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Lecture 18-19: Linear Modulations
Aliazam Abbasfar
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OutlineAmplitude Modulation
DSB/AM/SSB/VSB
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DSB modulation Double sideband modulation
xo(t) = Ac x(t) cos(ct)
Lowpass signal xI(t) = x(t), xQ(t) = 0 A(t), (t)= ?
Xo(t) = ½ Ac [ X(f-fc) + X(f+fc) ] Symmetric spectrum around fc Bandwidth : 2W Upper and lower sidebands
Transmitted power GXo(t) = ¼ Ac
2 [ GX(f-fc) + GX(f+fc) ] PXo = ½ Ac
2 PX = Pc PX
Pc = Unmodulated carrier power
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DSB demodulation Coherent demodulation
y(t) = 2A cos(ct) xo(t) = A Ac x(t) + A Ac x(t) cos(2ct) Filter out x(t) cos(2ct) by a LPF
z(t) = A Ac x(t) = K x(t)
Coherent demodulation Phase and frequency of the carrier is known
Phase offset z(t) = K cos() x(t) Lower gain
Frequency offset (f) z(t) = K cos(f t) x(t) Distortion
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AM modulation Amplitude modulation
xo(t) = Ac (1+x(t)) cos(ct) : modulation index (1+x(t)) > 0 (<= 1 if |x(t)|<1) Signal DC value = 0
Lowpass signal xI(t) = 1+x(t), xQ(t) = 0 A(t) = 1+x(t), (t)= 0
Xo(t) = ½Ac [(f-fc) + (f+fc) ] + ½ Ac [ X(f-fc) + X(f+fc) ]
Symmetric spectrum around fc Additional tone at fc
Transmitted power PXo = ½ Ac
2 (1+) PX = Pc (1+ PX)
Efficiency: AM = PX / (1+ PX) <= 50%
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AM demodulationEnvelope detection
Very simple circuits
Using non-linear circuitsHalf-wave/full-wave rectifier
Good for radio broadcastExpensive TX (only 1)Cheap RXs (many)
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SSB modulation Single sideband modulation
Send only one of the sidebands LSSB or USSB Filter out other sideband Signal usually has a DC hole
Xo(f) = X(f-fc)u(f-fc) ; f>0 Bandwidth : W Spectrally efficient Not symmetric
Transmitted power PXo = ½ PDSB = ½ Pc
PX
Good for FDM Low bandwidth Low power
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SSB modulation - 2Lowpass signal
xI(t) = ½ x(t), xQ(t) = ½ x(t)
IQ modulator
Weaver modulator
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SSB demodulation Coherent demodulation
y(t) = 2A cos(ct) xo(t) = ½ A Ac x(t) [1+cos(2ct)] - ½ A Ac x(t) sin(2ct) Filter out high freq. terms by a LPF
z(t) = ½ A Ac x(t) = K x(t)
Phase offset z(t) = K cos() x(t) + K sin() x(t) Lower gain + distortion
Frequency offset (f) z(t) = K cos(f t) x(t) + K sin(f t) x(t) Distortion
IQ demodulator Multiply with both cos(ct) and sin(ct) Complex demodulator No distortion
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VSB modulation Vestigial sideband modulation
Send one of the sidebands and and part of other Filter out part of other sideband Keeps signal DC components
Xo(f) = X(f-fc) H(f) ; f>0 Bandwidth > W Not symmetric
Transmitted power PSSB < PXo < PDSB
Used in video broadcast Low bandwidth Keeps low frequencies Low power
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VSB modulationH(f) has odd symmetry around fc
H(f) = (1 +j HVSB )/2
HVSB is a realizable filter
Lowpass signalxI(t)= ½ x(t), xQ(t) = ½ x(t)*hVSB(t)
IQ modulator
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VSB demodulation Coherent demodulation
y(t) = ½ A Ac x(t) [1+cos(2ct)] - ½ A Ac x’(t) sin(2ct) Filter out high frequency terms by a LPF
z(t) = ½ A Ac x(t) = K x(t)
Phase offset z(t) = K cos() x(t) + K sin() x’(t) Lower gain + distortion
Frequency offset (f) z(t) = K cos(f t) x(t) + K sin(f t) x(t) Distortion
Use IQ demodulator
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ReadingCarlson Ch. 4.2, 4.3 and 4.4
Proakis 2.5, 3.1, 3.2