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Frequency modulated signal with single tone modulation has a frequency deviation of 20 kHz and bandwidth of 60 kHz. The frequency of the modulating signal will be -
- a)5 kHz
- b)10 kHz
- c)20 kHz
- d)30 kHz
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
Frequency modulated signal with single tone modulation has a frequency...
Frequency modulation (FM) is a method of encoding information onto a carrier wave by varying its frequency. In FM, the frequency of the carrier wave is changed in accordance with the amplitude of the modulating signal.
Given that the frequency deviation of the FM signal is 20 kHz and the bandwidth is 60 kHz, we need to determine the frequency of the modulating signal.
1. Understanding frequency deviation:
- Frequency deviation refers to the maximum amount by which the carrier frequency deviates from its center frequency.
- In FM, the instantaneous frequency of the carrier wave is given by:
f_inst = f_c + Δf(t)
where f_inst is the instantaneous frequency, f_c is the center frequency, and Δf(t) is the frequency deviation at time t.
- In this case, the frequency deviation is given as 20 kHz, meaning the carrier frequency can deviate by a maximum of 20 kHz in either direction from the center frequency.
2. Relationship between frequency deviation and bandwidth:
- In FM, the bandwidth is directly proportional to the frequency deviation.
- The bandwidth of an FM signal is given by the Carson's rule:
Bandwidth = 2 * (Δf + f_m)
where Δf is the frequency deviation and f_m is the frequency of the modulating signal.
- In this case, the bandwidth is given as 60 kHz, and we need to find the frequency of the modulating signal.
3. Calculation:
- From the given information, we have:
Bandwidth = 2 * (Δf + f_m)
60 kHz = 2 * (20 kHz + f_m)
Dividing both sides by 2:
30 kHz = 20 kHz + f_m
Subtracting 20 kHz from both sides:
f_m = 30 kHz - 20 kHz
f_m = 10 kHz
Therefore, the frequency of the modulating signal is 10 kHz, which corresponds to option B.
Given that the frequency deviation of the FM signal is 20 kHz and the bandwidth is 60 kHz, we need to determine the frequency of the modulating signal.
1. Understanding frequency deviation:
- Frequency deviation refers to the maximum amount by which the carrier frequency deviates from its center frequency.
- In FM, the instantaneous frequency of the carrier wave is given by:
f_inst = f_c + Δf(t)
where f_inst is the instantaneous frequency, f_c is the center frequency, and Δf(t) is the frequency deviation at time t.
- In this case, the frequency deviation is given as 20 kHz, meaning the carrier frequency can deviate by a maximum of 20 kHz in either direction from the center frequency.
2. Relationship between frequency deviation and bandwidth:
- In FM, the bandwidth is directly proportional to the frequency deviation.
- The bandwidth of an FM signal is given by the Carson's rule:
Bandwidth = 2 * (Δf + f_m)
where Δf is the frequency deviation and f_m is the frequency of the modulating signal.
- In this case, the bandwidth is given as 60 kHz, and we need to find the frequency of the modulating signal.
3. Calculation:
- From the given information, we have:
Bandwidth = 2 * (Δf + f_m)
60 kHz = 2 * (20 kHz + f_m)
Dividing both sides by 2:
30 kHz = 20 kHz + f_m
Subtracting 20 kHz from both sides:
f_m = 30 kHz - 20 kHz
f_m = 10 kHz
Therefore, the frequency of the modulating signal is 10 kHz, which corresponds to option B.
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Community Answer
Frequency modulated signal with single tone modulation has a frequency...
Concept:
As per Carson’s rule, the bandwidth of a frequency modulated signal is defined as:
B.W. = 2 (Δf + fm)
Δ f = Frequency deviation of the modulated wave
fm = frequency of the modulating signal
As per Carson’s rule, the bandwidth of a frequency modulated signal is defined as:
B.W. = 2 (Δf + fm)
Δ f = Frequency deviation of the modulated wave
fm = frequency of the modulating signal
Calculation:
Given B.W. = 60 kHz and Δ f = 20 kHz
60k = 2 (20k + fm)
30k = 20k + fm
fm = 10 kHz
Given B.W. = 60 kHz and Δ f = 20 kHz
60k = 2 (20k + fm)
30k = 20k + fm
fm = 10 kHz
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Frequency modulated signal with single tone modulation has a frequency deviation of 20 kHz and bandwidth of 60 kHz. The frequency of the modulating signal will be -a)5 kHzb)10 kHzc)20 kHzd)30 kHzCorrect answer is option 'B'. Can you explain this answer?
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