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Communications 1

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Communications 1

Communications 1

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1. Communications 1 Hebat-Allah M. Mourad Professor Cairo University Faculty of Engineering Electronics & Communications Department

2. Text Book • Modern Digital and Analog Communication Systems Third edition B.P.Lathi - Chapters: 4 – 5 – 6 (1st term) 7 -11 (2nd term) • Communication systems, S. Haykin, John Wiley and Sons inc., 4th edition

3. Course Contents Introduction to modulation Different analog modulation techniques: Amplitude, Frequency and Phase -Transformation from analog to digital: Sampling, Quatization, PCM, DM, ADM -Introduction to satellite and mobile communications

4. Why Modulation? Mainly for two reasons 1 - Practical antenna dimensions lightvelocity Wavelengthfrequency Dimension is in the order of a quarter wavelength

5. Baseband Power Spectrum

6. Why Modulation? 2- Multiplexing Better utilization of the available frequency band Spectrum M3(f) M1(f) M2(f) MN(f) Frequency

7. Basic Modulation Types • s (t) = A (t) cos [Ө (t) ] • Ө (t) = ω t + φ (t) • ‘ Ac cos ωc t ‘ is called un-modulated carrier • Analog Modulation • Digital Modulation

8. m(t) modulated signal: s(t) Modulator Acos(2πfct+φ) Un-modulated carrier

9. Modulation Types (Analog Modulation)

10. Modulation Types (Digital Modulation)

11. Analog Modulation • Different analog modulation techniques • For each type:- - Mathematical presentation * Bandwidth * transmitted power - Modulators - Demodulators - Applications

12. 1- Amplitude Modulation (A.M)Conventional Amplitude Modulation • Consider a sinusoidal Carrier wave c(t) the un-modulated carrier. c(t) = Ac cos 2 π fc t = Ac cos ωc t Ac = carrier amplitude fc = carrier frequency • A.M is the process in which the amplitude of the carrier wave c(t) is varied about a mean value, linearly with the base band signal

13. 1-Amplitude Modulation • s(t) = Ac cos 2 π fc t + m(t) cos 2 π fc t = [Ac + m(t) ] cos 2 π fc t = modulated signal S(ω) = π Ac [ δ(ω + ωc) + δ(ω - ωc) ] + (1/2) [ M(ω + ωc) + M(ω - ωc) ]

14. 1- Amplitude Modulation • s(t)= un-modulated carrier + upper side band (U.S.B) + lower sideband (L.S.B.) • Bandwidth (B.W.) = 2W | S(ω) | | M(ω) | - ωc 0 + ωc - W 0 W

15. Condition : Ac + m(t) > 0 for all t Ac ≥ m(t)min (absolute –ve peak amp.) • Define: μ = modulation index = m(t)min / Ac • 0 ≤ μ ≤ 1 since there is no upper bound on Ac and Ac ≥ m(t)min • The envelope has the same shape of m(t) • Over modulation : μ > 1 • μ x 100 = percentage modulation

16. 1- Amplitude Modulation • Example: Let m(t) = Am cos 2 π fm t single tone signal Then s (t) = Ac cos 2 π fc t + Am cos 2 π fm t cos 2 π fc t s (t) = Ac [1 + μ cos 2 π fm t ] cos 2 π fc t μ = Am / Ac = modulation factor = modulation index

17. 1- Amplitude Modulation | S(ω) | πAc | M(ω) | π πμAc/2 ω - ωm ω 0 ωm fc -ωc-ωm ωc+ωm -ωc -ωc+ωm ωc-ωm - s (t) = Ac [1 + μ cos 2 π fm t ] cos 2 π fc t - B.W. = 2 fm - To get the power or energy : divide S(ω) by 2π, square the modulus and add all terms

18. 1- Amplitude Modulation • S(ω) = πAc [ (ω - ωc) + (ω - ωc) ] + (π Acμ/2) [ (ω +(ωc + ωm)) ] + (π Acμ/2) [ (ω -(ωc + ωm)) ] + (π Acμ/2) [ (ω -(ωc - ωm)) ] + (π Acμ/2) [ (ω +(ωc - ωm)) ]

19. 1- Amplitude Modulation • Un-modulated Power = carrier power= Ac2 / 2 • U.S.B power = L.S.B. power = μ2 Ac2 / 8 • Total side bands power = μ2 Ac2 / 4 • Pt = Pc + Ps = (Ac2 / 2) + (μ2 Ac2 / 4) = Pc [ 1+ (μ2 /2) ] η = Side band power = μ2 total power 2+ μ2

21. 1- Switching Modulators By multiplying the signal by any periodic waveform whose fundamental is ωc . This periodic function can be expressed using F.S. as:

22. Ψ(t) is a periodic pulse train • Ex: ring modulator,bridge modulators (different electronic circuits performing the switching operation)

23. For c >> m(t) , the diode acts as a switch controlled mainly by the value of ‘c’ Vbb’(t) = c cosωct + m(t) for c > 0 Vbb’(t) = 0 for c < 0

24. (1/W) > RC > Tc

25. Non-coherent demodulator

26. Amplitude Modulation • Virtues, limitations and modifications of A.M. • Advantages: Ease of Modulation and demodulation ( cheap to build the system) • Disadvantages - Waste of power. - Waste of B.W. • We trade off system complexity to overcome these limitations - DSB-SC - DSB-QAM - SSB - VSB

27. 2- Double Side bands Suppressed Carrier (DSB-SC) • The carrier component doesn’t appear in the modulated wave. • s(t) = m(t) cos ( 2 ω ct) • S(ω) = (1/2) [ M(ω - ωc) + M(ω - ωc) ] • Total power = side bands power = (1/2) m2(t) • B.W = 2W

28. DSB-SC Modulators • 1- Switching Modulators By multiplying the signal by any periodic waveform whose fundamental is ωc . This periodic function can be expressed using F.S. as:

29. Ψ(t) is a periodic pulse train • Ex: ring modulator,bridge modulators (different electronic circuits performing the switching operation)

30. DSB-SC Modulators x(t) m(t) • 2- Multiplier modulators • x(t)= m(t) cos 2 π fc t • X(f) = (½)[ M(f+fc) + M(f-fc)] X cos 2 πfct

31. DSB-SC Modulators • 3- Non linear modulators

32. DSB-SC Demodulators • Coherent (synchronous ) detection

33. Main problem : the carrier at the receiver must be synchronized in frequency and phase with the one at the transmitter. • Otherwise we can have serious problems in the demodulation as will be seen.

34. DSB-SC Demodulators m(t) cosωct eo(t) X L.P.F ~ cos[ (ωc+ ∆ ω )t + φ] Frequency shift Phase shift

35. DSB-SC Demodulators • eo(t) = m(t) cos ωct cos[ (ωc+ ∆ ω )t + φ] = (1/2) m(t) cos [ (∆ ω t) + φ] + cos [ (2 ωc +∆ ω) t + φ] • Second term will be suppressed by the L.P.F. • If ∆ ω =0 and φ = 0 eo(t) = (1/2) m(t) ( no frequency or phase error )

36. DSB-SC Demodulators • If ∆ω=0 eo(t) = (1/2) m(t) cos φ • If φ = constant, eo(t) is proportional to m(t) • Problems for φ either varying with time or equals to ± (π/2) • The phase error may cause attenuation of the output signal without causing distortion as long as it is constant.

37. DSB-SC Demodulators • If φ = 0 , ∆ω ≠ 0 eo(t) = (1/2) m(t) cos ∆ω t (Donald Duck) - The output is multiplied by a low frequency sinusoid, this causes attenuation and distortion of the output signal. - This could be solved by using detectors by square law device, or phase locked loops (PLL) (ex: Costas loop)

38. Carrier Acquisition in DSB-SC • Signal squaring method x(t) m(t) cos ωct S.L.D N.B.F(2fc) Freq div. by 2

39. (1/2)Accos φ m(t) Product modulator L.P.F cos(2πfct+φ) Phase Discriminator V.C.O -90 phase shift K sin 2 φ Product modulator L.P.F (1/2)Acsin φ m(t) Ac cos(2πfct)m(t) DSB-SC Demodulators • Costas Receiver

40. DSB-SC Demodulators • The L.O. freq. is adjusted to be the same as fc • Suppose that the L.O. phase is the same as the carrier wave: ‘I’ o/p = m(t) ‘Q’ o/p = 0 • Suppose that the L.O. phase drifts from its proper value by a small angle ‘φ’ radians. • ‘I’ o/p will be the same and ‘Q’ o/p will be proportional to sin φ ~ φ (for small φ)