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  • 1. Communication System Ass. Prof. Ibrar Ullah BSc (Electrical Engineering) UET Peshawar MSc (Communication & Electronics Engineering) UET Peshawar PhD (In Progress) Electronics Engineering (Specialization in Wireless Communication) MAJU Islamabad E-Mail: ibrar@cecos.edu.pk Ph: 03339051548 (0830 to 1300 hrs) 1
  • 2. Chapter-5 Angle Modulation • What is Angle modulation • What is the difference between frequency and phase modulation • What is direct and indirect modulation • Deviation sensitivity, phase deviation, modulation index • Bandwidth of angle-modulated wave 2
  • 3. Angle Modulation • Idea: The angle θ (t) of the carrier A Cos (Wc + θ (t))is modulated according to the modulating signal m(t): • The amplitude A remains constant. • This modulation type is called Angle modulation 3
  • 4. Angle Modulation Generalized sinusoidal function is given by: ϕ (t ) = A cos θ (t ) θ (t) = instantaneous phase (radians) Question: What is the instantaneous frequency? 4
  • 5. Angle Modulation A carrier can be represented as: ϕ (t ) = A cos θ (t ) dθ wi (t ) = dt t θ i (t ) = ∫ wi (t )dt 0 ϕ (t ) = angle modulated wave (Volt) A = peak carrier amplitude (Volt) wi = instantaneous angular frequency (rad/sec) θ i = instantaneous phase (radians) 5
  • 6. Phase Modulation (PM) The instantaneous phase of a harmonic carrier signal is varied in such a way that the instantaneous phase deviation i.e. the difference between the instantaneous phase and that of the carrier signal is linearly related to the size of the modulating signal at a given instant of time. In PM the angle θ (t ) varies linearly with m(t) θ i (t ) = wc t + k p m(t ) [ ϕ PM = A cos wc t + k p m(t ) wi (t ) = [ ] ] dθ i (t ) d wc t + k p m(t ) dm(t ) = = wc + k p dt dt dt Kp is the phase deviation sensitivity (rad/Volt) 6
  • 7. Frequency Modulation (PM) The frequency of a harmonic carrier signal is varied in such a way that the instantaneous frequency deviation i.e. the difference between the instantaneous frequency and the carrier frequency is linearly related to the size of the modulating signal at a given instant of time. If wi is varied linearly with the modulating signal we have FM and instantaneous frequency wi is given by: wi (t ) = wc + k f m(t ) t θ i (t ) = ∫ w (t )dt = w t + ∫ k i 0 ϕ FM = t c f m(t )dt 0 t   A cos  wc t + ∫ k f m(t ) 0   Kf is the frequency deviation sensitivity  rad / s   Volt    7
  • 8. Frequency Modulation (PM) PM θi (t ) = wc t + k p m(t ) ϕPM = A cos wc t + k p m(t ) [ ] wi (t ) = dθi (t ) d wc t + k p m(t ) dm(t ) = = wc + k p dt dt dt [ ] FM wi (t ) = wc +k f m(t ) t θi (t ) = ∫ w (t )dt = w t +∫ k i 0 ϕFM = t c f m(t ) dt 0 t   A cos wc t + ∫ k f m(t )  0   TASK: Make block diagrams of PM and FM modulators 8
  • 9. PM Modulator θi (t ) = wc t +k p m(t ) ϕPM = A cos wc t +k p m(t ) wi (t ) = PM d wc t +k p m(t ) dθi (t ) dm(t ) = = wc +k p dt dt dt [ Modulating signal source [ Phase modulator ] ] PM wave Direct A cos wc t Modulating signal source Differentiato r Frequency modulator A cos wc t PM wave Indirect 9
  • 10. FM Modulator FM wi (t ) = wc +k f m(t ) t θ (t ) = i t ∫w (t )dt =w t +∫k i c 0 ϕ = FM f m(t ) dt 0   A cos  c t +∫k f m(t )  w 0   Modulating signal source t Frequency modulator FM wave Direct A cos wc t Modulating signal source Integrator Phase modulator A cos wc t FM wave Indirect 10
  • 11. Frequency modulation of single frequency signal PM: m(t ) = Am cos( wmt ) ϕ PM (t ) = A cos( wc t + k p Am cos( wmt )) FM: m(t ) = Am cos( wmt ) t   ϕ FM (t ) = A cos  wc t + ∫ k f Am cos( wmt )dt  0   k f Am   = A cos  wc t + sin( wmt ) wm   11
  • 12. Example 5.1 p-212 12
  • 13. Example 5.1 p-212 13
  • 14. Transmission Bandwidth of FM Signal 14
  • 15. Transmission Bandwidth of FM Signal 15
  • 16. Transmission Bandwidth of FM Signal 16
  • 17. Transmission Bandwidth of FM Signal 17
  • 18. Transmission Bandwidth of FM Signal Summary of bandwidth relations 18
  • 19. Example-1 19
  • 20. Example-1 20
  • 21. Phase Modulation 21
  • 22. Phase Modulation 22
  • 23. 23
  • 24. 24
  • 25. 25
  • 26. 26
  • 27. 27
  • 28. 28
  • 29. 29
  • 30. 30
  • 31. 31
  • 32. 32
  • 33. Problem-5.3-2 33
  • 34. 34
  • 35. 35
  • 36. 36
  • 37. Problem: 37
  • 38. Solution: Input Signal m(t) Signal at point “b” Signal at point “c” Signal at point “d” Signal at point “e” 38