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From: Robert Baer
X-Mailer: Mozilla 4.75 [en] (Win98; U)
Subject: Re: SMPS transformer core power throughput calculation
Date: Fri, 13 Sep 2002 19:49:40 GMT
NNTP-Posting-Date: Fri, 13 Sep 2002 12:49:40 PDT
Organization: EarthLink Inc. -- http://www.EarthLink.net
Michael Denner wrote:
> I'm difficulty calculating power output from the switching frequency & core
> size. All the manufactures data I've come across present a graph of Po Vs
> core volume for all their cores with a switching frequency of 20Khz. Great
> if you want your psu to run at 20kHz!. Also there's generally three curves
> one for each drive topology eg push pull flyback or blocking. In the same
> breath they also state that the power output of the core increases with an
> increase in frequency, which is what I want to calculate!. But no where can
> I find a formula which will enable me to calculate what the output will be
> for a given frequency , flux density, and a core area or volume.
> A formula must exist because the Magnetic designer Demo program from
> intusoft has just that very feature. You select your core, input your
> frequency and out pops the maximum power that particular core can handle.
> How is this calculated?. Unfortunately I'm not using the cores in the demo
> data base and I can't afforded the £2600 price tag of the full version
> Does anyone have such an equation/formula?
> Best regards
Manufacturer data sheets of the core material and the specific core
shape and size may be of some help.
This is part of the "magic" involved, since there sems to be the
equivalent of 3 equations in 15 unknowns when it comes to transformer
design from scratch.
I have waded thru about 6 different books on this subject.
Everybody has a different approach, from a 10 step system to a 200+
step method; many have no units and all leave out the "magic" and assume
one has sufficent practical experience for the particular core materials
and/or types that they speak of.
I would dare say that even if you spent that money, you most likely
*not* get the equation/formula, and it is possible that it still would
not fit your requirements.
Power in a transformer core is porportional to the square of the cross
sectional arera of the core.
Some general equations, etc that may be useful:
Energy U(joules) = 0.5 * L(Henrys) * I(amps) * I(amps) = 1 Watt*second
In a flyback or switcher, each time the supply is switched across an
inductor, the current builds up along with the magnetic field in a nice
linear fashion, unless the core starts to saturate.
One can see that saturation as a rapidly increasing current, that
tends to look exponential (have seen it).
In any event, as long as it is linear (or close), the amount of energy
stored in the magnetic field can be calculated from the above equation,
using the peak current at the time of turnoff.
If one continues with the flyback case, the power available is
calculated by the energy multiplied by the number of pulses per second
("frequency" as used by all other workers).
Understanding this should go a long ways toward generalizing for
square wave drive, as the electronic case of superposition can be
applied (after all, we are still speaking of a linear system).
Besides the other equations you have seen, here are a few more:
L(henries) = u0(permeability units escape me) * N(turns, no units) *
N(turns, no units) * le(magnetic path length in meters) * Ae(core area
in square meters) .
Magnetic induction B(webers/metersquared *or* newtons/amp*meter *or*
tesla) = u0(permeability units escape me) * I(amps) * N(turns, no units)
Energy U(joules) = 0.5 * [ B(tesla) * B(tesla) ]/u0(permeability units
escape me) .
1 Tesla = 10^4 gauss = 1volt*second/metersquared = 1
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