Question

The phase margin of the system for which loop gain $GH\left(j\omega \right)=\frac{1}{(j\omega +1{)}^3}$is

• A. $-\pi$
• B. $\pi$
• C. 0
• D. $\pi /2$

Answer 1

The correct option is B $\pi$

PM is determined at gain cross over frequency
$\frac{1}{(\sqrt{1+{\omega }^2}{)}^3}=1$
$1+{\omega }^2=1$
$\therefore \omega =0$
$PM=\varphi +{180}^o$
$=-3ta{n}^{-1}0+{180}^o=0+{180}^o$
$={180}^o=\pi$