Circuit which create ac sine wave from dc pulsed signal
This is about as simple an analog inverter that I can simulate, but warning, not for the beginner with resonance issues.
The bridge diodes are 2f multipliers reduced to logic level with divide by 2 FF, then complementary inversion switches with a center tapped transformer with the tap having the isolated rectified power without filtering to low ripple DC.
This is purely an academic Q&A and has no practical use with some issues not mentioned.
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There is no "simple" circuit that does the reverse conversion of what a full wave bridge does on a sine wave.
However, it is possible to get there from here. Most of what you are asking about is an inverter. That's the reverse of a DC power supply. You put DC in, and AC power comes out.
Put a big enough capacitor on the output of the full wave bridge, you have DC with some ripple. That can be fed into an inverter to generate the same AC power as is going into the full wave bridge.
Note that not all inverters produce sine waves. You would specifically need a "true sine" output inverter. Square wave and "modified sine" used to be more common. Nowadays the extra electronics to create a sine wave isn't that much more expensive, and it's usually better for the load. True sine inverters are common now.
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