Question

The pole-zero map of a rational function $G\left(s\right)$ is shown below. When the closed counter $r$ is mapped into the $G\left(s\right)-plane$, then the mapping encircles.

• A. the point $-1+j0$ of the $G\left(s\right)-plane$ once in the counter-clockwise direction
• B. the origin of the $G\left(s\right)-plane$ once in the clockwise direction
• C. the origin of the $G\left(s\right)-plane$ once in the counter clockwise direction
• D. the point $-1+j0$ of the $G\left(s\right)-plane$ once in the clockwise direction

Answer 1

The correct option is B the origin of the $G\left(s\right)-plane$ once in the clockwise direction

s-plane contour is encircling 2-poles and 3-zeros in clockwise direction hence the corresponding $G\left(s\right)$ plane contour encircles origin 2-times in anti-clockwise direction
$\therefore$ Effectively once in clockwise direction.