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# communication system Chapter 5

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### communication system Chapter 5

1. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 12. Example 5.1 p-212 12
13. 13. Example 5.1 p-212 13
14. 14. Transmission Bandwidth of FM Signal 14
15. 15. Transmission Bandwidth of FM Signal 15
16. 16. Transmission Bandwidth of FM Signal 16
17. 17. Transmission Bandwidth of FM Signal 17
18. 18. Transmission Bandwidth of FM Signal Summary of bandwidth relations 18
19. 19. Example-1 19
20. 20. Example-1 20
21. 21. Phase Modulation 21
22. 22. Phase Modulation 22
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33. 33. Problem-5.3-2 33
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37. 37. Problem: 37
38. 38. Solution: Input Signal m(t) Signal at point “b” Signal at point “c” Signal at point “d” Signal at point “e” 38