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Registered Member #2099
Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1716
Strong work, Gren.
I like that you give the formula. IMHO, formulas given without an online calculator are better than online calculators given without a formula. I've found plenty of calculators that give wrong answers, even for reasonable input values. The two in this thread seem to give the same answers.
The B-max formula is not hard to get from basic EM principles, if you work in SI units and remember that μ0 = 4pi/10^7 henries per meter. In MS Excel, you can type =4e-7*pi(). [edit] Last night I wrote too late, and said an identical unit for μ0 was webers per volt-second. Wrong! The SI unit of magnetic permeability is, indeed, the henry per meter. That's identical to the "tesla per (ampere per meter)", as in μ = B / H.
But magnetic permeability has no place in the transformer core B_max formula. That formula is an application of Faraday's law of induction: V = dΦ/dt. Volts "per turn" = webers per second, so webers = volt-seconds.
SI flux unit: 1 weber is 1 tesla x 1 square meter; same as 10^8 maxwells. cgs flux unit: 1 maxwell is 1 gauss x 1 square cm. Flux change of 1 maxwell induces 10^-8 volt-seconds.
Gren's calculator gets an extra plus for having coefficients for both sine waves and square waves. Square waves have the lower RMS voltage for the same frequency and same flux swing (= integrated volt-seconds in one positive or negative half-cycle).
For |B_max| values close to saturation, you can squeeze out a bit more RMS voltage and peak voltage using "cresty" voltage waveforms. They form automatically if a sinusoidal primary voltage is too high (by, say, a factor of two), and the primary current is limited by a resistive ballast.
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Transformer B-Field Calculator
