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There is no such thing as "peak power". Mathematically it is simply double the RMS number and it overloads the circuit.
A transformer manufacturer might spec "peak power" to be double the RMS number for a minute or two before the transformer melts. But I think the weak old IRF540 Mosfets will melt first when they try to conduct 83A from the battery to the transformer.
Power output of a transformer is only limited by maximum permissible temperature rise.
If a transformer is continuously rated for 500 watts (or more commonly 500 VA) it could conceivably carry higher power than that for a short interval, if sufficient cool down periods are allowed for.
Would depend on things like whether steady state power is
thermally or core-saturation-limited (and temperature does
bother Bsat). If thermal then some interval can be withstood.
If at the edge of core saturation (and size, weight always
push this way) then maybe not much margin remains.
Cheapest would probably be a destructive test for some
sane stress-interval, and back off the rating by 50% or so.
Analyzing it depends on too many unknown factors.
just keep BMAX always below 300mT. Then calculate it from that. Of course it depends as said above, like how long is the peak, how hot is ambient , etc etc
Ferrite at 300mT is pretty much right at the limit of saturation.
Always better to design for a bit of margin to allow for slightly higher than expected input voltages.
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