Communication Systems

Prof. Chungming Kuo

Chapter 6

Double Sideband and Single Sideband (cont.)

Double Sideband and Single Sideband

This module will provide an introduction to amplitude modulation by considering double sideband (DSB) and single sideband (SSB).

Historically, these were not the earliest forms of amplitude modulation employed on a wide scale, but they relate very closely to concepts developed in the module frequency conversion.

Double Sideband and Single Sideband (cont.)

Hence, they will be covered before conventional amplitude modulation with a large carrier is introduced. The commercial AM broadcast system employs the latter system.

Amplitude Modulation Forms

Conventional Amplitude Modulation (Sometimes called AM-LC for AM with “large carrier.” When we use AM without any modifier, it will be assumed to mean conventional AM.)

Amplitude Modulation Forms (cont.)

Double Sideband (DSB) (Sometimes called DSB-SC, with SC representing “suppressed carrier.” We will refer to it simply as DSB.)

Single Sideband (SSB) Vestigial Sideband (VSB)

Essential Trigonometric Identities

cos A cos B 12

cos A B 12

cos A B

sin A sin B 12

cos A B 12

cos A B

Essential Trigonometric Identities (cont.)

sin A cos B 12

sin A B 12

sin A B

cos A sin B 12

sin A B 12

sin A B

Notation

vm t modulating or message signal (usually at baseband)

vc t carrier signal

vo t output of modulator

vr t received signal

vd t detected or demodulated signal

fc carrier frequency in hertz

c carrier frequency in radians per second 2 fc

W baseband bandwidth of modulating signal in hertz

BT transmission bandwidth of the modulated signal in hertz

Continuous Spectrum Signal ( )v t

t

( )V f

fWW

Discrete Spectrum Signal

( )v t

t

f1W Nf

T0

0

T

nC

Balanced Modulator

X( )ov t( )mv t

( ) cosc c cv t A t

Performs same operation as a mixer

Balanced Modulator EquationsContinuous Spectrum

vo t Kbvm t vc t KbAcvm t cos ct

Kvm t cos ct

vo t K2

vm t e j 2 fct K2

vm t e j 2 fct

Balanced Modulator EquationsContinuous Spectrum (cont.)

V o f K2

V m f fc K2

V m f fc

( )mv t

t

t

( )mV f

fWW

( )ov t ( )oV f

f

cf Wcf Wcf

Balanced Modulator EquationsDiscrete Spectrum

vm t Cn cos n1t n n1

N

W Nf1

Balanced Modulator EquationsDiscrete Spectrum (cont.)

vo t KbAc cos ct Cn cos n1t n n1

N

K Cn cos ct cos n1t n n1

N

Balanced Modulator EquationsDiscrete Spectrum (cont.)

vo t K2

Cn cos c n1 t n n1

N

K2

Cn cos c n1 t n n1

N

BT 2W

MODULATING SIGNAL SPECTRUM(a)

(b)

W f

f

DSB SPECTRUM

cf W cf Wcf

Example 1

Lowest frequency is 1 MHz-15 kHz

= 985 kHz

• A continuous-spectrum signal has components from near dc to 15 kHz and carrier is 1 MHz. Find range of DSB frequencies and bandwidth:

Example 1 (cont.)

Highest frequency is 1 MHz+15 kHz

= 1015 kHz

• A continuous-spectrum signal has components from near dc to 15 kHz and carrier is 1 MHz. Find range of DSB frequencies and bandwidth:

BT 2W 2 15 kHz 30 kHz

Example 2

LSB: 250 - 1 = 249 kHz

250 - 3 = 247 kHz

250 - 5 = 245 kHz

• A discrete-spectrum signal has components at 1, 3, and 5 kHz, and carrier has a frequency of 250 kHz. List DSB frequencies and find bandwidth:

Example 2 (cont.)

USB: 250 + 1 = 251 kHz

250 + 3 = 253 kHz

250 + 5 = 255 kHz

• A discrete-spectrum signal has components at 1, 3, and 5 kHz, and carrier has a frequency of 250 kHz. List DSB frequencies and find bandwidth:

BT 2W 2 5 kHz 10 kHz

Single Sideband (SSB) With SSB, only one of the two sidebands is

transmitted. It may be the lower sideband (LSB) or the upper sideband (USB). The transmission bandwidth is:

The most common method for generating SSB is the filter method illustrated on next two slides.

BT W

A DSB signal is first generated

WW

( )mV f

f

f

cf Wcf Wcf

1( )V f

cf

(a)

(b)

Spectral Plots for USB

cf cf W f

cf cf W f

( )A f

( )oV fcf

(c)

(d)

Spectral Plot for LSB

cfcf W f

cf W cf f

( )A f

( )oV fcf

cf

(e)

(f)

SSB Filter Method Generator

X1( )v t( )mv t

cosc cA t

BAND-PASSFILTER

( )ov t

SSB Equations for Discrete-Spectrum

vm t Cn cos n1t n n1

N

LSB : vo t K2

Cn cos c n1 t n n1

N

USB : vo t K2

Cn cos c n1 t n n1

N

Example 3

LSB: 985 kHz to 1 MHz

USB: 1 MHz to 1.015 MHz

• For system of Example 1, determine range of SSB frequencies and bandwidth for LSB and USB:

BT 15 kHz

Example 4

LSB: 249 kHz

247 kHz

245 kHz

• For system of Example 2, list SSB frequencies and determine bandwidth for LSB and USB.

Example 4 (cont.)

USB: 251 kHz

253 kHz

255 kHz

• For system of Example 2, list SSB frequencies and determine bandwidth for LSB and USB.

BT 5 kHz

Product Detection of DSB and SSB

X1( )v t( )rv t

( ) cosc c cv t A t

LOW-PASSFILTER

( )dv t

DSB Product Detection Analysis

vr t K rvm t cos ct

v1 Kbvrvc KbK r Acvm t cos ct cos ct

Bvm t cos2 ct

DSB Product Detection Analysis (cont.)

v1 t B2

vm t B2

vm t cos2 ct

vd t B2

vm t

DSB Detection Spectral Plots

( )rV f

f

f

f

cf Wcf W

1( )V f

WW 2 cf W 2 cf W

( )dV f

WW

SSB Product Detection Analysis

vr t K r

Cn

2cos c n1 t n

n1

N

vc t Kc cos ct

SSB Product Detection Analysis

v1 Kbvrvc Kb K r

Cn

2cos c n1 t n

n1

N

Ac cos ct

B2

Cn cos c n1 t n n1

N

cos ct

B4

Cn cos n1t n n1

N

B4

Cn cos 2 c n1 t n n1

N

SSB Product Detection Analysis (cont.)

vd t B4

vm t

SSB Detection Spectral Plots( )rV f

f

f

f

cf Wcf W

1( )V f

WW 2 cf W 2 cf W

( )dV f

WW

Effects of Non-Synchronization The preceding analysis has assumed that the carrier at the receiver is locked in frequency and phase with that at the transmitter.

This condition is referred to as synchronous product detection.Next, assume the following form for the receiver carrier:

vc t Ac cos c t

Results of Mathematical Analysis A rather detailed analysis at the receiver now yields the results below. Recall that the DSB signal was assumed as a continuous spectrum signal while the SSB signal was assumed as a discrete spectrum signal.

DSB : vd t B2

vm t cos t

SSB : vd t B4

Cn cos n1 t n n1

N

Comments

Both signals are distorted but effects on DSB are more serious.

DSB is useful in the following situations:– Systems in which a small pilot carrier is

transmitted.

Comments (cont.) DSB is useful in the following situations:

– Certain complex signal processing schemes that can extract a coherent reference.

– Automatic control systems of the “ac-carrier” types where reference carrier is available.

Summary The instantaneous product of a baseband sig

nal and a carrier yields a DSB signal. If one of the sidebands is eliminated, an SSB

signal is generated. For a baseband bandwidth W, the bandwidth

of a DSB signal is 2W, and the bandwidth of an SSB signal is W.

Summary (cont.) Theoretically, both DSB and SSB signals can

be demodulated by product detection. In practice, DSB requires an exact

synchronized reference while tolerable detection can be achieved with SSB without exact synchronization.