The group delay of the transfer function \(H\left( s \right) = \f
| The group delay of the transfer function \(H\left( s \right) = \frac{{s - 1}}{{s + 1}}\) is ______
A. π – 2 tan<sup>-1</sup> (ω)
B. <span class="math-tex">\(\frac{1}{{1 + \omega }}\)</span>
C. <span class="math-tex">\(\frac{2}{{{\omega ^2} + 1}}\)</span>
D. 2 tan<sup>-1</sup> (ω)
Please scroll down to see the correct answer and solution guide.
Right Answer is: C
SOLUTION
\(H{\left( s \right)_{s = j\omega }} = \frac{{j\omega - 1}}{{j\omega + 1}} \)
\(\theta \left( \omega \right) = \pi - 2{\tan ^{ - 1}}\left( \omega \right)\)
\({t_g}\left( \omega \right) = \frac{{ - d\theta \left( \omega \right)}}{{d\omega }} = \frac{2}{{1 + {\omega ^2}}}\)