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I see these double ended transformer drivers on many places, I know the working principles of these gate drive transformers but still don't have an idea about external components that I've marked with red. enter image description here

What's the purpose of capacitor connected series in primary, how the pnp bjt is working here, what's the purpose of these diodes and why two of them?

Thak you.

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What's the purpose of capacitor connected series in primary

The capacitor prevents DC current flowing in the transformer primary. DC current in the primary is to be avoided because it will cause the magnetic core to saturate and performance may seriously degrade.

how the pnp bjt is working here

It quickly turns off the MOSFET that follows it by actively dragging current from the charged gate.

what's the purpose of these diodes and why two of them?

Well you need at least one diode in order to produce the maximum gate drive voltage when turning on the associated MOSFET. Two diodes may be used to provide some dead-band area to avoid both MOSFETs conducting at once when the drive changeover occurs.

Maybe have a look at this website for extra details about driving MOSFETs via transformers. There is also this app note by MAXIM.

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