0
Derive the expression for frequency modulated wave.

Subject : Principle of Communication Engineering

Topic : Angle modulation and demodulation

Difficulty : High

pce(44) • 12k  views
0  upvotes
0
  • 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.

0  upvotes
Please log in to add an answer.

Next up

Read More Questions

If you are looking for answer to specific questions, you can search them here. We'll find the best answer for you.

Search

Study Full Subject

If you are looking for good study material, you can checkout our subjects. Hundreds of important topics are covered in them.

Know More