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The frequency response of G(s) = 1 plotted in the complex G(jω) [s(s + 1)(s + 2)]
plane (for 0 < ω < ∞) is
Correct Option: A
G(s) = | ||
s(s + 1)(s + 2) |
G(jω) = | ||
jω(jω + 1)(jω + 2) |
M = | ||
ω√ω² + 1 √ω² + 4 |
∠ φ = -90 - tan-1ω - tan-1 | ||
2 |
For ω = 0, M = ∞ ; ∠ φ = – 90
For ω = ∞, M = 0; ∠ φ = – 90 – 90 – 90 = – 270
So Cutting Real Axis
Imaginary part of G(jω) = 0
i.e. Img {G(jω)} = 0
⇒ Im | = 0 | |||
jω(-ω2 + 3)ω + 2 |
⇒ Im | = 0 | |||
-jω3 - 3ω2 + 2jω |
⇒ Im | = 0 | |||
- 3ω2 + j(2ω - ω3) |
⇒ Im | = 0 | |||
(3ω2)2 + (2ω - ω3)2 |
∴ 2ω – ω3 = 0
⇒ ω2 = 2 . ω = 0
Neglecting ω = 0, we have
ω = √2
∴ M |at ω = √2 = | = | ⇒ | < | 3 | |||||
√2 √3 √2 + 4 | √36 | 6 | 4 |