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It's known that the Quality factor Q is defined as :

Q = 2*pi*(Energy stored at resonance) / (Energy loss per cycle)

and for high Q resonators, It's known that Q can be also given by :

Q = Resonance frequency / 3dB Bandwidth

My question is, How can i prove that ? that both expressions of Q are equivalent if Q is large enough ?

I can prove it for many circuits, but i want a general rigorous proof of that.

Thank you in advance

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# About the Quality factor

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