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