GATE 2015 EE (EE2) – Question 35

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

The figure shows Nyquist loci for G1 and G2. Which choice is the Nyquist plot of their product?

Diagram for GATE 2015 EE (EE2) question 35

Option A in the figure
Option B in the figure
Option C in the figure
Option D in the figure

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Show answer and explanation

Correct answer: (B) Option B in the figure

Explanation

The intended normalized pair is an integrator and differentiator: G1(jω)=1/(jω) traces the negative imaginary axis from infinity to zero, while G2(jω)=jω traces the positive imaginary axis from zero to infinity.

Their product is identically 1, giving the point **+1 on the real axis, B**.

**Source qualification:** unscaled locus shapes alone do not specify magnitudes at matching frequencies. The exact unity point needs the intended reciprocal, unit-normalized pair; the displayed shapes by themselves cannot prove that normalization.

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