lecture 18-19: linear modulations aliazam abbasfar
Post on 28-Dec-2015
225 Views
Preview:
TRANSCRIPT
Lecture 18-19: Linear Modulations
Aliazam Abbasfar
OutlineAmplitude Modulation
DSB/AM/SSB/VSB
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
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
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%
AM demodulationEnvelope detection
Very simple circuits
Using non-linear circuitsHalf-wave/full-wave rectifier
Good for radio broadcastExpensive TX (only 1)Cheap RXs (many)
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
SSB modulation - 2Lowpass signal
xI(t) = ½ x(t), xQ(t) = ½ x(t)
IQ modulator
Weaver modulator
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
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
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
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
ReadingCarlson Ch. 4.2, 4.3 and 4.4
Proakis 2.5, 3.1, 3.2
top related