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For Bode plot of (1 + jωT) has
- a)slope of 20 dB/decade and phase angle + tan-1 (ωT)
- b)slope of - 20 dB/decade and phase angle + tan-1 (ωT)
- c)slope of 20 dB/decade and phase angle - tan-1 (ωT)
- d)slope of - 40 dB/decade and phase angle - tan-1(ωT)
Correct answer is option 'A'. Can you explain this answer?
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For Bode plot of (1 + jωT) hasa)slope of 20 dB/decade and phase angle ...
Bode Plot of (1 + jωT)
Slope of Bode Plot
The slope of the Bode plot is determined by the type of transfer function. For the given transfer function (1 + jωT), the slope of the Bode plot can be calculated as follows:
- At low frequencies, the magnitude of the transfer function is approximately 1, and the phase angle is approximately 0 degrees. Therefore, the slope of the Bode plot is 0 dB/decade.
- At high frequencies, the magnitude of the transfer function decreases at a rate of 20 dB/decade, and the phase angle approaches 90 degrees. Therefore, the slope of the Bode plot is 20 dB/decade.
Therefore, the overall slope of the Bode plot is 20 dB/decade.
Phase Angle of Bode Plot
The phase angle of the Bode plot can be calculated using the following formula:
θ = tan-1 (Im/Re)
where Im is the imaginary part of the transfer function, and Re is the real part of the transfer function.
For the given transfer function (1 + jωT), the phase angle can be calculated as follows:
- At low frequencies, the transfer function is approximately 1, and the phase angle is approximately 0 degrees.
- At high frequencies, the transfer function can be written as:
1 + jωT = jωT(1/ωT + j)
The imaginary part of the transfer function is ωT, and the real part of the transfer function is 1/ωT. Therefore, the phase angle can be calculated as:
θ = tan-1 (ωT/(1/ωT)) = tan-1 (ωT2)
Therefore, the phase angle of the Bode plot is tan-1 (ωT).
Conclusion
The Bode plot of (1 + jωT) has a slope of 20 dB/decade and a phase angle of tan-1 (ωT).
Slope of Bode Plot
The slope of the Bode plot is determined by the type of transfer function. For the given transfer function (1 + jωT), the slope of the Bode plot can be calculated as follows:
- At low frequencies, the magnitude of the transfer function is approximately 1, and the phase angle is approximately 0 degrees. Therefore, the slope of the Bode plot is 0 dB/decade.
- At high frequencies, the magnitude of the transfer function decreases at a rate of 20 dB/decade, and the phase angle approaches 90 degrees. Therefore, the slope of the Bode plot is 20 dB/decade.
Therefore, the overall slope of the Bode plot is 20 dB/decade.
Phase Angle of Bode Plot
The phase angle of the Bode plot can be calculated using the following formula:
θ = tan-1 (Im/Re)
where Im is the imaginary part of the transfer function, and Re is the real part of the transfer function.
For the given transfer function (1 + jωT), the phase angle can be calculated as follows:
- At low frequencies, the transfer function is approximately 1, and the phase angle is approximately 0 degrees.
- At high frequencies, the transfer function can be written as:
1 + jωT = jωT(1/ωT + j)
The imaginary part of the transfer function is ωT, and the real part of the transfer function is 1/ωT. Therefore, the phase angle can be calculated as:
θ = tan-1 (ωT/(1/ωT)) = tan-1 (ωT2)
Therefore, the phase angle of the Bode plot is tan-1 (ωT).
Conclusion
The Bode plot of (1 + jωT) has a slope of 20 dB/decade and a phase angle of tan-1 (ωT).
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For Bode plot of (1 + jωT) hasa)slope of 20 dB/decade and phase angle + tan-1 (ωT)b)slope of - 20 dB/decade and phase angle + tan-1 (ωT)c)slope of 20 dB/decade and phase angle - tan-1 (ωT)d)slope of - 40 dB/decade and phase angle - tan-1(ωT)Correct answer is option 'A'. Can you explain this answer?
Question Description
For Bode plot of (1 + jωT) hasa)slope of 20 dB/decade and phase angle + tan-1 (ωT)b)slope of - 20 dB/decade and phase angle + tan-1 (ωT)c)slope of 20 dB/decade and phase angle - tan-1 (ωT)d)slope of - 40 dB/decade and phase angle - tan-1(ωT)Correct answer is option 'A'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about For Bode plot of (1 + jωT) hasa)slope of 20 dB/decade and phase angle + tan-1 (ωT)b)slope of - 20 dB/decade and phase angle + tan-1 (ωT)c)slope of 20 dB/decade and phase angle - tan-1 (ωT)d)slope of - 40 dB/decade and phase angle - tan-1(ωT)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For Bode plot of (1 + jωT) hasa)slope of 20 dB/decade and phase angle + tan-1 (ωT)b)slope of - 20 dB/decade and phase angle + tan-1 (ωT)c)slope of 20 dB/decade and phase angle - tan-1 (ωT)d)slope of - 40 dB/decade and phase angle - tan-1(ωT)Correct answer is option 'A'. Can you explain this answer?.
For Bode plot of (1 + jωT) hasa)slope of 20 dB/decade and phase angle + tan-1 (ωT)b)slope of - 20 dB/decade and phase angle + tan-1 (ωT)c)slope of 20 dB/decade and phase angle - tan-1 (ωT)d)slope of - 40 dB/decade and phase angle - tan-1(ωT)Correct answer is option 'A'. Can you explain this answer? for Electrical Engineering (EE) 2024 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about For Bode plot of (1 + jωT) hasa)slope of 20 dB/decade and phase angle + tan-1 (ωT)b)slope of - 20 dB/decade and phase angle + tan-1 (ωT)c)slope of 20 dB/decade and phase angle - tan-1 (ωT)d)slope of - 40 dB/decade and phase angle - tan-1(ωT)Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for For Bode plot of (1 + jωT) hasa)slope of 20 dB/decade and phase angle + tan-1 (ωT)b)slope of - 20 dB/decade and phase angle + tan-1 (ωT)c)slope of 20 dB/decade and phase angle - tan-1 (ωT)d)slope of - 40 dB/decade and phase angle - tan-1(ωT)Correct answer is option 'A'. Can you explain this answer?.
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