Analog and Digital Communication Systems [chapters 1-6, 4 ed.]

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Amplitude Modulation

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So& 6.2

Double-8idebnd Supprewed Carrier

The most

, frcsueacr signal to ma&rlste (i.e., modify thc paramctgs of) another, highpl fmquency aSgnal. Mast commndy, IME other signal is a pure sinwid. We start, then, witb a pun siousoid $At) called the carrier waveform. It is givan this nune because it is used to COWthc infowstlon signal from the lransmitter to thc d v u . -Y. sXt)

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If,& h properly c h c n , thiserrria waveform can be efficiently transmitted. For ex.Bplc.supporepwentdd~tRqiwodesinthc~ge~lMHasnd3MHz gqapmklamDBrw~8thcmmbsrdi.blyseotovcr~uptorbostm ~hlfyaueLastriu~f.Obeinsbir~~@punrinuaoidrlcsrrisrdd .. ~ paolir-.m w a v d a y t h o f inLbCmpof1 MHEto3MHzison tb~diggmQn,andm*aauof~krylth~beured, ~wwutmOqusaticm~rbrpncediag~~csaiawavdonn

cmlomrQowbe~inawaytbat(a)LbCheJkmdsdl4~~ aed@)thcinf~mwcwiahtodb~w8u~mthc~wwavCdOW h a way that it a n be reawntd LbC &vet. In other words, we aie asking whether ~isaomswaythstthc~d~arvry(heinf~~.~~wisyss,ss we now illwuate. The right-hand side of Eq. (6.1) Coatpins thrae panuaaeff that may be wied: tbe amplitude A, the fnqucacyf, aod the phpM 0. Using &e information signal to vary A. f, or 0 tadstomnpUndc~~~aadpikrrcnodulmim,nspectlvely. Wewill~w~efIicht~misshievsdfweachofthescthraecuea

wmwillJsotbat~ifmcve~hr%arll~1y~~&tbe c h L separation of the signals at ibe rafdvu is poasibk. In asdi* are will find it

aiticslto~~atbirdpopcrty:TheinfanrstiwaSgnal~t)muub~mv~IMefromme~v~~wrvefam;it~oabeofmuohluetomodifyaau' rkrwavefomtacfficicatt radrtrtioaaprabilityifw~no(npmdua &I) BCClEnTely at thc receiver. l l t b ~ ~ t 4 8 o s a ~ ~ o f 4 w p l i i m o d ~ . ~ tmtmmts ofirequeacy mi modoI.tim follow in thc next chapter.

ffwc~tbe~~of@CmiaofBp(6.1).thef&~~wawfamisslts: ~ ~ (=tA(t)cos ) (zM#+ 0)

(6.2)

~fwqosacyf,sad~~BireeafbEsat.~~A(f)~*iorsomshoariar~-

~ w i r h ~ ~ ~ d t t r b o ~ w a w s l l l e s r r i s d ~ ~ c h a n s Wc6i1nplify~ea~by~thst0=O.~Wiunotdtscl;myoftbe

.bsdcd,siace~~,~y~toatimsshiftof~~~.Atimsshift

oatconddaddistatioaha~ans~

Sffi a2

DouMwidsbsnd SupprwMd Carrier

adogous to ths hipwmuk rssult that multipliion of a sinusoid by snorner m w a dMiearmd~hrqscaoia.'Ilratis,

If- A B by s(i), whcn a(t) cmtaim a d u r n of freqwaolss between 0 and f,chb~~caabcrppIhdtambytamtoylddarrscllt~all suauad~ofmefr#lucaciea. piSmr 6.3iadicaas that the modula*d wavtfm sdt) contains wmponcnts with fleqwmiu bstweenf, -.f and& +f,. As Aslong as signals in this range of frequencies &amnit nffbbttly a d an ratema of mwnable lag& can be conrtructcd, we have ~ved~6ntofthetwopmMenrs.Letwpl~insnatorpicaluldio~.~fmbe S L H z m d f c b c 1 M H e . ~ t h c n ~ o f ~ ~ b y c b s ~ w v iannis~~,~tolp05,oOoHt.

Tbcdobgecrivcis~ofWdgnrlr.We~etbatif~~~-

~lrl~alinu~of~fc~adaDaberiof~on~~modulrtard roidQf~f&~Pouisreuvfmnsdmetwo~cPriardowovcdq ~~~,~1&tf~df~rn~byitltlll~~..~hirisill.oltntsd drsdA.SlseshdlsdrraeWh~.wrrdLrtoWMou~

apatio&PaAM. m(l d@%OD

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Amplitude Modulation

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'ibir~onis~mthelpmemrrmcrssthrrtoscdmdrPwmC~cluria waveform. We Bnt draw tbe o d i m rt IA + s(t)] and -[A + s(t)].The h 4 waveform p a b d i d y bwhw Umsc tM ~ m ~We sU . ua fill in with a smooth. oscillpting wavcfonn

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oftBs~~~extsllc*damD.~beaaour*.ialbXof

afmDdDtties~mel~rbodsasucr.Tbs ua~bYlaul(iptgiqpwla).

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Mghw potential hpoint B, all fom diodss an short circuits. This is qui the switch king closed. The only limit to the rate of switching is i q s e d by the pwtkrl diodes an not ideal (i.c.. thefhve a oonmn eaphmx). ~he~csnalsobe~~ishcdu*lleastiv*ebcaonlc&viccssuchae %onopaatiog between outoff and nafmtioa~&tl:tmndotor act8 as an opens

The Mcood bmpdclass of modulator we d d e r is the square-low mod&or.

[s,W

+ s2(t)l2= s:(t) + s:(r) + 2st(t)s,(fl

Ifs~(t) i)tbP informah aud s ~ ( tis) the c a u k , we havf [s(t) + cos 2 . 6 3 = 2 0 + cos 9Irff

+ Zs(r)cos 2.62

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M-wave re&%aion is cquivaknt to tfic nuhawid opemion of rakingtbe solutcvalue.Theootpltoftbe&uistba 810)

= (A + dt11Wdrl

butsinceweaclsumthntA +s(t)aeva~nega?ivc,wccnaly(eowponeattof v;rlmrigrsioget

sr(t) = IA

+ dt)llddA

Amplitude Modulation

qplleriQnrintkistsd

AM *WD SUPERHETERODYNElW8WR

mvclope of a waveform as an o u t l i ~ mat ~ ~foUow thc puks of thc attemps to follow this outline. Our intuitive definition

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Tbe foregoing intuitive detiaitioa ib 18ot vay dsfyiog, since it applie.8 only to r nanow clam d s&. We lhrll now wrplorc a mihamtical ddinitioo of the a~vdope 1,

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'f?~~prranve&psfakso b o r n as t b e w n 1 ~ & ~ 6 ) ) ~ b p c o t m a & o f$a c ~ ) vrvetbnar(t)is~asihecompk~~of~~h~~ortrisr~irgi~

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h*tbi.~wrs'hrasdtbrtSV+fJlia~ID(h.hitoltbtaig h T b l r l r n o l t c l r o d o n w r b r s f .