GATE 2024 IN – Question 18

Control Systems · Stability and frequency response · 1 mark · Multiple choice

The sinusoidal transfer function corresponding to the polar plot shown, for $T>0$, is

$1-j\omega T$
$\dfrac{1-j\omega T}{1+j\omega T}$
$1+j\omega T$
$\dfrac1{1+j\omega T}$

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Correct answer: (A) $1-j\omega T$

Explanation

The locus begins at real value 1 and descends vertically as frequency increases. Its real part stays 1, and its imaginary part must decrease without bound.

Therefore it is $1-j\omega T$, **A**; the rational alternatives give curved loci.