-
The 3-dB bandwidth of a typical second-order system with the transfer function
C(s) = ωn2 R(s) s2 + 2ξωns + ωn2
is given by
-
- ωn √1 - 2ξ²
- ωn √(1 - ξ²) + √(ξ4 - ξ² + 1)
- ωn √(1 - 2ξ²) + √(4ξ4 - 4ξ² + 2)
- ωn √(1 - 2ξ²) + √(4ξ4 - 4ξ² + 2)
- ωn √1 - 2ξ²
Correct Option: C
| H(s) = | ||
| s2 + 2ξωns + ωn2 |
| H(jω) = | ||
| -ω2 + 2ξωn jω + ωn2 |
| [H(jω)] = | ||
| √(ω2n - ω2)2 + (ωξ + ωnω)2 |
[H(j0)] = 1
If ωc is the 3-dB frequency, then
| H(jωc) = | = 0.707 | |
| √(ω2n - ω2c)2 + (2ξ + ωnωc)2 |
⇒ ω4n = 0.5[ω4c - 2ω2c ω2n + 4 ξ2ω2n ω2c]
Rearranging,
0.5 ω4c - ω2c (ω2n - 2 ξ2 ω2n) - 0.5 ω ω2n = 0
Since ωc is real, hence (c) is correct.
