# Q-Factor

March 29, 2018

Back to: Sine Testing

The Q-factor of a resonance is the ratio of the resonance’s center frequency to its half-power bandwidth. It tells us how sharp, or steep, the resonance is.

(1)

(2)

#### Example

For example, if the center frequency of a resonance value was 97.91Hz, the equation to solve the Q-factor would be:

(3)

### Resonance Sharpness

In Figure 4.3, the left graph displays resonances with the same amplitude and center frequency but varying bandwidths. Notice the difference in sharpness between the three curves.

The right graph displays resonances with the same amplitude and bandwidth but varying center frequencies. On a linear axis, the difference in sharpness is not evident. However, it is on a logarithmic axis.

#### Example

Let’s refer back to Figure 4.1. The Q-factor of the 67.99Hz resonance was 25.4, 12.4 for the 142.1Hz resonance, and 68.5 for the 538.1Hz resonance. The 538.1Hz resonance was the sharpest.

The sharper the resonance, the quicker the resonance will resonate during a sine sweep. The Q-factor measures the difference between a resonance that slowly ramps up during a sine sweep (a wide resonance with a low Q-factor) and a resonance that quickly ramps up (a sharp resonance with a high Q-factor).

The sharper the resonance, the harder it is to control. For an in-depth discussion on this topic, see the following webinar on SRTD testing.