Half bridge DC-DC converter circuit analysis

I was trying to learn how the flyback and half bridge DC-DC converter is working.
For Flyback circuit,
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Understood output waveform is as follows.
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Keeping this understanding in mind, I was trying to analyze the Half bridge DC-DC converter working.
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MOSFET Part number: BUK7K17-60E

Current flow as per my understanding is

For M1 is conducting: VIN -> M1 -> T1-> C2->GND

For M2 is conducting: VIN-> C1 -> T1 -> M2 -> GND

Please correct me if I am wrong.

Also, any direction to the current and mosfet drain voltage characteristics (plots) will be appreciated.

Datasheet of LM5109B: Link

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