Bandwidth Calculator — सूत्र
## Closed-Loop Bandwidth
Bandwidth is the frequency at which the closed-loop magnitude response drops to -3 dB (70.7% of its DC value). It measures how fast the system can track inputs.
### Formula
**omega_BW = omega_n × sqrt(1 - 2*zeta² + sqrt(2 - 4*zeta² + 4*zeta⁴))**
Higher bandwidth means faster tracking but also more susceptibility to high-frequency noise. Good control design balances bandwidth against noise rejection.
Bandwidth is the frequency at which the closed-loop magnitude response drops to -3 dB (70.7% of its DC value). It measures how fast the system can track inputs.
### Formula
**omega_BW = omega_n × sqrt(1 - 2*zeta² + sqrt(2 - 4*zeta² + 4*zeta⁴))**
Higher bandwidth means faster tracking but also more susceptibility to high-frequency noise. Good control design balances bandwidth against noise rejection.
हल किया गया उदाहरण
A second-order system with omega_n = 20 rad/s and zeta = 0.7.
- 2*zeta² = 2 × 0.49 = 0.98
- Inner sqrt: sqrt(2 - 1.96 + 0.9604) = sqrt(1.0004) = 1.0002
- 1 - 0.98 + 1.0002 = 1.0202
- omega_BW = 20 × sqrt(1.0202) = 20 × 1.0100 = 20.20 rad/s
- f_BW = 20.20 / 6.283 = 3.215 Hz