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Topic 2

Topic 2. Amplitude Modulation. General Definition:. The amplitude of a sinusoidal carrier is varied in accordance with an message signal. Carrier: c(t)=A c cos(2πf c t) Message: m(t) with band -width W k a (volt -1 ): called Amplitude sensitivity

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Topic 2

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  1. Topic 2 Amplitude Modulation

  2. General Definition: The amplitude of a sinusoidal carrier is varied in accordance with an message signal Carrier: c(t)=Ac cos(2πfct) Message: m(t) with band -width W ka (volt-1): called Amplitude sensitivity Envelop of s(t) has the same shape as m(t) while: a) |kam(t)|<1 b) fc>>W

  3. Spectrum of AM signal

  4. Recall • Complex represent of real signals Where • Fourier transform in order calculating that is magnitude spectrum and phase spectrum of signal

  5. Recall • When signal is not period: T→∞ • Spacing of spectral lines 1/T→0 (spectrum become continuous) • Formula: (fn→f (Hz), ( )→V(f)df (V)) become • If there is frequency carrier f0 (bandpass signal), then V(f) is equivalent complex represent

  6. Limitations of AM and modified schemes • Amplitude modulation is wasteful of power: • Amplitude modulation is wasteful of bandwidth: • Modified schemes: • DSB-SC. • SSB

  7. Spectrum of DSB-SC

  8. Generation of DSB-SC

  9. Demodulation of DSB-SC

  10. Costa receiver

  11. Multiplexing of quadrate - carriers

  12. M(f) f XDSB(f) f HBPF(f) f XSSB(f) f Spectrum of SSB -W W

  13. m(t)cosωct XDSB(t) m(t) m(t) BPF XSSB(t) ∑ XSSB(t) -π/2 -π/2 m(t)sinωct Generation of SSB • Frequency .Phase-Shift Method Discrimitation Method • Minor produces upper-sideband • Plus produces lower-sideband

  14. XSSB(f) d(t) f -fc fc cos2πfct XSSB(t) LPF D(f) y(t) LPF -2fc -fc fc f Y(f) f Demodulation of SSB

  15. BPF ω2 Frequency Translation

  16. M1(f) m1(t) m1(t) BPF LPF ω1 M2(f) ω1 m2(t) BPF m2(t) ∑ Channel LPF M3(f) ω2 ω2 m3(t) BPF LPF m3(t) ω3 ω3 ω1 ω2 ω3 Multiplexing

  17. Problems • a) Verify that the message signal m(t) is recovered from a modulation DSB signal by first multiplying it by a local sinusoidal carrier and then passing the resultant signal through a low-pass filter as shown in Fig 2-7

  18. Probems b) Evaluate the effect of a phase error in local oscillator on synchronous DSB demodulation. c) Evaluate the effect of a small frequency error in local oscillator on synchronous DSB demodulation

  19. m(t)cosωct m(t) ∑ XSSB(t) -π/2 -π/2 m(t)sinωct Problems 2. Using the single-tone modulation signal m(t)=cosωmt verify that the output of the SSB generator of Fig is indeed an SSB signal and show that an upper-sideband (USB) or a lower-sideband (LSB) signal results from subtraction or addition at the summer

  20. d(t) cos2πfct XSSB(t) LPF y(t) Problems 3. Show that an SSB signal can be demodulated by the synchronous detector of fig : a) By sketching the spectrum of signal at each point b) By the time-domain expression of the signals at each point

  21. m(t)cosωct m(t) ∑ XSSB(t) -π/2 -π/2 m(t)sinωct Problems 4. Show that the system despised in fig..can be used to demodulate an SSB signal

  22. Problems 5. Sketch the ordinary AM signal for a singe-tone modulation with modulation index of μ=0.5 and μ=1 (μ=|min(m(t))|/A). Here ka=1 • The efficiency η of ordinary AM is defined as the percentage of the total power by the sideband, that is: Where Ps is the power carried by the sideband and Pt is the total power of AM signal • Find η for μ=0.5 • Show that for a singe-tone AM, ηmax is 0.33 percent at μ=1

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