Chapter 9. Amplitude Modulation

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Gerard Marsh
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1 Chapter 9. Amplitude Modulation 1

2 Goals Modulate and demodulate the double sideband-suppressed carrier (DSB-SC) amplitude modulation (AM) signals. Investigate the effects of frequency and phase errors on the demodulation performance. Modulate and demodulate AM signals by using the sampling and band pass filter (BPF) technique.

3 Double side-band suppressed carrier(dsb-sc) Amplitude modulations(am) DSB-SC, DSB-LC, SSB, VSB, etc. DSB-SC Modulated signal (tt)=ff tt cos(ωω cc tt) ff tt : information signal cos ωω cc tt : carrier signal, ωω cc = carrier frequency. Transmitter(modulator) structure ff tt (tt)=ff tt cos(ωω cc tt) cos ωω cc tt Spectrum of DSB-SC F tt = F tt = F ff tt cos(ωω cc tt) = 1 FF ωω + ωω cc + 1 FF ωω ωω cc Recall that multiplying sinusoid = frequency shift 3

4 Double side-band suppressed carrier(dsb-sc) DSB-SC Receiver (demodulator) structure (tt)=ff tt cos(ωω cc tt) gg(tt) LPF 1 ff tt : demodulated signal [CH19.B9] Proof: cos ωω cc tt :local carrier signal gg tt = tt cos ωω cc tt = ff tt cos(ωω cc tt) = ff(tt) 1+cos(ωω cctt) = 1 ff tt + 1 ff tt cos(ωω cctt) GG(ωω)= 1 FF ωω FF ωω ωω cc FF ωω + ωω cc Here, let us define LPF[x]: LPF[x] Ideal(Perfectly flat magnitude response within BW, no delay) LPF output of x. Then, LPF[GG(ωω)]= 1 FF ωω FF ωω ωω cc = 1 FF ωω FF ωω + ωω cc LPF gg tt = LPF 1 ff tt + 1 ff tt cos(ωω cctt) = 1 ff(tt) 4

5 Waveforms and Spectra of DSB-SC cos ωω cc tt LPF [CH9.1F4~1F6]If the BW of LPF is larger than W, noise power in the demodulated signal increases. [CH9.1F4~1F6]If the BW of LPF is smaller than W, the demodulated information is distorted. 5

6 Effect of phase error What if there exists a phase error between the carrier and the local carrier? Say, local carrier =cos ωω cc tt + θθ not cos ωω cc tt. Then, gg tt = tt cos ωω cc tt + θθ = ff tt cos(ωω cc tt)cos ωω cc tt + θθ = ff(tt) 1 cos ωω cctt + θθ + cos θθ = 1 ff tt cos ωω cctt + θθ + 1 ff tt cos θθ [CH9.A4] the demodulated signal(lpf output in the receiver) is given as: LPF gg tt = LPF 1 ff(tt) cos ωω cctt + θθ + 1 ff(tt)cos θθ =LPF 1 ff(tt) cos ωω cctt + θθ +LPF 1 ff(tt)cos θθ = 1 ff tt cos(θθ) Phase error results in decreased amplitude of the demodulated signal by the factor of cos(θθ). Special case: if θθ = ππ, then the signal disappears. 6

7 Effect of phase error [CH9.B]Consider the background noise nn tt is added to the received signal ff tt cos(ωω cc tt): Then, the multiplier output in the receiver gg tt = ff tt cos ωω cc tt + nn(tt) cos ωω cc tt + θθ = ff tt cos ωω cc tt cos ωω cc tt + θθ + nn(tt) cos ωω cc tt + θθ nn tt cos ωω cc tt + θθ = the noise component in gg tt. We denote nn θθ tt = nn tt cos ωω cc tt + θθ. [CH9.B10a] ACF of nn θθ tt IF ττ=0, RR nnθθ ττ = 0 = lim lim TT TT TT TT TT nn tt cos ωωcc tt+θθ dddd TT TT Two sample cases of nn θθ tt nn tt cos ωωcc tt+θθ nn tt cos ωω cc tt+θθ dddd =Power of nn θθ tt nn tt TT θθ = 0 = θθ = ππ/3 cos ωω cc tt + θθ nn θθ tt = nn tt cos ωω cc tt + θθ These samples illustrate that Power of nn θθ tt = Power of nn tt Power of cos(ωωtt+θθ), where power of cos(ωωtt+θθ) =1/ irrespective of θθ. RR nnθθ ττ = 0 =0.5 RR nn ττ = 0 7

8 Effect of phase error [CH9.B10a] (continued) ACF of nn θθ tt RR nnθθ ττ = Correlation between nn tt cos ωω cc tt + θθ and nn tt + ττ cos(ωω cc (tt + 8

9 Effect of phase error Demodulated signal (LPF output) = signal term + noise term = 1 ff tt cos(θθ) + LPF[nn θθ tt ] Signal amplitude decreases by the factor of cos θθ Signal power decreases by the factor of cos θθ On the other hand, noise power is constant irrespective of θθ [CH9.B4] Signal to Noise power Ratio (SNR) Signal power SNR(θθ) = Noise power =cos θθ SNR(θθ = 0) 1 Power of ff tt cos(θθ) = Power of LPF[nn θθ tt ] = cos θθ Power of 1 ff tt Power of LPF[nn θθ tt ] Phase error results in SNR decrease by the factor of cos θθ [CH9.B5] SNR loss =cos θθ =10llllll 10 cos θθ db 9

10 Effect of frequency error Now we consider the case when local carrier =cos ωω cc + ωω tt not cos ωω cc tt. We can rewrite local carrier = cos ωω cc tt + ωωtt =cos ωω cc tt + θθ where θθ= ωωtt. This implies that the frequency error results in linearly increasing phase error. [CH9.C1] So, we only need to change θθ into ωωtt in all the derivations for the phase error case. For example : demodulated signal= 1 ff tt cos( ωωtt) So, Signal to Noise power Ratio (SNR) SNR( ωωtt) =cos ωωtt SNR ωω = 0 SNR is time varying according to cos ωωtt. [CH9.C,C3,C6,C7] Even with a very tiny frequency error, cos ωωtt periodically changes from 0 to 1. [CH9.C,C3,C6,C7] Whenever cos ωωtt approaches 0, SNR instantaneously becomes 0. Critical problem! 10

11 Generating AM signal without Oscillator To generate carrier signal cos(ωω cc tt), we need an oscillator which is expensive. [CH9.3B] DSB-SC is equal to frequency shifting to center frequencies = ±ωω cc Recall, in chapter 7, frequency shifting is possible by sampling and BPF technique if we properly set the sampling frequency and properly design BPF. Sampling of ff tt by a periodic signal pp(tt) BPF nω 0 P1 ω 0 P n P 0 P 1 nω P 0 P 1 ω P n 0 0 BPF output =Spectrum of DSB-SC nω 0 P 0 P1 Pn BPF output spectrum=pp nn XX ωω + nnωω 0 + PP nn XX ωω nnωω 0 BPF output signal= ff(tt) PP nn cos nnωω 0 tt + θθ PPnn = DSB-SC modulated signal with a carrier signal = PP nn cos nnωω 0 tt + θθ PPnn [CH9.3B4] Parameter setting Condition 1: nnωω 0 =carrier frequency ωω cc, n=positive integer Condition : The sampling frequency ωω 0 Bandwidth of ff tt. Possible sampling frequency ωω 0 SSSSSSSSSSSS oooooo oooo ωω cc, ωω cc cc cc 3 4 under the condition 11

Chapter 10. Quadrature Multiplexing and Frequency Division Multiplexing

Chapter 10. Quadrature Multiplexing and Frequency Division Multiplexing 1 Goals Design a modulation and demodulation system for quadrature multiplexing (QM) amplitude modulation (AM). Design a frequency