Can someone explain how I can convert 220 V AC 60 Hz to 12/5 V DC, 500 mA/1A without using any transformer? Like Sonoff or Shelly power supply.
Thank you so much
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1A is a bit much for the classic trasformerless dropper (wh1ch just uses capacitors to produce a current source that's then regulated by a shunt regulator)
It appears that the Shelly uses a non-isoated buck converter to drop the up-to 350V it gets from the from rectified mains supply down to a lower voltage to run the system.
As a result every part of the circuit is live (and thus deadly)
If you want a safer power supply for experimenting consider using a phone charger.
Rectification followed by PWM and then smoothing using a capacitor. But since you want two output voltages, you would have to have two PWM's. Probably a regulator as well. This is just a high-level way of looking at it. Rectifier would have to be selected to accommodate the high voltage, and current requirements.
There are other ways of doing it.