I'm reading about the Q-factor from Wikipedia and here:
The Q-factor is defined as the resonant frequency divided by the bandwidth (the range of frequencies that oscillate with power greater than half of the power of the resonant frequency). Apparently, the definition is such, so that the amplitude against frequency plot resembles a sharper curve when the Q-factor is high.
But I don't understand why this is true. The numerator is the resonant frequency, not the amplitude of the resonant frequency. If the hold the bandwidth constant, why does the Q-factor improve simply by having the resonant frequency higher (moving the curve towards right/higher on the frequency domain plot)? If you look at the example pictures under the link I provided, you will see that the higher Q curve has a higher amplitude at the resonant frequency and the curve is less spread out. Naturally it would seem to me more intuitive to take the height of the curve and divide it by some number that characterises how spread out the curve is (here the bandwidth). Then a higher peak and less spread would give a higher Q/sharper "spike" on the plot.
It seems that there is something extremely simple that I'm misunderstanding but I'm just quite confused.