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GATE 2015 EC – Question 31

Control Systems · Frequency Response · 1 mark · Multiple choice

The polar plot of the transfer function $G(s) = \frac{10(s + 1)}{s + 10}$ for $0 \leq \omega < \infty$ will be in the

  1. first quadrant
  2. second quadrant
  3. third quadrant
  4. fourth quadrant

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Show answer and explanation

Correct answer: (A) first quadrant

Explanation

At $\omega = 0$ the value is 1, on the positive real axis. As $\omega$ rises, the zero at 1 adds positive phase and the pole at 10 subtracts less phase at first, so the phase is positive. At $\omega \to \infty$ the value tends to 10 with zero phase. The phase stays between 0° and 90°, so the plot is in the first quadrant.