# Frequency Modulation

May 26 • General, Notes • 4853 Views • No Comments on Frequency Modulation

Frequency Modulation
Let us consider the baseband signal f(t) and the unmodulated carrier ec(t)=Ecsin(wct+θo)
Before modulation the instantaneous frequency of the carrier was fc during frequency modulation
fc α f(t)
fc =kf f(t)
kf=proportionality constant called frequency sensitivity of the frequency modulator.
unit: Hz/volt if f(t) is a voltage sinal and Hz/amp if f(t) a current signal.
The total instantaneous frequency of the frequency modulated carrier signal is
fi=fc+ kff(t)
2 πfi=2 πfc+2 πkff(t)
wi=wc+2 πkif(t)
The total phase angle of the frequency modulated carrier signal is
wi=dθ(t)/d(t)
=>θ(t)= ʃwidt
=> θ(t)=wct+2πkfʃf(t)dt
From the above equation we can say that in frequency modulation the total phase angle of the carrier is varied in proportion to the integral of instantaneous value of baseband signal.
The instantaneous value of frequency modulated carrier signal is
efm(t)=Ecsin(wct+2πkfʃf(t)dt)
Generating FM signal by phase modulation

Here for the phase modulation baseband signal is f(t)
so, wct+θo α ʃf(t)dt
=> wct+θo =k ʃf(t)dt
for θo=0, efm(t)=Ecsin(wct+2πkfʃf(t)dt)
so we can say that if we integrate the baseband signal and then allow it phase modulate a carrier then we will get a FM carrier signal.
Modulation Index in FM:
Since frequency modulation is a version of angle modulation in frequency modulation the modulationindex is defined as the maximum change in angle of the carrier because of modulation, and it is denoted by β.
β=δ/fm
final FM equation: efm(t)=Ecsin(wct+ βsinwmt)
Percentage of modulation in FM:
It is defined as the ratio of actual frequency deviation to the maximum allowable frequency deviation.
% of modulation=
actual frequency deviation X 100 /maximum allowable frequency deviation.
For commercial Fm broadcasting the maximum allowable frequency deviation is 75KHz.