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The polar plot of a transfer function passes through the critical point (-1,0). Gain margin is
- a)Zero
- b)-1dB
- c)1dB
- d)Infinity
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
The polar plot of a transfer function passes through the critical poin...
Gain margin of a polar plot passing through the critical point is zero.
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The polar plot of a transfer function passes through the critical poin...
Understanding Gain Margin
Gain margin is an essential concept in control systems and stability analysis. It quantifies how much gain can be increased before the system becomes unstable.
Critical Point and Stability
- The critical point (-1, 0) on a polar plot indicates that the system's phase angle is 180 degrees with a gain of 1.
- If the polar plot passes through this point, it signifies that the system has reached the edge of stability.
Implications of Passing Through (-1, 0)
- When the plot touches (-1, 0), it suggests that the gain at this frequency is 0 dB, meaning the system is on the verge of instability.
- As the gain increases beyond this point, the system will start to oscillate, leading to potential instability.
Gain Margin Calculation
- Gain margin is defined as the difference between the gain at the critical phase (180 degrees) and 0 dB.
- Since the plot passes through (-1, 0), the gain margin is effectively zero because any increase in gain will bring the system to instability.
Conclusion
- Therefore, the correct answer is that the gain margin is zero.
- This indicates that the system is critically stable and any increase in gain will lead to instability.
By understanding these principles, one can effectively analyze and design control systems to achieve desired stability characteristics.
Gain margin is an essential concept in control systems and stability analysis. It quantifies how much gain can be increased before the system becomes unstable.
Critical Point and Stability
- The critical point (-1, 0) on a polar plot indicates that the system's phase angle is 180 degrees with a gain of 1.
- If the polar plot passes through this point, it signifies that the system has reached the edge of stability.
Implications of Passing Through (-1, 0)
- When the plot touches (-1, 0), it suggests that the gain at this frequency is 0 dB, meaning the system is on the verge of instability.
- As the gain increases beyond this point, the system will start to oscillate, leading to potential instability.
Gain Margin Calculation
- Gain margin is defined as the difference between the gain at the critical phase (180 degrees) and 0 dB.
- Since the plot passes through (-1, 0), the gain margin is effectively zero because any increase in gain will bring the system to instability.
Conclusion
- Therefore, the correct answer is that the gain margin is zero.
- This indicates that the system is critically stable and any increase in gain will lead to instability.
By understanding these principles, one can effectively analyze and design control systems to achieve desired stability characteristics.
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The polar plot of a transfer function passes through the critical point (-1,0). Gain margin isa)Zerob)-1dBc)1dBd)InfinityCorrect answer is option 'A'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about The polar plot of a transfer function passes through the critical point (-1,0). Gain margin isa)Zerob)-1dBc)1dBd)InfinityCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The polar plot of a transfer function passes through the critical point (-1,0). Gain margin isa)Zerob)-1dBc)1dBd)InfinityCorrect answer is option 'A'. Can you explain this answer?.
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