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GATE 2026 EE – Question 29

Control Systems · Stability analysis using Routh-Hurwitz and Nyquist criteria, Bode plots, Root loci · 1 mark · Multiple choice

The asymptotic Bode magnitude plot of a system is shown.

Which one of the following options best represents the transfer function of the system?

Diagram for GATE 2026 EE question 29
  1. $G(s)=\dfrac{1+\frac{s}{\omega_0}}{\frac{s}{\omega_0}}$
  2. $G(s)=\dfrac{\frac{s}{\omega_0}}{1+\frac{s}{\omega_0}}$
  3. $G(s)=\dfrac{1+\frac{s}{\omega_0}}{1-\frac{s}{\omega_0}}$
  4. $G(s)=\dfrac{1-\frac{s}{\omega_0}}{1+\frac{s}{\omega_0}}$

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Correct answer: (A) $G(s)=\dfrac{1+\frac{s}{\omega_0}}{\frac{s}{\omega_0}}$

Explanation

The magnitude falls at $-20$ dB/decade up to $\omega_0$ and is flat at 0 dB afterwards. A pole at the origin gives the $-20$ dB/decade slope, and a zero at $\omega_0$ flattens it: $G(s)=\dfrac{1+s/\omega_0}{s/\omega_0}$. For $\omega\ll\omega_0$, $|G|\approx\omega_0/\omega$, and for $\omega\gg\omega_0$, $|G|\to1$ (0 dB).