The converter topology should be clarified. The transformer itself can't act as a buck converter, there must be an output inductor performing energy storage. But that's probably what the OP intends.
Thanks, yes , i agree entirely, sorry if i didnt make it clear above.
Yes i certainly didnt mean the transformer acts as a buck converter.
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if the OP picks a duty cycle max..say 0.7...then take vin = 171v, vout = 120v at 120w....then design a CCM buck converter like that...ill show OP how OP can then very simply convert this into a pushpull of the same spec.
Note that I have used min vin = 171v when real vin min is 10v…….thats where the transformer will come into it….and where we will convert the miscreant buck into the swan-like pushpull
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Here is a push pull that meats your spec in the free simulator from ltspice…….convert to .asc format, then hit run.
I didn’t put any leakage in the transformer, …so you will need to add that and add some means of snubbing it
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I think one of the main things for the transformer, is getting the push pull design right first....and of course......you need to wind full layers of turns in general otherwise its too difficult to wind a layer on top of the one you've just wound....you can always cheat and use double or triple strands to fill the layer if need be........do you know how to use the core's "AL" value to find the inductance....also, use a ferrite thats fairly matched to your f(sw)
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I dont think theres a formula for doing a transformer, since you are limited to offtheshelf cores generally...so pick one....wind it.......see if it meets the criteria above...if not, pick a different core........you can make an excel spreadsheet which makes it quick to do this.....often you pick a core too small, and it would be in saturation, so you just choose the next size up....or often, you find your turns simply dont fit on the bobbin..they overflow it..so again, you need to pick the next size up and re-do it.
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all the maths you need to do the transformer is in this doc
https://massey276.wixsite.com/maths
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Actually sorry I mentioned a current doubler rectifier above…..this could be do-able, but not worth it for your spec, as you have a high step up ratio and rel’y low output current.
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Do you understand the difference between magnetising current and power current in a push pull?
This is key to winding the txfmr.
The attached sim shows an expression for the magnetising current so that you can see it in the pushpull ltspice simulation attached