Question

The number and direction of encirclements around the point $-1+j0$ in the complex plane by the Nyquist plot of
$G\left(s\right)=\frac{1-s}{4+2s}is$

• A. zero
• B. one, anti-clockwise
• C. one, clockwise
• D. two, clockwise

Answer 1

The correct option is A zero

$G\left(s\right)=\frac{1-s}{4+2s}$
$and\angle G\left(s\right)=-{\tan }^{-1}\omega -{\tan }^{-1}\frac{\omega }{2}$
$ats=0,|G\left(s\right)|=\frac{1}{4}=0.25$
$and\angle G\left(s\right){|}_{\omega =0}=0^{\circ }$
$ats=\infty ,|G\left(s\right)|=-\frac{1}{2}=-0.5$
$and\angle G\left(s\right){|}_{\omega =\infty }=-{180}^{\circ }$

Nyquist plot is

Hence, number of encirclements of $(-1+j0)=0$