Subject: Re: Core gapping techniques and general SMPS magnetics stuff
Date: Fri, 20 Dec 2002 13:41:44 -0800
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On Fri, 20 Dec 2002 07:16:40 GMT, analog wrote:
>Patrick Lawler, Chris Carlen wrote:
>>> So I will have to gap my cores. How do you folks gap E-cores for
>>> prototype/low volume applications? Obviously it's not that hard to
>>> figure out a way, but I'm curious how others do it too. I'll probably
>>> cut out some shim material, epoxy it to the outer legs, and hold the
>>> halves together gently in a vice until it all sets up. Then I can soak
>>> it in acetone later for a day if I want to disassemble it.
>> I'll avoid the many posts in this thread discussing magnetic principles,
>> and just give the short formulas I use. The formulas are first-order,
>> and do not take into account core non-linearity (not a problem with
>> ferrites, except above 3000 Gauss :) ), fringing flux (possibly an issue
>> with 'large' gaps). Add your own design margins. They should get you
>> 95% of the way to a solution.
>> 1) Determine the number of turns needed to avoid saturation:
>> N = (L*Ipk*10^8)/(Bsat*Ae)
>> 2) Determine the gap necessary to support the peak current:
>> lg = (0.4*pi*N*Ipk/Bsat)-(le/ur)
>> N is inductor turns
>> L is the desired inductance (Henries)
>> Ipk is the peak inductor current (Amperes)
>> Bsat is the core material saturation level (Gauss)
>> Ae is the core cross-sectional area (cm^2)
>> le is the path length of the core (cm)
>> ur is the relative permeability of the core
>> lg is the desired center-leg gap distance (cm)
>Bravo! That's the the same method I also have used and suggested to Chris,
>but with all the proper pesky unit conversion factors included as well as
>the (le/ur) term which is important for very small gaps.
>As I recall, there also should be correction factors for fringing effects.
>These are significant with large gaps and with gaps unshrouded by windings,
>such as typically is the case for outer leg gaps. In either case the flux
>path through air is larger than expected, leading to greater energy storage.
>As I dimly recall, 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 to account for flux bulging.
The formula I use came from McLymans' book, "Transformer and Inductor Design
Handbook". The calculated inductance is multiplied by the correction factor:
Lff = Lcalc * FF
The formula is given as:
FF = 1+ (lg/sqrt(Ae))*ln(2*G/lg)
sqrt means square root
ln is the natural log
lg is the gap length
Ae is the core cross-sectional area
G is the winding width of the bobbin (how wide can the copper winding be)
All units are the same unit of measurement (all in mm, all in cm, etc.)
>> If you don't want to grind the center leg, split the value of lg in half,
>> and put each spacer in the outer legs of the core. I don't worry about
>> gluing the shims in place. I just tape the core halves together tightly,
>> so the gap is accurate and the shims don't fall out.
>Did you know, when ac flux is significant in an inductor wound with many
>layers, a distributed gap actually can significantly reduce the proximity
>effect losses in the windings by halving their average distance to the gap?
>However, if outer leg gaps are intolerable, don't despair, for there is a
>clever and perhaps little know technique to avoid proximity losses even
>with a center leg only gapped design. In parallel to the normal, multi-
>layered winding, which will continue to carry the bulk of the dc current,
>a single layer of small wire is first wound on the bobbin. Because it is
>nearest to the gap, this winding will carry almost all of the ac magnetizing
>current for the core and prevent proximity currents from building in the
>multiple layers of the main winding. One caveat, though, the two parallel
>windings must have *exactly* the same number of turns to avoid generating
>huge circulating currents and rendering the whole exercise pointless.
>Fun stuff, huh? -- analog
As I said, the two formulas in my first posting take care of 95% of the design.
And everyone knows that 95% of work is done in 5% of the time.
The other 5% of the work takes 95% of the time. :)
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