I have seen previous similar answers about radio transmission, but looking at the following scheme I am not sure about the role C3 plays in the circuit. I guess it is needed to remove the DC signal from the transistor's base, but I cannot exactly figure out how it acts. Could you please help me?
closed as off-topic by Leon Heller, laptop2d, Chris Stratton, Harry Svensson, Chupacabras Aug 1 '18 at 12:26
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Internally to the BJT is a parasite called "Miller capacitance". It can be regarded as a capacitor between collector and base and is typically, for normal transistors, in the region of 10 pF. It reduces the gain of a transistor at high frequencies because it injects a signal current back into the base: -
The effect of C3
With C3 present, that injected current instead of flowing into the base, finds a lower impedance path down to ground and this extends the high frequency performance of a BJT circuit that uses the emitter as its input (as in the case of your oscillator because positive oscillatory feedback is fed to the emitter).
In this circuit C3 does not block dc, it helps maintain a dc voltage at the transistor's base. It's part of the transistor's biasing arrangement.
Oh, and jamming a broadcast FM signal is illegal, at least in the U.S.
Energy is only stored in circulating-path networks. C3 and C4 complete one of the RF-energy-loops.