-
For the transfer function
G(s) H(s) = 1 s (s + 1)(s + 0.5)
the phase cross-over frequency is_____ rad/sec
-
- 0.707
- 707
- 7.07
- None of the above
Correct Option: A
| G(s) H(s) = | ||
| s (s + 0.5) (s + 1) |
| G(jω) H(jω) = | ||
| jω (jω + 0.5) (jω + 1) |
φ = ∠ G (jω) H (jω)
= - 90° - tan-1 2 ω - tan-1 ω
At phase cross-over point, = – 180°
∴ tan– 1 ω + tan– 1 2ω = 90°
| ⇒ tan– 1 | = 90° | |
| 1 - 2ω2 |
| ⇒ | = tan 90° = ∞ | |
| 1 - 2ω2 |
∴ 1 - 2ω2 = 0
| ⇒ ω = | = 0.707 rad /sec | |
| √2 |
