Whether the transformer is "planar" or not, what I do is:
Pick a core.
Pick a maximum flux density that does not produce saturation or excessive heat at the frequency in question, at the maximum temperature that the core is anticipated to achieve.
Figure out how many primary turns are needed to keep the maximum flux density that low.
Figure out how much I-squared-R loss you get at the current in question at the frequency in question at the maximum wire temperature foreseen.
Keep in mind that the skin effect is significant at frequencies in the
10's of KHz and higher for any wire size likely to carry 12 amps. Resistance of copper wire is also roughly proportional to absolute temperature, but the variation with temperature is less (probably closer to proportional to square root of absolute temperature) once the skin effect has boosted resistance a lot.
There are charts and formulas for predicting resistance of a given wire size at a given frequency.
I would suggest Litz wire with a high strand count for 8 volts 12 amps at frequencies in the 10's of KHz and higher, since that is likely to allow substantially smaller wire that will allow a smaller core. And I would try to find some data on the resistance of the Litz wire in question at the frequency in question.
And after that, test and verify that the transformer does not overheat, since most published skin-effect-related resistance increase figures are for isolated straight wire and the figures can be different in a winding.
I don't understand how the ferroxcube cores work. There is a core (E) and a plate (PLT). When I calculate my transformer's core loss density do I take the Ve of the E plus the Ve of the PLT into account?
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