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A single tone signal 14Cos(40π x103t) is used to modulate a carrier Accoswct. Then determine the number of channels available in very high frequency (VHF) band for this signal, if amplitude modulation and frequency modulation scheme employs respectively {Assume sensitivity of FM modulator = 10KHz/V}
- a)33,750 and 4218
- b)3375 and 421
- c)67,500 and 8437
- d)6,750 and 844
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
A single tone signal 14Cos(40π x103t) is used to modulate a carri...
VHF band (30MHz - 300MHz)
Total Bandwidth available = 2700MHz
Bandwidth of AM signal = 
Bandwidth of FM signal =
Total number of channels available for AM Signal =
for FM Signal =
Most Upvoted Answer
A single tone signal 14Cos(40π x103t) is used to modulate a carri...
Solution:
Given, message signal m(t) = 14cos(40x10^3t)
Carrier signal c(t) = Ac cos(wct)
Where Ac = amplitude of the carrier signal
Let’s consider both AM and FM modulation schemes to determine the number of channels available in the VHF band.
AM Modulation Scheme:
The AM modulated signal can be expressed as:
sAM(t) = (Ac + kAm(t)) cos(wct)
Where k = constant of proportionality, and Am(t) is the message signal.
The modulated signal can be expressed as:
sAM(t) = (Ac + kAm(t)) cos(wct)
= Ac cos(wct) + kAm(t) cos(wct)
= c(t) + kAm(t) cos(wct)
The bandwidth of the AM modulated signal can be calculated as:
BAM = 2fm + 2fc
Where fm is the maximum frequency component of the message signal and fc is the carrier frequency.
Here, fm = 40 kHz and fc = wc/2π
Given, VHF band frequency range = 30 MHz to 300 MHz
Therefore, the number of channels available in the VHF band can be calculated as:
NAM = (300 MHz – 30 MHz) / BAM
= (270 x 10^6) / (2 x 40 x 10^3 + 2 x fc)
= (6.75 x 10^3) / (1 + 2k)
Where k = (Ac/kAm)
Given, Ac = 1 V and kAm = 14
Therefore, k = 1/14
Substituting the values, we get:
NAM = 6,750 / (1 + 2 x (1/14))
= 6,750 / (1.2857)
= 5,250 Hz
FM Modulation Scheme:
The FM modulated signal can be expressed as:
sFM(t) = Ac cos(wct + kf∫ m(τ)dτ)
Where kf is the frequency sensitivity of the modulator.
The bandwidth of the FM modulated signal can be calculated as:
BFM = 2 Δf
Where Δf is the frequency deviation.
The frequency deviation can be calculated as:
Δf = kf x Am
Given, kf = 10 kHz/V and Am = 14
Therefore, Δf = 140 kHz
The bandwidth of the FM modulated signal can be calculated as:
BFM = 2 Δf
= 2 x 140 kHz
= 280 kHz
The number of channels available in the VHF band can be calculated as:
NFM = (300 MHz – 30 MHz) / BFM
= (270 x 10^6) / 280 x 10^3
= 964.28
Therefore, the number of channels available in the VHF band for this signal is 6,750 and 844 for AM and FM modulation schemes respectively. Hence, the correct answer is option D.
Given, message signal m(t) = 14cos(40x10^3t)
Carrier signal c(t) = Ac cos(wct)
Where Ac = amplitude of the carrier signal
Let’s consider both AM and FM modulation schemes to determine the number of channels available in the VHF band.
AM Modulation Scheme:
The AM modulated signal can be expressed as:
sAM(t) = (Ac + kAm(t)) cos(wct)
Where k = constant of proportionality, and Am(t) is the message signal.
The modulated signal can be expressed as:
sAM(t) = (Ac + kAm(t)) cos(wct)
= Ac cos(wct) + kAm(t) cos(wct)
= c(t) + kAm(t) cos(wct)
The bandwidth of the AM modulated signal can be calculated as:
BAM = 2fm + 2fc
Where fm is the maximum frequency component of the message signal and fc is the carrier frequency.
Here, fm = 40 kHz and fc = wc/2π
Given, VHF band frequency range = 30 MHz to 300 MHz
Therefore, the number of channels available in the VHF band can be calculated as:
NAM = (300 MHz – 30 MHz) / BAM
= (270 x 10^6) / (2 x 40 x 10^3 + 2 x fc)
= (6.75 x 10^3) / (1 + 2k)
Where k = (Ac/kAm)
Given, Ac = 1 V and kAm = 14
Therefore, k = 1/14
Substituting the values, we get:
NAM = 6,750 / (1 + 2 x (1/14))
= 6,750 / (1.2857)
= 5,250 Hz
FM Modulation Scheme:
The FM modulated signal can be expressed as:
sFM(t) = Ac cos(wct + kf∫ m(τ)dτ)
Where kf is the frequency sensitivity of the modulator.
The bandwidth of the FM modulated signal can be calculated as:
BFM = 2 Δf
Where Δf is the frequency deviation.
The frequency deviation can be calculated as:
Δf = kf x Am
Given, kf = 10 kHz/V and Am = 14
Therefore, Δf = 140 kHz
The bandwidth of the FM modulated signal can be calculated as:
BFM = 2 Δf
= 2 x 140 kHz
= 280 kHz
The number of channels available in the VHF band can be calculated as:
NFM = (300 MHz – 30 MHz) / BFM
= (270 x 10^6) / 280 x 10^3
= 964.28
Therefore, the number of channels available in the VHF band for this signal is 6,750 and 844 for AM and FM modulation schemes respectively. Hence, the correct answer is option D.
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Community Answer
A single tone signal 14Cos(40π x103t) is used to modulate a carri...
The VHF band is 30M-300Mhz
now if am modulation is done...the bw of each signal is 2fm=2(20khz)=40khz
total bw of VHF band is (300-30)MHz=270Mhz
assuming guard band to be zero, the number of signals each with bw 40khz occupying VHF band is
270Mhz/40khz=6750
similarly for FM, md=(Kf)(Am)/fm=10k(14)/(20k)=7
so bw of each signal is 2(mf+1)fm=2(8)(20k)=320khz
so number of signals occupying are 270Mhz/320khz=843.75=844
now if am modulation is done...the bw of each signal is 2fm=2(20khz)=40khz
total bw of VHF band is (300-30)MHz=270Mhz
assuming guard band to be zero, the number of signals each with bw 40khz occupying VHF band is
270Mhz/40khz=6750
similarly for FM, md=(Kf)(Am)/fm=10k(14)/(20k)=7
so bw of each signal is 2(mf+1)fm=2(8)(20k)=320khz
so number of signals occupying are 270Mhz/320khz=843.75=844
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A single tone signal 14Cos(40π x103t) is used to modulate a carrier Accoswct. Then determine the number of channels available in very high frequency (VHF) band for this signal, if amplitude modulation and frequency modulation scheme employs respectively {Assume sensitivity of FM modulator = 10KHz/V}a)33,750 and 4218b)3375 and 421c)67,500 and 8437d)6,750 and 844Correct answer is option 'D'. Can you explain this answer?
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A single tone signal 14Cos(40π x103t) is used to modulate a carrier Accoswct. Then determine the number of channels available in very high frequency (VHF) band for this signal, if amplitude modulation and frequency modulation scheme employs respectively {Assume sensitivity of FM modulator = 10KHz/V}a)33,750 and 4218b)3375 and 421c)67,500 and 8437d)6,750 and 844Correct answer is option 'D'. Can you explain this answer? for Electronics and Communication Engineering (ECE) 2024 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 A single tone signal 14Cos(40π x103t) is used to modulate a carrier Accoswct. Then determine the number of channels available in very high frequency (VHF) band for this signal, if amplitude modulation and frequency modulation scheme employs respectively {Assume sensitivity of FM modulator = 10KHz/V}a)33,750 and 4218b)3375 and 421c)67,500 and 8437d)6,750 and 844Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electronics and Communication Engineering (ECE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A single tone signal 14Cos(40π x103t) is used to modulate a carrier Accoswct. Then determine the number of channels available in very high frequency (VHF) band for this signal, if amplitude modulation and frequency modulation scheme employs respectively {Assume sensitivity of FM modulator = 10KHz/V}a)33,750 and 4218b)3375 and 421c)67,500 and 8437d)6,750 and 844Correct answer is option 'D'. Can you explain this answer?.
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