Transcript Document

Outline
•Analog-to-Digital Conversion - Sampling
•Digital Modulation Schemes
•Revisit Analog Modulation Schemes
•Amplitude Modulation (AM)
•Frequency Modulation (FM)
Modulation Process
•Information-bearing signals (e.g., voice, video) are called
baseband signals. Other terms for information-bearing signals
are message signal and modulating wave.
•Modulation is defined as the process by which some
characteristics of a carrier signal (typically a cosine wave) is
varied in accordance with a message signal.
•Modulation process is required to shift the frequency content
of our message signals to a range that is acceptable by the
transmission medium. (e.g., above 30 KHz for wireless
transmission).
Modulation Types
Analog Modulation:
Message signal is analog (a.k.a
continuous-time).
Digital Modulation:
Message signal is digital
(a.k.a discrete-time).
•Amplitude Modulation (AM)
•Amplitude Shift Keying (ASK)
•Frequency Modulation (FM)
•Frequency Shift Keying (FSK)
•Phase Modulation (PM)
•Phase Shift Keying (PSK)
Digital Modulation Schemes
Digital Modulation Schemes
Figure 4-8
WCB/McGraw-Hill
Amplitude Change
 The McGraw-Hill Companies, Inc., 1998
Figure 4-9
Frequency Change
WCB/McGraw-Hill
 The McGraw-Hill Companies, Inc., 1998
Figure 4-10
WCB/McGraw-Hill
Phase Change
 The McGraw-Hill Companies, Inc., 1998
Figure 5-24
Amplitude Shift Keying
Also known as Symbol Rate
WCB/McGraw-Hill
 The McGraw-Hill Companies, Inc., 1998
Figure 5-27
Frequency Shift Keying
WCB/McGraw-Hill
 The McGraw-Hill Companies, Inc., 1998
Figure 5-29
WCB/McGraw-Hill
Phase Shift Keying
 The McGraw-Hill Companies, Inc., 1998
Figure 5-30
PSK
Constellation
WCB/McGraw-Hill
 The McGraw-Hill Companies, Inc., 1998
Figure 5-31
WCB/McGraw-Hill
Quadrature PSK - QPSK
4-PSK
 The McGraw-Hill Companies, Inc., 1998
Figure 5-32
QPSK
Constellation
WCB/McGraw-Hill
 The McGraw-Hill Companies, Inc., 1998
Figure 5-33
8-PSK
Constellation
WCB/McGraw-Hill
 The McGraw-Hill Companies, Inc., 1998
Figure 5-35
WCB/McGraw-Hill
4-QAM and 8-QAM
Constellations
 The McGraw-Hill Companies, Inc., 1998
Figure 5-36
WCB/McGraw-Hill
8-QAM Signal
 The McGraw-Hill Companies, Inc., 1998
Figure 5-37
16-QAM
Constellation
WCB/McGraw-Hill
 The McGraw-Hill Companies, Inc., 1998
Figure 5.17
Bit and baud
Table 5.1 Bit and baud rate comparison
Modulation
Units
Bits/Baud
Baud rate
Bit Rate
Bit
1
N
N
4-PSK, 4-QAM
Dibit
2
N
2N
8-PSK, 8-QAM
Tribit
3
N
3N
16-QAM
Quadbit
4
N
4N
32-QAM
Pentabit
5
N
5N
64-QAM
Hexabit
6
N
6N
128-QAM
Septabit
7
N
7N
256-QAM
Octabit
8
N
8N
ASK, FSK, 2-PSK
Sampling – Pulse Amplitude Modulation
(PAM)
Sampling – Pulse Amplitude Modulation (PAM)
Quantized PAM Signal
Figure 3.11
Illustration of the quantization process. (Adapted from
Bennett, 1948, with permission of AT&T.)
Figure 5-20-continued
From Analog to PCM
WCB/McGraw-Hill
 The McGraw-Hill Companies, Inc., 1998
Figure 5-20-continued
From Analog to PCM
WCB/McGraw-Hill
 The McGraw-Hill Companies, Inc., 1998
Figure 5-20-continued
From Analog to PCM
WCB/McGraw-Hill
 The McGraw-Hill Companies, Inc., 1998
Figure 5-19
Pulse Coded Modulation
WCB/McGraw-Hill
 The McGraw-Hill Companies, Inc., 1998
Nyquist’s Sampling Theorem
A band-limited signal of finite energy, which has no frequency
components higher than W Hertz, may be completely described
by specifying the values of the signal at instants of time separated
by (1/2W) seconds or can be recovered from a knowledge of its
samples taken at a rate of 2W samples per second.
fs = 2 × W
Sampling
frequency
Bandwidth
of signal
Impact of Sampling on the Frequency Domain
Sampling frequency = message bandwidth
Message signal cannot be recovered from the sampled signal !!
Impact of Sampling on the Frequency Domain
Message signal
Frequency Content
Frequency Content of the
sampled message signal
Message bandwidth
fs = 2 × W
Sampling frequency
•Revisit Analog Modulation Schemes
•Amplitude Modulation (AM)
•Frequency Modulation (FM)
•How to produce AM Signal?
Amplitude Modulation
Amplitude Modulation
Modulating
signal v (t)
VAM(t)
S
Carrier Amplitude
cos C t
vC
Carrier Frequency
Carrier Signal: ct   vc  cosct
Message Signal or modulating signal: vS t   vS cosS t
Modulated Signal: VAM t  
vS
M
vC
VAM t  
VAM t  
vC  vS (t ) cosct
 vS

vC 1  cosS t  cosct
 vC

vC 1 M cosS t  cosct
Modulation Index
Amplitude Modulation
vS
M
vC
• Modulation Index M is determined by the peak
amplitudes of the carrier and the modulating signal.
• In practice, carrier signal amplitude vC is usually
fixed and the M ratio is changed by varying the
amplitude of the modulating signal vS.
• Hence, higher vS produce higher M but M < 1.
• M is kept as high as possible to ensure good SNR of
the received AM signal for recovery.
• When M > 1, over-modulated carrier signal distorts
the information – Clipping or saturation.
Amplitude Modulation
Envelope of the
modulated signal
has the same shape
with the message
signal.
Illustrating the amplitude modulation process.
(a) Baseband signal vs(t).
(b) AM wave for M < 1 for all t.
(c) AM wave for M > 1 for some t.
Envelope is distorted
vS
M
vC
AM : Double-sided band (DSB)
AM Signal: VAM t   vC  vS (t ) cosct
where modulating signal:
Thus,VAM t 

vC cosCt
vS t   vS cosS t

Carrier
Component
Wasted energy in
carrier component
because it contains
no information
Action: To suppress
the carrier
vS
2

vS cosS t. cosCt
Double-side band components
(DSB)
cos C  S t  cos C  S t

(LSB)
(USB)
Lower side band
Upper side band
Amplitude Modulation
AM is the earliest type of modulation in history.
Its main advantage is its simplicity. – linear modulation
technique
AM is wasteful in power consumption. Although the carrier
signal does not carry any information, it is still transmitted.
AM is wasteful in bandwidth usage. The upper sideband is
reflection of the lower sideband. One sideband is sufficient to
express the frequency content of the message signal. Yet, AM still
transmits one unnecessary sideband.
Spectrum of AM wave
(a) Spectrum of AM Signal: both carrier and double-sided bands
|v|
fS
fc-fS
fc
fc+fS
f
(b) Spectrum of Double-Sided Band - Carrier Suppression (DSB-SC)
|v|
fc-fS
fc
fc+fS
f
Double Sideband-Suppressed Carrier Modulation (DSB-SC)
Modulating
signal
DSB-SC signal
vS(t)
cos C t
Carrier Frequency
• Balance Modulator
vS cosS t
vc  cosct
vS(t)
-90o
-90o
vS sin S t
vc  sin ct
Carrier
Oscillator
vC(t)

DSB-SC
Double Sideband-Suppressed Carrier
Modulation (DSB-SC)
modulating signal:
DSB-SC signal:
Single Sideband-Suppressed Carrier Modulation (SSB-SC)
Modulating
signal
DSB-SC
signal
vS(t)
cos C t
Sideband
filter
(crystal
filter)
SSB-SC
signal
Carrier Frequency
Bandpass filter applied
at the DSB-SC signal to
generate SSB-SC signal.
Problem: It is very difficult and costly to design a bandpass
filter that is sharp enough to select only one sideband !
Demodulation of AM signal
Modulating
signal
DSB-SC signal
vS t   vS cosS t
cos C t
• Balance Modulator
Carrier Frequency
vC vS
cos C  S t  cos C  S t 
2
vS cosS t
vc  cosct
vS(t)
-90o
-90o
vS sin S t
vc  sin ct
Carrier
Oscillator

DSB-SC
vC(t)
vC vS
cos C  S t  cos C  S t 
2
Demodulation of AM signal
• Most basic: Envelope detector (for AM signal only)
Charging/Discharging voltage
AM signal
vAM(t)
•
•
•
•
•
•
+
–
diode D
vs(t)
R
C
Cc
To remove DC component
& smoothen vs(t)
As VAM(t) increases in amplitude, the diode conducts (forward bias) and capacitor C start to
charge-up very quickly to 1st peak vp1 with a time constant  = Cr, where r is the diode’s
forward resistance (usually very small when diode is conducting).
As VAM(t) decreases in amplitudes, the diode switch-off (reverse bias) and capacitor C start to
discharge slowly with a time constant  = CR, where R must be greater than r.
When VAM(t) increases again, D conducts and C charges up rapidly to 2nd peak vp2 and when
VAM(t) decreases again D is off and C discharges slowly and this is repeated according to the
amplitude of VAM(t) signal.
If CR is too small, C discharge too rapidly; results in ripple amplitude in demodulated output.
If CR is too large, C discharge too slowly; vs(t) fails to follow the envelope results in
distortion (or diagonal clippling) in demodulated output.
Hence, time constant  must be optimum.
Optimum AM Demodulation
Ripple amplitude in AM
Demodulation – RC too small
Diagonal Clipping/distortion in
AM Demodulation – RC too large
Demodulation of (DSB-SC) signal (1)
• Synchronous detection
Vx
DSB-SC signal
vDSBSC
Low
Pass
Filter
 vS t . cosCt
cos C t
Vx  vDSBSC  cosct
local oscillator
• Local oscillator produce the exactly coherent
oscillation output that is synchronized with the
original carrier in both frequency and phase.
• The output is then filter by low-pass filter that
only allowed the desired signal to pass through.
|v|
fS
fc-fS
fc
fc+fS
Recovered
modulating
signal
f
 vS t . cosCt  cosCt
 vS t . cosC t
2
vS t 

.1  cos 2C t 
2
vS (t ) vS (t )


cos 2c t
2
2
Desired
signal
Unwanted
signal
Demodulation of (DSB-SC) signal (2)
• Costal Loop / Phase Lock Loop (PLL)
vS (t ) cosC t
vS (t )
cos   cos 2C   
2
vS (t )
cos  
2
Output:
LPF
vc  cosct   
DSB-SC
VCO
-90o
vS (t ) sin C t
-90o
Loop
filter
vc  sinct   
vS (t )
sin   sin 2C   
2
LPF

vS (t )
sin  
2
• The frequency fc is know a priori to the demodulator and generated by the voltage
control oscillator, VCO.
• PLL circuit (VCO + Loop filter) try to lock the phase so that local oscillation is
synchronized with original fc.of the DSBSC signal.
• Once synchronization is achieved, the difference in phase   will be eliminated,
thereby, recover the modulating signal.
Frequency Modulation (FM)
v
s
fC
fi
In FM, the information is conveyed by varying the frequency of the carrier
signal fC in step with the instantaneous amplitude of the modulating signal
vs.
Frequency Modulation (FM)
• FM signal is produced by a frequency modulator which converts the voltage
variation in the modulating signal vs to a frequency variation of the carrier signal
vs(t)
Frequency
Modulator
fi
• The “instantaneous” frequency fi is the sum of carrier frequency fC and the
“frequency deviation” f as the result of the ‘amplitude-frequency’ conversion.
fi  fc  f
where
f  k f .vs ; k f is conversion gain (unit : Hz / volt )
• When no modulating signal is applied, the output
frequency is the same as the carrier frequency
since f  0 ; no deviation is observed.
• When a modulating signal is applied, the
instantaneous output frequency fi will start to
vary/deviate from fc with the amount of f .
• The conversion can be seen from the graph
fi
Hz
kf = volt
fc
Conversion gain
vs
0
Frequency Modulation (FM)
Carrier Signal:
Constant
speed
ct   vc  cos2f ct 
FM Modulated Signal:
2
1
st   vc  cos i 
Angular displacement :
Fact in FM :
(Distance = speed × time)
Instantaneous frequency fi of the cosine wave is:
1 d  i t 
f i t  

2
dt
i  2f i  t
Instantaneous
angular
displacement
varying
speed
Frequency Modulation (FM)
• General FM signal
can be expressed as:
where i is the instantaneous
angular displacement:
• Recall that instantaneous
frequency i of FM:
• hence i can be re-written as:
VFM (t )  vC . cos i
 i   i dt  2  f i dt
fi  fC  f
 i  2

f  k f vs
 fC  k f .vs cosst
f C  k f vs cos  s t
 dt
 2 f C  1 dt  2 k f vs  cos  s t dt
FM modulation index:

k f vs
fs
f

fs
 C t  2 k f vs
 C t 
k f vs
fs
sin st
2 f s
sin s t
 C t   sin st
Frequency Modulation (FM)
• Therefore, FM signal can be expressed as:
VFM (t )  vC . cos Ct   sin st 
FM modulation index:
f k f vs


fs
fs
Carrier frequency is varied or deviated
by the amount of  sin s t
FM is a non-linear modulation.
FM signal envelope is constant.
•  controls the amount of frequency change in FM signal.
• In FM,  can be greater than 1: ( > 1), since f can be set independent of fs
and both values are not bounded by fC.
• However, fs must be kept smaller than fC in order for FM to work successfully.
Frequency Modulation
Carson’s Rule:
The transmission bandwidth required by a frequency
modulated signal is given below.
 1
BT  2  f max  1  
 
FM modulation index:
Maximum frequency deviation
f k f vs


fs
fs
Example
A message signal with a bandwidth of 15 KHz is to be used to frequency
modulate a carrier signal at 400 KHz. Given that maximum frequency
deviation is 75 KHz. According to Carson’s Rule, what is the
transmission bandwidth required for the frequency modulated signal?
1) message bandwidth ?
f s or W  15 KHz
2) maximum frequency deviation ?
3) modulation index ?
f  75 KHz
f 75


5
f s 15
4) Using Carson’s rule, the required transmission bandwidth:
 1
 1
BT  2  f  1    2  75 1    180KHz
 5
 
Tutorial
1- What is Amplitude Modulation ?
Amplitude modulation is the process by which the
amplitude of a carrier signal is varied according to a
message signal.
2- What frequency range will be covered by a 412 KHz carrier
signal after it has been amplitude modulated by an audio signal
that is bandlimited to 24 KHz ?
Due to amplitude modulation, the frequency spectrum of
the audio signal will shift to the carrier signal frequency.
The frequency range from (412-24) KHz to (412+24) KHz
will be covered by the amplitude modulated signal.
Tutorial
3- Consider the video signal that has a frequency
content between 0 Hz and 6 MHz. What is the required
transmission bandwidth if Frequency Modulation is used
with a maximum frequency deviation of 30 MHz
according to Carson’s Rule ?
maximum frequency deviation ?
f  30 MHz
modulation index ?
f

5
6 MHz
 1
 1
BT  2  f  1    2  30 1    72 MHz
 5
 
Tutorial
With aid of diagram, explain the process of amplitude modulation?
Your answer should include the carrier signal, modulating signal
and the AM signal itself.
Tutorial
4- What is Amplitude Shift Keying (ASK)?
ASK is a digital modulation technique where the amplitude of
a carrier signal is varied to transmit ones and zeros.
5- What is Phase Shift Keying (PSK)?
PSK is a digital modulation technique where the phase of a
carrier signal is varied to transmit ones and zeros.
6- What is Frequency Shift Keying (FSK)?
FSK is a digital modulation technique where the frequency of a
carrier signal is varied to transmit ones and zeros.
Tutorial
7- Sketch the ASK modulated signal for a bit pattern of
01100101. Use a cosine wave as the carrier signal!
Tutorial
8- Sketch the PSK modulated signal for a bit pattern of
01100101. Use a cosine wave as the carrier signal!
Tutorial
Briefly explain the Pulse Amplitude Modulation (PAM) and
Quantisation process.
PAM converts the analog signal to a series of pulse-trains with
different amplitude corresponding to the amplitude of the
analog signal at different interval in time.
Quantisation is a process to convert these pulse-trains
amplitude from analog value to discrete value by binary level
representation. The number levels (L) that can be represented
is corresponding to the number of bit (N) used. L = 2N
Tutorial
With the aid of block diagram, describe how a analog signal is
sent using a digital system with PAM.