whatever the input current looks like for a full bridge, you can make a flyback whose input current will look the same….ie a train of trapezoids of a certain shape profile.
But yes, flybacks are disfavoured mainly because of the energy dissipation in the RCD clamp which is related to leakage L, but more than that energy is dissipated in the RCD, and also turn off switching losses are bad, because the vds is shooting up to vin + vrefrerred + v(leakage spike).
Also, all the output current goes through the flyback diode.
And in flyback, the primary fets see more than vin in the off state....but we don't always hold that against the flyback because that is also the case for the pushpull and the one transistor forward converter with reset winding, as well as the active clamp forward converter
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The real badboy about the flyback, is that at fet turn off, the current flow in the leakage L keeps ‘ramming’ its current through the primary, and indeed into the RCD clamp, the problem is that you end up with some of your power current then getting dissipated in the RCD clamp….because the secondary diode doesn’t switch on quickly enough to suddenly start shipping power current at the exact point of turn off of the primary fet….why is the turn on of the secondary diode delayed?……mainly because of the leakage L in the txfmr.
So in the flyback your Leakage L is a gangster that forces some of your precious power current into the RCD clamp, where it gets dissipated.