Bandwidth Calculator

Calculate the -3 dB bandwidth of a second-order closed-loop system from natural frequency and damping ratio.

rad/s

Bandwidth (omega_BW)

20.201 rad/s

Bandwidth3.215 Hz

Bandwidth (omega_BW) vs Natural Frequency (omega_n)

Vedi formula →

Formula

## 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.

Esempio Risolto

A second-order system with omega_n = 20 rad/s and zeta = 0.7.

  1. 012*zeta² = 2 × 0.49 = 0.98
  2. 02Inner sqrt: sqrt(2 - 1.96 + 0.9604) = sqrt(1.0004) = 1.0002
  3. 031 - 0.98 + 1.0002 = 1.0202
  4. 04omega_BW = 20 × sqrt(1.0202) = 20 × 1.0100 = 20.20 rad/s
  5. 05f_BW = 20.20 / 6.283 = 3.215 Hz