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An angle modulated signal is given by s(t) = cos 2
p
(2 x 106t + 30 sin 150t + 40 cos 150t). The maximum frequency and phase deviations of s(t) are- a)10.5 kHz, 140prad
- b)6 kHz and 80prad
- c)10.5 kHz, 100prad
- d)7.5 kHz, 100prad
Correct answer is option 'D'. Can you explain this answer?
Verified Answer
An angle modulated signal is given by s(t) = cos 2p (2 x 106t + 30 sin...
s(t) = cos 2
p
(2 x 10+16t + 30 sin 150t + 40 cos 150t)
Phase deviation = 100
p
Frequency deviation = 7.5 kHz.
Most Upvoted Answer
An angle modulated signal is given by s(t) = cos 2p (2 x 106t + 30 sin...
Given: s(t) = cos 2π (2 × 106t 30 sin 150t 40 cos 150t)
To find: Maximum frequency and phase deviations
Solution:
Frequency Modulation (FM) equation:
s(t) = Ac cos [2πfc t + kf ∫ m(t) dt]
where,
Ac = carrier amplitude
fc = carrier frequency
kf = frequency sensitivity
m(t) = modulation signal
Given signal:
s(t) = cos 2π (2 × 106t 30 sin 150t 40 cos 150t)
This signal can be written as:
s(t) = cos 2π (2 × 106t 60 sin (2π × 25t) 80 cos (2π × 25t))
Carrier frequency fc = 2 × 106 Hz
Modulation index:
μ = (Maximum frequency deviation) / (Modulation frequency)
Here, modulation frequency = 25 Hz
Maximum frequency deviation = 80 Hz
μ = 80 / 25 = 3.2
Maximum frequency deviation:
Δf = kf × m
Here, maximum value of m(t) = 80
kf = Δf / m
kf = 80 / 80 = 1 Hz/V
Maximum frequency deviation = Δf = kf × m = 1 × 80 = 80 Hz
Phase deviation:
Δθ = kp × m
where,
kp = phase sensitivity
For FM modulation,
kp = 2π × Δf / fm
kp = 2π × 80 / 25 = 2π × 3.2
kp = 20π rad/V
Maximum phase deviation = Δθ = kp × m = 20π × 80 = 1600π rad
Maximum phase deviation in radians = 1600π ≈ 5026 rad
Maximum phase deviation in degrees = (Maximum phase deviation in radians) × (180 / π) ≈ 287.5°
Hence, the maximum frequency deviation is 80 Hz and the maximum phase deviation is 100π rad (or 287.5°). Therefore, option D is the correct answer.
To find: Maximum frequency and phase deviations
Solution:
Frequency Modulation (FM) equation:
s(t) = Ac cos [2πfc t + kf ∫ m(t) dt]
where,
Ac = carrier amplitude
fc = carrier frequency
kf = frequency sensitivity
m(t) = modulation signal
Given signal:
s(t) = cos 2π (2 × 106t 30 sin 150t 40 cos 150t)
This signal can be written as:
s(t) = cos 2π (2 × 106t 60 sin (2π × 25t) 80 cos (2π × 25t))
Carrier frequency fc = 2 × 106 Hz
Modulation index:
μ = (Maximum frequency deviation) / (Modulation frequency)
Here, modulation frequency = 25 Hz
Maximum frequency deviation = 80 Hz
μ = 80 / 25 = 3.2
Maximum frequency deviation:
Δf = kf × m
Here, maximum value of m(t) = 80
kf = Δf / m
kf = 80 / 80 = 1 Hz/V
Maximum frequency deviation = Δf = kf × m = 1 × 80 = 80 Hz
Phase deviation:
Δθ = kp × m
where,
kp = phase sensitivity
For FM modulation,
kp = 2π × Δf / fm
kp = 2π × 80 / 25 = 2π × 3.2
kp = 20π rad/V
Maximum phase deviation = Δθ = kp × m = 20π × 80 = 1600π rad
Maximum phase deviation in radians = 1600π ≈ 5026 rad
Maximum phase deviation in degrees = (Maximum phase deviation in radians) × (180 / π) ≈ 287.5°
Hence, the maximum frequency deviation is 80 Hz and the maximum phase deviation is 100π rad (or 287.5°). Therefore, option D is the correct answer.
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An angle modulated signal is given by s(t) = cos 2p (2 x 106t + 30 sin 150t + 40 cos 150t). The maximum frequency and phase deviations of s(t) area)10.5 kHz, 140p radb)6 kHz and 80p radc)10.5 kHz, 100p radd)7.5 kHz, 100p radCorrect answer is option 'D'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2025 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about An angle modulated signal is given by s(t) = cos 2p (2 x 106t + 30 sin 150t + 40 cos 150t). The maximum frequency and phase deviations of s(t) area)10.5 kHz, 140p radb)6 kHz and 80p radc)10.5 kHz, 100p radd)7.5 kHz, 100p radCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An angle modulated signal is given by s(t) = cos 2p (2 x 106t + 30 sin 150t + 40 cos 150t). The maximum frequency and phase deviations of s(t) area)10.5 kHz, 140p radb)6 kHz and 80p radc)10.5 kHz, 100p radd)7.5 kHz, 100p radCorrect answer is option 'D'. Can you explain this answer?.
An angle modulated signal is given by s(t) = cos 2p (2 x 106t + 30 sin 150t + 40 cos 150t). The maximum frequency and phase deviations of s(t) area)10.5 kHz, 140p radb)6 kHz and 80p radc)10.5 kHz, 100p radd)7.5 kHz, 100p radCorrect answer is option 'D'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2025 is part of Electronics and Communication Engineering (ECE) preparation. The Question and answers have been prepared according to the Electronics and Communication Engineering (ECE) exam syllabus. Information about An angle modulated signal is given by s(t) = cos 2p (2 x 106t + 30 sin 150t + 40 cos 150t). The maximum frequency and phase deviations of s(t) area)10.5 kHz, 140p radb)6 kHz and 80p radc)10.5 kHz, 100p radd)7.5 kHz, 100p radCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An angle modulated signal is given by s(t) = cos 2p (2 x 106t + 30 sin 150t + 40 cos 150t). The maximum frequency and phase deviations of s(t) area)10.5 kHz, 140p radb)6 kHz and 80p radc)10.5 kHz, 100p radd)7.5 kHz, 100p radCorrect answer is option 'D'. Can you explain this answer?.
Solutions for An angle modulated signal is given by s(t) = cos 2p (2 x 106t + 30 sin 150t + 40 cos 150t). The maximum frequency and phase deviations of s(t) area)10.5 kHz, 140p radb)6 kHz and 80p radc)10.5 kHz, 100p radd)7.5 kHz, 100p radCorrect answer is option 'D'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electronics and Communication Engineering (ECE).
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