Hi!
How exactly does an FM transmitter work?
What does every single component do in the process?
Please explane in detale..
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I'm not sure how much you know, but the basic circuit you have shown is an oscillator where the oscillator frequency can be slightly modified by the microphone. The values of L and that 36 pF capacitor are creating a tank circuit which defines the carrier frequency. Do you need more than this?
Another thought I had, I think this configuration is a Colpitts oscillator. You could possibly look that up for more information.