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Due to an addition of pole at origin, the polar plot gets shifted by ___ at ω = 0?
- a)-45°
- b)-60°
- c)-90°
- d)-180°
Correct answer is option 'C'. Can you explain this answer?
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Due to an addition of pole at origin, the polar plot gets shifted by _...
Introduction
In control systems and signal processing, the addition of poles in the transfer function can significantly affect the behavior of the system. A pole at the origin alters the phase response of the system, especially at low frequencies.
Effect of a Pole at the Origin
- A pole at the origin contributes a phase lag of 90 degrees to the system's response.
- This means that for every pole added at the origin, the phase of the output signal will lag behind the input signal by 90 degrees.
Polar Plot Shift
- In a polar plot, the phase shift impacts the angle of the plot as a function of frequency (ω).
- At ω = 0, the introduction of a pole at the origin will shift the plot downwards by 90 degrees.
Conclusion
- Therefore, when a pole is added at the origin, the polar plot is effectively shifted by -90 degrees at ω = 0.
- This shift is crucial for understanding system stability and frequency response.
The correct answer is option C: -90°.
In control systems and signal processing, the addition of poles in the transfer function can significantly affect the behavior of the system. A pole at the origin alters the phase response of the system, especially at low frequencies.
Effect of a Pole at the Origin
- A pole at the origin contributes a phase lag of 90 degrees to the system's response.
- This means that for every pole added at the origin, the phase of the output signal will lag behind the input signal by 90 degrees.
Polar Plot Shift
- In a polar plot, the phase shift impacts the angle of the plot as a function of frequency (ω).
- At ω = 0, the introduction of a pole at the origin will shift the plot downwards by 90 degrees.
Conclusion
- Therefore, when a pole is added at the origin, the polar plot is effectively shifted by -90 degrees at ω = 0.
- This shift is crucial for understanding system stability and frequency response.
The correct answer is option C: -90°.
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Due to an addition of pole at origin, the polar plot gets shifted by _...
Addition of pole causes instability to the system.
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