Tiny Li-Ion Charger with no Chip. Schematic & how does it work.

I'm testing a tiny 18650 Li-Ion / Li-Pol cell charger and then taking it to bits, including an autopsy of the transformer. It contains a 2-transistor switching power supply with no optocoupler and a Li-Ion charging circuitry with no dedicated charging chip. There are just two transistors and a TL431 voltage reference. I reverse engineer the schematic and explain how does the switching power supply and the charging circuitry work.

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