The formula to calculate the Bandwidth Frequency is:
fb=ωn(√1−(2ζ2)+√ζ4−(4ζ2)+2)
Bandwidth Frequency is the range of frequencies over which the magnitude of the frequency domain drops to 70.7% from its zero frequency value. Natural Frequency of Oscillation refers to the frequency at which a physical system or structure will oscillate or vibrate when it is disturbed from its equilibrium position. Damping Ratio in a control system is defined as the ratio with which any signal gets decayed.
Let's assume the following values:
Using the formula:
fb=23(√1−(2⋅0.12)+√0.14−(4⋅0.12)+2)=54.9696597723011
| Natural Frequency (ωn) | Damping Ratio (ζ) | Bandwidth Frequency (fb) |
|---|---|---|
| 20 | 0.1 | 47.799704149827065 |
| 21 | 0.1 | 50.189689357318414 |
| 22 | 0.1 | 52.579674564809771 |
| 23 | 0.1 | 54.969659772301128 |
| 24 | 0.1 | 57.359644979792478 |
| 25 | 0.1 | 59.749630187283827 |