- 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

depends on the instantaneous amplitude of modulating signal i.e*Wc**δ=kVm cos Wmt*where

frequency deviation sensitivity of FM*k=*Again, instantaneous frequency is:

*Wi=Wc+δ*---------------------(i)*Wi=Wc+kVm cos Wmt*The frequency modulated signal is represented mathematically as

------------------------(ii)*Vfm=Vc sin θ*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*----------------------------------------(iii)*θ= Wct+Mf sin Wmt*where

(modulation Index)=*Mf**(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.