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My textbook says that

"$Q$ factor is an especially important quantity for electrical ossicilations trasnmitting radio waves. When selecting radio and television stations it is essential that the transmitting and receiving circuits are tuned to the same resonance frequency"

However why must the two circuits tuned to the same resonance frequency? Also, how is Q factor related to the whole set up?

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  • $\begingroup$ If the two circuits were not tuned to the same frequency then you would not get the station or channel you want. Like the expression "tune your radio" $\endgroup$
    – BioPhysicist
    Commented Oct 18, 2018 at 15:08

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However why must the two circuits tuned to the same resonance frequency? Also, how is Q factor related to the whole set up?

The transmitted signal carries some information, which is conveyed by modulating the carrier, which leads to the expansion of the bandwidth of the transmitted signal. For simplicity, we can assume that the expansion is symmetric, so that the carrier frequency is in the middle of the transmitted bandwidth.

In order to receive this information, the bandwidth of the receiver has to be at least as wide as the bandwidth of the transmitted signal, but not much wider, so that the stations transmitting at neighboring frequencies are not picked up as well.

Under these constraints and taking into account symmetry, mentioned earlier, for the best reception (maximum overlap), the resonant frequency of the receiver has to be aligned with the carrier frequency of the transmitter.

The Q factor of the receiver is important because it defines the receiver's bandwidth.

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