Powering the switching IC is not such a problem, as the top of C4 – the Cuk capacitor, is at a relatively stable dc voltage relative to local-IC-0V, and so a three-terminal regulator (LDO or dc-dc) could easily do that, maybe with a diode to prevent the regulators input capacitor from messing with the Cuk capacitor, or Cuk capacitors triangle wave from pushing through the regulator.
However, the traditional T元41+optocoupler feedback used in isolated ac-dc power supplied could easily cross this, I claim…. The graph right shows the horrendous waveform across which feedback signals would have to jump – the local IC 0V is a -34V 333kHz square wave relative to the output’s 0V. There is a huge drawback with this scheme, as neither the input+output 0V (triangle symbol in circuit diag), nor the negative output, have a dc connection to the IC’s local 0V. LTspice note: I had to delay the start of the input ramp to avoid giving the simulation tool a headache. And if LTspice has done its work well, it looks like this technique would indeed work as the output (lower line on graph left) settles to -2x the input voltage in this converter, whose input fet (top fet in diagram above) has a 2:1 on-off ratio.
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