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Zener diode parallel to RC circuit

In the left hand side part there is a diode in series to parallel RC network. And in the right hand side there is a zener diode in parallel with series RC network.

How do these sub circuits operate? Is the second one (on the right) used for filtering electronic noise?

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That's not a zener. That is a Schottky diode needed for its fast response on the secondary side of the flyback. The RC in parallel will be acting as a snubber to manage its response (power loss, ringing)

The primary side D+RC is to deal with the leakage inductance of the transformer. The diode ensures the RC is in circuit only during turn-off. The C will absorb the energy stored in the leakage inductance (increasing the voltage to a controlled level) and the R is to discharge before the next switch event

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