EE354 : Communications System I

EE354 : Communications System I 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 = PcPX • 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 PcPX • 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), xQ(t) =  ½ x(t)*hVSB(t) • IQ modulator HVSB

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

EE354 : Communications System I