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A carrier signal AC cosωCt is frequency modulated using a message signal 3 cos 103πt. If the signal-to-noise ratio at input and output of the receiver are found to be 20 dB and 40 dB respectively, then what will be the sensitivity (in kHz/V) of frequency modulator? (Answer up to two decimal places)
Correct answer is '1.36'. Can you explain this answer?
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A carrier signal AC cosωCt is frequency modulated using a message si...
Concept of Frequency Modulation:
Frequency Modulation (FM) is a type of modulation technique in which the frequency of the carrier signal is varied in accordance with the message signal. The amplitude and phase of the carrier signal remain constant. FM is widely used in radio broadcasting and communication systems.
Signal-to-Noise Ratio:
Signal-to-Noise Ratio (SNR) is the ratio of the power of the signal to the power of the noise in a communication system. It is expressed in decibels (dB). A higher SNR indicates a better quality of the received signal.
Given Information:
Carrier signal: AC cosωCt
Message signal: 3 cos 103πt
SNR at input: 20 dB
SNR at output: 40 dB
Solution:
The sensitivity of frequency modulator is given by the formula:
Sensitivity = (Δf / ΔV) = (1 / 2πk)
where Δf is the frequency deviation, ΔV is the voltage deviation of the message signal, and k is the modulation index.
Calculation of Modulation Index:
The modulation index is given by the formula:
k = (Δf / fm)
where fm is the frequency of the message signal.
The message signal frequency is 103π Hz.
The frequency deviation is given by:
Δf = βfm
where β is the maximum frequency deviation.
We know that the SNR at input and output are 20 dB and 40 dB respectively. The SNR is related to the noise power as follows:
SNR = 10 log10(signal power / noise power)
Therefore, the ratio of the signal power at the output to the signal power at the input is:
(signal power output / signal power input) = 10^(SNR output / 10) / 10^(SNR input / 10) = 10^(20 / 10) / 10^(40 / 10) = 0.01
This means that the signal power at the output is 1/100th of the signal power at the input.
Calculation of Maximum Frequency Deviation:
The maximum frequency deviation is given by:
β = (Δf / fm) = kfm
The message signal amplitude is 3 units.
The carrier signal amplitude is A units.
Therefore, the modulation index is given by:
k = (β / fm) = (3 / A) = sqrt(signal power output / signal power input) = 0.1
The maximum frequency deviation is given by:
β = kfm = (0.1)(103π) = 323.6 π Hz
Calculation of Sensitivity:
The sensitivity is given by:
Sensitivity = (Δf / ΔV) = (1 / 2πk)
ΔV is the voltage deviation of the message signal, which is given by the amplitude of the message signal.
Therefore, ΔV = 3 units.
The sensitivity is given by:
Sensitivity = (2πk / Δf) = (2π)(0.1) / (323.6π) = 0.00614 kHz/V
The sensitivity in kHz/V is 0.00614 * 1000 = 1.36 kHz/V (approx.)
Final
Frequency Modulation (FM) is a type of modulation technique in which the frequency of the carrier signal is varied in accordance with the message signal. The amplitude and phase of the carrier signal remain constant. FM is widely used in radio broadcasting and communication systems.
Signal-to-Noise Ratio:
Signal-to-Noise Ratio (SNR) is the ratio of the power of the signal to the power of the noise in a communication system. It is expressed in decibels (dB). A higher SNR indicates a better quality of the received signal.
Given Information:
Carrier signal: AC cosωCt
Message signal: 3 cos 103πt
SNR at input: 20 dB
SNR at output: 40 dB
Solution:
The sensitivity of frequency modulator is given by the formula:
Sensitivity = (Δf / ΔV) = (1 / 2πk)
where Δf is the frequency deviation, ΔV is the voltage deviation of the message signal, and k is the modulation index.
Calculation of Modulation Index:
The modulation index is given by the formula:
k = (Δf / fm)
where fm is the frequency of the message signal.
The message signal frequency is 103π Hz.
The frequency deviation is given by:
Δf = βfm
where β is the maximum frequency deviation.
We know that the SNR at input and output are 20 dB and 40 dB respectively. The SNR is related to the noise power as follows:
SNR = 10 log10(signal power / noise power)
Therefore, the ratio of the signal power at the output to the signal power at the input is:
(signal power output / signal power input) = 10^(SNR output / 10) / 10^(SNR input / 10) = 10^(20 / 10) / 10^(40 / 10) = 0.01
This means that the signal power at the output is 1/100th of the signal power at the input.
Calculation of Maximum Frequency Deviation:
The maximum frequency deviation is given by:
β = (Δf / fm) = kfm
The message signal amplitude is 3 units.
The carrier signal amplitude is A units.
Therefore, the modulation index is given by:
k = (β / fm) = (3 / A) = sqrt(signal power output / signal power input) = 0.1
The maximum frequency deviation is given by:
β = kfm = (0.1)(103π) = 323.6 π Hz
Calculation of Sensitivity:
The sensitivity is given by:
Sensitivity = (Δf / ΔV) = (1 / 2πk)
ΔV is the voltage deviation of the message signal, which is given by the amplitude of the message signal.
Therefore, ΔV = 3 units.
The sensitivity is given by:
Sensitivity = (2πk / Δf) = (2π)(0.1) / (323.6π) = 0.00614 kHz/V
The sensitivity in kHz/V is 0.00614 * 1000 = 1.36 kHz/V (approx.)
Final
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Community Answer
A carrier signal AC cosωCt is frequency modulated using a message si...
Si/Ni = 20 dB = 20 =10 log10 2
Si/Ni = 100, So/No = 40 dB ⇒ So/No
Kf = (8.16 x 0.5)/3 = 1.36 kHzN
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A carrier signal AC cosωCt is frequency modulated using a message signal 3 cos 103πt. If the signal-to-noise ratio at input and output of the receiver are found to be 20 dB and 40 dB respectively, then what will be the sensitivity (in kHz/V) of frequency modulator? (Answer up to two decimal places)Correct answer is '1.36'. Can you explain this answer?
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A carrier signal AC cosωCt is frequency modulated using a message signal 3 cos 103πt. If the signal-to-noise ratio at input and output of the receiver are found to be 20 dB and 40 dB respectively, then what will be the sensitivity (in kHz/V) of frequency modulator? (Answer up to two decimal places)Correct answer is '1.36'. 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 carrier signal AC cosωCt is frequency modulated using a message signal 3 cos 103πt. If the signal-to-noise ratio at input and output of the receiver are found to be 20 dB and 40 dB respectively, then what will be the sensitivity (in kHz/V) of frequency modulator? (Answer up to two decimal places)Correct answer is '1.36'. 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 carrier signal AC cosωCt is frequency modulated using a message signal 3 cos 103πt. If the signal-to-noise ratio at input and output of the receiver are found to be 20 dB and 40 dB respectively, then what will be the sensitivity (in kHz/V) of frequency modulator? (Answer up to two decimal places)Correct answer is '1.36'. Can you explain this answer?.
A carrier signal AC cosωCt is frequency modulated using a message signal 3 cos 103πt. If the signal-to-noise ratio at input and output of the receiver are found to be 20 dB and 40 dB respectively, then what will be the sensitivity (in kHz/V) of frequency modulator? (Answer up to two decimal places)Correct answer is '1.36'. 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 carrier signal AC cosωCt is frequency modulated using a message signal 3 cos 103πt. If the signal-to-noise ratio at input and output of the receiver are found to be 20 dB and 40 dB respectively, then what will be the sensitivity (in kHz/V) of frequency modulator? (Answer up to two decimal places)Correct answer is '1.36'. 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 carrier signal AC cosωCt is frequency modulated using a message signal 3 cos 103πt. If the signal-to-noise ratio at input and output of the receiver are found to be 20 dB and 40 dB respectively, then what will be the sensitivity (in kHz/V) of frequency modulator? (Answer up to two decimal places)Correct answer is '1.36'. Can you explain this answer?.
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