Lecture 18-19: Linear Modulations Aliazam Abbasfar

Outline Amplitude Modulation DSB/AM/SSB/VSB

DSB modulation Double sideband modulation x o (t) = A c x(t) cos(  c t) Lowpass signal x I (t) = x(t), x Q (t) = 0 A(t), (t)= ? X o (t) = ½ A c [ X(f-f c ) + X(f+f c ) ] Symmetric spectrum around f c Bandwidth : 2W Upper and lower sidebands Transmitted power G Xo (t) = ¼ A c 2 [ G X (f-f c ) + G X (f+f c ) ] P Xo = ½ A c 2 P X = P c P X P c = Unmodulated carrier power

DSB demodulation Coherent demodulation y(t) = 2A cos( c t) x o (t) = A Ac x(t) + A Ac x(t) cos(2 c t) Filter out x(t) cos(2 c t) 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 x o (t) = A c (1+x(t)) cos(  c t)  : modulation index (1+x(t)) > 0 (<= 1 if |x(t)|<1) Signal DC value = 0 Lowpass signal x I (t) = 1+x(t), x Q (t) = 0 A(t) = 1+x(t), (t)= 0 X o (t) = ½A c [(f-f c ) + (f+f c ) ] + ½ A c [ X(f-f c ) + X(f+f c ) ] Symmetric spectrum around f c Additional tone at f c Transmitted power P Xo = ½ A c 2 (1+  ) P X = P c (1+  P X ) Efficiency:  AM =   P X / (1+  P X ) <= 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 X o (f) = X(f-f c )u(f-f c ) ; f>0 Bandwidth : W Spectrally efficient Not symmetric Transmitted power P Xo = ½ P DSB = ½ P c P X Good for FDM Low bandwidth Low power

SSB modulation - 2 Lowpass signal x I (t) = ½ x(t), x Q (t) =  ½ x(t) IQ modulator Weaver modulator

SSB demodulation Coherent demodulation y(t) = 2A cos( c t) x o (t) = ½ A A c x(t) [1+cos(2 c t)] - ½ A A c x(t) sin(2 c t) 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( c t) and sin( c t) 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 X o (f) = X(f-f c ) H(f) ; f>0 Bandwidth > W Not symmetric Transmitted power P SSB < P Xo < P DSB Used in video broadcast Low bandwidth Keeps low frequencies Low power

VSB modulation H(f) has odd symmetry around f c H(f) = (1 +j H VSB )/2 H VSB is a realizable filter Lowpass signal x I (t)= ½ x(t), x Q (t) =  ½ x(t)*h VSB (t) IQ modulator

VSB demodulation Coherent demodulation y(t) = ½ A A c x(t) [1+cos(2 c t)] - ½ A A c x’(t) sin(2 c t) 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

Reading Carlson Ch. 4.2, 4.3 and 4.4 Proakis 2.5, 3.1, 3.2