Does this provide galvanic isolation from an AC supply?
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If that is your aim I agree, even though there are commercial products which use this approach.This is not a safe or prudent approach to obtaining power from the AC line.
Hypothetically then..This is not a safe or prudent approach
If I have this right then what's needed for "won't kill you when you touch it" isolation is just one big bipolar eletrolytic cap. In this case at least 700 µF works ok along with a 2mF filter cap. I'm simulating it with a constant-power load of 1 kW. The final output is supposed to be 12v which to me suggests the use of a buck regulator. The buck regulator not requiring a transformer, just an inductor. The idea here is that the whole thing works out being much cheaper than a 60hz transformer at this power level, though i can't speak for Mhz range SMPSs. But before 1 good idea comes 100 bad ones.In theory you only need one of the capacitors since there is no return path.