None of the inductors suggested have very high current Irms(A). The Irms(A) of the torroid I am using is 10A and even that gets hot.
So the question is will the design above still need a high current coupled inductor.
*Glances back at the OP*, oh yeah, a couple amps will be needed, won't it. Well, most of these are families, should be able to find something bigger SRF or LPD or whatever. Or that inverter transformer is looking quite good, despite its size and cost.
Probably most of the heat in your toroid was core loss, so that it's practically irrelevant if the winding is rated 10A or 100A. With a waveform that peaky, you get a lot of excess heating -- another good reason to use a tapped winding or transformer.
The other question I have is if I use a coupled 4.7uH 1:1 inductor why use the extra 10uH one ?
Edit: Because the suggested 1:10 inductor is only 27uH and I will need the extra 10uH ?
If I use a 1:1 I could leave it out ?
What extra 10?
Inductance depends on operating frequency and desired current ripple. 4.7uH might be enough, or you may need to raise the frequency, or deal with the higher ripple (increased losses, especially in the inductor and main filter caps).
I was looking for values near the original primary inductance, but I didn't check if that was consistent with the controller's operating point. The datasheets for those controllers are very detailed, do take a look and double-check the original author's work.
This is the datasheet for the 6265 1:10 Ratio
Not quite the same circuit example as Tim's above though.
That's an interesting one. Must be... self-excited oscillator, for single-cell battery or solar or thermopile or energy harvesting purposes? So, the capacitors are there to help shift charge around, without having to put too many different windings on the poor little transformer. Something like that. It's not a good method to use at scale; you can get away with it at low voltages because, with so little voltage to begin with, you're going to get crap efficiency anyway (anything over 50% is good), and since you're only doing this for a couple watts at most, the parts are small and you can afford to overkill them a bit, so they'll tolerate hacks like turn-on switching into a capacitor load.
Notice the current path from MOSFET drain, through the transformer, coupling cap, sync rect, and output filter, back to ground. When the transistor turns on, it delivers a huge gulp of current to charge that capacitor, which means big switching losses.
Tim