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Polar plot of sinusoidal transfer function is a plot of:
- a)magnitude and phase angle
- b)magnitude versus frequency
- c)phase angle versus frequency
- d)none of the above
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Polar plot of sinusoidal transfer function is a plot of:a)magnitude an...
Polar plot:
- The polar plot of a transfer function G(jω) is the plot of the magnitude of G(jω) versus the phase angle of G(jω) as ω is varied from 0 to positive infinity.
- For all pole systems, type indicates the starting point of the polar plot and order indicates the ending point of the polar plot.
The sinusoidal transfer function G(jω) is a complex function and it is given by
G(jω) = Re [G(jω)] + j Im [G(jω)]
G(jω) = |G(jω)| ∠ G(jω)
= M ∠ϕ Polar form
From the above equation,
G(jω) may be represented as a phasor of magnitude M and phase angle ϕ
The starting points (ω = 0) of a polar plot for different types of minimum phase systems is given below:
G(jω) = Re [G(jω)] + j Im [G(jω)]
G(jω) = |G(jω)| ∠ G(jω)
= M ∠ϕ Polar form
From the above equation,
G(jω) may be represented as a phasor of magnitude M and phase angle ϕ
The starting points (ω = 0) of a polar plot for different types of minimum phase systems is given below:
- As seen from the above figure, when a zero is added the type decreases, and the end of the polar plot shifts by +90°.
- When a pole is added, the type of the system increases, and hence the end of the polar plot shifts by -90°.
Therefore, the Polar plot of the sinusoidal transfer function is a plot of magnitude and phase angle.
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Community Answer
Polar plot of sinusoidal transfer function is a plot of:a)magnitude an...
Definition:
Polar plot of a sinusoidal transfer function is a plot that shows the magnitude and phase angle of the transfer function as a function of frequency.
Explanation:
- Magnitude: The magnitude of the transfer function represents the ratio of the output amplitude to the input amplitude. It is plotted on the radial axis of the polar plot.
- Phase Angle: The phase angle of the transfer function represents the phase shift between the input and output signals. It is plotted on the angular axis of the polar plot.
Interpretation:
- The magnitude and phase angle of a sinusoidal transfer function provide valuable information about the system's behavior at different frequencies.
- By analyzing the polar plot, engineers can determine the system's stability, gain margin, and phase margin.
Significance:
- The polar plot helps in understanding how a system responds to different frequencies and aids in designing control systems.
- It is a useful tool for characterizing the frequency response of a system and identifying potential issues such as resonance or instability.
In conclusion, a polar plot of a sinusoidal transfer function is a representation of both magnitude and phase angle, making it a valuable tool for analyzing system behavior in the frequency domain.
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Polar plot of sinusoidal transfer function is a plot of:a)magnitude and phase angleb)magnitude versus frequencyc)phase angle versus frequencyd)none of the aboveCorrect answer is option 'A'. Can you explain this answer?
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