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The polar plot of a transfer function passes through (-1, 0) point. The gain margin is
- a)zero
- b)- 1 dB
- c)1 dB
- d)infinity
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The polar plot of a transfer function passes through (-1, 0) point. Th...
When polar plot passes through (-1, 0) the system is on limit of stability and gain margin is zero.
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The polar plot of a transfer function passes through (-1, 0) point. Th...
Explanation:
Polar Plot Passing Through (-1, 0) Point:
- In a polar plot, the point (-1, 0) represents a frequency where the phase angle is -180 degrees and the magnitude is 1.
- This point is significant because it indicates the frequency at which the system's gain crossover frequency occurs.
Gain Margin:
- The gain margin is a measure of how much the system's gain can be increased before it becomes unstable.
- It is defined as the amount of gain that can be added to the system before the phase margin becomes zero.
Interpretation of Polar Plot Passing Through (-1, 0) Point:
- When the polar plot passes through the point (-1, 0), it means that the system's gain crossover frequency is at -180 degrees phase angle and 1 magnitude.
- This indicates that the system is critically stable at this frequency.
Gain Margin Calculation:
- Since the gain margin is zero when the polar plot passes through the (-1, 0) point, it means that any further increase in gain will push the system towards instability.
- Therefore, the gain margin in this case is zero.
Therefore, the correct answer is option 'A' - zero gain margin.
Polar Plot Passing Through (-1, 0) Point:
- In a polar plot, the point (-1, 0) represents a frequency where the phase angle is -180 degrees and the magnitude is 1.
- This point is significant because it indicates the frequency at which the system's gain crossover frequency occurs.
Gain Margin:
- The gain margin is a measure of how much the system's gain can be increased before it becomes unstable.
- It is defined as the amount of gain that can be added to the system before the phase margin becomes zero.
Interpretation of Polar Plot Passing Through (-1, 0) Point:
- When the polar plot passes through the point (-1, 0), it means that the system's gain crossover frequency is at -180 degrees phase angle and 1 magnitude.
- This indicates that the system is critically stable at this frequency.
Gain Margin Calculation:
- Since the gain margin is zero when the polar plot passes through the (-1, 0) point, it means that any further increase in gain will push the system towards instability.
- Therefore, the gain margin in this case is zero.
Therefore, the correct answer is option 'A' - zero gain margin.
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