Quality factor via bandwidth

The quality factor of the system can be defined in terms of its resonant frequency and the resonance width, referred to as full width at half maximum, i.e. it is the bandwidth over which the vibration power is greater than half the power at the resonant frequency.

Notes:

1. An equivalent definition uses angular frequencies instead of linear ones.

2. There is another definition that is approximately equivalent to this one at high quality factor values.

Links:

1. Wikipedia.

quality_factor

quality_factor of the oscillator.

Symbol:

Q

Latex:

\(Q\)

Dimension:

dimensionless

resonant_frequency

Oscillator’s resonant temporal_frequency.

Symbol:

f_r

Latex:

\(f_\text{r}\)

Dimension:

frequency

resonance_width

Resonance width, or full width at half maximum, of the peak in the graph of the dissipated power as a function of driving frequency, i.e. the difference between the frequencies at which the dissipated power is half the peak dissipated power, which happens at the resonant frequency, vid. figure. See temporal_frequency.

Symbol:

Delta(f)

Latex:

\(\Delta f\)

Dimension:

frequency

law

Q = f_r / Delta(f)

Latex:

\[Q = \frac{f_\text{r}}{\Delta f}\]