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The polar plot of the open loop transfer function of a feedback control system intersects the real axis at -2. The gain margin of the system is
  • a)
    -5dB
  • b)
    0dB
  • c)
    -6dB
  • d)
    40dB
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The polar plot of the open loop transfer function of a feedback contro...
Answer: c
Explanation: Gain margin of the system is inverse of the intersect on the real axis and calculated in decibels.
G(s) = 1+s / s(1+0.5s).
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Most Upvoted Answer
The polar plot of the open loop transfer function of a feedback contro...
Explanation:
The polar plot of the open-loop transfer function of a feedback control system can be used to analyze the stability and performance of the system. It represents the frequency response of the system in the complex plane.

Polar Plot and Intersecting the Real Axis:
The polar plot is a graph that shows the magnitude and phase of the transfer function as a function of frequency. In the polar plot, the magnitude is represented by the distance from the origin to a point on the plot, and the phase is represented by the angle from the positive real axis to the line connecting the origin and the point.

When the polar plot intersects the real axis, it means that the transfer function has a pole or a zero at that particular frequency. In this case, the polar plot intersects the real axis at -2, indicating that the transfer function has a pole or a zero at that frequency.

Gain Margin:
The gain margin of a system is a measure of how much the gain of the system can be increased before the system becomes unstable. It is defined as the amount of gain at the frequency where the phase of the open-loop transfer function is -180 degrees.

In this case, since the polar plot intersects the real axis at -2, it means that the phase at that frequency is -180 degrees. Therefore, the gain margin can be determined by finding the gain at that frequency.

Answer:
Since the polar plot intersects the real axis at -2, the gain margin of the system is the gain at that frequency. Therefore, the correct answer is option 'C', which is -6dB.
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