sinusoidal modulating waveform of amplitude 5 V and a frequency of 2 KHz is applied to FM generator, which has a frequency sensitivity of 40 Hz/volt. Calculate the frequency deviation, modulation index, and bandwidth.
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Given, the amplitude of modulating signal, Am=5V
Frequency of modulating signal, fm=2KHz
Frequency sensitivity, kf=40Hz/volt
We know the formula for Frequency deviation as
Δf=kfAm
Substitute kf and Am values in the above formula.
Δf=40×5=200Hz
Therefore, frequency deviation, Δf is 200Hz
The formula for modulation index is
β=Δffm
Substitute Δf and fm values in the above formula.
β=2002×1000=0.1
Here, the value of modulation index, β is 0.1, which is less than one. Hence, it is Narrow Band FM.
The formula for Bandwidth of Narrow Band FM is the same as that of AM wave.
BW=2fm
Substitute fm value in the above formula.
BW=2×2K=4KHz
Therefore, the bandwidth of Narrow Band FM wave is 4KHz.
Explanation:
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