GATE 2014 EC (EC1) – Question 57
Using asymptotic Bode plots, find phase margin (degrees) of $G(s)=10/((s+0.1)(s+1)(s+10))$.
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Correct answer: 42 to 48
Explanation
The DC gain is10/[0.1×1×10]=10, or20dB. Beyond0.1rad/s the magnitude falls at20dB/decade and reaches0dB at1rad/s. At that frequency the straight-line phase contributions from poles0.1,1,10are−90°,−45°,0°, respectively. Thus phase margin=180−135=**45°**. The question explicitly requests asymptotic plots.