communication systems prof. chungming kuo. chapter 6 double sideband and single sideband (cont.)
TRANSCRIPT
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.