The pole-zero map of a rational function {G}( {s}) is shown below. When the closed contour \Gamma is mapped into the {G}( {s}) -plane, then the mapping encircles.

Correct Answer is : the origin of the G(s) -plane once in the clockwise direction.

the origin of the {G}( {s}) -plane once in the counter-clockwise direction.

the point -1+j 0 of the G(s) -plane once in the counter-clockwise direction.

the origin of the G(s) -plane once in the clockwise direction.

the point -1+j 0 of the {G}( {s}) -plane once in the clockwise direction.

GATE Electronics and Communications (EC) 2020 Solved Papers

Question : 30 of 65

Marks: +1, -0

The pole-zero map of a rational function

{G}( {s})

is shown below. When the closed contour

Γ

is mapped into the

{G}( {s})

-plane, then the mapping encircles.

the origin of the ${G}( {s})$ -plane once in the counter-clockwise direction.
the point $-1+j 0$ of the $G(s)$ -plane once in the counter-clockwise direction.
the origin of the G(s) -plane once in the clockwise direction.
the point $-1+j 0$ of the ${G}( {s})$ -plane once in the clockwise direction.

Solution:

Given number of closed loop poles 2 in contour and number of closed loop 3 zero in contour.

{P}=2

and

{Z}=3 .

So effective number of encirclements to the origin is once in clockwise direction.

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