I have following 2nd order system:
(2*d*w0*s+w0^2)/(s^2+2*d*w0*s+w0^2)
where "w0" is the undamped natural frequency and "d" is the damping. Is there an equation what describes a relationship between the undamped natural frequency and a bandwidth of this system?
The half-power (-3 dB) bandwidth is conveniently related to the damping d and the undamped natural frequency w0 through the quality factor Q, as follows: (-3 dB bandwidth in radians/sec) = w0/Q or (-3 dB bandwidth in Hz) = f0/Q, where w0 = (2 pi f0) and Q = w0/(2 d).
Dear Steven Baker, thank you for your answer. Is there any book where I can find these equations?
What I gave is just the bandwidth of the resonance defined by the denominator of your expression. Your expression (ratio) would correspond to the transfer function, for example, of a low-pass filter comprised of a series inductor L followed by a shunt branch comprised of a resistor R and capacitor C in series to ground. The -3 dB bandwidth of the low-pass filter is approximately w0 = sqrt(1/LC), independent of the damping. The damping only has an effect in the vicinity of frequency w0. If your context is electrical, you should be able to find plenty of information in any text on filter analysis.
Finally, I have found the answer, I want to share it as it was very useful for me. See attached. The formula is in pg. 21.
Credits to: Dr. Kevin Craig, Rensselaer Polytechnic Institute.
- Badges
- Science topic