Question

The magnitude and phase of the transfer function \(G(s) = \frac{1}{{s + 1}}\) at ω = 1 is:
1. 0.707 and 45º
2. -3 dB and 0.78 rad
3. 0.707 and -45º
4. 3 dB and -90º

Answer 1

Correct Answer - Option 3 : 0.707 and -45º

Concept:

The magnitude of the transfer function can be found by replacing s with jω and then taking the magnitude and phase of the transfer function. 

Analysis:

\(G(s) = \frac{1}{{s + 1}}\)

\(G(jω ) = \frac{1}{{jω + 1}}\)

\(|G(jω )| = \frac{1}{\sqrt{ω^2 + 1^2}}\)

∠ G(jω) = - tan-1(ω/1)

at ω = 1, 

\(|G(jω )| = \frac{1}{\sqrt{2}} = 0.707\)

∠ G(jω) = - tan-1(1/1) = - 45°