From: "Christopher R. Carlen"
Subject: Re: Deriving H for magnetic cores
Date: Wed, 18 Dec 2002 17:56:55 -0800
Organization: Sandia National Laboratories, Albuquerque, NM USA
NNTP-Posting-Date: Thu, 19 Dec 2002 00:55:44 +0000 (UTC)
User-Agent: Mozilla/5.0 (X11; U; Linux i686; en-US; rv:1.1) Gecko/20020826
X-Accept-Language: en-us, en
John Woodgate wrote:
> You've already gone over the heads of half the people here, I suspect.
> You are considering a far too sophisticated model to analyse, too. Start
> with a single circular conductor.
I've done that already. The toroid's not hard. I got the right answer
> Just leave out such high-level complications. This was supposed to be a
> learning process, wasn't it?
Yes, but with a practical goal. I have to ultimately design a real
>>H=N*I/(2*pi*r) in units of (A/m) of course.
> Yes, but a FAR simpler model would have given you that, and we could ALL
> understand it.
I'll respond to this in your other post....
>>Next we generalize this to a core with an effective path length of Le in
>>meters. The point of this is that we are dealing with all sorts of core
>>geometries, and so it is necessary to generalize the result to cores
>>other than the toroid. We define the effective length Le to mean the
>>following: Le is that length of a contour C chosen such that the H over
>>that contour, multiplied by the cross sectional area of the core (taken
>>perpendicular to dl_vec at the intersection of the area surface with C),
>>yields the same value of flux as the result of the general calculation
>>of the flux PHI:
>>PHI = B_vec . ds_vec
>>With Le defined in this manner then we can disconnect the core geometry
>>from the above formula with one further step, that is to replace the r
>>dependence with a contour length dependence. (Note that this whole
>>argument for Le is related to one or another of the mean value theorems
>>of mathematics, but I can't explain it rigorously anymore.)
> Well, you are still right, but your reasoning is arcane.
Why is it arcane? If you wanted to prove it rigorously, you'd have to
whip out the mean value theorem, I bet.
>>H=N*I/Le in units of (A/m).
> Still right.
>>I will have to deal with B on another day, as I have to get to work.
> B = uH. u is in general not constant but a non-linear function of H and
> previous history - it has 'memory'. That makes things really exciting.
> Forget the vectors; KISS.
But they're so much fun!
Christopher R. Carlen
Principal Laser/Optical Technologist
Sandia National Laboratories CA USA