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Registered Member #142
Joined: Sat Feb 11 2006, 01:19PM
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Posts: 102
killah, I have that Amidon pamphlet, the one that folds out. Has lots of information in there. The formula you posted applies to a sine wave. Pi sqrt 2 =~ 4.44, which they give as an approximation. Not that you need more accuracy, but it illuminates the theory a little bit. They say "peak" but they mean rms. If you drive it with a square wave, it becomes B= ___VPk * 100_____ 4 * Ac * Nt * F
Registered Member #142
Joined: Sat Feb 11 2006, 01:19PM
Location:
Posts: 102
It looks like Amidon made a typo in the equation on page 9 we have been discussing. I believe that 10^2 in the numerator is incorrect. It should be 10^8. Amidon uses gauss and centimeters, in other words the cgs (centimeter gram second) system consistently throughout the data book. The correct cgs equation with B expressed in gauss and Ae in cm^2 is
B = (E x 10^8) / (4.44 Ae N f)
In mks, with B expressed in Teslas and Ae in m^2, the equation is
B = E / (4.44 Ae N f)
(And be aware, that is not the only error in their data book. The graph at the bottom of page 6 has an expression for magnetizing force that leaves out a factor of Pi on the right side of the equation. I didn't find any other mistakes, but those two are bad enough.)
I would also like to point out, in regard to the power to core size and frequency relationship you asked about, one can actually induce a solution from Amidon's data. Look for a relationsip between frequency versus flux density table in the data table in the middle of page 9. You might notice that frequency varies as the square of B in that table to a close approximation, which yields an expression for B in terms of the square root of f. Merge it with the equation for B lower down on page 9 (using the correct power of ten this time), eliminating B and yielding a single expression in terms of Ae, N, f and E: E = .007 Ae N sqrt f with Ae expressed in cm^2. In mks, with Ae expressed in m^2 that becomes E = 70 Ae N sqrt f
Edit: I just noticed where that lost 10^6 went. Amidon says f = frequency (MHz) so for 100 kHz, for example, you would plug 0.1 into their version of the equation.
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Toroidial Core Power Calculation