\[Q=\frac{f_r}{\Delta f}\]
Variables
Qquality factor
frresonant frequency (Hz)
df[Δf]bandwidth between half-power frequencies (Hz)
Description
What is this formula?
The Quality Factor measures the sharpness of a resonance peak. A high-Q system resonates strongly within a narrow frequency range, while a low-Q system responds over a wider frequency range.
When to use it
Use this formula when evaluating resonant systems, filters, oscillators, acoustic resonators, mechanical vibrations, and energy storage efficiency.
Example
Given:
fr = 1000 Hz
Δf = 20 Hz
Formula:
Q = fr/Δf
Substitution:
Q = 1000/20
Q = 50
Result:
Q = 50
Applications
Mechanical resonators.
Acoustic resonators.
Electronic filters.
Oscillators.
Vibration analysis.
Control systems.