Chapter 3: Amplitude Modulation 7/13/2010 1
Chapter 3: A
mplitu
de M
odulatio
n
7/13/2010
1
Intro
ductio
n
Objective
To co
nvey in
form
ation th
rough a m
edium sep
arating th
e tran
smitter an
d receiver
Inform
ation:
Baseb
and sig
nal 0
≤f ≤
WIf m
atches th
e chan
nel b
and: b
aseban
d tran
smissio
nOtherw
ise, may b
e block
ed by th
e chan
nel: m
odulatio
n
Modulatio
nSome ch
aracteristic of a carrier
is varied in acco
rdan
ce with a
modulatin
g sig
nal (in
form
ation)
Modulatin
g w
ave m(t)
Carrier c(t)
Modulated
wave s(t)
Contin
uous‐w
ave modulatio
n: sin
usoidal w
ave as carrier
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2
m(t)
c(t)
s(t)Modulato
r
Intro
ductio
n (co
ntd.)
Dem
odulatio
nTo resto
re the o
riginal b
aseban
d sig
nal m
(t)
Reverse th
e modulatio
n process
Contin
uous‐w
ave modulatio
n: sin
usoidal w
ave as carrier
Modulate th
e amplitu
de A
c
The am
plitu
de o
f a sinusoidal carrier w
ave is varied in
accordan
ce with th
e baseb
and sig
nal
Modulate th
e angle
The an
gle (freq
uen
cy or p
hase) o
f a sinusoidal carrier w
ave is varied
in acco
rdan
ce with th
e baseb
and sig
nal
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3
)2
cos()
(
ftA
tc
c
ft
2
Band‐pass Sign
alA gen
eral modulated
signal:
a(t): th
e envelo
peof th
e ban
d‐pass sig
nal
φ(t): th
e phase
of th
e signal
W
e have:
where
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4
Band‐pass Sign
alIn‐phase co
mponen
t:
Quad
rature co
mponen
t:
The p
hase d
iagram
:
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5
Amplitu
de M
odulatio
nA process in
which th
e amplitu
de o
f the carrier w
ave c(t)
is varied ab
out a m
ean valu
e, linearly
with th
e baseb
and sig
nal m
(t)
Sinusoidal carrier w
ave c(t):
Carrier freq
uen
cy: fcBaseb
and sig
nal: m
(t)
Amplitu
de‐m
odulated
(AM) w
ave:
K
a : amplitu
de sen
sitivity (volt‐1),a co
nstan
t desig
n
factor
K
a A
m = µ: m
odulatio
n facto
r7/13/20
106
Example: C
hoices o
f Ka
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7
Amplitu
de M
odulatio
n (co
ntd.)
Like sam
plin
g m
(t)with th
e positive im
pulses in
c(t)
Objective:
The en
velop of s(t)
has essen
tially the sam
e shap
e as m(t)
Conditio
ned on
[a] T
he am
plitu
de o
f ka m
(t)is alw
ays less than unity
Ensu
res [1+ka m
(t)] is always p
ositive (n
o phase reversal)
Since an
envelo
p sh
ould alw
ays be a p
ositive fu
nctio
n
Overm
odulated
: when |k
a m(t)|>
1
Envelo
p co
uld be n
egative
Carrier p
hase reversals w
hen th
e envelo
p acro
ss zero
envelo
p
disto
rtion
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8
Amplitu
de M
odulatio
n (co
ntd.)
an
d
[b]The carrier freq
uen
cy fcis m
uch greater th
an th
e highest freq
uen
cy componen
t Wof th
e baseb
and sig
nal
m(t)
Otherw
ise, an en
velop w
ith can
not b
e visu
alized or d
etected satisfacto
rily
Nyq
uist–
Shan
non sam
plin
g th
eorem
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9
Spectru
m of s(t)
The F
ourier tran
sform of th
e AM w
ave s(t)
Two delta fu
nctio
ns: scaled
by A
c /2, at ±fc
Two versio
ns o
f the b
aseban
d sp
ectrum
Scaled
by k
a Ac /2
Moved
to ±fc
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10
Spectru
m of s(t) (co
ntd.)
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11
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12
Spectru
m of M
odulated
Voice Sig
nal
‐fc‐fc +
4K
‐fc ‐4K
fcfc +
4K
fc ‐4K
S(f)
f
Spectru
m of s(t)
(contd.)
The sp
ectrum of m
(t)in [–
W, 0
] is completely visib
le if fc
> W
Otherw
ise, overlap
…
Upper sid
eban
d: fc
< f < fc +
W
Lower sid
eban
d: fc
‐W
< f < fc
Sym
metric w
ith reg
ard to fc
No overlap
if fc> W
Tran
smissio
n ban
dwidth B
Tfor an
AM w
ave
Twice th
e messag
e ban
dwidth: B
T= 2W
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13
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14
Example 3
.1
Desig
n facto
r: modulatio
n facto
r µ
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15
Example 3
.1 (co
ntd.)
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16
Assu
ming 1 o
hm resisto
r:
Ratio
of th
e total sid
eban
d
power to
the to
tal power
of s(t):
Ratio
n of th
e carrier power
to th
e total p
ower o
f s(t):
Example 3
.1 (co
ntd.)
µ
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17
Implem
entatio
n: Sw
itching M
odulato
r
C(t)
has a larg
e amplitu
de
The d
iode acts lik
e an id
eal switch
Zero
imped
ance w
hen v
1 (t) > 0,
block
ed otherw
ise
Rl = 1
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18
Implem
entatio
n: Sw
itching M
odulato
r (co
ntd.)
The in
put vo
ltage:
W
hen |m
(t)| «A
c , the o
utput vo
ltage is:
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19
Implem
entatio
n: Sw
itching M
odulato
r (co
ntd.)
Perio
dic p
ulse train
of d
uty cycle eq
ual to
one‐h
alf, and
perio
d T
0 =1/fc , rep
resented
by its F
ourier series:
Substitu
ting it in
to v
2 (t), we h
ave
Componen
t:
Unwan
ted co
mponen
ts:
Delta fu
nctio
ns at 0
, ±2fc , ±
4fc , …
Baseb
and sp
ectrum m
oved
to 0, ±
3fc , ±5fc , …
Rem
oved
from w
ith a b
and‐pass filter [fc ‐W
, fc +W
]
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20
Implem
entatio
n: En
velop Detecto
r
Reco
ver the o
riginal m
odulatin
g w
ave from received
modulated
wave
s(t)
m(t)
Envelo
p detecto
r:
Used
in alm
ost all co
mmercial A
M rad
io receivers
W
orks if: fc >
Wan
d m
odulatio
n facto
r µ< 10
0%
[1] P
ositive h
alf‐cycle: C ch
arges up rap
idly
to th
e peak
value o
f s(t)
[2] When S(t)
falls bello
w th
e peak
: the d
iode is reverse‐b
iased an
d is sh
ut
off; C
disch
arges slo
wly
[3] W
hen S(t)
rises above th
e C vo
ltage ag
ain, C ch
arges u
p rap
idly
again to
the p
eak valu
e
NOTE: th
e envelo
p sh
ould be p
ositive fo
r the d
iode to
work
Slowly:
Rap
idly:
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21
Envelo
p Detecto
r Example
A sin
usoidal A
M w
ave with 50
% m
odulatio
n
The rip
ples at th
e carrier frequen
cy can be rem
oved
by a lo
w‐pass filter
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22
AM Discu
ssions
Stren
gth
Easy to
implem
ent
Low co
st, good fo
r mass p
roductio
n
Lim
itations
Not en
ergy efficien
t:
Carrier carries n
o in
form
ation
Tran
smissio
n of carrier w
ave represen
ts a waste o
f energ
y
May tak
e a consid
erable h
igh portio
n of th
e total en
ergy
Larg
e transm
it power also
cause in
terference to
others
Not b
andwidth efficien
t:
Req
uires tw
ice the m
essage b
andwidth to tran
smit: B
T= 2W
Sym
metry: u
pper an
d lo
wer sid
eban
ds: o
ne is su
fficient
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23
AM Discu
ssions (co
ntd.)
Trad
e off system
complexity fo
r improved
utilizatio
n of co
mmunicatio
n reso
urces
(C
omplexity ) vs. (B
andwidth an
d en
ergy)
Solutio
ns:
Double sid
eban
d‐su
ppressed
carrier (DSB‐SC)
Suppress th
e carrier from s(t)
to save tran
smit p
ower
Still n
eed 2W
Vestig
ial sideb
and (V
SB) m
odulatio
n
Inclu
de o
ne sid
eban
d an
d th
e vestige o
f the o
ther sid
eban
d
TV: sig
nifican
t componen
ts at low freq
uen
cy
Still n
eed to tran
smit carrier
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24
AM Discu
ssions (co
ntd.)
Solutio
ns (co
ntd.):
Single sid
eban
d (S
SB) m
odulatio
n
Only u
se the u
pper o
r the lo
wer sid
eban
d
Voice: n
eglig
ible lo
w freq
uen
cy componen
ts
Optim
al form of m
odulatio
n
Minim
um tran
smit p
ower
Minim
um tran
smissio
n ban
dwidth
But, at th
e cost o
f increased
cost o
f complexity
Double Sid
eband –Suppressed
Carrier M
odulatio
n (D
SB‐SC
)AM sig
nal:
DSB‐SC: rem
ove th
e carrier, consists o
f the p
roduct o
f m(t)
and c(t)
Conseq
uen
ce: phase reversal
The en
velop is n
ot co
nserved
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25
m(t)
c(t)
s(t)
DSB
‐SC (co
ntd.)
Fourier tran
sform of s(t) is
If M
(f)is in
[‐W, W
], moves th
e baseb
and sig
nal sp
ectrum
to ±fc
No carrier co
mponen
t (pulses at ±
fc ), but still h
ave BT=
2W
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26
DSB
‐SC Im
plem
entatio
nMultip
lier is hard
er to im
plem
ent th
an Switch
ing
Modulato
r
Ring m
odulato
rThe fo
ur d
iodes fo
rm a rin
g pointin
g to th
e same w
ay
Contro
lled by a sq
uare‐w
ave carrier c(t)of freq
uen
cy fcW
hen sw
itched on: co
nstan
t forw
ard resistan
ce rf
W
hen sw
itched off: co
nstan
t back
ward
resistance r
b
One h
alf‐cycle: outer d
iodes are sw
itched on an
d th
e inner d
iodes are sw
itched off
The o
ther h
alf‐cycle: outer d
iodes are sw
itched off an
d
the in
ner d
iodes are sw
itched on
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27
Ring M
odulato
r (contd.)
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28
Ring M
odulato
r (contd.)
W
orks lik
e a co
mmutato
r
The o
utput in
one h
alf‐cycle h
as the sam
e vo
ltage b
ut d
ifferent
polarity, as th
e output
in th
e other h
alf cycle
Use th
e square carrier
c(t)to sam
ple m
(t)
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29
Ring M
odulato
r (contd.)
No output at th
e carrier freq
uen
cy fcAlso called
double‐
balan
ced m
odulato
rBalan
ced baseb
and sig
nal
Balan
ced sq
uare‐w
ave carrier
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30exp
and
Ring M
odulato
r (contd.)
Baseb
and sp
ectrum m
oved
(and scaled
) to odd harm
onics
of th
e square‐w
ave carrier c(t)
Use a b
and‐pass filter
If fc
> W
: use a b
and‐pass filter [fc
‐W, fc
+ W
] to rem
ove
unwan
ted co
mponen
ts
If fc
< W : sid
eban
d overlap
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31
fc3fc
2fc
w
w
Dem
odulatio
n: C
oheren
t Detecto
rFirst m
ultip
lying s(t)
with a lo
cally gen
erated sin
usoidal
waveAssu
ming perfect syn
chronizatio
n
coheren
t
Modulate s(t)
again w
ith th
e same carrier
Then lo
w‐pass filterin
g th
e product
rem
ove u
nwan
ted co
mponen
ts with a lo
w‐pass filter
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32
Coheren
t Detecto
r (contd.)
A phase d
ifference φ
betw
een th
e transm
itter and receiver carrier
The o
utput sig
nal is
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33
Coheren
t Detecto
r (contd.)
After th
e low‐pass filter, w
e have
Quad
rature n
ull effect: w
hen φ
= ±π/2, co
sφ=0
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34
Solutio
n: C
ostas R
eceiver
Perfect syn
chronizatio
n: very h
ard in a d
istributed
netw
ork en
vironmen
t
Costas R
eceiverUses tw
o co
heren
t detecto
rs with th
e same in
put s(t),
but th
e carriers are π/2
apart
In‐phase co
heren
t detecto
r, or I‐ch
annel
Quad
rature‐p
hase co
heren
t detecto
r, or Q
‐chan
nel
Quad
rature‐p
hase
π/2
apart
A neg
ative feedback
contro
l system to stab
ilize the
phase d
riftsAssu
ming sm
all phase d
rifts
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35
Costas R
eceiver
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36
A m
ultip
lier follo
wed by a
low‐pass filter
Stab
ilizes φat 0
Quadratu
re‐Carrier M
ultip
lexing
Exp
loit th
e quad
rature n
ull effect fo
r good use
Quad
rature‐carrier m
ultip
lexing or q
uad
rature‐
amplitu
de m
odulatio
n(Q
AM)
Use tw
o D
SB‐SC m
odulated
waves to
occu
py th
e same
ban
d, yet allo
ws sep
aration of th
e two baseb
and sig
nals
at the receiver
Two carriers w
ith 90 phase sh
ift
Dem
odulate s(t)
usin
g th
e two carriers, resp
ectivelyThe q
uad
rature n
ull effect elim
inate th
e unwan
ted base
ban
d sig
nal
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37
Quadratu
re‐Carrier M
ultip
lexing
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38
Quadratu
re‐Carrier M
ultip
lexing
(contd.)
Can use th
e Costas receiver
Or sen
d a p
ilot sig
nal o
utsid
e the p
ass‐ban
d of th
e modulated
signal
A lo
w power sin
usoidal to
ne w
hose freq
uen
cy and
phase are related
to th
e carrier wave c(t)
Used
at the receiver fo
r synch
ronizatio
n
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39
Single‐Sid
eband M
odulatio
nObjective
Only tran
smit th
e upper o
r lower sid
eban
d
Optim
al: min power an
d m
in ban
dwidth
Concep
tually easier
First g
enerate a d
ouble‐sid
eban
d sig
nal
Pass it th
rough an id
eal b
and‐pass filter, e.g
., [fc , fc +W
]
Challen
ge
Hard
to co
nstru
ct an id
eal filter (i.e., with a zero
transitio
n ban
d)
Tak
e advan
tage o
f properties o
f the sig
nal sp
ectrum
Good fo
r voice: very little en
ergy b
elow fa =
300Hz
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40
Single‐Sid
eband M
odulatio
n
(contd.)
The tran
sition ban
d of th
e filter is 2fa ,Greatly sim
plifies th
e desig
n of th
e SSB filter
Hilb
ert transfo
rm
Dem
odulatio
nCoheren
t dem
odulatio
n is req
uired
Syn
chronizatio
n
Low power p
ilot carrier in
additio
n to th
e selected sid
eban
d
Usin
g highly stab
le oscillato
rs in both th
e transm
itter and
receiver to gen
erate carrier
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41
f
|H(f)|
fcfc +
fafc ‐fa
fcfc +
fafc ‐fa
Single‐Sid
eband M
odulatio
n
(contd.)
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42
Vestigial Sid
eband M
odulatio
nVSB
For sig
nals d
o not h
ave an en
ergy g
ap at th
e orig
in
Sen
d: o
ne sid
eban
d + vestig
e of th
e other sid
eban
d
The filter is allo
wed to have a n
onzero
transitio
n ban
d
The q
uestio
n: h
ow m
uch vestig
e?
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43
VSB
(contd.)
7/13/2010
44
VSB
: Design
of H
(f)Modulated
signal sp
ectrum
Dem
odulatio
n w
ith a syn
chronous lo
cal carrier
For d
istortio
nless rep
roductio
n
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45
After lo
w‐pass filter:
VSB
(contd.)
Finally w
e have
Allo
ws a g
reat deal o
f flexibility in
choosin
g H
(f)
|H
(f)|=0.5 at th
e carrier frequen
cy
The cu
toff p
ortio
n aro
und fc
exhibits o
dd sym
metry
Sum is o
ne w
ithin fc ‐fv
≤f ≤
fc +fv
Out sid
e the b
and, i.e., |f| >
fc +W
, H(f)
can be arb
itrary
Them
e Example –
VSB
for TV
VSB fo
r commercial T
V broad
cast: analo
g an
d digital
TV ch
annel: 6
MHz: [54
MHz, 6
0 M
Hz]
Pictu
re and so
und: m
1 (t)an
d m
2 (t)
Analo
g TV
Pictu
re
Pictu
re carrier : 55.25 MHz
VSB: 25%
of th
e lower sid
e ban
d (1.25 M
Hz)+
upper sid
eban
d (4
.5 MHz) +
pictu
re carrier
Sound so
und
Sound carrier: 59
.75 MHz
Ban
dwidth: 0
.25 MHz
Two facto
rs
Video sig
nal h
as large b
andwidth an
d sig
nifican
t low‐freq
uen
cy co
nten
t VSB m
odulatio
n
SSB can
not b
e used
Dem
odulato
r should be ch
eap fo
r mass p
roductio
n
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47
VSB
for TV
(contd.)
7/13/2010
48
Idealized
amplitu
de sp
ectrum of a
transm
itted TV sig
nal
Amplitu
de resp
onse o
f VSB sh
aping
filter in th
e receiver
VSB
for TV
(contd.)
VSB can
also be u
sed fo
r digital T
V
Consid
erations
Back
ward
compatib
le: fit into 6 M
Hz T
V ch
annels
Use d
igital co
ding of vid
eo sig
nals
Low co
st dem
odulato
r circuitry fo
r mass p
roductio
n
Sound, vid
eo an
d co
lor are all in
tegrated
as one
data stream
W
ill be d
iscussed
in Chap
ter 9
Carrier at 54
.155 MHz is also
transm
itted
7/13/2010
49
VSB
for TV
(contd.)
Idealized
amplitu
de sp
ectrum of V
SB m
odulated
digital T
V sig
nal
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50
Them
e Example –
Frequen
cy‐Divisio
n M
ultip
lexing
Multip
lexing th
rough sig
nal p
rocessin
gA number o
f indep
enden
t signals are co
mbined in
to a
composite sig
nal su
itable fo
r transm
ission over a co
mmon
chan
nel
Sep
arating sig
nals in
time: tim
e‐divisio
n m
ultip
lexing
Sep
arating sig
nals in
frequen
cy: frequen
cy‐divisio
n
multip
lexing
FDM
Low‐pass sig
nals/lo
w‐pass filter
Modulato
rs shift th
e spectru
m to m
utually exclu
sive freq
uen
cy intervals
Ban
d‐pass filters to
restrict the m
odulated
signals
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51
Block D
iagram of FD
M System
7/13/2010
52
FDM Illu
stration
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53
FDM Exam
ple
GSM800 digital
chan
nelized
cellular
system
The o
ne‐w
ay ban
dwidth
is 12.5 MHz
The R
F ch
annel sp
acing
is 200 kHz
Eight u
sers share an
RF
chan
nel
Guard
ban
ds
To m
inim
ize cross‐talk
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54
Summary
Amplitu
de m
odulatio
n:
Modulate th
e amplitu
de o
f a sinusoidal carrier
A fo
rm of co
ntin
uous‐w
ave modulatio
n
Four typ
es, how do th
ey work, p
ros an
d co
ns
Stan
dard
amplitu
de m
odulatio
n (A
M)
Double sid
eban
d‐su
ppressed
carrier (DSB‐SC) m
odulatio
n
Single‐sid
eban
d (S
SB) m
odulatio
n
Vestig
ial sideb
and m
odulatio
n
Two dem
odulatio
n tech
niques
Coheren
t dem
odulatio
n
Nonco
heren
t detectio
n
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Example:
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Example (co
ntd.)
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