Upload
others
View
13
Download
0
Embed Size (px)
Citation preview
Dr. Ahmed El-Mahdy COMM 601: Modulation I
COMM 601: Modulation I
Lecture 2
Conventional Amplitude Modulation
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Amplitude Modulation
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Amplitude Modulation
• Also known as “Linear Modulation”.
• Applications:
- AM radio
- TV video broadcasting (VSB)
- Point to point communications (SSB)
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Double Side Band
Suppressed
Carrier
(DSB)
Conventional
AM
Amplitude Modulation
Single side band
(SSB)
Vestigial side
Band
(VSB)
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Conventional Amplitude Modulation
frequencycarriertheis
amplitude.carriertheis:where
2cos
:by defined vecarrier wa sinusoidal aConsider
c
c
cc
f
A
tfAc(t)
c(t)
modulator. theof senstivity amplitude theis:
2cos)(1
:as described becan signal (AM) modulated amplitudeAn
signal). g(modulatin signalmessagethedenotes)(Let
a
cac
kwhere
tftmkAs(t)
tm
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Conventional Amplitude Modulation
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Spectrum of AM Signal
M(f)
-W 0 W f fc -W fc fc+ W f-fc -W -fc -fc+ W 0
Wf c
S(f)
1
BT=2W
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Spectrum of AM Signal
f
Wf c
BT=2W
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Spectrum of AM Signal (Cont.)
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Transmission Bandwidth of Conventional AM
AM is Wasteful of Bandwidth
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Conventional Amplitude Modulation
The envelope of s(t) has the same shape as
the baseband signal m(t) provided that two
requirements are satisfied:
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Conventional Amplitude Modulation
(c)). Fig.in (asdistortion
envelope exhibits signal modulated thecase, In this
zero. thecrosses)]([1 whenever reversal
phasecarrier in resulting modulated,over becomes
signalcarrier then the,1)(such that large
ismodulator theof senstivity amplitude he When t
envelope. therepresents]1[
Then positive.alwaysis)]([1
that ensurescondition this(b), Fig.in shown As
allfor1)(
:unity than less is of magnitude The (1)
tmk
tmk
m(t)k A
tmk
ttmk
m(t)k
a
a
ac
a
a
a
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Conventional Amplitude Modulation
distorted. be willand 0 around be will
spectrum theofpart becauserily satisfacto detected be
not can envelope thesatisfied,not iscondition thisIf
:isThat(t).
signal theof component frequency hightest the
an greater thmuch is frequency carrier The)2(
c
c
f
Wf
m
W
f
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Conventional AM: Basic definitions
2
-
-ve sign
)](1[ tmkA ac
Envelope
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Conventional AM: Average transmitted power
See Appendix
(At the end of this
Lecture)
Assume m(t) has zero mean
])(1[2
])()(21[2
)](1[2
)(2
1
222
222
22
2
tmkA
tmktmkA
tmkA
tCP
ac
aac
ac
avg
)(1)(
2cos)(1
tmkAtCThen
tftmkAs(t)Since
ac
cac
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Conventional AM: Modulation efficiency
Modulation Efficiency:
is the ratio between side band power (that conveys information) to
the total power
)(1
)(
)(2
1
2
1
)(2
1
100powerTotal
power band side
22
22
2222
222
tmk
tmk
tmkAA
tmkA
a
a
acc
ac
Dr. Ahmed El-Mahdy COMM 601: Modulation I
22
2
2
2
])(max1[2
]])(max1[[2
1
])](1[[max2
1
)(max2
1
tmkA
tmkA
tmkA
tCP
ac
ac
ac
PEP
Peak Envelope Power of Conventional AM:
Conventional AM: Peak Envelope Power
is the power that would be obtained if the envelope attains its
maximum value
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Remarks on Transmitted Power of Conventional AM
AM is Wasteful of Power
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Conventional AM with single tone modulating signal
mamamm
a
mm
a
AkAkAA
k
tfAtm
tmtmk
2
)(Then
)2cos)( :signal modulating sinusiodalFor
2
)(min)(max(factor)index Modulation Since
10
Then
1)2cos(.1)(Since
tfAkeitmk mmaa
tftfAs(t) cmc 2cos2cos1
For single tonee
Dr. Ahmed El-Mahdy COMM 601: Modulation I
tfAtm mm 2cos
mmm ffff
AfM
2
MODULATING SIGNAL
MODULATED (AM) SIGNAL
CARRIER UPPER SIDEBNAND LOWER SIDEBNAND
Conventional AM with single tone modulating signal
tftfAts cmc 2cos2cos1
tftfAtfAts mcccc 2cos.2cos2cos
tfftffA
tfAts mcmcc
cc
2cos2cos2
2cos
mcmcc
mcmcc
ccc
ffffffA
ffffffA
ffffA
fS
4
4
2
Dr. Ahmed El-Mahdy COMM 601: Modulation I
AMPLITUDE MODULATED SIGNAL
MODULATING SIGNAL
VAc 52
VAm 5.22
mTfB 2V
Ac 25.14
Hzf
Hzf
VA
k
VA
m
c
c
a
m
10
200
10
1.0
5
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Conventional AM with single tone modulating signal
2
2
2
2
2
2
2
2
22
22
2
21
2
)(1
)(
m
m
m
m
a
a
A
A
A
A
tmk
tmk
3
1max 1When
For sinusoidal
modulating signal
ma Ak tfAtm mm 2cos
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Conventional AM with single tone modulating signal
]2
1[2
]2
1[2
)(22
222
2
222
22 c
avgm
m
ca
ccavg
AP
A
A
Atmk
AAP
22
22
22
]1[2
]1[2
])(max1[2
cPEPm
m
ca
cPEP
APA
A
Atmk
AP
tfAtm mm 2cos
ma Ak
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Conventional AM with multi-tone modulating signal
: efficiency theand formulaspower above in the thisUse
...
,...;Then
2cos....)2cos)2cos1
2cos....))2cos)2cos(1
2cos)(1:signalmodulatedThe
....)2cos)2cos)( :signal modulating tone-Multi
2
2
2
1
2211
2211
2211
2211
avg
avg
mama
cmmammac
cmmmmac
cac
mmmm
AkAk
tftfAktfAkA
tftfAtfAkA
tftmkAs(t)
tfAtfAtm
Proof is not required
]2
1[2
22avgc
avg
AP
22
]1[2
avgc
PEP
AP
2
2
2 avg
avg
1thatsuch avg
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Example: Conventional AM
is the modulation
index
1, mA
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Example: Conventional AM (cont.)
tt
tftfAs(t)
AkAk
tfAtm
cmc
m
ama
mm
5102cos]20002cos5.01[5
2cos2cos1
5.0
)2cos()(
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Example: Conventional AM (cont.)
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Example: Conventional AM (cont.)
14)625.0(4)5.2(2)( 222
fSPavg
)( fS
f
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Example: Conventional AM (cont.)
22
]1[2
cPEP
AP
]2
1[2
22 c
avg
AP
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Appendix:
Power Calculations
The following formulas are valid for
all types of modulations
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Appendix: Power CalculationsNormalized average power: (using complex envelope C(t))
2
)(2
1tCPavg
Peak envelope power: (using complex envelope C(t))
Modulation Efficiency:
100powerTotal
power band side
2)(max2
1tCPPEP
Dr. Ahmed El-Mahdy COMM 601: Modulation I
Appendix: Power CalculationsTime average:
For Non-periodic signal:
2/
2/
)(1
lim
T
TT
dttxT
x
0
00
)(1
T
dttxT
x
When x(t) is periodic with period To:
signalrealais)(tx
periodsignaltheis0T