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.
Answers
Explanation:
Solution
Given, the equation of an FM wave as
s(t)=20cos(8π×106t+9sin(2π×103t))
We know the standard equation of an FM wave as
s(t)=Accos(2πfct+βsin(2πfmt))
We will get the following values by comparing the above two equations.
Amplitude of the carrier signal, Ac=20V
Frequency of the carrier signal, fc=4×106Hz=4MHz
Frequency of the message signal, fm=1×103Hz=1KHz
Modulation index, β=9
Here, the value of modulation index is greater than one. Hence, it is Wide Band FM.
We know the formula for modulation index as
β=Δffm
Rearrange the above equation as follows.
Δ=βfm
Substitute β and fm values in the above equation.
Δ=9×1K=9KHz
Therefore, frequency deviation, Δf is 9KHz.
The formula for Bandwidth of Wide Band FM wave is
BW=2(β+1)fm
Substitute β and fm values in the above formula.
BW=2(9+1)1K=20KHz
Therefore, the bandwidth of Wide Band FM wave is 20KHz
Formula for power of FM wave is
Pc=Ac22R
Assume, R=1Ω and substitute Ac value in the above equation.
P=(20)22(1)=200W
Therefore, the power of FM wave is 200 watts