Transcript session 15-16

Lecture 15,16:
Linear Modulations
Aliazam Abbasfar
Outline
 Amplitude Modulation
 DSB/AM/SSB/VSB
DSB modulation
 Double sideband modulation
 xo(t) = Ac x(t) cos(wct)
 Lowpass signal
 xI(t) = x(t), xQ(t) = 0
 A(t), Q(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 Ac2 [ GX(f-fc) + GX(f+fc) ]
 PXo = ½ Ac2 PX = Pc PX
 Pc = Unmodulated carrier power
DSB demodulation
 Coherent demodulation
 y(t) = 2A cos(wct) xo(t)
= A Ac x(t) + A Ac x(t) cos(2wct)
 Filter out x(t) cos(2wct) 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(f) x(t)
 Lower gain
 Frequency offset (Df)
 z(t) = K cos(2pDf t) x(t)
 Distortion
AM modulation
 Amplitude modulation
 xo(t) = Ac (1+mx(t)) cos(wct)
 m : modulation index
 (1+mx(t)) > 0 (m<= 1 if |x(t)|<1)
 Signal DC value = 0
 Lowpass signal
 xI(t) = 1+mx(t), xQ(t) = 0
 A(t) = 1+mx(t), Q(t)= 0
 Xo(t) = ½Ac [d(f-fc) + d (f+fc) ] +
½m Ac [ X(f-fc) + X(f+fc) ]
 Symmetric spectrum around fc
 Additional tone at fc
 Transmitted power
 PXo = ½ Ac2 (1+m2) PX = Pc (1+m2 PX)
 Efficiency: hAM = m2PX / (1+m2 PX) <= 50%
AM demodulation
 Envelope detection
 Very simple circuits
 Using non-linear circuits
 Half-wave/full-wave rectifier
 Good for radio broadcast
 Expensive 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 - 2
 Lowpass signal
 xI(t) = ½ x(t), xQ(t) =  ½ x(t)
 IQ modulator
 Weaver modulator
SSB demodulation
 Coherent demodulation
 y(t) = 2A cos(wct) xo(t)
= ½ A Ac x(t) [1+cos(2wct)] - ½ A Ac x(t) sin(2wct)
 Filter out high freq. terms by a LPF

z(t) = ½ A Ac x(t) = K x(t)
 Phase offset
 z(t) = K cos(f) x(t) + K sin(f) x(t)
 Lower gain + distortion
 Frequency offset (Df)
 z(t) = K cos(2pDf t) x(t) + K sin(2pDf t) x(t)
 Distortion
 IQ demodulator
 Multiply with both cos(wct) and sin(wct)
 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 modulation
 H(f) has odd symmetry around fc
 H(f) = (1 +j HVSB )/2
 HVSB is a realizable filter

 Lowpass signal
 xI(t)= ½ x(t),
 IQ modulator
xQ(t) =  ½ x(t)*hVSB(t)
VSB demodulation
 Coherent demodulation
 y(t) = ½ A Ac x(t) [1+cos(2wct)] - ½ A Ac x’(t) sin(2wct)
 Filter out high frequency terms by a LPF

z(t) = ½ A Ac x(t) = K x(t)
 Phase offset
 z(t) = K cos(f) x(t) + K sin(f) x’(t)
 Lower gain + distortion
 Frequency offset (Df)
 z(t) = K cos(2pDf t) x(t) + K sin(2pDf t) x(t)
 Distortion
 Use IQ demodulator
Reading
 Carlson Ch. 4.2, 4.3 and 4.4
 Proakis 2.5, 3.1, 3.2