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The Q-factor is often defined as Q = resonance frequency/bandwidth. Suppose we take this definition and take two LC circuits which both have Q=1, but the first resonant circuit has a resonance frequency of 1 and the second one has a resonance frequency of 10.

This means that the first circuit has a bandwidth of 1 and the second one has a bandwidth of 10. But if this is the case, I would say intuitively that the second circuit is less selective because it has a bigger bandwidth. But the Q are the same so one says the selectivity is the same. It seems weird to me that in the formula of the Q we don't just have Q = 1/bandwidth. Why is that?

Edit:

But does it makes sense to say that the Q factor characterizes the pic in the frequency domain even though in the figure just down here the shapes are exactly the same but the Q factors are different?

enter image description here

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    \$\begingroup\$ Q is perhaps best appreciated as a figure of merit, as an analogy its easy to make a 1 ohm resistor to the nearest ohm, it is extremely to difficult to fabricate a 1MegOhm resistor to the nearest ohm \$\endgroup\$
    – sstobbe
    Commented Jul 2, 2017 at 17:03
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    \$\begingroup\$ You are confusing the resonant frequency with bandwidth. Bandwidth of the circuit can be the same at resonant frequencies of 1MHz and 100MHz (though harder in practice with real components). \$\endgroup\$
    – filo
    Commented Jul 2, 2017 at 17:26

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