Subject : Principle of Communication Engineering

Topic : Angle modulation and demodulation

Difficulty : High

• If the frequency of carrier signal is varied in accordance with the instantaneous amplitude of the modulating signal, then it is called as frequency modulation.
• In FM the amplitude of carrier remains constant. The variation in carrier frequency from the umodulated carrier is called frequency deviation (δ).

• FM is non-linear process & information contain in frequency deviation.

  Mathematical Expression of FM:

• Instantaneous frequency of frequency modulated wave is;

  Wi=Wc+δ

• The frequency deviation above or below Wc depends on the instantaneous amplitude of modulating signal i.e

  δ=kVm cos Wmt

  where k= frequency deviation sensitivity of FM

• Again, instantaneous frequency is:

  Wi=Wc+δ

  Wi=Wc+kVm cos Wmt ---------------------(i)

• The frequency modulated signal is represented mathematically as

  Vfm=Vc sin θ ------------------------(ii)

  where θ instantaneous phase & it can be determine from instantaneous frequency as

  Wi = dθ /dt

  Wi dt = dθ

  ∫dθ= ∫Wi dt

  Substituting the value of Wi from equation (i) in above equation;

  θ= ∫ (Wc+kVm cos Wmt ) dt

  θ= Wct+ (kVm/Wm) sin Wmt

  θ= Wct+Mf sin Wmt ----------------------------------------(iii)

  where Mf (modulation Index)= (kVm/Wm)

  Substituting the value of θ from equation (iii) in equation (ii);

  Vfm=Vc sin (Wct+Mf sin Wmt)

  Above is the equation of frequency modulation.