What is the merit of fractional bandwidth?
$$f_{fractional}=\frac{f_{higher}-f_{lower}}{f_{mid}}$$
The same absolute bandwidth will have a smaller fractional bandwidth, if the mid frequency is higher, ok. It is reciprocal to the Q-factor, ok. Still, I could not find a good explanation why I would use the fractional bandwidth to describe for example a filter instead of absolute.
The only source I found is this page, look for paragraph How to judge fractional and relative bandwidth?
Best Answer
In some cases it works out to be more convenient. Some things (like human perception of pitch, and filter responses) respond to frequency logarithmically. That is, higher frequency octaves have more bandwidth than low frequency octaves.
It's the same reason low-pass or high-pass filter topologies have their roll-off described in dB/octave rather than dB/Hz. For example, we know that all first-order filters have a roll-off of 6dB/octave. This holds if we are designing a filter for 1kHz or 1GHz.
The same sort of issue applies to band-pass and band-reject filters. If we took a band-pass filter 100Hz wide at 1kHz, then scaled all the component values to move it up to 1GHz, then its bandwidth would be 100MHz. However, it would have the same fractional bandwidth.
Thus, it's convenient to specify the bandwidth of a particular topology as a fractional bandwidth because it does not change as the passband is moved by scaling all the component values.