What is the half-power bandwidth of a resonant circuit that has a resonant frequency of 3.7 MHz and a Q of 118?
Why Half-power (-3 dB) bandwidth of a resonant circuit is BW = f0 / Q. With f0 = 3.7 MHz and Q = 118, BW = 3,700,000 / 118 = 31,356 Hz, about 31.4 kHz. Higher Q means a narrower, sharper response for the same resonant frequency.
Watch out The 436.6 kHz figure comes from multiplying 3.7 MHz by 118 instead of dividing, and 15.7 kHz is that correct result cut in half, as if the formula used 2Q.
BW = f divided by Q. Q is quality, and high quality means narrow. Divide, never multiply.
3700 over 118 is about 31.4, which is 10 pi, easy to spot. 15.7 is 5 pi, half the answer: the divide-by-2Q trap.