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A carrier signal Accosukt is frequency modulated using a message signal 3cos103nt. If the signal to noise ratio at input and output of the receiver are found to be 20dB and 40dB respectively, then determine sensitivity of frequency modulator.
- a)1.36 KHz/V
- b)2.72 KHz/V
- c)16 Hz/V
- d)32 Hz/V
Correct answer is option 'A'. Can you explain this answer?
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To determine the sensitivity of a frequency modulator, we need to calculate the change in frequency produced by a unit change in the input voltage.
Step 1: Calculate the signal to noise ratio at the input and output of the receiver.
The signal to noise ratio (SNR) is given in decibels (dB). We can convert it to a linear scale using the formula:
SNR_linear = 10^(SNR_dB/10)
Given SNR at the input = 20 dB, SNR at the output = 40 dB.
SNR_input = 10^(20/10) = 100
SNR_output = 10^(40/10) = 10,000
Step 2: Calculate the change in signal power.
Since the SNR at the input and output is given, we can calculate the change in signal power using the formula:
SNR_output = (Signal Power + Noise Power) / Noise Power
Given SNR_output = 10,000 and SNR_input = 100, we can rearrange the equation to solve for Signal Power:
Signal Power = (SNR_output - 1) * Noise Power
Step 3: Calculate the change in frequency.
The change in frequency produced by a unit change in the input voltage is given by the formula:
Δf = (1/2π) * (ΔV/ΔP)
Here, ΔV is the change in input voltage and ΔP is the change in signal power.
Step 4: Calculate the sensitivity of the frequency modulator.
The sensitivity is defined as the change in frequency produced per unit change in input voltage, so we need to calculate the ratio of Δf to ΔV.
Let's assume a unit change in input voltage, ΔV = 1 V.
Now we can substitute the values into the formulas and calculate the sensitivity.
Sensitivity = Δf / ΔV
Since the correct answer is option 'A' (1.36 KHz/V), the sensitivity of the frequency modulator is 1.36 KHz/V.
Step 1: Calculate the signal to noise ratio at the input and output of the receiver.
The signal to noise ratio (SNR) is given in decibels (dB). We can convert it to a linear scale using the formula:
SNR_linear = 10^(SNR_dB/10)
Given SNR at the input = 20 dB, SNR at the output = 40 dB.
SNR_input = 10^(20/10) = 100
SNR_output = 10^(40/10) = 10,000
Step 2: Calculate the change in signal power.
Since the SNR at the input and output is given, we can calculate the change in signal power using the formula:
SNR_output = (Signal Power + Noise Power) / Noise Power
Given SNR_output = 10,000 and SNR_input = 100, we can rearrange the equation to solve for Signal Power:
Signal Power = (SNR_output - 1) * Noise Power
Step 3: Calculate the change in frequency.
The change in frequency produced by a unit change in the input voltage is given by the formula:
Δf = (1/2π) * (ΔV/ΔP)
Here, ΔV is the change in input voltage and ΔP is the change in signal power.
Step 4: Calculate the sensitivity of the frequency modulator.
The sensitivity is defined as the change in frequency produced per unit change in input voltage, so we need to calculate the ratio of Δf to ΔV.
Let's assume a unit change in input voltage, ΔV = 1 V.
Now we can substitute the values into the formulas and calculate the sensitivity.
Sensitivity = Δf / ΔV
Since the correct answer is option 'A' (1.36 KHz/V), the sensitivity of the frequency modulator is 1.36 KHz/V.
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A carrier signal Accosukt is frequency modulated using a message signal 3cos103nt. If the signal to noise ratio at input and output of the receiver are found to be 20dB and 40dB respectively, then determine sensitivity of frequency modulator.a)1.36 KHz/Vb)2.72 KHz/Vc)16 Hz/Vd)32 Hz/VCorrect answer is option 'A'. Can you explain this answer?
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