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GATE 2015 EE – Question 63

Control Systems · Mathematical modelling and representation of systems, Feedback principle, Transfer function, Block diagrams and Signal flow graphs · 2 marks · Multiple choice

The transfer function of a second order real system with a perfectly flat magnitude response of unity has a pole at $(2 - j3)$. List all the poles and zeroes.

  1. Poles at $(2 \pm j3)$, no zeroes.
  2. Poles at $(\pm 2 - j3)$, one zero at origin.
  3. Poles at $(2 - j3)$, $(-2 + j3)$, zeroes at $(-2 - j3)$, $(2 + j3)$.
  4. Poles at $(2 \pm j3)$, zeroes at $(-2 \pm j3)$.

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Show answer and explanation

Correct answer: (D) Poles at $(2 \pm j3)$, zeroes at $(-2 \pm j3)$.

Explanation

A real system has complex poles in conjugate pairs, so the poles are at $2 \pm j3$. A flat unit magnitude response means an all-pass system, where every pole at $p$ has a matching zero at $-p$. So the zeroes are at $-2 \mp j3$, which is $-2 \pm j3$.