TELE3113 Analogue and DigitalCommunications

DSB-SC Modulation

Wei Zhang

w.zhang@unsw.edu.au

School of Electrical Engineering and Telecommunications

The University of New South Wales

DSB-SC Modulation (1)

Double sideband-suppressed carrier (DSB-SC) modulation

consists of the product of the message signal m(t) and the

carrier wave c(t), as given by

s(t) = c(t)m(t)

= Ac cos(2πfct)m(t).

The Fourier transform of the DSB-SC modulated signal is

S(f) =Ac

2[M(f − fc) + M(f + fc)]

where we used the relation:

m(t) exp(j2πfct) ⇔ M(f − fc) Shifting PropertyTELE3113 - DSB-SC Modulation. August 5, 2009. – p.1/10

DSB-SC Modulation (2)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−1

−0.5

0

0.5

1Carrier Wave c(t)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1−10

−5

0

5

10Message Signal m(t)

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

−5

0

5

DSB−SC Modulated Signal s(t)

TELE3113 - DSB-SC Modulation. August 5, 2009. – p.2/10

DSB-SC Modulation (3)

)( fS

)( fM

W W− 0

0 Wfc −− Wfc +− cf− Wfc − Wfc + cf

)0(2

MAc

)0(M

f

f

Upper sideband

Lower sideband

Spectrum of message signal

Spectrum of DSB-SC modulated signal

TELE3113 - DSB-SC Modulation. August 5, 2009. – p.3/10

DSB-SC Modulation (4)

The modulated signal s(t) undergoes a phase reversalwhenever the message signal m(t) crosses zero.

The envelope of the modulated signal s(t) is different from

the message signal. So the simple demodulation using an

envelop detection is not an option for DSB-SC modulation.

TELE3113 - DSB-SC Modulation. August 5, 2009. – p.4/10

Example of DSB-SC Modulation

Consider DSB-SC modulation of a single-tone message signal

m(t) = Am cos(2πfmt). The modulated signal is therefore given

by

s(t) = AmAc cos(2πfmt) cos(2πfct).

The FT of the DSB-SC modulated signal is given by

S(f) =AmAc

4δ(f − fc − fm) +

AmAc

4δ(f + fc + fm)

+AmAc

4δ(f − fc + fm) +

AmAc

4δ(f + fc − fm).

TELE3113 - DSB-SC Modulation. August 5, 2009. – p.5/10

Coherent Detection (1)

Product modulator

Local oscillator

Low-pass filter

Modulated wave )(ts )(tv

Demodulated signal )(tvo

)2cos(' φπ +tfAcc

Suppose in the receiver the local oscillator can provide thesame frequency, but arbitrary phase difference φ, measured

with respect to the carrier wave c(t).

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Coherent Detection (2)

Denote the local oscillator signal by A′

ccos(2πfct + φ). The

detector output is therefore

v(t) = A′

ccos(2πfct + φ)s(t)

= AcA′

ccos(2πfct + φ) cos(2πfct)m(t)

=1

2AcA

′

ccos(4πfct + φ)m(t) +

1

2AcA

′

ccos(φ)m(t),

where we used the relation

cos(θ1) cos(θ2) =1

2cos(θ1 + θ2) +

1

2cos(θ1 − θ2).

TELE3113 - DSB-SC Modulation. August 5, 2009. – p.7/10

Coherent Detection (3)

Consider the output of the product modulator,

v(t) =1

2AcA

′

ccos(4πfct + φ)m(t) +

1

2AcA

′

ccos(φ)m(t).

The Fourier transform of v(t) is given by

V (f) =1

4AcA

′

c[M(f − 2fc) + M(f + 2fc)]

+1

2AcA

′

ccos(φ)M(f).

The first term is a high-frequency signal centered at ±2fc and the

second term is a low-frequency signal centered at 0.

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Coherent Detection (4)

After the low-pass filtering the signal v(t), at the filter output we

obtain

vo(t) =1

2AcA

′

ccos(φ)m(t).

As long as the phase error φ is constant, the detector output

provides an undistorted version of the message signal m(t).

In practice, however, the phase error φ varies randomly with

time, thereby causing the coherent detection difficult.

Therefore, the local oscillator in the receiver must

synchronize in both frequency and phase with the carrier

wave c(t).

TELE3113 - DSB-SC Modulation. August 5, 2009. – p.9/10

Costas Loop: carrier phase recovery

Product modulator

Low-pass filter

DSB-SC wave )(ts

Demodulated signal

)2cos( φπ +tfc

Product modulator

Low-pass filter

)()cos(21

tmAc

φ

090− Phase-shifter

)2sin( φπ +tfc

Voltage-controlled oscillator

Phase discriminator

)()sin(2

1tmA

cφ

I-channel

Q-channel

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