ANALOG

COMMUNI
CATIONS
 (
R15A0409)ANALOGCOMMUNI
CATI
ONS

CourseObjecti
ves:
Obj
ectiveofthecour sei sto:
 Emphasi zeont hestudyofpr i
nci plesofcommuni cat
iontheory
.
 Focusont hef undament alsofcommuni cati
onsystem.
 Intr
oducet het echniquesoft ransmi tti
ngandr eceivi
nginformati
onsignalsusing
analog car r
ier modul ati
on t echni ques ( AM,FM,PM) and ev aluatet heir
performancel ev el
s( SNR)inthepr esenceofchannel noi
se.
 Establi
shf oundat i
onf orunder standi ngt herel
ati
onshipamongv ari
oust echnical
factor
susef ulindesi gning&oper ati
ngcommuni cati
onsy st
em.

UNI
TI
AMPLI TUDE MODULATI ON: I ntroduct ion t o communi cat ion sy stem, Need f or
modul ation,FrequencyDi visionMul ti
plexing,Ampl it
udeModul ation:Def inition,Ti me
domai nandf r
equencydomai ndescr i
ption,si nglet onemodul ation,powerr elationsi n
AM wav es,Gener ation ofAM wav es:squar el aw Modul at or,Swi t
chi ng modul ator,
Det ect i
onofAM Wav es: Squar el awdet ect or,Env elopedet ect or.
DSB- SCmodul ation:Doubl esi debandsuppr essedcar riermodul ati
on, ti
medomai nand
frequencydomai ndescr i
pti
on, Gener ati
onofDSBSCWav es:Bal ancedModul at ors, Ring
Modul ator ,
Detect i
onofDSBSCwav es: Coher entdet ecti
on, COSTASLoop.
Radi oTr ansmi t
ters-Cl assifi
cat i
onofTr ansmi tters.AM Tr ansmi tterbl ockdi agr am and
expl anationofeachbl ock.
UNI TI I
SSBMODULATI ON:Fr equencydomai ndescr ipti
on,Fr equencydi scri
mi nat ionmet hod
forgener at
ionofAM SSBModul at edWav e,Hi lbertTr ansf or m &i t
sPr oper ties,Ti me
domai ndescr i
ption,Phasedi scrimi nat i
onmet hodf orgener at i
ngAM SSBModul ated
wav es.Demodul ationofSSBWav es.
Vest igialsidebandmodul ation:Fr equencydescr ipti
on,Gener ationofVSBModul ated
wav e,Ti me domai n descr iption,Env elope det ection ofa VSB Wav e pl us Car ri
er,
Compar i
sonofAM Techni ques, Appl icationsofdi fferentAM Sy stems.
UNI TI II
ANGLEMODULATI ON:Basi cconcept s,Fr equencyModul ation:Si nglet onef requency
modul ation,Spect r
um Anal ysisofSi nusoi dal FM Wav e,Nar rowbandFM, Wi debandFM,
Const antAv er
agePower ,Tr ansmi ssionbandwi dthofFM Wav e.Gener ationofFM
Wav es:Indi r
ectFM,Di rectFM:Var actorDi odeandReact anceModul ator .Det ectionof
FM Wav es:Bal ancedFr equencydi scriminat or,Zer ocr ossi ngdet ect
or ,Phasel ocked
l
oop,Compar i
sonofFM &AM.,Pr e-
emphasi s&de- emphasi s,FM Tr ansmi tterbl ock
diagr am andexpl anationofeachbl ock.
UNI TI V
NOI SE:Noi seincommuni cationSy st em, Whi teNoi se,Nar rowbandNoi se–I nphaseand
Quadr aturephasecomponent s.Noi seBandwi dth,Noi seFi gur e,Noi seTemper ature,
Noi sei nDSB&SSBSy stem Noi sei nAM Sy stem, NoiseinAngl eModul ationSy stem, and
Threshol def f
ectinAngl eModul ationSy stem.
UNITV
RECEIVERS: Radio Receiver, Recei
ver Types: Tuned r adi
o f requency recei
ver,
Super
het r
odyne recei
ver- RF sect i
on, Fr
equency mi xer
s, tracking, Int
ermedi
ate
fr
equency,AGC. Recei ver Parameters & Char act
eri
sti
cs,FM Recei ver and i
ts
comparisonwithAM Receiver
.
PULSEMODULATI ON:Ty pesofPul semodul ati
on,PAM:Gener ati
on( Singl
epolari
ty,
doubl
epol ar
ity
)andDemodul at
ion.PWM:Gener ation&demodul at
ionofPWM,PPM,
Generat
ionanddemodul ati
onofPPM.

TEXTBOOKS:
1.Communi cat
ionSy
stems-SimonHay ki
n,2ndEditi
on,Wil
eyPubl
icat
ions.
2.Communi cat
ionSy
stems–B. P.Lathi
,BSPublicati
on,2006.
3.Pri
nci
plesofCommunicati
onSy st
ems–HTaub&D.Schi l
li
ng,
Gautam Sahe,
TMH,20073r dEdi
ti
on.

REFERENCES:
1.Elect
ronics&Communi cationSyst
em –Geor geKennedyandBer nar
dDav i
s,
TMH2004.
2.Communi cati
onSy st
emsSecondEdi tion–R. P.Si
ngh,
SPSapr e,
TMH, 2007.
3.Analog&Di gi
talCommuni cati
on–K. Sam Shanmugam, Wil
ey2005
4.Fundament alsofCommuni cati
onSystems-JohnG.Pr oaki
s,Masond,Sal
ehiPEA,
2006.
5.Elect
ronicCommuni cat
ionSy st
ems-Modul at
ion&Transmissi
on-Robert
nd
J.Schoenbeck, 2 Edi ti
on,PHI
 UNI
T-I
I
ntr
oduct
iont
oCommuni
cat
ionSy
stem

Communi
cati
oni
sthepr
ocessbywhi
chi
nfor
mat
ioni
sexchangedbet
ween
i
ndi
vi
dual
sthr
oughamedium.

Communicati
oncanal
sobedefi
nedast
het
ransf
erofi
nfor
mat
ionf
rom onepoi
nti
n
spaceandti
metoanot
herpoi
nt.

Thebasi
cbl
ockdi
agr
am ofacommuni
cat
ionsy
stem i
sasf
oll
ows.

 Transmitter:Couplesthemessagei ntot hechannel usinghighfrequencysi

gnal
s.
 Channel:Themedi um usedf ortr
ansmi ssi
onofsignal s
 Modul at
ion:Itistheprocessofshi f
ti
ngt hef r
equencyspect rum ofasignal
to
afrequencyr angeinwhi chmor eeffi
cienttransmissioncanbeachi eved.
 Receiver
: Restoresthesignal t
oitsori
ginalform.
 Demodul ati
on: I
tisthepr ocessofshif
t i
ngthef r
equencyspect rum backtothe
ori
ginalbasebandf requencyr angeandr econstr
uctingt heori
ginalf
orm.

Modul
ati
on:

Modul
ati
oni
sapr
ocesst
hatcausesashi
fti
nther
angeoff
requenci
esi
nasi
gnal
.

•Si
gnal
sthatoccupyt
hesamer
angeoff
requenci
escanbesepar
ated.

•Modul
ati
onhel
psi
nnoi
sei
mmuni
ty,
att
enuat
ion-dependsont
hephy
sical

medi
um.Thebel
owf
igur
eshowst
hedi
ff
erentki
ndsofanal
ogmodul
ati
onschemes

t
hatar
eav
ail
abl
e
Modulat
ioni
soperati
onper
for
medatt
het
ransmi
tt
ert
oachi
eveef
fi
cientandr
eli
abl
e
i
nfor
mationt
ransmissi
on.

Foranal
ogmodulati
on,
iti
sfrequencytransl
ati
onmet
hodcausedbychangi
ngt
he
appropr
iat
equant
it
yinacarr
iersignal
.

I
tinv
olv
est
wowav
efor
ms:

 Amodulat
ingsignal
/basebandsignal
–repr
esent
sthemessage.
 Acar
ri
ersignal
–dependsont y
peofmodulati
on.

•Oncet
hisi
nfor
mat
ioni
srecei
ved,
thel
owf
requencyi
nfor
mat
ionmustber
emov
ed
f
rom t
hehi
ghf
requencycar
ri
er.•
Thi
spr
ocessi
sknownas“
Demodul
ati
on”
.

Needf
orModul
ati
on:

 Basebandsi gnalsar eincompat ibl

efordi
recttr
ansmi
ssi
onovert
hemedi
um
so,modul ati
onisusedt oconv ey(baseband)si
gnal
sfr
om onepl
acet
o
another.
 All
owsf requencyt ranslati
on:
o Fr equencyMul t
iplexi
ng
o Reducet heant ennahei ght
o Av oidsmi xingofsi gnals
o Nar rowbandi ng
 Eff
icienttr
ansmi ssion
 Reducednoi seandi nt
er f
erence

Ty
pesofModul
ati
on:

Thr
eemai
nty
pesofmodul
ati
ons:

Anal
ogModul
ati
on

 Ampl
i
tudemodul
ati
on
 Example:Doubl e sideband with carr
ier(
DSB-WC) ,Double-sideband
suppressedcar r
ier(DSB-SC),Singlesidebandsuppressedcarri
er(
SSB- SC)
,
vest
igialsi
deband( VSB)
 Anglemodul at
ion( f
requencymodulati
on&phasemodul ati
on)
Example:Nar row band f r
equency modulat
ion ( NBFM),Wideband
fr
equency modul at
ion (WBFM) ,Nar r
owband phase modul ati
on (NBPM),
Widebandphasemodul ati
on( NBPM)

Pul
seModul
ati
on

 Carri
eri
sat rai
nofpulses
 Example:PulseAmpli
tudeModul
ati
on(
PAM)
,Pul
sewi
dthmodul
ati
on(
PWM),
PulsePosit
ionModulati
on(PPM)

Di
git
alModul
ati
on

 Modul
ati
ngsi
gnal i
sanalog
o Example:Pulse Code Modul ati
on (PCM),Delta Modul
ati
on (
DM) ,
Adapti
veDel t
aModul ation(ADM),Dif
fer
enti
alPulseCodeModulati
on
(DPCM),AdaptiveDiff
erenti
alPul
seCodeModul at
ion(
ADPCM)etc.
 Modul
ati
ngsi
gnal i
sdigit
al(bi
narymodulat
ion)
o Example:Ampl i
tudeshiftkeyi
ng(ASK),f
requencyShi
ftKeyi
ng(FSK),
PhaseShiftKeyi
ng( PSK)etc

Fr
equencyDi
vi
sionMul
ti
plex
ing

Multi
plexi
ngi sthenamegivent
otechni
ques,whichal
lowmorethanonemessaget o
betransferr
edv i
athesamecommuni cati
onchannel.Thechannelinthi
scont ext
couldbeat ransmissi
onl
ine,e.
g.atwi
stedpairorco-
axi
alcabl
e,aradi
osystem ora
fi
breopticsystem et
c.

FDM isder
ivedfrom AM techni
quesinwhichthesignalsoccupythesamephysical
‘
li
ne’buti
ndiff
erentfr
equencybands.Eachsignaloccupiesi
tsownspecif
icbandof
fr
equenci
esallt
hetime,i
.e.themessagessharethechannelbandwidt
h.

 FDM –messagesoccupynar
rowbandwi
dth–al
lthet
ime.
 Fi
g.1.Fr
equencyDi
vi
sionMul
ti
plex
ing

Ampl
i
tudeModul
ati
on(
AM)

Amplit
udeModulat
ionistheprocessofchangi
ngtheampl
it
udeofarel
ati
vel
yhigh
fr
equencycar
ri
ersignali
naccordancewit
ht heampl
it
udeofthemodul
ati
ngsignal
(I
nfor
mati
on).

Thecarri
erampli
tudevar
iedli
nearl
ybythemodulati
ngsignalwhi
chusual
lyconsi
sts
ofarangeofaudi
of r
equenci
es.Thefr
equencyofthecar
rieri
snotaf
fect
ed.
  Appli
cationofAM -Radi
obr oadcast
ing,
TVpi
ctur
es(
video)
,facsi
mil
etr
ansmi
ssi
on
 FrequencyrangeforAM -535kHz–1600k Hz
 Bandwidth-10k Hz

Var
iousf
ormsofAmpl
i
tudeModul
ati
on

•Conv ent
ionalAmpl
it
udeModul
ati
on(Alt
ernat
ivel
yknownasFul
lAM or
DoubleSidebandLar
gecar
ri
ermodulat
ion(DSBLC)/Doubl
eSi
debandFul
l
Carr
ier(DSBFC)

•Doubl
eSi
debandSuppr
essedcar
ri
er(
DSBSC)modul
ati
on

•Si
ngl
eSi
deband(
SSB)modul
ati
on

•Vest
igi
alSi
deband(
VSB)modul
ati
on

Ti
meDomai
nandFr
equencyDomai
nDescr
ipt
ion

I
tist
hepr
ocesswher
e,t
heampl
i
tudeoft
hecar
ri
eri
svar
iedpr
opor
ti
onal
to
t
hatoft
hemessagesi
gnal
.

Letm (t
)bethebase-bandsi
gnal
,m( t
)←→ M (
ω)andc(t
)bet
hecar r
ier
,c(
t)
=Accos(
ωct).f
cischosensuchthatf
c>>W, wher
eW i
sthemaxi
mum f
requency
componentof
m(t)
.Theamplit
udemodulatedsi
gnali
sgiv
enby

s(
t)=Ac[
1+kam(
t)]cos(
ωct
)

Four
ierTr
ansf
orm onbot
hsi
desoft
heabov
eequat
ion

S(
ω)=πAc/
2(δ(
ω−ωc)+δ(
ω+ωc)
)+kaAc/2(
M(ω−ωc)+M(
ω+

ωc)
)kai
saconst
antcal
l
edampl
i
tudesensi
ti
vi
ty.

kam(
t)<1andi
tindi
cat
esper
cent
agemodul
ati
on.

Fi
g.2.Ampl
i
tudemodul
ati
oni
nti
meandf
requencydomai
n
Si
ngl
eToneModul
ati
on:

Consi
deramodulati
ngwavem(t)t
hatconsi
stsofasi
ngl
etoneorsi
ngl
e
fr
equencycomponentgi
venby

Expandi
ngt
heequat
ion(
2),
weget
 Fi
g.3.Fr
equencyDomai
nchar
act
eri
sti
csofsi
ngl
etoneAM

Powerr
elat
ionsi
nAM wav
es:

Consi
dert
heexpr
essi
onf
orsi
ngl
etone/
sinusoi
dal
AM wav
e
Ther
ati
ooft
otal
sidebandpowert
othet
otal
poweri
nthemodul
atedwav
eisgi
venby

Thi
srat
ioi
scal
l
edt
heef
fi
ciencyofAM sy
stem

Gener
ati
onofAM wav
es:

Twobasi
campli
tudemodul
ati
onpri
nci
plesar
edi
scussed.Theyar
esquar
elaw
modul
ati
onandswit
chi
ngmodulat
or.

Squar
eLawModul
ator

Whentheout
putofadevi
cei
snotdir
ectl
yproport
ionalt
oinputt
hroughoutthe
oper
ati
on,t
hedevi
ceissai
dtobenon-
li
near
.TheInput-
Outputrel
ati
onofanon-li
near
devi
cecanbeexpr
essedas

Whent
heoutputi
sconsi
deredupt
osquar
eofthei
nput,
thedevi
cei
scal
l
edasquar
e
l
awdevi
ceandthesquar
elawmodulat
ori
sasshowninthef
igur
e4
 Fig.
4.SquareLawModul at
or
Consideranon-l
ineardevicetowhi chacar r
ierc(t
)=Accos(
2πfct
)andan
i
nformationsi
gnalm( t
)arefedsi mult
aneousl
yasshowni nf i
gure4.The
tot
alinputt
othedeviceatanyinst
antis

Thereforethesquarelawdev i
ceout
put0Vconsi
stsoft
hedccomponentatf
=0.Thei nformati
onsi gnalr
angi
ngfr
om 0t
oW Hzanditssecondhar
monics
aresignalatfcand2fc.
Spect
rum i
sasshownbel
ow
Swit
chingModul
ator

Fi
g.5.Swit
chingModul
ator
Thet
otal
inputf
ort
hedi
odeatanyinstanti
sgi
venby
 Whent hepeakampl itudeofc( t
)ismai ntained mor et hanthatof
i
nformationsignal,theoper ationisassumedt obedependentononl yc(t)
i
rrespecti
veofm( t)
.
Whenc( t
)isposi t
ive,v2=v1si
ncethediodeisfor wardbiased.Si
mi l
arl
y,
whenc( t)i
snegat i
ve,v2=0si ncediodeisreversebiased.Baseduponabov e
operati
on,swit
chingr esponseoft hediodeisperiodicr ect
angularwavewi t
h
anampl i
tudeunityandi sgiv
enby

Therequi
redAM si
gnalcent
redatfccanbeseparat
edusi
ngbandpass
fi
l
ter.Thelowercutoff
-fr
equencyforthebandpassfi
lt
ershoul
dbebet ween
wandf c-
wandt heuppercut-
offf
requencybet
weenfc+wand2f c.Thefi
lt
er
outputisgiv
enbytheequati
on
Det
ect
ionofAM wav
es

Demodulat
ionistheprocessofrecoveri
ngthei
nformati
onsi
gnal
(baseband)
fr
om t
heincomingmodul at
edsignalattherecei
ver
.Therear
etwomethods,t
heyare
Squar
elawDetectorandEnvelopeDetector

Squar
eLawDet
ect
or

Consi
deranon-
li
neardevi
cetowhi
chtheAM si
gnals(
t)i
sappl
i
ed.Whent
hel
evel
of
s(
t)i
sverysmal
l,out
putcanbeconsi
der
eduptosquar
eofthei
nput
.
Thedev i
ceoutputconsist
sofadccomponentatf=0,i nformat
ionsignalrangi
ng
fr
om 0-W Hzandi t
ssecondharmonicsandf r
equencybandscenteredatfcand2f c.
The requi
red i
nfor
mation can be separ
ated usi
ng low pass f
ilt
erwi t
h cutof f
fr
equencyrangi
ngbetweenW andf c-
w.Thef i
l
teroutputi
sgivenby

Whentheinformati
onlevelisver
ylow,t
henoiseef
fecti
ncr
easesatt
her
ecei
ver
,
hencet
hesystem cl
ari
tyi
sv er
ylowusi
ngsquar
elawdemodul
ator
.

Env
elopeDet
ect
or

Iti
sasimpleandhighlyeff
ecti
vesyst
em.Thismethodi
susedinmostoft
he
commer
cial
AM r
adi
or ecei
ver
s.Anenv
elopedet
ect
ori
sasshownbel
ow.
 Fi
g.7.Env
elopeDet
ect
or

Dur
ingt heposit
ivehalfcy cl
esoftheinputsi
gnals,t
hediodeDi sforward
biasedandt hecapaci
torCchar gesuprapi
dlytothepeakoftheinputsignal
.When
theinputsignalfal
lsbelow thi
sv al
ue,t
hediodebecomesr ever
sebi asedandt he
capacit
orCdi schar
gesthroughtheloadr
esist
orRL.

Thedischar
geprocessconti
nuesunti
lthenextposi
ti
vehal
fcycl
e.Whenthe
i
nputsignalbecomesgr eatert
han thevol
tageacrossthecapaci
tor
,thediode
conduct
sagainandtheprocessi
srepeat
ed.

Thechargeti
meconst ant(
rf+Rs)
Cmustbeshor tcomparedwit
hthecar
ri
er
peri
od,t
hecapacit
orchargesrapi
dlyandther
ebyfoll
owst heappl
iedv
olt
ageupto
theposi
tiv
epeakwhent hediodeisconducti
ng.
Thatisthechargi
ngti
meconst
ant
shal
lsat
isfyt
hecondi
ti
on,

Where ‘ W’ is band wi dt
h of t he message si
gnal
.Theresul
tist
hatt
he
capaci
torvol
tageordet
ect
oroutputi
snear
lyt
hesameast
heenvel
opeofAM wave.

Adv
ant
ages and Di
sadv
ant
ages of

AM:
Adv
ant
agesofAM:
  Gener
ati
onanddemodulat
ionofAM waveareeasy
.
 AM syst
ems ar e cost effect
ive and easy t
o bui
l
d.

Di
sadv
antages:
 AM cont ains unwant ed car
ri
er component
,hence i
t r
equir
es
moretr
ansmi ssionpower.
 The t ransmi ssi
on bandwidt
h is equal t o twi
ce the
messagebandwi dth.

Toovercomet heseli
mit
ati
ons,t
heconventi
onalAM sy
stem i
smodi
fi
edatthe
costofincreased system complexi
ty.Ther
efor
e,three t
ypes ofmodi
fi
ed AM
syst
emsarediscussed.

DSBSC (
Doubl
e Si
de Band Suppr
essed Car
ri
er) modul
ati
on:I
nDSBC
modul
ati
on,t
hemodul
atedwav
econsi
stsofonl
ytheupperandl
owersi
debands.
Tr
ansmi
tt
edpoweri
ssav
edt
hrought
hesuppr
essi
onoft
hecar
ri
erwav
e,butt
he
channel
bandwi
dth r
equi
rement i
s t
he same
as bef
ore.

SSBSC (
Singl
e Si
de Band Suppr
essed Car
ri
er)modul
ati
on:The SSBSC
modul
atedwav
econsi
stsofonl
ytheuppersi
debandorl
owersi
deband.SSBSCi
s
sui
tedf
ort
ransmi
ssi
on of v
oice si
gnal
s. I
t i
s an opt
imum f
orm of
modul
ati
on i
nthati
trequi
res t
he mi
nimum t
ransmi
ssi
on powerand mi
nimum
channel
bandwi
dth.Di
sadv
ant
agei
sincr
easedcostandcompl
exi
ty.

VSB(
Vest
igi
alSi
deBand)modul
ati
on:I
nVSB,onesi
debandi
scompl
etel
y
passedandj
ustat
raceorv
est
igeoft
heot
hersi
debandi
sret
ained.Ther
equi
red
channelbandwi
dthi
sther
efor
einexcessoft
hemessagebandwi
dthbyanamount
equalt
othewi
dth oft
hev
est
igi
alsi
deband.Thi
smet
hod i
ssui
tabl
efort
he
t
ransmi
ssi
onofwi
debandsi
gnal
s.
 DSB-
SCMODULATI
ON

DSB-
SCTi
medomai
nandFr
equencydomai
nDescr
ipt
ion:

DSBSCmodul at
orsmakeuseoft hemultiply
ingact ioni
nwhi chthe
modulati
ngsignal
mul ti
pli
esthecarr
ierwave.I
nt hi
ssy stem, t
hecarri
ercomponent
i
seli
mi nat
edandbot hupperandlowersidebandsar etransmi t
ted.Asthecarri
er
componentissuppressed,thepowerrequi
redfortransmi ssi
onislessthanthatof
AM.

Consequent
ly,t
hemodulat
edsignal
s(t
)undergoesaphaser
ever
sal
,whenev
ert
he
messagesignalm(
t)cr
osseszeroasshownbelow.

Fi
g.1.(
a)DSB-
SCwav
efor
m(b)DSB-
SCFr
equencySpect
rum

Theenvel
opeofaDSBSCmodul at
edsi gnali
stheref
oredi
ff
erentf
rom t
he
messagesi
gnalandtheFour
iert
ransf
orm ofs(t)i
sgivenby
Gener
ati
onofDSBSCWav
es:

Bal
ancedModul
ator(
ProductModul
ator
)

A bal anced modul atorconsi

sts oftwo standard ampli
tude modulat
ors
arrangedinabal ancedconf i
gurati
onsoastosuppressthecarri
erwaveasshowni n
thef ol
lowingbl ockdi agram.I ti
sassumedt hatt
heAM modul at
orsareidenti
cal
,
exceptf orthesi gnr ever
saloft hemodulat
ingwaveappliedtotheinputofoneof
them.Thus, theout putoft hetwomodulat
orsmaybeexpr essedas,
Hence,ex
ceptfort
hescal
ingfact
or2ka,t
hebalancedmodul
atorout
puti
sequalt
o
t
heproductoft
hemodulat
ingwaveandthecar
ri
er.

Ri
ngModul
ator

Ri
ngmodulat
orist
hemostwi
del
yusedpr
oductmodul
atorf
orgener
ati
ngDSBSC
waveandi
sshownbel
ow.

Thefourdiodesfor
m ar i
nginwhi cht heyal
lpointinthesamedi rect
ion.Thediodes
are contr
oll
ed by square wav e carri
erc(t
)off r
equency fc,which is appli
ed
l
ongitudi
nall
ybymeansoft wocent er-t
appedtransformers.Assumingthediodesare
i
deal,whent hecar
rierisposit
ive,theouterdiodesD1andD2ar eforwardbiased
whereast heinnerdiodesD3andD4ar er eversebiased,sot hatthemodul at
or
multi
pli
esthebasebandsi gnalm( t
)byc( t
).Whent hecar r
ieri
snegative,t
hediodes
D1andD2ar ereversebiasedandD3andD4ar ef orward,andt hemodul at
or
multi
pli
esthebasebandsignal –m( t
)byc(t)
.

Thus t
he ri
ng modul at
orinitsidealf
orm is a pr
oductmodul
atorf
or
squarewavecarr
ierandt hebasebandsi
gnalm(
t).Thesquar
ewavecar
ri
ercanbe
expandedusi
ngFourierseri
esas

From t
heaboveequati
onitiscleart
hatoutputf r
om t
hemodulat
orconsists
enti
rel
yofmodulat
ionpr
oducts.I
ft hemessagesi gnalm(t
)isbandli
mitedtot he
fr
equencyband−w<f<w, theoutputspect
rum consist
sofsi
debandscentr
edatf c.
Det
ect
ionofDSB-
SCwav
es:

Coher
entDet
ect
ion:

Themessagesi gnalm(
t)canbeuni
quel
yrecoveredfr
om aDSBSCwaves( t
)
byfi
rstmult
iply
ings(t)wit
halocal
l
ygener
atedsi
nusoidalwaveandthenl
ow pass
fi
l
ter
ingtheproductasshown.

Itis assumed thatt he l

ocaloscill
ator si
gnalis exactl
y coherentor
synchroni
zed,inbothfrequencyandphase,withthecarri
erwav ec(t)usedinthe
productmodul atort
o generates(t
).Thismet hodofdemodul at
ioni sknownas
coherentdet
ectionorsy
nchronousdetect
ion.

Fi
g.6.
Spect
rum ofout
putoft
hepr
oductmodul
ator
 From t
hespectr
um,i
tisclearthattheunwantedcomponent(f
ir
stter
mi nthe
expr
ession)can be r
emoved by the low-pass f
il
ter
,prov
ided t
hatt he cut
-of
f
fr
equencyofthef
il
teri
sgr
eatert
hanW butl essthan2fc-
W.Thefi
lt
eroutputi
sgiven
by

Thedemodul
atedsi
gnal
vo(
t)i
sther
efor
epr
opor
ti
onal
tom(
t)whent
hephaseer
rorϕ
i
sconstant
.

Cost
asRecei
ver(
Cost
asLoop)
:

Cost
asrecei
verisasynchr
onousrecei
versy
stem,sui
tabl
efordemodulat
ing
DSBSCwaves.I
tconsistsoft
wocoherentdet
ector
ssuppli
edwitht
hesamei nput
si
gnal
,

Fi
g.7.Cost
asRecei
ver

Thef
requencyoft helocalosci
ll
atori
sadj
ustedtobethesameast hecarri
er
fr
equencyfc.Thedet ectori
nt heupperpathisr
eferr
edtoasthein-
phasecoherent
detect
ororI -
channel,andthati nthelowerpat
hi sref
err
edtoast hequadrat
ure-
phasecoherentdetectororQ-channel
.

Thesetwodetect
orarecoupledt
ogethertofor
m anegati
vefeedbacksyst
em
desi
gnedi nsuchawayast omaintaint
helocalosci
ll
atorsy
nchr
onouswi t
hthe
carr
ierwave.Suppose
the local osci l
l
ator signal i
s of t he same phase as t he carrerc(
i t)=
Accos(2πfct
)wav eusedt ogener
atetheincomi ngDSBSCwav e.Thenwef i
ndthatt he
I-
channelout putcontainsthedesireddemodul atedsignalm( t),whereast heQ-
channeloutputiszeroduet oquadr at
urenul lef
fectoftheQ- channel.Supposet hat
thelocaloscil
lat
orphasedr i
ftsf
rom it
spr opervaluebyasmal langleϕradians.The
I-
channelout put wil
lr emain essenti
allyunchanged,but t here willbe some
signalappearing at the Q-channel out put,whi ch i
s pr oporti
onal tosin( )≈
f
orsmal lϕ.

ThisQ-channeloutputwi l
lhavesamepol ari
tyast heI
-channeloutputforone
dir
ecti
on ofl ocaloscil
latorphase dr iftand opposi
te polar
ityfort he opposi
te
dir
ecti
onofl ocaloscil
latorphasedr if
t.Thusbycombi ni
ngt heI-channelandQ-
channeloutputsinaphasedi scr
iminator(whi
chconsistsofamul ti
pli
erfoll
owedby
aLPF),adccont r
olsi
gnalisobt ai
nedt hataut
omatical
lycorr
ectsforthelocalphase
err
orsinthevoltage-
controll
edoscil
lator.

Radi
oTr
ansmi
tt
ers

Ther
ear etwoappr oachesingenerat
inganAM si gnal
.Theseareknownas
l
ow andhi ghlevelmodulati
on.They'r
eeasyt oidentif
y:Alow l
evelAM transmi
tt
er
perfor
mst heprocessofmodul at
ionnearthebegi nni
ngofthet r
ansmit
ter.Ahigh
l
ev elt
ransmit
terperf
ormst hemodulati
onstepl ast,att
helastor"fi
nal"ampli
fi
er
stageinthetr
ansmitt
er.Eachmet hodhasadv antagesanddisadvant
ages,andboth
areincommonuse.

Low-
Lev
elAM Tr
ansmi
tt
er:

Fi
g.8.Low-
Lev
elAM Tr
ansmi
tt
erBl
ockDi
agr
am

Ther
ear etwosignalpathsint hetransmi t
ter
,audiofrequency( AF)andr adio
frequency( RF).TheRFsi gnaliscr eatedint heRFcarrieroscill
ator
.Att estpointA
theosci l
lat
or'soutputsignalispresent.Theout putofthecarrieroscil
l
atorisaf air
ly
smal lACv oltage,perhaps200t o400mVRMS.Theosci l
l
atori sacr i
ti
calstagei n
anyt ransmi t
ter.Itmustpr oduceanaccur ateandst eadyf requency.Ev er
yr adio
stati
oni sassi gnedadi ff
erentcarrierfr
equency .Thedial(ordi spl
ay)ofar eceiver
displaysthecar ri
erf
requency.Ift
he
oscil
l
atordri
ftsofffr
equency ,t
her ecei
verwillbeunabletorecei
vet hetr
ansmi t
ted
si
gnalwithoutbei
ngr eadj
usted.Wor seyet,i
ftheoscil
l
atordrif
tsontothefrequency
beingusedbyanot herradi
ost ati
on,int
erfer
encewilloccur.Twocircuitt
echniques
arecommonl yusedtostabil
i
zet heoscil
lat
or,buff
eri
ngandv olt
ageregulat
ion.

Thebuf f
erampl i
fi
erhassomet hi
ngt odowi thbuffer
ingorpr otect
ingt he
oscil
lat
or.Anoscill
atorisalit
tl
el i
keanengi ne(wi
ththespeedoft heenginebei ng
si
mi l
art otheoscil
lator
'sfrequency)
.Ifthel oadont heengineisincreased( the
engineisaskedt odomor ewor k),theenginewillr
espondbysl owingdown.An
oscil
lat
oractsi nav erysi
mi l
arfashion.Ifthecur
rentdrawnf r
om theosci ll
ator'
s
outputisincr
easedordecreased,theoscil
l
atormayspeeduporsl owdownsl ightl
y.

Buf ferampl if
ierisar elati
velylow- gai
nampl i
fi
ert hatfollowst heosci l
lat
or.It
hasaconst antinputi mpedance( r
esist
ance).Ther efore,italway sdr awst hesame
amountofcur r
entf rom theosci l
lator.Thishelpstopr event"pul l
ing"oft heoscill
ator
frequency . The buf f
er ampl if
ier i s needed because of what 's happening
"downst ream"oft heosci l
lat
or.Ri ghtafterthisstagei sthemodul ator .Becausethe
modul atori sanonl inearampl if
ier,itmaynothav eaconst anti nputr esist
ance- -
especiallywheni nformationi spassi ngintoit.Butsi ncet herei sabuf feramplif
ier
betweent heosci l
latorandmodul ator,t
heosci l
latorseesast eadyloadr esi
stance,
regardlessofwhatt hemodul atorstageisdoi ng.

VoltageRegul ation:Anosci l
latorcanal sobepul ledofffrequencyi fitspower
supplyv oltageisn'theldconst ant.Inmostt r
ansmi tt
ers,thesuppl yv olt
aget othe
oscil
l
atori sregulatedataconst antv alue.Ther egulatedvoltagev al
uei soften
between5and9v olts;zenerdi odesandt hree-ter
mi nalregul
atorI Csar ecommonl y
used v oltage regulator s.Vol tage r egul at
ion is especi al
lyi mpor tant when a
tr
ansmi tt
eri sbeingpower edbybat teriesoranaut omobi le'
selectricalsystem.Asa
batt
erydi scharges,itst erminalv ol
tagef all
s.TheDCsuppl yvoltagei nacarcanbe
anywher ebet ween12and16v olt
s,dependi ngonengi neRPM andot herelectr
ical
l
oadcondi ti
onswi t
hint hev ehi
cle.

Modulator:Thest abi
li
zedRFcar r
iersi
gnalf eedsoneinputoft hemodulator
stage.Themodul atorisavariabl
e-gai
n( nonl
inear)ampli
fi
er.Towor k,itmusthav e
anRFcar ri
ersignalandanAFi nf or
mat i
onsi gnal.Inalow-l
eveltransmitt
er,t
he
powerl evel
sar el ow intheoscil
lator,buff
er,andmodul atorstages;typi
call
y,t
he
modul at
oroutputi saround10mW ( 700mVRMSi nto50ohms)orless.

AFVol t
ageAmpl if
ier:Inor derf ort hemodul atortof uncti
on,itneedsan
i
nfor mationsi gnal
.Ami crophonei sonewayofdev elopi
ngt heintell
igencesignal
,
howev er,itonl ypr oducesaf ew mi l
liv
ol t
sofsi gnal.Thi ssi mplyisn'tenought o
operatet hemodul ator,soav ol
tageampl i
fierisusedt oboostt hemi crophone'
s
si
gnal .Thesi gnallevelatt heoutputoft heAFv olt
ageampl i
fierisusuallyatleast1
vol
tRMS;i tishighl ydependentupont het ransmitter'sdesign.Not i
cet hattheAF
ampl i
fierint hetransmi t
terisonl ypr ovidi
ngav ol
tagegai n,andnotnecessar i
lya
currentgai nf orthemi crophone'ssi gnal.Thepowerl evel
sar equi t
esmal latthe
outputoft hisampl i
f i
er;
af ewmW atbest .
 RFPowerAmpl i
fi
er:Attestpoi ntDt hemodul atorhascr eatedanAM si gnalby
i
mpr essingthei nformationsignalf rom t estpoi ntCont othest abi
lizedcar ri
ersi
gnal
from t estpoi ntB att hebuf ferampl ifi
erout put.Thi ssignal( testpoi ntD)i sa
compl eteAM si gnal,buthasonl yaf ewmi ll
iwat tsofpower .TheRFpowerampl i
fi
er
i
snor mal l
ybui ltwithsev eralstages.Thesest agesi ncreasebot ht hev olt
ageand
currentoft heAM si gnal.Wesayt hatpowerampl if
icati
onoccur swhenaci rcui
t
providesacur rentgai n.Inordert oaccur atelyampl if
yt hetinyAM si gnalfrom the
modul ator,t heRFpowerampl ifi
erst agesmustbel i
near.Youmi ghtr ecal
lthat
ampl if
iersar edi vi
dedupi nto" classes,"accor dingt otheconduct i
onangl eoft he
acti
v edev icewi t
hin.ClassA andcl assB ampl i
fi
ersar econsi deredt obel i
near
ampl if
iers,sot heRFpowerampl i
fi
erst ageswi llnormal l
ybeconst ructedusingone
orbot hoft heset ypeofampl i
fi
er s.Ther efore,thesi gnalattestpoi ntEl ooksjustli
ke
thatoft estpointD; it'
sjustmuchbi ggeri nv olt
ageandcur r
ent.

Ant
ennaCoupl er
:Theant ennacoupl erisusuall
ypartofthel astorfi
nalRF
powerampl if
ier
,andassuch,i snotr eall
yasepar ateacti
vestage.Itperfor
msno
ampli
ficat
ion,andhasnoact i
vedev i
ces.Itperfor
mst woimport
antj obs:I
mpedance
matchingandf ilt
eri
ng.ForanRFpowerampl ifi
ertofunct
ioncorrectl
y,i
tmustbe
suppl
iedwi t
hal oadresist
anceequal t
ot hatforwhichi
twasdesigned.

Theant ennacoupl eralsoact sasal ow- passfil

ter.Thi
sfil
teringreducesthe
ampl i
tudeofhar monicener gi
est hatmaybepr esentint hepowerampl i
fi
er'
soutput.
(Allampl if
ier
sgener atehar moni cdistorti
on,ev en"li
near"ones.)Forexampl e,the
transmittermaybet unedt ooper ateon1000kHz.Becauseofsmal lnonli
neari
ti
esin
theampl ifi
ersoft hetransmi t
ter,thetr
ansmi t
terwillal
sopr oduceharmoni cenergi
es
on2000kHz( 2ndhar monic),3000kHz( 3r
dhar monic),andsoon.Becauseal ow-
passf i
lt
erpassest hef undament alfr
equency( 1000kHz)andr ej
ectst heharmonics,
wesayt hatharmoni cat t
enuationhast akenplace.

Hi
gh-
Lev
elAM Tr
ansmi
tt
er:

Fi
g.9.Low-
Lev
elAM Tr
ansmi
tt
erBl
ockDi
agr
am

Thehigh-
leveltr
ansmitt
erofFigure9i sverysimi
l
artothelow-l
eveluni
t.The
RFsecti
onbeginsjustli
kethelow-l
eveltransmi
tter;t
her
eisanoscil
lat
orandbuf f
er
ampli
fi
er.Thedif
ferenceinthehi
ghlev eltr
ansmitt
eriswher
et hemodulati
ontakes
pl
ace.I
nsteadof
addingmodulat
ioni
mmedi at
elyaft
erbuffering,
thi
st y
peoft ransmi
tterampli
fiest
he
unmodulat
edRFcarri
ersignalf
ir
st.Thus, t
hesignal
satpoi ntsA,B,
andDi nFi
gure9
al
llookli
keunmodulat
edRFcar ri
erwav es.Theonl ydiff
erenceist
hatt heybecome
bi
ggerinvol
tageandcurr
entastheyappr oachtestpointD.

Themodulationprocessi nahi gh-leveltransmi tt

ert akespl acei nthelastor
fi
nal poweramplifi
er.Becauseoft hi
s,anaddi ti
onal audioampl i
fiersecti
oni sneeded.
Inor dertomodulateanampl ifi
erthatisr unningatpowerl ev elsofsev eralwatt
s( or
mor e),comparablepowerl evel
sofi nformat i
onar er equir
ed.Thus,anaudi opower
ampl if
ierisrequir
ed.Thef i
nalpowerampl if
ierdoesdoubl e-dutyinahi gh-l
evel
transmi t
ter
.Fir
st,itprovi
despowergai nf ortheRFcar ri
ersi gnal,j
ustl i
ketheRF
powerampl i
fi
erdidi nthelow-l
eveltransmi tter.Inaddi t
iont opr ov
idi
ngpowergai n,
thefinalPAalsoper for
mst hetaskofmodul ati
on.Thef inalpowerampl i
fi
erinahi gh-
l
ev eltransmit
terusuallyoperatesincl assC,whi chi sahi ghlynonl i
nearampl ifi
er
class.

Compar
ison:

LowLev
elTr
ansmi
tt
ers

 Canpr oduceanyki
ndofmodulat
ion;
AM, FM, orPM.
 Requireli
nearRFpowerampl
i
fier
s,whichreduceDCeff
ici
encyandi
ncr
eases
producti
oncosts.

Hi
ghLev
elTr
ansmi
tt
ers

 HavebetterDCeff
ici
encythanl
ow-
lev
eltransmi
tter
s,andar
ever
ywel
lsui
ted
forbatt
eryoper
ati
on.
 Arerestr
ict
edtogener
ati
ngAM modulat
iononly
.
 UNI
T-I
I
I
ntr
oduct
ionofSSB-
SC

StandardAM andDSBSCr equi

retransmissionbandwi dt
hequalt ot wi
cet he
messagebandwi dth.Inboththecasesspect rum containstwosi debandsofwi dthW
Hz,each.Butt heupperandl owersidesar euniquelyr el
atedt oeachot herbyt he
vi
rtueoft hei
rsymmet r
yaboutt hecarr
ierfrequency.Thatis,giventheampl i
tudeand
phasespect r
aofeithersi
deband, t
heothercanbeuni quel
ydet ermined.Thusifonly
onesi debandi stransmit
ted,andi fbotht hecar r
ierandt heothersidebandar e
suppressedatt het r
ansmitt
er,noi nfor
mat ionislost .Thiskindofmodul ati
oni s
cal
ledSSBSCandspect ralcompar i
sonbet weenDSBSCandSSBSCi sshowni nthe
fi
gures1and2.

Fr
equencyDomai
nDescr
ipt
ion
si
debandi stransmi tted;theresulti
ngSSBmodul at
edwav ehast hespect rum showni
n
fi
gure
6.Simil
arl
y,thelowersi debandisrepresentedi ndupl
icatebythef requenciesbelow
fcandt hoseabov e- fcandwhenonl ythel owersidebandi st ransmitted,the
spectr
um oft hecor r
espondingSSBmodul at edwav eshowni nf i
gure5. Thust he
essenti
alfunction oft he SSB modul ati
on ist otr
anslat
et he spect r
um oft he
modulati
ngwav e, eit
herwi thorwi t
houtinversion,toanewl ocationint hefrequency
domain.The adv antage ofSSB modul ation isr educed bandwi dth and t he
el
iminati
onofhi ghpowercar ri
erwav e.Themai ndisadvantagei st hecostand
complexit
yofitsimpl ement at
ion.

Gener
ati
onofSSBwav
e:

Fr
equencydi
scr
imi
nat
ionmet
hod

Consi
dert hegenerati
onofSSBmodul atedsignalcont ai
ningtheupperside
bandonl y.From apr acti
calpointofview,themostsev ererequir
ementofSSB
generati
onarisesfrom theunwantedsideband,thenear estcomponentofwhi chis
separatedfr
om thedesi r
edsidebandbyt wicet helowestf r
equencycomponentof
themessagesi gnal
.Iti
mpl i
esthat,f
ort
hegener ati
onofanSSBwav etobepossible,
themessagespect rum musthav eanenergygapcent eredatt heori
ginasshowni n
fi
gure7.Thisrequir
ementi snatur
all
ysati
sfi
edbyv oicesignals,whoseener
gygapi s
about600Hzwi de.
 Thef
requencydi
scr
iminat
ionorfi
l
termethodofSSBgenerat
ionconsi
stsofa
productmodulat
or,whi
chproducesDSBSCsignalandaband-passfil
tert
oextract
thedesir
edsidebandandr
ejectt
heotherandi
sshowninthefi
gure8.

Appli
cati
onoft hi
smet hodrequi
resthatthemessagesignalsat
isfi
estwocondi
ti
ons:
1.Themessagesi gnalm(t)hasnolow-f
requencycont
ent.Example:
speech,
audi
o,music.
2.ThehighestfrequencycomponentW oft hemessagesignalm(t)i
smuchless
thanthecarr
ierfrequencyfc.

Then,undert hesecondi
ti
ons,t
hedesi
redsi
debandwi
llappeari
nanon-
over
lappingi
ntervalinthespect
rum i
nsuchawaythati
tmaybeselect
edbyan
appr
opriatef
il
ter
.

Indesigni
ngthebandpassfi
lt
er,thefoll
owingrequi
rement
sshouldbesat
isf
ied:
1.Thepassbandofthefil
teroccupiesthesamef r
equencyr
angeasthe
spect
rum oft
hedesi
redSSBmodul
atedwav e.

2.Thewi
dthoft
heguar
dbandoft
hef
il
ter
,separ
ati
ngt
hepassbandf
rom t
he
st
opband,wheretheunwant
edsidebandoft hef
il
teri
nputl
i
es,i
stwi
cet
hel
owest
fr
equencycomponentoft
hemessagesignal
.

When itis necessaryto generate an SSB modulat

ed wave occupyi
ng a
frequencybandthatismuchhi gherthanthatofthemessagesignal
,i
tbecomesv ery
diff
icul
ttodesignanappr opr
iat
ef i
l
terthatwil
lpassthedesir
edsidebandandreject
theot her
.Insuchasi t
uati
oni ti
snecessar yt or
esorttoamul t
ipl
e-modul
ati
on
processsoast oeaset hefi
lt
eri
ng
requir
ement
.Thisapproachi
sil
l
ust
rat
edi
nthef
oll
owi
ngf
igur
e9i
nvol
vi
ngt
wo
stagesofmodul
ati
on.

TheSSBmodul atedwav eatt hefi

rstfi
l
teroutputisusedast hemodulating
wav eforthesecondproductmodul ator
,whichproducesaDSBSCmodul atedwav e
withaspectrum t
hatissymmet ri
call
yspacedaboutt hesecondcarr
ierf
requencyf 2.
Thef r
equencyseparat
ionbetweent hesidebandsoft hi
sDSBSCmodul atedwav ei s
eff
ectivel
ytwicethefi
rstcar
ri
erfrequencyf1,ther
ebypermitt
ingthesecondfil
terto
removet heunwantedsideband.

Hi
l
ber
tTr
ansf
orm &i
tsPr
oper
ti
es:

TheFour i
ertransformi susef ulforev aluatingthef requencycont entofanener gy
si
gnal ,orinalimiti
ngcaset hatofapowersi gnal
.Itprovidesmat hemat i
calbasi sf or
analyzinganddesi gni ngt hef r
equencysel ecti
vefil
tersforthesepar ati
onofsi gnal s
ont hebasi softheirf requencycont ent.Anot hermet hodofsepar ati
ngt hesi gnal sis
basedonphasesel ect i
vity,which uses phase shi fts between t he appr opr i
ate
si
gnal s( component s)to achiev e the desired
separation.In caseofa si nusoi
dalsi gnal ,thesimpl estphaseshi tof180o i
f s
obtainedby“ Idealtransf ormer ”(
polari
tyr eversal
).Whent hephaseangl esofal lthe
o
component sofagi vensi gnalareshi f
tedby90,t her esult
ingf unct
ionoft i
mei s
cal
ledt he“Hil
berttransf orm”oft hesignal .
Consi deranLTIsy stem wi tht r
ansferfunctiondefinedbyequat i
on1
 Thedev i
cewhi chpossessessuchapr opert
yiscalledHilberttransfor
mer.
Whenevera signalis appl
ied tot he Hil
berttransf
ormer,the ampl i
tudes ofal l
fr
equencycomponentsoft hei nputsignalr
emai nunaff
ected.I
tpr oducesaphase
o o
shi
ftof-90 foral
lposit
ivefrequencies,whi
leaphaseshi f
tsof90 f orallnegati
ve
fr
equenciesoft
hesignal.

I
fx(
t)i
saninputsi
gnal
,theni
tsHi
l
ber
ttr
ansf
ormeri
sdenot
edbyxˆ
(t)and
showni
nthef
oll
owi
ngdiagr
am.
Now consi
deranyinputx(t
)tot heHil
berttr
ansf
ormer
,whichisanLTIsyst
em.Let
theimpul
seresponseoftheHi l
bertt
ransfor
merisobt
ainedbyconv
olv
ingthei
nput
x(t
)andimpul
seresponseh(t)ofthesyst
em.
Pr
oper
ti
es:

Ti
meDomai
nDescr
ipt
ion:

Theti
medomaindescr
ipt
ionofanSSBwav
es(
t)i
nthecanoni
cal
for
mis
gi
venbyt
heequati
on1.
 Fol
l
owi
ngt
hesamepr
ocedur
e,wecanf
indt
hecanoni
cal
repr
esent
ati
onf
oranSSB
wave
s(
t)obt
ainedbyt
ransmi
tt
ingonl
ythel
owersi
debandi
sgi
venby

Phasedi
scr
imi
nat
ionmet
hodf
orgener
ati
ngSSBwav
e:

Ti
medomai ndescr
ipt
ionofSSBmodul
ati
onl
eadstoanothermethodofSSB
gener
ati
onusi
ngtheequati
ons9or10.Thebl
ockdi
agram ofphasedi
scri
minat
ori
s
asshowninfi
gur
e15.
 Thephasedi scri
mi nat
orconsi st
softwoproductmodulat
orsIandQ, suppl
ied
wit
hcar r
ierwavesin-
phasequadr aturetoeachother
.Theincomingbasebandsignal
m(t)isappliedtopr oductmodul atorI,pr
oduci
ngaDSBSC modul atedwav ethat
contai
nsr ef
erencephasesi debandssy mmetri
call
yspacedaboutcarrierf
requency
fc.

TheHilberttr
ansf
orm mˆ( t
)ofm ( t)isappl
iedtopr oductmodulat
orQ,
produci
ngaDSBSCmodul atedthatcontai
nssidebandshavingidenti
calampl
it
ude
spectr
atothoseofmodul at
orI,butwithphasespect
rasucht hatvect
oraddi
ti
onor
subtr
acti
onoft hetwomodul at
oroutputsresul
tsi
ncancell
ationofonesetofside
bandsandrei
nforcementoftheotherset.

Theuseofaplussignatthesummingjunct
iony
iel
dsanSSBwavewi
thonl
y
t
helowersi
deband,whereastheuseofami nussi
gnyiel
dsanSSBwavewi
thonl
y
t
heuppersi
deband.Thi
smodul at
orci
rcui
tiscal
l
edHart
leymodul
ator
.

Demodul
ati
onofSSBWav
es:
I
ntr
oduct
iont
oVest
igi
alSi
deBandModul
ati
on

Vesti
gialsi
debandi sat
y peofAmpl it
udemodul ati
oninwhichonesi deband
i
scompl etel
ypassedal ongwit
ht raceortai
lorvesti
geoft heot
hersideband.VSBis
acompr omisebet weenSSBandDSBSCmodul ation.InSSB,wesendonl yoneside
band,theBandwi dt
hr equir
edt
osendSSBwav eisw.SSBi snotappropr
iat
ewayof
modul at
ionwhent hemessagesi gnalcontai
nssignif
icantcomponentsatextr
emely
l
owf requenci
es.Toov ercomethisVSBisused.

Fr
equencyDomai
nDescr
ipt
ion

Thefol
l
owi
ngFigi
ll
ust
rat
est
hespect
rum ofVSBmodul
atedwav
es(
t)wi
thr
espect
tot
hemessagem (
t)(
bandl
i
mit
ed)

Assumet hatt
heLowersidebandismodif
iedi
ntot
hev est
igi
alsi
deband.The
vest
igeoft helowersideband compensat
esfortheamountr emoved f
rom the
uppersi
deband.Thebandwidthr
equir
edtosendVSBwaveis
 Thevest
igeoftheUppersidebandcompensatesf
ort
heamountr
emov
ed
f
rom t
heLowersideband.Thebandwidthrequi
redt
osendVSBwavei
sB=w+fv,
wher
ef vi
sthewidt
hoft hevest
igi
alsideband.

Therefore,
VSBhasthevi
rt
ueofconservi
ngbandwidthalmostaseff
icient
lyas
SSBmodul at
ion,whi
l
eret
aini
ngtheexcel
l
entlow-f
requencybaseband
char
acter
isti
csofDSBSCanditi
sstandardf
orthetransmissi
onofTVsignals.

Gener
ati
onofVSBModul
atedWav
e

VSBmodul
atedwavei
sobt
ainedbypassi
ngDSBSCt
hroughasi
debandshapi
ngf
il
ter
asshowni
nfigbel
ow.

Fi
g.17.Bl
ockDi
agr
am ofVSBModul
ator

Theexactdesi
gnoft
hisfi
lt
erdependsonthespect
rum oftheVSBwaves.
Therel
ati
onbetweenfi
lt
ert
ransf
erfunct
ionH(f
)andthespectrum ofVSBwavesi
s
gi
venby

S(
f)=Ac/
2[M(
f-f
c)+M(
f+f
c)]
H(f
) (
1)

WhereM(f
)ist
hespectrum ofMessageSignal
.Now,
wehav et
odetermi
nethe
speci
fi
cat
ionf
orthef
il
tert
ransferf
unct
ionH(f
)Itcanbeobt
ainedbypassi
ngs(
t)t
oa
coherentdetectoranddeter
miningthenecessarycondi
ti
onf orundi
stor
tedversionof
themessagesi gnalm(t)
.Thus,s( t)i
smul t
ipl
i
edbyal ocall
ygenerat
edsi nusoi
dal
wav ecos( 2πfct)whi
chi ssynchronouswiththecarri
erwav eAccos(2πfct
)inbot h
frequencyandphase, asi
nfigbelow,
 Thespect
rum ofVo(
f)i
sinf
igbel
ow,

Si
mil
arl
y,thetr
ansf
erfunct
ionH(f)oft
hefil
terf
orsendi
ngLowersi
debandal
ong
wi
ththevesti
geoftheUppersi
debandisshowninfi
gbelow,
Ti
meDomai
nDescr
ipt
ion:

Timedomainr epr
esentat
ionofVSBmodul atedwav e,procedur
ei ssimil
art
o
SSBModulatedwaves.Lets(t
)denoteaVSBmodul atedwav eandassumi ngthats(
t)
cont
aini
ng Uppersideband al
ong wit
htheVest igeoft heLowersi deband.VSB
modulat
edwav es(t)ist heoutputfr
om Sidebandshapi ngf i
lt
er,whosei nputi
s
DSBSCwav e.Thef
il
tertr
ansferf
uncti
onH(f
)isofthef or
m asi nfigbel
ow,

Fi
g(2)Lowpassequi
val
entt
oH(
f)
Note:
1.I
fvest
igi
alsi
debandi
sincr
easedt
oful
lsi
deband,
VSBbecomesDSCSB,
i
.e.
,mQ(
t)=0.
Env
elopedet
ect
ionofaVSBWav
epl
usCar
ri
er
Compar
isonofAM Techni
ques:

Appl
i
cat
ionsofdi
ff
erentAM sy
stems:

 Ampli
tudeModulati
on:AM radi
o,Shor
twaveradi
obr
oadcast
 DSB-
SC: Dat
aModems, Col
orTV’scol
orsi
gnal
s.
 SSB:
Telephone
 VSB:TVpict
uresignal
s
 UNI
TII
I
ANGLEMODULATI
ON
 Basi
cconcept
s
 Fr
equencyModul
ati
on
 Si
ngl
etonef
requencymodul
ati
on
 Spect
rum Anal
ysi
sofSi
nusoi
dal
FM Wav
e
 Nar
rowbandFM,
WidebandFM,
Const
antAv
eragePower
 Tr
ansmi
ssi
onbandwi
dthofFM Wav
e
 Gener
ati
onofFM Wav
es:
oI
ndi
rectFM,
Dir
ectFM:
Var
act
orDi
odeandReact
ance
Modul
ator
 Det
ect
ionofFM Wav
es:
o Bal
ancedFr
equencydi
scr
imi
nat
or,
Zer
ocr
ossi
ngdet
ect
or,
Phasel
ockedl
oop
 Compar
isonofFM &AM
 Pr
e-emphasi
s&de-
emphasi
s
 FM Tr
ansmi
tt
erbl
ockdi
agr
am andexpl
anat
ionofeachbl
ock
I
nst
ant
aneousFr
equency

Thef
requencyofacosi
nef
unct
ionx(
t)t
hati
sgi
venby

x(
t)cos
ct0

i ocsi
sequalt ncei
tisaconst
antwi
thr ot
espectt ,andt
hephaseoft
hecosi
nei
s
t ant0.Theangl
heconst eoft ne(
hecosi t)=ct+0i
sal
i
nearr
elat
ionshi
pwi
th
r ot(
espectt ast
rai
ghtl
i
newi
t opeofcandy
hsl –int
erceptof0)
.Howev
er,
forot
her
si
nusoi
dalf
unct
ions,t
hef
requencymayi
tsel
fbeaf
unct
ionoft
ime,andt
her
efor
e,
weshoul
dnott
hinki
nter
msoft
heconst
antf
requencyoft
hesi
nusoi
dbuti
nter
ms
oft
heI
NSTANTANEOUSf
requencyoft
hesi
nusoi
dsi
ncei
tisnotconst
antf lt
oral .
Consi
derf
orexampl
ethef
oll
owi
ngsi
nusoi
d
y
(t)c
os
(t
),

e(
wher t)i
saf
unct
ionoft
ime.Thef
requencyofy
(t)i
nthi
scasedependsont
he
f
unct
ionof(
t)andmayi
tsel
fbeaf
unct
ionoft
ime.Thei
nst
ant
aneousf
requencyof
y
(t)gi
venabovei
sdefinedas
d(t)
( t
) .
i
dt

Asacheckupf
ort
hisdef
ini
ti
on,
weknowt
hatt
hei
nst
ant
aneousf
requencyofx(
t)i
s
equalt
oit
sfr
equencyatal
lti
mes(
sincet
hei
nst
ant
aneousf
requencyf
ort
hat
f
unct
ioni
sconst )andi
ant oc.Cl
sequalt ear
lyt
hissat
isf
iest
hedef
ini
ti
onoft
he
i
nst
ant
aneousf
r nce(
equencysi t)=
ct+0andt
her
ef ei
or (t)=c.
I
fweknow t
hei
nst
ant
aneousf
requencyofsomesi
nusoi
dfr
om –t
osomet
imet
,
wecanf
indt
heangl
eoft
hatsi
nusoi
datt
imetusi
ng
t

(
t)
i(
)d.


Changi
ngt e(
heangl t)ofsomesi
nusoi
dist
hebasesf
ort
het
wot
ypesofangl
e
modul
ati
on:
PhaseandFr
equencymodul
ati
ont
echni
ques.

PhaseModul
ati
on(
PM)

I
nthi
sty
peofmodul
ati
on,
thephaseoft
hecar
ri
ersi
gnal
isdi
rect
lychangedbyt
he
messagesi
gnal
.Thephasemodul
atedsi
gnal
wil
lhav
ethef
orm
 gPM (
t)A
cos
ctkpm (
t)
,

eAi
wher saconst
ant
,ci
sthecar
ri
erf
requency
,m(
t)i
sthemessagesi
gnal
,andkp
i
sapar
amet
ert
hatspeci
fi
eshowmuchchangei
ntheangl
eoccur
sforev
eryuni
tof
changeof
m(
t).Thephaseandi
nst
ant
aneousf
requencyoft
hissi
gnal
are

PM (
t)ctkpm (t)
,
dm (
t) km (
t).
( t)  
k
i c p c p
dt

So,
thef
requencyofaPM si
gnal
ispr
opor
ti
onal
tot
heder
ivat
iveoft
hemessagesi
gnal
.

Fr
equencyModul
ati
on(
FM)

Thi
sty
peofmodul
ati
onchangest
hef
requencyoft
hecar
ri
er(
nott
hephaseasi
nPM)
di
rect
lywiththemessagesignal.TheFM modul
atedsi
gnal
is
t
 
gFM (
t)Acosctkf m()d,
  

ekfi
wher sapar
amet
ert
hatspeci
fi
eshowmuchchangei
nthef
requencyoccur
sfor
ev
eryuni
tchangeofm(
t).Thephaseandi
nst
ant
aneousf
requencyoft
hisFM ar
e

FM (
t)ct m ()d,

kf
t
d 
i(
t)ckf  )
m( dckfm (
t).
dt
 

Rel
ati
onbet
weenPM andFM

PM andFM ar
eti
ght
lyr
elat
edt
oeachot
her
.Weseef
rom t
hephaseandf
requency
t

r
elat
ionsf
orPM andFM gi
venabov
ethatr
epl ngm(
aci t)i
nthePM si
gnal m (
wi
th
 )d


dm (
tgi
vesaPM si
gnal
.Thi
s
gi
vesanFM si
gnal
andr
epl ngm(
aci t)i
ntheFM si
gnal )
wi
thi
sil
l
ust
rat
edi
nthef
oll
owi
ngbl
ockdi
agr
ams. dt
 Fr
equencyModul
ator(
FM)

t
m (t)d

Phase
m(
t) Modulat
o gFM(
t)
(

)d
r(PM)

PhaseModul
ator(
PM)

dm (
t)
Fr
equenc
d(
) dt
m(
t) y gPM(
t)
dt Modulat
o
r(FM)

Fr
equencyModul
ati
on

InFr
equencyModulat
ion(
FM)theinst
antaneousvalueoftheinfor
mati
on
si
gnalcont
rol
sthefr
equencyoft
hecarr
ierwave.Thisi
sil
lustr
atedinthefol
l
owing
di
agrams.

Noti
cethatast
heinfor
mati
onsignali
ncr
eases,t
hef r
equencyofthecar
ri
er
i
ncreases,andasthei
nformati
onsi
gnaldecr
eases,t
hefrequencyofthecar
ri
er
decreases.
 Thef
requencyf
ioft
hei
nfor
mat
ionsi
gnalcont
rol
sther
ateatwhi
cht
hecar
ri
er
f
requencyi
ncr
easesand decr
eases.Aswi
th AM,f
imustbel han f
esst c.The
ampl
i
tudeoft
hecar
ri
err
emai
nsconst
antt
hroughoutt
hispr
ocess.
Whent
hei
nfor
mat
ionv
olt
ager
eachesi
tsmaxi
mum v
aluet
hent
hechangei
n
f
requencyoft
hecar
ri
erwi
l
lhav
eal
sor
eachedi
tsmaxi
mum dev
iat
ionabov
ethe
nomi
nalv
alue.Si
mil
arl
ywhent
hei
nfor
mat
ionr
eachesami
nimum t
hecar
ri
erwi
l
lbe
ati
tsl
owestf
requencybel
ow t
he nomi
nalcar
ri
erf
requencyv
alue.When t
he
i
nfor
mat
ionsi
gnal
iszer
o,t
hennodev
iat
ionoft
hecar
ri
erwi
l
loccur
.
Themaxi
mum changet
hatcanoccurt
othecar
ri
erf
rom i
tsbasev
aluef
cis
cal
l
edt
hef
requencydev
iat
ion,andi
sgi
vent
hesy
mbolf
c.Thi
sset
sthedy
nami
c
r
ange(
i.
e.v
olt
ager
ange)oft
het
ransmi
ssi
on.Thedy
nami
crangei
sther
ati
ooft
he
l
argestandsmal
l
estanal
oguei
nfor
mat
ionsi
gnal
sthatcanbet
ransmi
tt
ed.
Bandwi
dthofFM andPM Si
gnal
s
Thebandwi
dthoft
hedi
ff
erentAM modul
ati
ont
echni
quesr
angesf
rom t
he
bandwi
dthoft
hemessagesi
gnal(
forSSB)t
otwi
cet
hebandwi
dthoft
hemessage
si
gnal
(forDSBSCandFul
lAM)
.WhenFM si
gnal
swer
efi
rstpr
oposed,
itwast
hought
t
hatt
hei
rbandwi
dthcanber
educedt
oanar
bit
rar
il
ysmal
lval
ue.Compar
edt
othe
bandwi
dthofdi
ff
erentAM modul
ati
ont
echni
ques,t
hiswoul
dint
heor
ybeabi
g
adv
ant
age.I
twasassumedt
hatasi
gnalwi
thani
nst
ant
aneousf
requencyt
hat
changesov angeoffHzwoul
erofr dhav
eabandwi
dthoffHz.Whenexper
iment
s
wer
edone,i
twasdi
scov
eredt
hatt
hiswasnott
hecase.I
twasdi
scov
eredt
hatt
he
bandwi
dthofFM si
gnal
sforaspeci
fi
cmessagesi
gnalwasatl
eastequalt
othe
bandwi
dthoft
hecor
respondi
ngAM si
gnal
.Inf
act
,FM si
gnal
scanbecl
assi
fi
edi
nto
t
wot
ypes:Nar
rowbandandWi
debandFM si
gnal
sdependi
ngont
hebandwi
dthof
eachoft
hesesi
gnal
s
Nar
rowbandFM andPM

Thegener
alf
orm ofanFM si
gnal
thatr
esul
tswhenmodul
ati
ngasi sm(
gnal t)i
s
t
 
gFM (
t)A ctkf
cos )
m( d.
  

Anar
rowbandFM orPM si
gnal
sat
isf
iest
hecondi
ti
on

kfa(
t) 1

ForFM and
 kpm(
t) 1

ForPM,
wher
e
t

t)
a( )
m( d,


suchthatachangeinthemessagesi
gnal
doesnotr
esul
tsi
nal
otofchangei
nthe
i
nstantaneousf
requencyoft
heFM si
gnal
.

Now,
wecanwr
it
etheabov
eas

gFM ( cos
t)A ctkfa(
t).
St
art
ingwit
hFM, toevaluat
ethebandwidthoft
hissi
gnal
,weneedtoexpandi
tusi
ng
apowerser
iesexpansion.So,
wewi l
ldefi
neasli
ghtl
ydif
fer
entsi
gnal

gˆ
M (
F ejtka(t)A
t)A c f
ejt
ejkfa(t).
c

Remembert
hat

ejc f Acos  n ,
 tka(
t)
gˆ
F t)A
M( ctkat)
f ( jA
si ctka(
t)
f

s
o

t)Re
gFM ( gˆ t)
FM ( 
.

Nowwecanexpandt
het
erm ejka(t) gˆ
f t),
FM ( whi
chgi
ves
i
n

j
ct
 j2kf2a2( 3 33
t) j t) j4kf4a4(
kf a ( t) 
ˆ
g ( t)A
e  1j
ka(t)    
FM f
 2 ! 3 ! 4 ! 



 k2a2(
t k3a3(
j t k4a4(
t) 
) )

Aejctj
ka( ejctf
t) ejct f
ejctf ejct 
f

 2! 3! 4! 


ncekfanda(
Si t
)ar
ereal
(a(
t)i
sr ealbecausei
tist
hei
ntegr
alofareal
funct
ion
jct
m(t
)),andsi
nce Re{e }=cos( ct
) ejct}=
and Re{j
–si
n(ct)
, then
 t)Re
gFM ( gˆ t
FM (


) k2a2(
t) k3a3(
t) k4a4(
t) 

A t)ka(
cos( t)si
n(t)f cos(
t)f si
n(t)f t) 
cos(
c f c c c c
 2! 3! 4! 



Theassumpt
ionwemadef
ornar
r s(kfa(
owbandFM i t)1)
.Thi
sassumpt
ionwi
l
lresul
tin

makingal
lthet
ermswi
th kfa(
t)gr
eat
ert
han1t
obesmal
lcompar
edt
othef
ir
st
powersof

gFM (
t)
twoter
ms.So,t
hefol
l
owi
ngi
sar
easonabl
e
appr
oximat
ionf
or

gFM (Narrowband)( 
t)Acos
(ct)kfa(
t when kfa(
t) 1.
)
sin( ,
ct)

I
tmustbest
ressedt
hatt
heabov
eappr
oxi
mat
ioni
sonl
yval
i
dfornar
rowbandFM
si
gnal
sthatsat
isf
ythecondi
ton(kfa(
i t)1)
.Theabov
esi
gnali
ssi
mpl
ytheaddi
ti
on

(
oract
ual
l
ythesubt
ract
ion)ofacosi
ne(
thecar
ri
er)wi
thaDSBSCsi
gnal
(butusi
nga
si
neast
hecar
ri
er)
.Themessagesi
gnalt
hatmodul
atest
heDSBSCsi snotm(
gnali t)
buti
tsi
ntegr
atona(
i t).Oneoft
hepr
oper
ti
esoft
heFour
iert
ransf
ormi
nfor
msust
hat
t
hebandwi
dthofasi m(
gnal t
)and
i
tsi
ntegr
atona(
i t)(
andi
tsder
ivat
ivet
oo)ar
ethesame(
ver
if
ythi
s).Ther
efor
e,t
hebandwi
dth
oft
henar
rowbandFM si
gnal
is

BW FM (Narrowband)BW DSBSC2BW m (t)

.
Wewi
l
lseel
atert
hatwhent
hecondi
ti kf<<1)i
on( snotsat
isf
ied,t
hebandwi
dthof
t
heFM si
gnalbecomeshi
ghert
hatt
wicet
hebandwi
dthoft
hemessagesi
gnal
.
Si
mil
arr
elat
ionshi
pshol
dforPM si
gnal
s.Thati
s

gPM (Narrowband)( 
t)A ct)kpm (
cos( t) when kp
m(t) 1,

si
n( 
ct),

and

BW PM (Narrowband)BW DSBSC2BW m (t)

.
Const
ruct
ionofNar
rowbandFr
equencyandPhaseModul
ator
s

Theaboveapproxi
mati
onsfornarrowbandFM andPM canbeeasi
l
yusedt
o
const
ructmodulat
orsf
orbothtypesofsignal
s
 k<
f <1

m(
t)
t at
()



(


d
) X k
f

si
n(ct
)
–/
2  A gFM(
Nar
rowBand
(
)
t)

cosct
(
)

Nar
rowbandFM Modul
ator

kp<<1

m(
t)

X k
p

si
n(ct
)

–/
2  A gPM(
Nar
rowBand(
)t)

cos(
 ct
)

Nar
rowbandPM Modul
ator

Gener
ati
onofWi
debandFM Si
gnal
s

Consi
dert
hef
oll
owi
ngbl
ockdi
agr
am

Nar
rowband
m(
t) P gFM (WB)(
t)
FM (.)
Modul
ator

gFM (NB)(
t)
AssumeaBPFi sincludedi n
t
hisblocktopassthesi gnal
wit
ht hehi
ghestcar r
ier
f
reuqnecyandrejectallother
s

Anar
rowbandFM si
gnalcanbegener
atedeasi
l
yusi
ngt
hebl
ockdi
agr
am oft
he
nar
rowbandFM modul
atort
hatwasdescr
ibedi
napr
evi
ousl
ect
ure.Thenar
rowband
FM modul
atorgener
atesanar
rowbandFM si
gnalusi
ngsi
mpl
ecomponent
ssuchas
an i
ntegr
ator(
an OpAmp)
,osci
l
lat
ors,mul
ti
pli
ers,and adder
s.The gener
ated
nar
rowbandFM si
gnalcanbeconv
ert
edt
oawi
debandFM si
gnalbysi
mpl
ypassi
ng
i
tthr
oughanon–l
i
neardev
icewi
thpowerP.Bot
hthecar
ri
erf
requencyandt
he
f
requencydev
iat
ionfoft
henar
rowbandsi
gnal
ar
eincr
easedbyaf orP.Somet
act imes,
thedesi
redi
ncr
easei
nthecar
ri
erf
requency
andt
hedesi
redi
ncr nfar
easei edi
ff
erent
.Int
hiscase,wei easeft
ncr othe
desi
redv
alueanduseaf
requencyshi
ft
er(
mul
ti
pli
cat
ionbyasi
nusoi
dfol
l
owedbya
BPF)t
ochanget
hecar
ri
erf
requencyt
othedesi
redv
alue.

SI
NGLE-
TONEFREQUENCYMODULATI
ON

Ti
me-
Domai
nEx
pressi
on

Si
ncet
heFM wav
eisanonl
i
nearf
unct
ionoft
hemodul
ati
ngwav
e,t
he
f
requencymodul
ati
oni
sanonl
i
nearpr
ocess.Theanal
ysi
sofnonl
i
near
pr
ocessi
sthe di
ff
icul
ttask.I
nthi
ssect
ion,we wi
l
lst
udysi
ngl
e-t
one
f
requencymodul
ati
oni
ndet
ailt
osi
mpl
i
fyt
heanal
ysi
sandt
ogett
hor
ough
under
standi
ngaboutFM.

Letusconsi
derasi
ngl
e-t
onesi
nusoi
dal
messagesi
gnal
def
inedby

n(
t)=Ancos(
2nƒ
nt) (
5.13)

Thei
nst
ant
aneousf
requencyf
rom Eq.(
5.8)i
sthen

(
ƒt)=ƒ
c+kAnc
ƒ os(
2nƒ
nt)=ƒ
c+∆ƒ
cos(
2nƒ
nt) (
5.14)
wher
e

∆ƒ=k
ƒAn
 i
st hemodulat
ioni
ndexoft
heFM wav
e.Ther
efor
e,t
hesi
ngl
e-t
oneFM wav
eis
expressedby

sFM(
t)=Accos[
2nƒ
ct n(
+þƒsi 2nƒ
nt)
] (
5.18)

Thi
sist
hedesi
redt
ime-
domai
nexpr
essi
onoft
hesi
ngl
e-t
oneFM wav
e

Si
mil
arl
y,si
ngl
e-t
onephasemodul
atedwav
emaybedet
ermi
nedf
rom Eq.
as

sPM(
t)=Accos[
2nƒ
ct+kpAncos(
2nƒ
nt)
]

or
,sPM(
t)=Accos[
2nƒ
ct+þpcos(
2nƒ
nt)
] (
5.19)

wher
e
þp=k
pAn (
5.20)
i
sthemodul
ati
oni
ndexoft
hesi
ngl
e-t
onephasemodul
ated
wav
e.Thef
requencydev
iat
ionoft
hesi
ngl
e-t
onePM wav
eis

Spect
ral
Anal
ysi
sofSi
ngl
e-ToneFM Wav
e
Theabov
eEq.canber
ewr
it
tenas
j
2nƒt j
þsi
n(2nƒt)
sFM(
t)=Re{
Ace e }
c n

Forsi
mpl
i
cit
y,t
hemodul
ati
oni
ndexofFM hasbeenconsi
der
edasþi
nst
ead
ofþƒaf
ter
war
d.Si
ncesn(
i 2nƒ
nt)i
sper
iodi
cwi
thf
undament
alper
iodT=
1⁄
ƒ j
þsi
n(2nƒt)
n,thecompl
exexpont
iale n isal
soper
iodi
cwi
tht
hesame
f
undament
alper
iod.Ther
efor
e,t
hiscompl
exexponent
ial
canbeexpandedi
n
Four
ierser
iesr
epr
esent
ati
onas

wher
etheFour
ierser
iescoef
fi
cient
scnar
eobt
ainedas
 TRANSMI
SSI
ONBANDWI
DTHOFFM WAVE

Thet
ransmi
ssi
onbandwi
dthofanFM wav
edependsont
hemodul
ati
oni
ndex
þ.Themodul
ati
oni
ndex
,ont
heot
herhand,dependsont
hemodul
ati
ngampl
i
tude
andmodul
ati
ngf
requency
.Iti
sal
mosti
mpossi
blet
odet
ermi
net
heexactbandwi
dth
oft
heFM wav
e.Rat
her
,weusear
ule-
of-
thumbexpr
essi
onf
ordet
ermi
ningt
heFM
bandwi
dth.

Forsi
ngl
e-t
onef
requencymodul
ati
on,
theappr
oxi
mat
edbandwi
dthi
s
det
ermi
nedbyt
heexpr
essi
on

Thi
sexpr
essi
oni
sregar
dedast
heCar
son’
srul
e.TheFM bandwi
dth
det
ermi
nedbyt
hisr
uleaccommodat
esatl
east98%oft
het
otal
power
.

Foranar
bit
rar
ymessagesi
gnal
n(t
)wi
thbandwi
dthormaxi
mum f
requencyW,
t
hebandwi
dthoft
hecor
respondi
ngFM wav
emaybedet
ermi
nedbyCar
son’
srul
e
as

GENERATI
ONOFFM WAVES
FM wav
esar
enor
mal
l
ygener
atedbyt
womet
hods:
indi
rectmet
hodanddi
rectmet
hod.

I
ndi
rectMet
hod(
Armst
rongMet
hod)ofFM Gener
ati
on
I
nthi
smet
hod,nar
row-
band FM wav
eisgener
ated f
ir
stbyusi
ng phase
modul
atorandt
hent
hewi
debandFM wi
thdesi
redf
requencydev
iat
ioni
s
obt
ainedbyusi
ngf
requencymul
ti
pli
ers.
Theabov
eeqi
stheexpr
essi
onf
ornar
rowbandFM wav
e

I
nthi
scase

Fi
g:Nar
rowbandFM Gener
ator

Thef
requencydev
iat
ion∆ƒi
sver
ysmal
linnar
row-
bandFM wav
e.Topr
oduce
wi
debandFM,
wehav
etoi
ncr
easet
hev
alueof∆ƒt
oadesi
redl
evel
.Thi
sisachi
eved
bymeansofoneormul
ti
plef
requencymul
ti
pli
ers.Af
requencymul
ti
pli
erconsi
stsof

anonl
i
neardev
iceandabandpassf
il
t .Thent
er hor
dernonl
i
neardev
icepr
oducesa
dccomponentandnnumberoff
requencymodul
atedwav
eswi
thcar
ri
erf
requenci
es
ƒ
c,2ƒ
c,…nƒ
candf
requencydev
iat
ions∆ƒ
,2∆ƒ
,…n∆ƒ
,respect
ivel
y.I
fwewantanFM

wav
ewi
thf
requencydev
iat
ionof6∆ƒ
,thenwemayusea6t
hor
dernonl
i
neardev
ice

orone2nd or
derandone3r
d or
dernonl
i
neardev
icesi
ncascadef
oll
owedbya
bandpassf
il
tercent
eredat6ƒ
c.Nor
mal
l
y,wemayr
equi
rev
eryhi
ghv
alueoff
requency
dev
iat
ion.Thi
saut
omat
ical
l
yincr
easest
hecar
ri
erf
requencybyt
hesamef
act
or
whi
chmaybehi
ghert
hant
her
equi
redcar
ri
erf
requency
.Wemayshi
ftt
hecar
ri
er
f
requencyt
othedesi
redl
evelbyusi
ngmi
xerwhi
chdoesnotchanget
hef
requency
dev
iat
ion.

Thenar
rowbandFM hassomedi
stor
ti
onduet
otheappr
oxi
mat
ionmadei
n
der
ivi
ng t
he expr
essi
on ofnar
rowband FM f
rom t
he gener
alexpr
essi
on.Thi
s
pr
oducessomeampl
i
tudemodul
ati
oni
nthenar
rowbandFM whi
chi
sremov
edby
usi
ngal
i
mit
eri
nfr
equencymul
ti
pli
er.
Di
rectMet
hodofFM Gener
ati
on

I
nthi
smet
hod,
thei
nst
ant
aneousf
requencyƒ
(t)oft
hecar
ri
ersi
gnal
c(t
)isv
ari
ed
di
rect
lywi
tht
hei
nst
ant
aneousv
alueoft
hemodul
ati
ngsi
gnal
n(t
).Fort
his,
an
osci
l
lat
ori
susedi
nwhi
chanyoneoft
her
eact
ivecomponent
s(ei
therCorL)oft
he
r
esonantnet
wor
koft
heosci
l
lat
ori
svar
iedl
i
near
lywi
thn(
t).Wecanuseav
aract
or
di
odeorav
ari
capasav
olt
age-v
ari
abl
ecapaci
torwhosecapaci
tancesol
ely
dependsont
her
ever
se-
biasv
olt
ageappl
i
edacr
ossi
t.Tov
arysuchcapaci
tance
l
i
near
lywi
thn(
t),
wehav
etor
ever
se-
biast
hedi
odebyt
hef
ixedDCv
olt
ageand
oper
atewi
thi
nasmal
ll
inearpor
ti
onoft
hecapaci
tance-
vol
tagechar
act
eri
sti
ccur
ve.
Theunmodul
atedf
ixedcapaci
tanceC0i
sli
near
lyv
ari
edbyn(
t)sucht
hatt
he
r
esul
tantcapaci
tancebecomes

C(
t)=C0−kn(
t)

wher
etheconst
antki
sthesensi
ti
vi
tyoft
hev
aract
ordi
ode(
measur
edi
n
capaci
tanceperv
olt
).

f
ig:
Har
tl
eyosci
l
lat
orf
orFM gener
ati
on

Theabov
efi
gur
eshowst
hesi
mpl
i
fieddi
agr
am oft
heHar
tl
ey
osci
l
lat
ori
nwhi
chi
simpl
ement
edt
heabov
edi
scussedscheme.The
f
requencyofosci
l
lat
ionf
orsuchanosci
l
lat
ori
sgi
ven
i
sthe f
requency sensi
ti
vi
ty oft
he modul
ator
.The Eq.(
5.42)i
sthe r
equi
red
expr
essi
onf
ort
hei
nst
ant
aneousf
requencyofanFM wav
e.I
nthi
sway
,wecan
gener
ateanFM wav
ebydi
rectmet
hod.
Di
rectFM maybegener
atedal
sobyadev
icei
nwhi
cht
hei
nduct
anceoft
he
r
esonantci
rcui
tisl
i
near
lyv
ari
ed bya modul
ati
ng si
gnaln(
t);i
nthi
scase t
he
modul
ati
ngsi
gnal
bei
ngt
hecur
rent
.
Themai
nadv
ant
ageoft
hedi
rectmet
hodi
sthati
tpr
oducessuf
fi
cient
lyhi
gh
f
requencydev
iat
ion,t
husr
equi
ri
ngl
i
ttl
efr
equencymul
ti
pli
cat
ion.But
,ithaspoor
f
requencyst
abi
l
ity
.Af
eedbackschemei
susedt
ost
abi
l
izet
hef
requencyi
nwhi
ch
t
heout
putf
requencyi
scompar
edwi
tht
heconst
antf
requencygener
atedbyhi
ghl
y
st
abl
ecr
yst
alosci
l
lat
orandt
heer
rorsi
gnal
isf
eedbackt
ost
abi
l
izet
hef
requency
.

DEMODULATI
ONOFFM WAVES
Thepr
ocesst
oext
ractt
hemessagesi
gnalf
rom af
requencymodul
atedwav
e
i
sknownasf
requencydemodul
ati
on.Ast
hei
nfor
mat
ioni
nanFM wav
eiscont
ained
i
nit
sinst
ant
aneousf
requency
,thef
requencydemodul
atorhast
het
askofchangi
ng
f
requencyv
ari
ati
onst
oampl
i
tudev
ari
ati
ons.Fr
equencydemodul
ati
onmet
hodi
s
gener
all
ycat
egor
izedi
ntot
wot
ypes:di
rectmet
hodandi
ndi
rectmet
hod.Underdi
rect
met
hodcat
egor
y,wewi
l
ldi
scussaboutl
i
mit
erdi
scr
imi
nat
ormet
hodandunder
i
ndi
rectmet
hod,
phase-
lockedl
oop(
PLL)wi
l
lbedi
scussed.
Li
mit
erDi
scr
imi
nat
orMet
hod

Recal
l
ingt
heexpr
essi
onofFM si
gnal
,
t

s(
t)=Accos[
2nƒ
ct+2nkƒƒn(
t)dt
]
0

I
nthi
smet
hod,
ext
ract
ionofn(
t)f
rom t
heabov
eequat
ioni
nvol
vest
het
hree
st
eps:
ampl
i
tudel
i
mit
,di
scr
imi
nat
ion,
andenv
elopedet
ect
ion.
A.Ampl
i
tudeLi
mit

Dur
ingpr
opagat
ionoft
heFM si
gnalf
rom t
ransmi
tt
ert
orecei
vert
he
ampl
i
tudeoft
heFM wav
e(supposedt
obeconst
ant
)mayunder
gochanges
duet
ofadi
ngandnoi
se.Ther
efor
e,bef
oref
urt
herpr
ocessi
ng,t
heampl
i
tude
oft
heFM si
gnali
sli
mit
edt
oreducet
heef
fectoff
adi
ngandnoi
sebyusi
ng
l
i
mit
erasdi
scussedi
nthesect
ion5.
9.Theampl
i
tudel
i
mit
ati
onwi
l
lnotaf
fect
t
hemessagesi
gnalast
heampl
i
tudeofFM doesnotcar
ryanyi
nfor
mat
ionof
t
hemessagesi
gnal
.

B.Di
scr
imi
nat
ion/Di
ff
erent
iat
ion

I
nthi
sst
epwedi
ff
erent
iat
etheFM si
gnal
asgi
venby

Her
ebot
htheampl
i
tudeandf
requencyoft
hissi
gnal
aremodul
ated.
I
nthi
scase,t
hedi
ff
erent
iat
ori
snot
hingbutaci
rcui
tthatconv
ert
s
changei
nfr
equencyi
ntocor
respondi
ngchangei
nvol
tageorcur
rentasshown
i
nFi
g.5.
11.Thei
deal
dif
fer
ent
iat
orhast
ransf
erf
unct
ion

H(
jw)=j
2nƒ
 Fi
gur
e:Tr
ansf
erf
unct
ionofi
deal
dif
fer
ent
iat
or.

I
nst
eadofi
dealdi
ff
erent
iat
or,
anyci
rcui
tcanbeusedwhosef
requency
r
esponsei
sli
nearf
orsomebandi
nposi
ti
vesl
ope.Thi
smet
hodi
sknownas
sl
opedet
ect
ion.Fort
his,l
i
nearsegmentwi
thposi
ti
vesl
opeofRChi
ghpass
f
il
terorLCt
ankci
rcui
tcanbeused.Fi
gur
e5.
13showst
heuseofanLCci
rcui
t
asadi
ff
erent
iat
or.Thedr
awbacki
sthel
i
mit
edl
i
nearpor
ti
oni
nthe

sl
opeoft het
ankcir
cui
t.Thi
sisnotsui
tabl
eforwi
debandFM wher
ethepeak
fr
equencydev
iat
ioni
shigh.

Fi
gur
e:UseofLCt
ankci
rcui
tasadi
ff
erent
iat
or.

Abettersol
ut i
oni
sther
ati
oorbal
ancedsl
opedetect
orinwhichtwo
ankc
t ir
cui
tstunedatƒ c+∆ƒandƒ
c−∆ƒar
eusedtoextendt
helinearpor
ti
onas
showni
nbelowf igur
e.
 Fi
gur
e:Fr
equencyr
esponseofbal
ancedsl
opedet
ect
or.

Anotherdetect
orcal
l
edFoster-
seel
ydiscriminatorel
i
minat
est
wot
ankci
rcui
ts
butst
il
loffert
hesamel i
nearastherat
iodetector.

C.Env
elopeDet
ect
ion

Thethi
rdstepi
stosendt
hedi
ff
erent
iat
edsi
gnal
tot
heenv
elopedet
ect
ort
orecov
er
themessagesi
gnal
.

Phase-
LockedLoop(
PLL)asFM Demodul
ator
APLLconsi
stsofamul
ti
pli
er,al
oopf
il
ter
,andaVCOconnect
edt
oget
hert
o
f
orm af
eedbackl
oopasshowni
nFi
g.5.
15.Lett
hei
nputsi
gnalbeanFM
wav
easdef
inedby

s(
t)=Accos[
2nƒ
ct+∅1(
t]
)

Fi
g:PLLDemodul
ator
Lett
heVCOout
putbedef
inedby

v
VCO(
t)=Avsn[
i 2nƒ
ct+∅2(
t]
)

wher
e t

∅2(
t)=2nkvƒ
v()
tdt
0

Thehi
gh-
fr
equencycomponenti
sremov
edbyt
hel
ow-
passf
il
ter
ingoft
he
l
oopf
il
ter
.Ther
efor
e,t
hei
nputsi
gnal
tot
hel
oopf
il
tercanbeconsi
der
edas

Thedi
ff
erence∅2(
t)−∅1(
t)=∅e(
t)const
it
utest
hephaseer
ror
.Letus
assumet
hatt
hePLLi
sinphasel
ocksot
hatt
hephaseer
rori
sver
ysmal
l
.
Then,
Si
ncet
hecont
rol
vol
tageoft
heVCOi
spr
opor
ti
onal
tot
hemessagesi
gnal
,
(
vt)i
sthedemodul
atedsi
gnal
.
Weobser
vet
hatt
heout
putoft
hel
oopf
il
terwi
thf
requencyr
esponseH(
ƒ)i
s
t
hedesi
redmessagesi
gnal
.Hencet
hebandwi
dthofH(
ƒ)shoul
dbet
hesameast
he
bandwi
dthW oft
hemessagesi
gnal
.Consequent
ly,
thenoi
seatt
heout
putoft
he
l
oopf
il
teri
sal
sol
i
mit
edt
othebandwi
dthW.Ont
heot
herhand,
theout
putf
rom t
he
VCOi
sawi
debandFM si
gnal
wit
hani
nst
ant
aneousf
requencyt
hatf
oll
owst
he
i
nst
ant
aneousf
requencyoft
her
ecei
vedFM si
gnal
.

PREEMPHASI
SANDDEEMPHASI
SNETWORKS

I
n FM,t
he noi
se i
ncr
eases l
i
near
lywi
thf
requency
.Byt
his,t
he hi
gher
f
requencycomponent
sofmessagesi
gnal
arebadl
yaf
fect
edbyt
henoi
se.Tosol
ve
t
hispr em,wecanuseapr
obl eemphasi
sfi
l
teroft
ransf
erf
unct
ionHp(
ƒ)att
he
t
ransmi
tt
ert
oboostt
hehi
gherf
requencycomponent
sbef
oremodul
ati
on.Si
mil
arl
y,
att
her
ecei
ver
,thedeemphasi
sfi
l
teroft
ransf
erf
unct
ionHd(
ƒ)canbeusedaf
ter
demodul
atort
oat
tenuat
ethehi
gherf
requencycomponent
sther
ebyr
est
ori
ngt
he
or
igi
nal
messagesi
gnal
.
Thepr
eemphasi
snet
wor
kandi
tsf
requencyr
esponsear
eshowni
nFi
gur
e5.
19
(
a)and(
b)r
espect
ivel
y.Si
mil
arl
y,t
hecount
erpar
tfordeemphasi
snet
wor
kis
showni
nFi
gur
e5.
20.

Fi
gur
e;(
a)Pr
eemphasi
snet
wor
k.(
b)Fr
equencyr
esponseofpr
eemphasi
snet
wor
k.
 Fi
gur
e(a)Deemphasi
snet
wor
k.(
b)Fr
equencyr
esponseofDeemphasi
snet
wor
k.

I
nFM broadcast
ing,
ƒ1 andƒ
2ar
enor
mal
l
ychosent
obe2.
1kHzand30k
Hz
r
espect
ivel
y.

Thef
requencyr
esponseofpr
eemphasi
snet
wor
kis
Compar
isonofAM andFM:
S.
NO AMPLITUDEMODULATI ON FREQUENCYMODULATI ON
1. Bandwidthi
sv er
ysmallwhi
chi
sone I
trequi
resmuchwiderchannel
(7t
o15
ofthebi
ggestadvant
age ti
mes)ascomparedtoAM.
2. Theamplit
udeofAM si
gnalvar
ies Theampl i
tudeofFM signal
isconst
ant
dependi
ngonmodulati
onindex
. andindependentofdepthofthe
modulati
on.
3. Ar
eaofr
ecept
ioni
slar
ge Theareofr ecept
ionissmallsi
ncei
tis
l
imit
edt oli
neofsi ght
.
4. Tr
ansmit
ter
sarerel
ati
vel
y Tr
ansmit
ter
sar
ecompl
exandhence
si
mple&cheap. ex
pensi
ve.
5. Theav eragepoweri nmodul atedwav e Theav er
agepoweri nfr
equency
i
sgr eaterthancar ri
erpower .Thi s modulatedwav eissameas
addedpoweri sprovi
dedbymodul ating contai
nedinun-modulatedwav e.
source.
6. Mor esuscept ibletonoiseinterference Noi secanbeeasi l
yminimized
andhasl owsi gnaltonoiseratio,itis ampl it
udevariat
ionscanbeel i
minat
ed
mor ediff
iculttoeliminateeffectsof byusi ngli
miter.
noise.
7. i
tisnotpossi bletooperatewi t
hout i
tispossibl
et ooperat
esev er
al
i
nterfer
ence. i
ndependenttransmitt
ersonsame
fr
equency.
8. Themaxi mum valueofmodulat
ion Norestr
ict
ionispl
acedon
i
ndex modulat
ionindex.
=1, otherwiseover-modul
ati
onwould
resultindist
ort
ions.

FM Tr
ansmi
tt
er
TheFM t
ransmi
tt
eri
sasi
ngl
etr
ansi
storci
rcui
t.I
nthet
elecommuni
cat
ion,
t
hef
requencymodul
ati
on(
FM)
transf
erst
hei
nfor
mat
ionbyv
ary
ingt
hef
requencyof
car
ri
erwav
eaccor
dingt
othemessagesi
gnal
.Gener
all
y,t
heFM t
ransmi
tt
eruses
VHFr
adi
ofr
equenci
esof87.
5to108.
0MHzt
otr
ansmi
t&r
ecei
vet
heFM si
gnal
.Thi
s
t
ransmi
tt
er accompl
i
shes t
he most excel
l
ent r
ange wi
th l
ess power
. The
per
for
manceandwor
kingoft
hewi
rel
essaudi
otr
ansmi
tt
erci
rcui
tisdependsont
he
i
nduct
ioncoi
l&v
ari
abl
ecapaci
tor
.Thi
sar
ti
clewi
l
lexpl
ainaboutt
hewor
kingoft
he
FM t
ransmi
tt
erci
rcui
twi
thi
tsappl
i
cat
ions.
TheFM t
ransmi
tt
eri
sal
ow powert
ransmi
tt
erandi
tusesFM wav
esf
or
t
ransmi
tt
ingt
hesound,t
hist
ransmi
tt
ert
ransmi
tst
heaudi
osi
gnal
sthr
ought
he
car
ri
erwav
ebyt
hedi
ff
erenceoff
requency
.Thecar
ri
erwav
efr
equencyi
sequi
val
ent
t
otheaudi
osi
gnaloft
heampl
i
tudeandt
heFM t
ransmi
tt
erpr
oduceVHFbandof88
t
o108MHZ.
Plesef
oll
owt
hebel
owl
i
nkf
or:Knowal
lAboutPowerAmpl
i
fier
sforFM
Tr
ansmi
tt
er
 Bl
ockDi
agr
am ofFM Tr
ansmi
tt
er

Wor
kingofFM Tr
ansmi
tt
erCi
rcui
t
Thef
oll
owi
ngci
rcui
tdi
agr
am showst
heFM t
ransmi
tt
erci
rcui
tandt
her
equi
red
el
ect
ri
calandel
ect
roni
ccomponent
sfort
hisci
rcui
tist
hepowersuppl
yof9V,
r
esi
stor
,capaci
tor
,tr
immercapaci
tor
,induct
or,
mic,
transmi
tt
er,
andant
enna.Letus
consi
dert
hemi
crophonet
ounder
standt
hesoundsi
gnal
sandi
nsi
det
hemi
cther
eis
apr
esenceofcapaci
ti
vesensor
.Itpr
oducesaccor
dingt
othev
ibr
ati
ont
othechange
ofai
rpr
essur
eandt
heACsi
gnal
.

FM Tr
ansmi
tt
erci
rcui
t

Thef
ormat
ionoft
heosci
l
lat
ingt
ankci
rcui
tcanbedonet
hrought
het
ransi
storof
2N3904byusi
ngt
hei
nduct
orandv
ari
abl
ecapaci
tor
.Thet
ransi
storusedi
nthi
s
ci
rcui
tisanNPNt
ransi
storusedf
orgener
alpur
poseampl
i
ficat
ion.I
fthecur
renti
s
passedatt
hei
nduct
orL1andv
ari
abl
ecapaci
tort
hent
het
ankci
rcui
twi
l
losci
l
lat
eat
t
her
esonantcar
ri
erf
requencyoft
heFM modul
ati
on.Thenegat
ivef
eedbackwi
l
lbe
t
hecapaci
torC2t
otheosci
l
lat
ingt
ankci
rcui
t.

Togener
atet
her
adi
ofr
equencycar
ri
erwav
est
heFM t
ransmi
tt
erci
rcui
t
r
equi
resanosci
l
lat
or.Thet
ankci
rcui
tisder
ivedf
rom t
heLCci
rcui
ttost
oret
he
ener
gyf
orosci
l
lat
ions.
Thei
nputaudi
osi
gnalf
rom t
hemi
cpenet
rat
edt
othebaseoft
het
ransi
stor
,whi
ch
modul
atest
heLCt
ankci
rcui
tcar
ri
erf
requencyi
nFM f
ormat
.Thev
ari
abl
ecapaci
tor
i
susedt
ochanget
her
esonantf
requencyf
orf
inemodi
fi
cat
iont
otheFM f
requency
band.Themodul
atedsi
gnalf
rom t
heant
ennai
sradi
atedasr
adi
owav
esatt
heFM
f
requencybandandt
heant
ennai
snot
hingbutcopperwi
reof20cm l
ongand24
gauge.I
nthi
sci
rcui
tthel
engt
hoft
heant
ennashoul
dbesi
gni
fi
cantandher
eyoucan
uset
he25-
27i
nchesl
ongcopperwi
reoft
heant
enna.

Appl
i
cat
ionofFm Tr
ansmi
tt
er
 TheFM t
ransmi
tt
ersar
eusedi
nthehomesl
i
kesoundsy
stemsi
nhal
l
stof
il
lthe
soundwi
tht
heaudi
osour
ce.
 Thesear
eal
sousedi
nthecar
sandf
it
nesscent
ers.
 Thecor
rect
ional
faci
l
iti
eshav
eusedi
ntheFM t
ransmi
tt
erst
oreducet
hepr
ison
noi
sei
ncommonar
eas.
Adv
ant
agesoft
heFM Tr
ansmi
tt
ers

 TheFM t
ransmi
tt
ersar
eeasyt
ouseandt
hepr
icei
slow
 Theef
fi
ci
encyoft
het
ransmi
tt
eri
sver
yhi
gh
 I
thasal
argeoper
ati
ngr
ange
 Thi
str
ansmi
tt
erwi
l
lrej
ectt
henoi
sesi
gnal
from anampl
i
tudev
ari
ati
on.
 UNI
TIV
NOISE
 Noi
sei
ncommuni
cat
ionSy
stem,
 Whi
teNoi
se
 Narr
owbandNoi
se–I
nphaseandQuadr
atur
ephase
component
s
 Noi
seBandwi
dth
 Noi
seFi
gur
e
 Noi
seTemper
atur
e
 Noi
sei
nDSB&SSBSy
stem
 Noi
sei
nAM Sy
stem
 Noi
sei
nAngl
eModul
ati
onSy
stem
 Thr
eshol
def
fecti
nAngl
eModul
ati
onSy
stem
Noi
sei
ncommuni
cat
ionsy
stem

 Noi
sei
sunwantedsignalthataff
ectswant
edsignal
 Noi
sei
srandom si
gnalthatexist
sincommunicati
on
sy
stemsEf
fectofnoi
se

 Degradessystem perf
ormance(Analoganddigi
tal
)
 Receiv
ercannotdi
stingui
shsignalf
rom noi
se
 Effi
ci
encyofcommuni cat
ionsystem
r
educesTy
pesofnoi
se

 Thermalnoise/
whit
enoi
se/
Johnsonnoi
seorf
luct
uat
ionnoi
se
 Shotnoise
 Noisetemperat
ure
 Quanti
zati
onnoise

Noisetemperat
ure
Equiv
alentnoi
setemperaturei
snotthephy
sical
temperat
ureofampli
fi
er,buta
theor
etical
const
ruct
,thatisanequi
val
entt
emperatur
ethatpr
oducesthatamount
ofnoisepower

=( −1)

Whi
tenoi
se
Oneofthev er
yimportantrandom pr
ocessesisthewhit
enoiseprocess.
Noi
sesinmanypr acti
cal
situati
onsareapproxi
matedbyt hewhit
enoiseprocess.
Mosti
mportantl
y,thewhit
enoi seplaysani
mpor t
antrol
einmodelli
ngofWSS
si
gnal
s.

Awhitenoiseprocess isarandom pr
ocesst
hathasconst
antpowerspect
ral
densi
tyatallf
requenci
es.Thus
where isarealconst
antandcal
l hei
edt ntensi
tyoft
hewhi
tenoi
se.Thecor
respondi
ng
aut
ocor
rel
ati
onfuncti
onisgi
venby

wher
e i
stheDi
racdel
ta.

Theav
eragepowerofwhi
tenoi
se

Theaut
ocor
rel
ati
onf
unct
ionandt
hePSDofawhi
tenoi
sepr
ocessi
sshowni
n
Fi
gure1bel
ow.

f
ig:
aut
ocor
rel
ati
onandpsdofwhi
tenoi
se

NARROWBANDNOI
SE(
NBN)

Inmostcommuni cati
onsy stems,weareoftendeal
ingwithband-passfil
ter
ingof
signal
s.Widebandnoisewillbeshapedint
obandl i
mitednoi
se.Ifthebandwi dt
hof
thebandli
mi t
ednoiseisrelati
vel
ysmallcomparedtothecarr
ierfrequency,
wer ef
er
tothisasnarr
owbandnoise.

t
henar
rowbandnoi
sei
sexpr
essedasas

wherefcisthecar
ri
erf
requencywit
hint
hebandoccupi
edbyt se.x(
henoi t
)and
yt
()areknownasthequadrat
urecomponent
soft sen(
henoi t
).TheHiber
t
t
ransfor
m of
 n(t
)is
Proof
.
TheFour
iert
ransf
orm ofn(
t)i
s

^(f)bet ^
LetN heFour
iert
ransf
orm ofn^(t
). I
nthef
requencydomai
n,N
f
()=N(
f)[
-jsgn(
f)]
. Wesi
mpl
ymul
ti
plyal
lposi
ti
vef
r sofN(
equencycomponent f)
jandal
by- lnegat
ivef
r sofN(
equencycomponent f)byj
.Thus

Thequadr
atur
ecomponent t
sx()andy
(t)cannowbeder
ivedf
rom equat
ions

x(
t)=n(t
) ct+n^
co2f t
()sin2fct \
and
yt
()=n(t
)cos2fct-n^
(t)sin2fct

Fi
g:gener
ati
onofnar
rowbandnoi
se
 Fi
g:Gener
ati
onofquadr
atur sofn(
ecomponent t)
.

 Fi
l
ter
satt
her
ecei
verhav
eenoughbandwi
dtht
o
passt
hedesi
redsi
gnal
butnott
oobi
gtopass
excessnoi
se.
 Nar
rowband(
NB)f
ccent
erf
requencyi
smuchbi
ggert
hatt
hebandwi
dth.
 Noi
seatt
heout
putofsuchf
il
ter
siscal
l
ednar
rowbandnoi
se(
NBN)
.
 NBNhasspect
ral
concent
rat
edaboutsomemi
d-bandf
requencyf
c
 Thesampl
efunct
ionofsuchNBNn(
t)appear
sasasi
newav
eoff
requencyf
c
whi
chmodul
atessl
owl
yinampl
i
tudeandphase
Noi
sef
igur
e
TheNoi
sef
igur
eist
heamountofnoi
sepoweraddedbyt
heel
ect
roni
cci
rcui
tr
yint
he
r
ecei
vert
othet
her
malnoi
sepowerf
rom t
hei
nputoft
her
ecei
ver
.Thet
her
malnoi
se
att
hei
nputt
other
ecei
verpassest
hrought
othedemodul
ator
.Thi
snoi
sei
spr
esent
i
nther
ecei
vechannelandcannotber
emov
ed.Thenoi
sef
igur
eofci
rcui
tsi
nthe
r
ecei
versuchasampl
i
fier
sandmi
xer
s,addsaddi
ti
onalnoi
set
other
ecei
vechannel
.
Thi
srai
sest
henoi
sef
looratt
hedemodul
ator
.

Noi
seBandwi
dth

Af
il
ter
’sequi
val
entnoi
sebandwi
dth(
ENBW)i
sdef
inedast
hebandwi
dthofaper
fect
r
ect
angul
arf
il
tert
hatpasses t
he same amountofpoweras t
he cumul
ati
ve
bandwi
dthoft
hechannelsel
ect
ivef
il
ter
sint
her
ecei
ver
.Att
hispoi
ntwewoul
dli
ke
t
o know t
he noi
se f
loori
n ourr
ecei
ver
,i.
e.t
he noi
se poweri
nthe r
ecei
ver
i
nter
medi
atef
requency(
IF)f
il
terbandwi
dtht
hatcomesf
rom kTB.Si
ncet
heuni
tsof
kTBar
eWat
ts/Hz,cal
cul
atet
henoi
sef
loori
nthechannelbandwi
dthbymul
ti
ply
ing
t
henoi
sepoweri
na1Hzbandwi
dthbyt
heov
eral
lequi
val
entnoi
sebandwi
dthi
nHz.

NOI
SEI
NDSB-
SCSYSTEM:
Lett
het
ransmi
tt
edsi
gnal
is

Ther
ecei
vedsi
gnalatt
heout
putoft
her
ecei
vernoi
se-l
i
mit
ingf
il
ter:Sum oft
his
si
gnalandf
il
ter
ednoi
se.
Afi
l
ter
ednoi
sepr
ocesscanbeexpr
essedi
nter
msofi
tsi
n-
phaseandquadr
atur
ecomponent
sas

enc(
wher t)i
si phasecomponentandns(
n- t)i
squadr
atur
ecomponent
Recei
vedsi
gnal
(Addi
ngt
hef
il
ter
ednoi
set
othemodul
atedsi
gnal
)

Demodul
atet
he r
ecei
ved si
gnalbyf
ir
stmul
ti
ply
ing r
(t)bya l
ocal
l
ygener
ated
si
nusoi
dcos(
2fct+ )
,wher
eist
hephaseoft
hesi
nusoi
d.Thenpassi
ngt
hepr
oduct

si
gnal
thr
oughani
deal
lowpassf
il
terhav
ingabandwi
dthW.

Thel
owpassf
il
terr
eject
sthedoubl
efr
equencycomponent
sandpassesonl
ythel
owpass
component
s.

theeffectofaphasedi
ff
erencebet
weent
her
ecei
vedcar
ri
erandal
ocal
l
ygener
ated
carr
ierat
2
t
her
ecei
ver
isadr
opequal
tos
oc()i
nther
ecei
vedsi
gnal

power
.Phase-
lockedl
oop

Theeffectofaphase-
lockedl
oopi
stogener
atephaseoft
her
ecei
vedcar
ri
eratt
he
recei
ver.

I
faphase-
lockedl
oopi
sempl
oyed,
then =0andt
hedemodul
ator
i
scal
l
edacoher
entorsy
nchr
onousdemodul
ator
.

I
nouranal
ysi
sint
hissect
ion,
weassumet
hatwear
eempl
oyi
ngacoher
ent

demodul
ator
.Wi
tht
hisassumpt
ion,
weassumet
hat =0

Ther
efor
e,att
her
ecei
verout
put
,themessagesi
gnal
andt
henoi
secomponent
sar
e
addi
ti
veandwear
eabl
etodef
ineameani
ngf
ulSNR.Themessagesi
gnal
poweri
s
gi
venby
PowerPM i
sthecont
entoft
he

messagesi
gnal
Thenoi
sepoweri
sgi
venby

Thepowercont
entofn(
t)canbef
oundbynot
ingt
hati
tist
her
esul
tofpassi
ngnw(
t)
t
hroughaf
il
terwi
thbandwi
dthBc.
Ther
efor
e,t
hepowerspect
ral
densi
tyofn(
t)i
s
gi
venby

whi
chi
sident
ical
tobasebandSNR.

I
nDSB-
SCAM,
theout
putSNRi
sthesameast
heSNRf
orabasebandsy
stem.DSB-
SCAM doesnotpr
ovi
deanySNRi
mpr
ovementov
erasi
mpl
ebaseband
communi
cat
ionsy
stem.

NOI
SEI
NSSB-
SCSYSTEM:

LetSSBmodul
atedsi
gnal
is
I
nputt
othedemodul
ator

Assumpt
ion:
Demodul
ati
onwi
thani
deal
phaser
efer
ence.
Hence,
theout
putoft
hel
owpassf
il
teri
sthei
n-phasecomponent(
wit
ha
coef
fi
cientof½)oft
hepr
ecedi
ngsi
gnal
.

Thesi
gnal
-t
o-noi
ser
ati
oinanSSBsy
stem i
sequi
val
entt
othatofaDSBsy
stem.

Noi
sei
nConv
ent
ional
AM

Wher
e ai
sthemodul
ationi
ndex
mn(
t)i
snor
malizedsothati
tsmi
nimum v
al s-
uei 1

I
fasynchr
onousdemodulat
ori
semploy
ed,
thesi
tuati
onisbasi
cal
l
ysi
mil
ar
t
otheDSBcase,exceptt e1+amn(
hatwehav t)i
nsteadofm(t)
.
  I
npr
act
ical
appl
i
cat
ions,
themodul
ati
oni
ndexai
sint
her
angeof0.
8-0.
9.

 Powercont
entoft
henor
mal
i
zedmessagepr
ocessdependsont
hemessage
sour
ce.

 Speechsi
gnal
s:Lar
gedy
nami
cr PM i
ange, sabout0.
1.

 Theov
eral
ll
ossi
nSNR,
whencompar
edt
oabasebandsy
stem,
is
af
act
orof0.
075orequi
val
entt
oal
ossof11dB.

Ther
easonf
ort
hisl
ossi
sthatal
argepar
toft
het
ransmi
tt
erpoweri
susedt
o
sendt
hecar
ri
ercomponentoft
hemodul
atedsi
gnalandnott
hedesi
redsi
gnal
.
Toanal
yzet
heenv
elope-
det
ect
orper
for
mancei
nthepr
esenceofnoi
se,we
mustusecer
tai
nappr
oxi
mat
ions.

Thi
sisar
esul
toft
henonl
i
nearst
ruct
ureofanenv
elopedet
ect
or,
whi
chmakesanexact
anal
ysi
sdi
ff
icul
t

I
nthi
scase,
thedemodul
atordet
ect
stheenv
elopeoft
her
ecei
vedsi
gnal
andt
he
noi
sepr
ocess.
Thei
nputt
otheenv
elopedet
ect
ori
s

Ther
efor
e,t
heenv
elopeofr(t)i
sgi
venby
Nowweassumethatthesi nr(t)i
gnalcomponenti smuchst
rongert
han
t
henoi
secomponent
.Then

Ther
efor
e,wehav
eahi
ghpr
obabi
l
ityt
hat

Af
terr
emov
ingt
heDCcomponent
,weobt
ain

whi
chi
sbasi
cal
l
yt (
hesameasyt)f
ort
hesy
nchr
onousdemodul
ati
on
withoutt
he½coef f
ici
ent
.
Thiscoeff
ici
ent
,ofcourse,hasnoef
fectont
hef
inalSNR.Soweconcl
udet
hat
,
undert
he assumpt
ion ofhi
gh SNR att
he r
ecei
veri
nput
,the per
for
mance of
sy
nchr
onousandenv
elopedemodul
ator
sist
hesame.

Howev
er,i
fthepr
ecedi
ngassumpt
ioni
snott
rue,t
hati
s,i
fweassumet
hat
,at
t
her
ecei
veri
nput
,thenoi
sepoweri
smuchst
rongert
hant
hesi
gnal
power
,Then
Weobser
vet
hat
,att
hedemodul
atorout
put
,thesi
gnalandt
henoi
secomponent
s
ar
enol
ongeraddi
ti
ve.I
nfact
,thesi
gnalcomponenti
smul
ti
pli
edbynoi
seandi
sno
l
ongerdi
sti
ngui
shabl
e.I
nthi
scase,
nomeani
ngf
ulSNRcanbedef
ined.Wesayt
hat
t
hissy
stem i
soper
ati
ngbel
owt
het
hreshol
d.Thesubj
ectoft
hreshol
dandi
tsef
fect
ont
heper
for
manceofacommuni
cat
ionsy
stem wi
l
lbecov
eredi
nmor
edet
ail
whenwedi
scusst
henoi
seper
for
mancei
nangl
emodul
ati
on.

Ef
fectoft
hreshol
dinangl
emodul
ati
onsy
stem:

FM THRESHOLDEFFECTFM t
hreshol
disusual
l
ydef
inedasaCar
ri
er-
to-
Noi
ser
ati
o
atwhi
chdemodul
atedSi
gnal
-t
o-Noi
ser
ati
ofal
l
s1dBbel
ow t
hel
i
nearr
elat
ionshi
p.
Thi
sist
he ef
fectpr
oduced i
n an FM r
ecei
verwhen noi
se l
i
mit
sthe desi
red
i
nfor
mat
ionsi
gnal
.Itoccur
satabout10dB,asear
li
erst
atedi
n5t
hei
ntr
oduct
ion,
whi
chi
satapoi
ntwher
etheFM si
gnal
-t
o-Noi
sei
mpr
ovementi
smeasur
ed.Bel
ow
t
heFM t
hreshol
dpoi
nt,t
henoi
sesi
gnal(
whoseampl
i
tudeandphasear
erandoml
y
v
ary
ing)mayi
nst
ant
aneousl
yhav
eampl
i
tudegr
eat
ert
hant
hatoft
hewant
edsi
gnal
.
Whent
hishappens,t
henoi
sewi
l
lpr
oduceasuddenchangei
nthephaseoft
heFM
demodul
atorout
put
.Inanaudi
osy
stem,t
hissuddenphasechangemakesa“
cli
ck”
.
I
nvi
deoappl
i
cat
ionst
het
erm“
cli
cknoi
se”i
susedt
odescr
ibeshor
thor
izont
albl
ack
andwhi
tel
i
nest
hatappearr
andoml
yov
erapi
ctur
e

Ani
mpor
tantaspectofanal
ogueFM sat
ell
i
tesy
stemsi
sFM t
hreshol
def
fect
.InFM
sy
stemswher
ethesi
gnall
eveli
swel
labov
enoi
ser
ecei
vedcar
ri
er-
to-
noi
ser
ati
oand
demodul
atedsi
gnal
-t
o-noi
ser
ati
oar
erel
atedby
:

Theexpr
essi
onhowev
erdoesnotappl
ywhent
hecar
ri
er-
to-
noi
ser
ati
odecr
eases
bel
ow acer
tai
npoi
nt.Bel
ow t
hiscr
it
icalpoi
ntt
hesi
gnal
-t
o-noi
ser
ati
odecr
eases
si
gni
fi
cant
ly.Thi
sis
knownast
heFM t
hreshol
def
fect(
FM t
hreshol
disusual
l
ydef
inedast
hecar
ri
er-
to-
noi
ser
ati
oatwhi
cht
hedemodul
atedsi
gnal
-t
o-noi
ser
ati
ofal
l1dBbel
owt
hel
i
near
r
elat
ionshi
pgi
veni
nEqn9.I
tgener
all
yisconsi
der
edt
ooccuratabout10dB)
.

Bel
ow t
heFM t
hreshol
dpoi
ntt
henoi
sesi
gnal(
whoseampl
i
tudeandphasear
e
r
andoml
yvar
ying)
,mayi
nst
ant
aneousl
yhav
eanampl
i
tudegr
eat
ert
hant
hatoft
he
want
edsi
gnal
.Whent
hishappenst
henoi
sewi
l
lpr
oduceasuddenchangei
nthe
phaseoft
heFM demodul
atorout
put
.Inanaudi
osy
stem t
hissuddenphasechange
makesa"
cli
ck"
.Inv
ideoappl
i
cat
ionst
het
erm"
cli
cknoi
se"i
susedt
odescr
ibeshor
t
hor
izont
albl
ackand whi
tel
i
nest
hatappearr
andoml
yov
era pi
ctur
e,because
sat
ell
i
tecommuni
cat
ionssy
stemsar
epowerl
i
mit
edt
heyusual
l
yoper
atewi
thonl
ya
smal
ldesi
gnmar
ginabov
etheFM t
hreshol
dpoi
nt(
per
hapsaf
ew dB)
.Becauseof
t
hisci
rcui
tdesi
gner
shav
etr
iedt
odev
iset
echni
quest
odel
ayt
heonsetoft
heFM
t
hreshol
def
fect
.Thesedev
icesar
egener
all
yknownasFM t
hreshol
dext
ensi
on
demodul
ator
s.Techni
quessuchasFM f
eedback,
phasel
ockedl
oopsandf
requency
l
ockedl
oopsar
eusedt
oachi
evet
hisef
fect
.Bysucht
echni
quest
heonsetofFM
t
hreshol
def
fect
scanbedel
ayedt
il
ltheC/
Nrat
ioi
sar
ound7dB.

Noi
sei
nAngl
eModul
atedSy
stems

Li
keAM,
noi
seper
for
manceofangl
emodul
atedsy
stemsi
schar
act
eri
zedbypar
amet
erγ

Not
e:i
fbandwi
dthr
ati
oisi
ncr
easedbyaf
act
or2.
Then i
ncr
easesbyaf
act
or4

Thi
sexchangeofbandwi
dthandnoi
seper
for
mancei
sani
mpor
tantf
eat
ureofFM
 UNI
T-V
Recei
ver
s
I
ntr
oduct
iont
oRadi
oRecei
ver
s:

I
nr adi
ocommuni cat
ions,ar adi
or ecei
ver(
receiv
erorsimpl
yr adi
o)isan
elect
roni
cdev i
cethatr
eceiv
esr adi
owav esandconvertsthei
nfor
mati
oncarri
edby
them toausablef
orm.

Ty
pesofRecei
ver
s:

TunedRadi
oFr
equencyRecei
ver
:

Fi
g.1.TRFRecei
ver
Pr
obl
emsi
nTRFRecei
ver
s:
Fi
g.2.Bl
ockdi
agr
am ofSuperhet
erody
neRecei
ver
.
Char
act
eri
sti
csofRadi
oRecei
ver
:
Fi
g.3.Ty
pical
Fidel
i
tycur
ve
Bl
ocksi
nSuperhet
erody
neRecei
ver
:

 Basicpri
nciple
o Mi xi
ng
o Intermedi atef r
equencyof455KHz
o Gangedt uning
 RFsecti
on
o Tuni ngci rcuit
s–r ejecti
nterf
erenceandreducenoisef
igur
e
o Wi debandRFampl ifi
er
 LocalOscil
lator
o 995KHzt o2105KHz
o Tracki ng
 IFampli
fi
er
o Ver ynar rowbandwi dthClassAampl i
fi
er–selects455KHzonl
y
o Prov idesmuchoft hegain
o Doubl etunedci r
cuits
 Detect
or
o RFi sf il
teredtoground
1.RFAmpl
i
fier
:
 2.Mi
xer

Separ
atel
yExci
tedMi
xer
:

Fi
g.5Separ
atel
yExci
tedFETMi
xer
Sel
fExci
tedMi
xer
:

Fi
g.6.Sel
fExci
tedMi
xer

3.Tr
acki
ng
4.Local
Osci
l
lat
or

5.I
FAmpl
i
fier

Fi
g.7TwoSt
ageI
FAmpl
i
fier
Choi
ceofI
nter
medi
ateFr
equency
:

6.Aut
omat
icGai
nCont
rol

Fi
g.8.Si
mpl
eAGCci
rcui
t
 Fi
g.9.Del
ayedAGCci
rcui
t

Fi
g.10.Responseofr
ecei
verwi
thv
ari
ousAGCci
rcui
ts.
FM Recei
ver
:

Fi
g.11.FM Recei
verBl
ockdi
agr
am
Compar
isonswi
thAM Recei
ver
s
Ampl
i
tudeLi
mit
er:
 PULSEMODULATI
ON

I
ntr
oduct
ion:

Pul
seModul
ati
on

 Carri
eri
sat rai
nofpulses
 Example:PulseAmpli
tudeModul
ati
on(
PAM)
,Pul
sewi
dthmodul
ati
on(
PWM),
PulsePosit
ionModulati
on(PPM)

Ty
pesofPul
seModul
ati
on:
⚫ Thei
mmedi
ater
esul
tofsampl
i
ngi
sapul
se-
ampl
i
tudemodul
ati
on(
PAM)si
gnal

⚫ PAM i
sananalogschemeinwhichtheampli
tudeofthepul
seis
pr
oport
ional
totheampli
tudeofthesi
gnal
attheinst
antofsampli
ng

⚫ Anot
heranal
ogpul
se-f
ormi
ngtechni
quei
sknownaspul
se-durat
ion
modulat
ion(
PDM).Thi
sisal
soknownaspul
se-wi
dthmodulat
ion(PWM)

⚫ Pul
se-
posi
ti
onmodul
ati
oni
scl
osel
yrel
atedt
oPDM

Pul
seAmpl
i
tudeModul
ati
on:

InPAM,ampli
tudeofpul
sesi
svar
iedi
naccor
dancewi
thi
nst
ant
aneousv
alue
ofmodul
ati
ngsi
gnal.

PAM Gener
ati
on:

Thecar
rieri
sinthefor
m ofnarrowpulseshav
ingfrequencyfc.Theunif
orm
sampli
ngtakesplacei
nmulti
pli
ert
ogeneratePAM si
gnal.Samplesarepl
acedTs
secawayfrom eachot
her.
 Fi
g.12.PAM Modul
ator

⚫ Theci
rcui
tissi
mpl
eemi
tt
erf
oll
ower
.
⚫ I
ntheabsenceoft
hecl
ocksi
gnal
,theout
putf
oll
owsi
nput
.
⚫ Themodul
ati
ngsi
gnal
isappl
i
edast
hei
nputsi
gnal
.
⚫ Anot
heri
nputt
othebaseoft
het
ransi
stori
sthecl
ocksi
gnal
.
⚫ Thefr
equencyoft
hecl
ocksi
gnali
smadeequalt
othedesi
redcar
ri
erpul
se
tr
ainf
requency
.
⚫ Theampli
tudeofthecl
ocksi
gnal
ischosent
hehighl
evel
isatgr
oundlevel
(0v
)
andlow l
evelatsomenegati
vevolt
agesuff
ici
entt
obringthetr
ansist
orin
cut
offr
egion.
⚫ Whencl
ockishi
gh,cir
cui
toper
atesasemi
tt
erf
oll
owerandt
heout
putf
oll
ows
i
nthei
nputmodul
atingsi
gnal
.
⚫ Whencl
ocksi
gnal
isl
ow,
transi
stori
scut
offandout
puti
szer
o.
⚫ Thust
heout
puti
sthedesi
redPAM si
gnal
.

PAM Demodul
ator
:
⚫ ThePAM demodul
atorci
rcui
twhi
chisjustanenvel
opedetect
orfol
l
owedbya
secondor
derop-
ampl owpassfi
l
ter(t
ohav egoodfi
lt
eri
ngcharact
eri
sti
cs)i
s
asshownbel
ow

Fi
g.13.PAM Demodul
ator
Pul
seWi
dthModul
ati
on:
⚫ I
nthi
stype,t
heamplit
udei
smaintainedconst
antbutt
hewidthofeachpul
se
i
svar
iedinaccor
dancewit
hinst
antaneousval
ueoftheanal
ogsignal
.

⚫ I
nPWM i
nfor
mat
ioni
scont
ainedi
nwi
dthv
ari
ati
on.Thi
sissi
mil
art
oFM.

⚫ I
npulsewidt
hmodul
ati
on(PWM),thewidt
hofeachpulsei
smadedi
rect
ly
pr
oport
ional
tot
heampli
tudeoft
heinf
ormati
onsignal
.

Pul
sePosi
ti
onModul
ati
on:
⚫ Inthistype,t
hesampledwaveform hasf
ixedampl
it
udeandwidt
hwher eas
thepositionofeachpul
sei
sv ari
edasperinst
ant
aneousval
ueoftheanalog
signal.

⚫ PPM si
gnal
isf
urt
hermodi
fi
cat
ionofaPWM si
gnal
.

PPM &PWM Modul

ator
:

Fi
g.14.PWM &PPM Modul
ator

• ThePPM si
gnal
canbegener
atedf
rom PWM si
gnal
.

• ThePWM pul
sesobtai
nedatthecomparat
oroutputar
eappl
i
edt
oamono
st
abl
emultiv
ibr
atorwhi
chisnegati
veedgetr
igger
ed.
 • Henceforeacht
rai
li
ngedgeofPWM si
gnal,t
hemonost
abl
eoutputgoes
hi
gh.I
tremainshi
ghforafi
xedti
medecidedbyi
tsRCcomponents.

• Thusast
hetrail
i
ngedgesofthePWM signal
keepsshif
ti
nginpropor
ti
on
wit
hthemodulati
ngsi
gnal
,thePPM pul
sesalsokeepshi
ft
ing.

• Ther
efor
eall
thePPM pul
seshavethesameampl i
tudeandwi
dth.The
i
nfor
mationi
sconvey
edviachangi
ngposit
ionofpulses.

Fi
g.15.PWM &PPM Modul
ati
onwav
efor
ms

PWM Demodul
ator
:

Fi
g.16.PWM Demodul
ator
 ⚫ Tr
ansi
storT1wor
ksasani
nver
ter
.

⚫ Dur
ingt
imei
nter
val
A-Bwhent
hePWM si
gnal
ishi
ght
hei
nputt
otr
ansi
stor
T2i
slow.

⚫ Theref
ore,
dur
ingt
histi
mei nt
erv
alT2i
scut
-of
fandcapaci
torCi
schar
ged
thr
oughanR-Ccombinat
ion.

⚫ Duri
ngti
mei nt
erv
alB-CwhenPWM si
gnal
isl
ow,
thei
nputt
otr
ansi
storT2i
s
hi
gh,anditget
ssatur
ated.

⚫ Thecapaci
torCdi
schar
gesr
api
dlyt
hroughT2.
Thecol
l
ect
orv
olt
ageofT2
dur
ingB-Cislow.
⚫ Thus,
thewavef
orm att
hecol
lectorofT2i
ssi
mil
art
osaw-
toot
hwav
efor
m
whoseenvel
opeist
hemodulati
ngsignal.
⚫ Passi
ngi
tt ough2ndor
hr derop-
ampLowPassFi
l
ter
,gi
vesdemodul
atedsi
gnal
.

PPM Demodul
ator
:

Fi
g.17.PPM Demodul
ator

⚫ Thegapsbetweent
hepulsesofaPPM si
gnal
cont
aint
hei
nfor
mat
ion
regar
dingt
hemodulat
ingsi
gnal
.
⚫ Dur
inggapA-Bbet
weenthepul
sesthetr
ansi
stori
scut
-of
fandt
hecapaci
tor
Cgetschar
gedthr
oughR-Ccombi
nati
on.
⚫ Dur
ingt
hepul
sedurat
ionB-
Cthecapaci
tordi
schar
gest
hrought
ransi
storand
t
hecoll
ect
orv
olt
agebecomeslow.
⚫ Thus,
wavefor
m acrosscol
l
ect
ori
ssaw-
toot
hwav
efor
m whoseenv
elopei
s
themodul
ati
ngsignal
.

⚫ Passi
ngi
tt ough2ndor
hr derop-
ampLowPassFi
l
ter
,gi
vesdemodul
atedsi
gnal
.