I
think they should be for review in a few days.
Christopher R. Carlen
Principal Laser/Optical Technologist
Sandia National Laboratories CA USA