Amplitude modulation

Transcription

1 Uni. Inroduion pliude odulion odulion i proe o vrying one o he hrerii o high requeny inuoidl he rrier in ordne wih he innneou vlue o he oduling he inorion ignl. The high requeny rrier ignl i heilly repreened by he equion.. Where o innneou vlue o he oine wve --i xiu vlue --rrier requeny --phe relion wih repe o he reerene ny o he l hree hrerii or preer o he rrier n be vried by he oduling ege ignl, giving rie o pliude, requeny or phe odulion repeively. Need or odulion:. ribiliy o nenn In he udio requeny rnge, or eiien rdiion nd reepion, he rniing nd reeiving nenn u hve ize oprble o he wvelengh o he requeny o he ignl ued. I i luled uing he relion λ. The wvelengh i 75 eer Hz in he brod bnd, bu KHz, he wvelengh urn ou o be 300 Kiloeer. pril nenn or hi vlue o wvelengh i uniginble nd ipoible.. odulion or ee o rdiion For eiien rdiion o elerognei wve, he nenn dienion required i o he order o o. I i poible o onru pril nenn only by inreing he requeny o he be bnd ignl. 3. odulion or uliplexing The proe o obining everl ignl or iulneou rniion on ingle hnnel i lled uliplexing. In order o ue hnnel o rni he dieren

2 be bnd ignl inorion he e ie, i beoe neery o rnle dieren ignl o o ke he oupy dieren requeny lo or bnd o h hey do no inerere. Thi i oplihed by uing rrier o dieren requenie.. Nrrow bnding: Suppoe h we wn o rni udio ignl rnging ro 50-0 Hz uing uible nenn. The rio o highe o lowe requeny i 00. Thereore n nenn uible or ue one end o he requeny rnge would be enirely oo hor or oo long or he oher end. Suppoe h he udio peru i rnled o h i oupie he rnge ro o Hz. Then he rio o highe o lowe requeny beoe.0. Thu he proe o requeny rnlion i ueul o hnge widebnd ignl o nrrow bnd ignl. lower requenie, he ee o liker noie nd bur noie re evere.. pliude odulion In pliude odulion, he pliude o he rrier ignl i vried by he oduling/ege/inorion/be-bnd ignl, in ordne wih he innneou vlue o he ege ignl. Th i pliude o he rrier i de proporionl o he innneou vlue pliude o he oduling ignl. I i he inorion ignl nd he rrier ignl i vried proporionl o he o i he rrier, he pliude o. The pek pliude o rrier er odulion ny inn i given by [ ]. The rrier ignl er odulion or he oduled ignl i repreened by he equion.. o --. k o --.3 where k i lled pliude eniiviy o he odulor. The equion.3 i he ndrd expreion or pliude oduled ignl. Le o be he ege ignl o requeny nd pek pliude. Then ingle-one oduled ignl i given by he equion.. k o o

3 where o o o o ---. i lled odulion index or deph o odulion. The odulion index o ye i deined he rio o pek pliude o ege ignl o pek pliude o rrier ignl The ollowing igure. how he ege, rrier nd pliude oduled wveor. Figure.: ege, rrier nd pliude oduled ignl Noe: i lo lled deph o odulion. peiie he ye lriy. inree, he ye lriy lo inree. + 3

4 Conider he pliude oduled wveor hown in igure.. Figure.: ege nd pliude oduled ignl We hve he odulion index given by Fro he igure., we ge x in x x Dividing he equion.7 by.9, we ge x in x in ---.9

5 x in x in Here x i he xiu pliude nd in i iniu pliude o he oduled ignl. odulion index h o be governed uh h i i lwy le hn uniy; oherwie i reul in iuion known over-odulion >. The overodulion our, whenever he gniude o he pek pliude o he oduling ignl exeed he gniude o he pek pliude o he rrier ignl. The ignl ge diored due o over odulion. Beue o hi liiion on, he ye lriy i lo liied. The wveor or dieren vlue o odulion index re hown in igure.3. Figure.3: wveor or dieren vlue o Noe: I he odulion index exeed uniy he negive pek o he oduling wveor i lipped nd phe reverl rher hn lped level. Exple. goe negive, whih heilly pper oduling ignl oni o yeril ringulr wve, whih h zero d oponen nd pek-o-pek volge v. I i ued o pliude odule rrier o pek volge 0v. Clule he odulion index? The pliude o he oduling ignl i 5.5 The odulion index i vol 5

6 .3 Single one pliude odulion/ Sinuoidl Conider oduling wve requeny oponen given by where Le h oni o ingle one or ingle o ---. i pek pliude o he inuoidl oduling wve i he requeny o he inuoidl oduling wve be he pek pliude nd be he requeny o he high requeny rrier ignl. Then he orreponding ingle-one wve i given by o Co ---. Le x nd in denoe he xiu nd iniu vlue o he envelope o he oduled wve. Then ro he bove equion., we ge x in Expnding he equion., we ge x x o o o The Fourier rnor o i obined ollow. in in ---. Thu he peru o n wve, or he peil e o inuoidl odulion oni o del union requenie i hown in igure..,, nd. The peru or poiive 6

7 C Figure.: Frequeny-doin hrerii o ingle one. Frequeny peru o wve: Conider he ndrd expreion or wve k o o. The rrier requeny hn he highe requeny oponen W o he ege ignl. i. e., W W i lled he ege bndwidh. The Fourier rnor S o wve i given by i uh greer k Suppoe h he be bnd ignl W W hown in igure.5. i bnd liied o he inervl Figure.5: Speru o ege nd wve 7

8 igure.5, or or Fro he equion.5, he peru o wve obined i hown in W. Thi peru oni o wo del union weighed by he, nd ourring, nd wo verion o he be bnd peru rnled in requeny by. Fro he peru, he ollowing poin re noed. i For poiive requenie, he highe requeny oponen o he wve i W, nd he lowe requeny oponen i W. The dierene beween hee wo requenie deine he rniion bndwidh whih i exly wie he ege bndwidh W. B T or n wve, B T W ii For poiive requenie, he porion o he peru o n wve lying bove he rrier requeny, i reerred o he Upper Side Bnd USB, where he yeri porion below, i lled he Lower Side Bnd LSB. For negive requenie, he USB i he porion o he peru below porion bove overlp. nd he LSB i he. The ondiion W enure h he ide bnd do no The wve i volge or urren wve. In eiher e, he verge power delivered o reior by i opried o hree oponen. Crrier power = Upper ide-requeny power = Lower ide-requeny power = 8 8 Exple. rrier wve o requeny 0 Hz nd pek vlue 0 i pliude oduled by 5 KHz ine wve o pliude 6. Deerine he odulion index nd pliude o he ide requenie The ide requenie re Hz nd Hz. 8

9 9 The pliude o ide requenie i given by vol *0.5 verge power or inuoidl ower relion in Conider he expreion or ingle one/inuoidl wve Co Co Co Thi expreion onin hree oponen. They re rrier oponen, upper ide bnd nd lower ide bnd. Thereore verge power o he wve i u o hee hree oponen. Thereore he ol power in he pliude oduled wve i given by USB LSB r Where ll he volge re r vlue nd i he reine, in whih he power i diiped. r C LSB LSB 8 USB USB 8 Thereore ol verge power i given by USB LSB ---.9

10 given by 33% =. The rio o ol ide bnd power o he ol power in he oduled wve i SB SB / / The rio i lled he eiieny o ye nd i ke xiu vlue o Exple.3 brod rdio rnier rdie 0KW, when he odulion perenge i 60. How uh o hi i rrier power. / KW 0.6 / Exple. rdio rnier rdie 0 KW nd rrier power i 8.5 KW. Clule odulion index Eeive volge nd urren or inuoidl In ye, he oduled nd unoduled urren re neery o lule he odulion index ro he. The eeive or r vlue o volge E o he oduled wve i deined by he equion E. 0

11 Siilrly he eeive or roo en qure volge E o rrier oponen i deined by E. Now uing he relion, We ge, E E iilr rguen pplied o urren, yield I I Where I i he r urren o oduled wve nd I i he r urren o unoduled rrier. Noe: The xiu power in he wve i =.5, when =. Thi i iporn, beue i i he xiu power h relevn pliier u be pble o hndling wihou diorion. Exple.5 00 W rrier i oduled o deph o 7.5 %. Clule ol power in he oduled wve. n: =5.5w Exple.6 The nenn urren o n rnier i 8 p, when only he rrier i en, bu i inree o 8.93, when he rrier i oduled by ingle ine wve. Find perenge odulion. Deerine he nenn urren when he peren odulion hnge o 0.8. n: =70.%, I =9.9.7 Noninuoidl odulion When inuoidl rrier ignl i oduled by non-inuoidl oduling ignl, he proe i lled Non-inuoidl odulion. Conider high requeny inuoidl ignl o nd he non-inuoidl ege ignl hown in igure.6. The non-inuoidl oduling ignl h line peru h i ny requeny oponen o dieren pliude.

12 Figure.6: Non-inuoidl ege ignl nd peru The expreion or he non-inuoidl i given by The ol verge power n be obined by dding he verge power or eh oponen, k o k o o S Hene he eeive odulion index n be deined e pliude odulor Two bi pliude odulion priniple re diued. They re qure lw odulion nd wihing odulion. Squre lw odulor When he oupu o devie i no direly proporionl o inpu hroughou he operion, he devie i id o be non-liner. The Inpu-Oupu relion o non-liner devie n be expreed in in 3in in... When he in pu i very ll, he higher power er n be negleed. Hene he oupu i pproxiely given by 0 O in in When he oupu i onidered up o qure o he in pu, he devie i lled qure lw devie nd he qure lw odulor i hown in he igure.7.

13 3 Figure.7: Squre lw odulor Conider non liner devie o whih rrier = o nd n inorion ignl re ed iulneouly hown in igure.7. The ol inpu o he devie ny inn i o in in he level o he inpu i very ll, he oupu n be onidered up o qure o he inpu,., i.e 0 in in O o o o o ] [ o o ] o [ ] o [ Tking Fourier rnor on boh ide, we ge 0 0 Thereore he qure lw devie oupu 0 oni o The d oponen = 0. The inorion ignl rnging ro 0 o W Hz nd i eond hroni. Signl nd.

14 Frequeny bnd enered wih deviion o W, Hz. The required ignl wih rrier requeny n be epred uing bnd p iler he ou pu o he qure lw devie. The iler hould hve lower uo requeny rnging beween W nd -W nd upper u-o requeny beween +W nd Thereore he iler ou pu i = I = o o o o, we ge = o o Copring hi wih he ndrd repreenion o ignl, k o Thereore odulion index o he oupu ignl i given by = The oupu ignl i ree ro diorion nd enuion only when W > W or 3W. Swihing odulor Conider eionduor diode ued n idel wih o whih he rrier ignl igure.8. o nd inorion ignl re pplied iulneouly hown Figure.8: Swihing odulor

15 5 The ol inpu or he diode ny inn i given by o v v When he pek pliude o i inined ore hn h o inorion ignl, he operion i ued o be dependen on only irrepeive o. When i poiive, v =v ine he diode i orwrd bied. Siilrly, when i negive, v =0 ine diode i revere bied. Bed upon bove operion, wihing repone o he diode i periodi rengulr wve wih n pliude uniy nd i given by Thereore he diode repone o i produ o wihing repone p nd inpu v. v =v *p pplying he Fourier Trnor, we ge The diode oupu v oni o d oponen =0. Inorion ignl rnging ro 0 o w Hz nd ininie nuber o requeny bnd enered,, 3,, n n n n p o, 0, 6 o 3 o n n p 6 o 3 o o

16 The required ignl enered n be epred uing bnd p iler. The lower uo-requeny or he bnd p iler hould be beween w nd -w nd he upper u-o requeny beween +w nd. The iler oupu i given by he equion For ingle one inorion, le S o o S o o Thereore odulion index, The oupu ignl i ree ro diorion nd enuion only when -w>w or >w. Deodulion o : - Deodulion i he proe o reovering he inorion ignl be bnd ro he inoing oduled ignl he reeiver. There re wo ehod. Squre lw deodulor Conider non-liner devie o whih he ignl i pplied. When he level o i very ll, oupu n be onidered upo qure o he inpu. Non Liner devie v o Low Filer Figure: Deodulion o uing qure lw devie ' Thereore o o in in I i he inorion ignl 0-wHz nd inpu ignl o he non-liner devie i given by o k o i he rrier, 6

17 7 o o pplying Fourier rnor on boh ide, we ge The devie oupu oni o d oponen =0, inorion ignl rnging ro 0-W Hz nd i eond hroni nd requeny bnd enered nd. The required inorion n be epred uing low p iler wih u o requeny rnging beween W nd -w. The iler oupu i given by DC oponen + ege ignl + eond hroni The d oponen ir er n be eliined uing oupling pior or rnorer. The ee o eond hroni o inorion ignl n be redued by inining i level very low. When i very low, he iler oupu i given by When he inorion level i very low, he noie ee inree he reeiver, hene he ye lriy i very low uing qure lw deodulor. Envelop deeor I i iple nd highly eeive ye. Thi ehod i ued in o o he oeril rdio reeiver. n envelop deeor i hown below. o o o o k K o o K K K K K W o o ' K K o K

18 Figure: Envelope deeor During he poiive hl yle o he inpu ignl, he diode D i orwrd bied nd he pior C hrge up rpidly o he pek o he inpu ignl. When he inpu ignl ll below hi vlue, he diode beoe revere bied nd he pior C dihrge hrough he lod reior L. The dihrge proe oninue unil he nex poiive hl yle. When he inpu ignl beoe greer hn he volge ro he pior, he diode ondu gin nd he proe i repeed. The hrge ie onn r + C u be hor opred wih he rrier period, he pior hrge rpidly nd here by ollow he pplied volge up o he poiive pek when he diode i onduing. Th i he hrging ie onn hll iy he ondiion, r On he oher hnd, he dihrging ie-onn L C u be long enough o enure h he pior dihrge lowly hrough he lod reior L beween he poiive pek o he rrier wve, bu no o long h he pior volge will no dihrge he xiu re o hnge o he oduling wve. Th i he dihrge ie onn hll iy he ondiion, where W i bnd widh o he ege ignl. The reul i h he pior volge or deeor oupu i nerly he e he envelope o wve. C LC W 8

19 dvnge o : Generion nd deodulion o wve re ey. ye re o eeive nd ey o build. Didvnge: onin unwned rrier oponen, hene i require ore rniion power. The rniion bndwidh i equl o wie he ege bndwidh. To overoe hee liiion, he onvenionl ye i odiied he o o inreed ye oplexiy. Thereore, hree ype o odiied ye re diued. DSBSC Double Side Bnd Suppreed Crrier odulion: In DSBC odulion, he oduled wve oni o only he upper nd lower ide bnd. Trnied power i ved hrough he uppreion o he rrier wve, bu he hnnel bndwidh requireen i he e beore. SSBSC Single Side Bnd Suppreed Crrier odulion: The SSBSC oduled wve oni o only he upper ide bnd or lower ide bnd. SSBSC i uied or rniion o voie ignl. I i n opiu or o odulion in h i require he iniu rniion power nd iniu hnnel bnd widh. Didvnge i inreed o nd oplexiy. SB eigil Side Bnd odulion: In SB, one ide bnd i opleely ped nd ju re or veige o he oher ide bnd i reined. The required hnnel bndwidh i hereore in exe o he ege bndwidh by n oun equl o he widh o he veigil ide bnd. Thi ehod i uible or he rniion o wide bnd ignl. Double Side Bnd Suppreed Crrier odulion DSBSC odulor ke ue o he uliplying ion in whih he oduling ignl uliplie he rrier wve. In hi ye, he rrier oponen i eliined nd boh upper nd lower ide bnd re rnied. he rrier oponen i uppreed, he power required or rniion i le hn h o. I i he ege ignl nd DSBSC oduled wve i given by o = o i he rrier ignl, hen 9

20 Conequenly, he oduled ignl under goe phe reverl, whenever he ege ignl roe zero hown below. Figure: Crrier, ege nd DSBSC wve or The envelope o DSBSC oduled ignl i hereore dieren ro he ege ignl nd he Fourier rnor o i given by S For he e when be bnd ignl i liied o he inervl W<<W hown in igure below, we ind h he peru S o he DSBSC wve i illured below. Exep or hnge in ling or, he odulion proe iply rnle he peru o he be bnd ignl by. The rniion bndwidh required by DSBSC odulion i he e h or. Figure: ege nd he orreponding DSBSC peru 0

21 ing odulor: - ing odulor i he o widely ued produ odulor or genering DSBSC wve nd i hown below. Figure: ing odulor The our diode or ring in whih hey ll poin in he e direion. The diode re onrolled by qure wve rrier o requeny, whih i pplied longiudinlly by en o wo ener-pped rnorer. uing he diode re idel, when he rrier i poiive, he ouer diode D nd D re orwrd bied where he inner diode D3 nd D re revere bied, o h he odulor uliplie he be bnd ignl by. When he rrier i negive, he diode D nd D re revere bied nd D3 nd D re orwrd, nd he odulor uliplie he be bnd ignl by. Thu he ring odulor in i idel or i produ odulor or qure wve rrier nd he be bnd ignl. The qure wve rrier n be expnded uing Fourier erie n n o n n Thereore he ring odulor ou pu i given by n n o n n Fro he bove equion i i ler h oupu ro he odulor oni enirely o odulion produ. I he ege ignl i bnd liied o he requeny bnd w w, he oupu peru oni o ide bnd enered.

22 Blne odulor rodu odulor blned odulor oni o wo ndrd pliude odulor rrnged in blned onigurion o o uppre he rrier wve hown in he ollowing blok digr. I i ued h he odulor re idenil, exep or he ign reverl o he oduling wve pplied o he inpu o one o he. Thu, he oupu o he wo odulor y be expreed, k o k o pliude odulor- o Oillor dder - pliude odulor- Figure: Blned odulor Subring ro, Hene, exep or he ling or k, he blned odulor oupu i equl o he produ o he oduling wve nd he rrier. Deodulion o DSBSC oduled wve by Coheren deeion The ege ignl n be uniquely reovered ro DSBSC wve by ir uliplying wih lolly genered inuoidl wve nd hen low p ilering he produ hown. k o

23 Figure: Coheren deeor I i ued h he lol oillor ignl i exly oheren or ynhronized, in boh requeny nd phe, wih he rrier wve ued in he produ odulor o genere. Thi ehod o deodulion i known oheren deeion or ynhronou deeion. Le o be he lol oillor ignl, nd o be he DSBSC wve. Then he produ odulor oupu v i given by v o o v o o The ir er in he bove expreion repreen DSBSC oduled ignl wih rrier requeny, nd he eond er repreen he led verion o ege ignl. uing h he ege ignl i bnd liied o he inervl w w, he peru o v i ploed hown below. Figure: Speru o oupu o he produ odulor 3

24 Fro he peru, i i ler h he unwned oponen ir er in he expreion n be reoved by he low-p iler, provided h he u-o requeny o he iler i greer hn W bu le hn -W. The iler oupu i given by The deoduled ignl v o i hereore proporionl o when he phe error i onn. Single one DSBSC odulion Conider inuoidl oduling ignl nd he rrier ignl o.. The orreponding DSBSC oduled wve i given by o ingle requeny o o Thu he peru o he DSBSC oduled wve, or he e o inuoidl oduling wve, oni o del union loed. nd uing pere ynhroni beween he lol oillor nd rrier wve in oheren deeor, he produ odulor oupu onin he high requeny oponen nd led verion o originl inorion ignl. The Low Filer i ued o epre he deired ege ignl. v o o o o o Co eeiver Co loop Co reeiver i ynhronou reeiver ye, uible or deoduling DSBSC wve. I oni o wo oheren deeor upplied wih he e inpu ignl, h i he inoing DSBSC wve o bu wih individul lol oillor ignl h re in phe qudrure wih repe o eh oher hown below.

25 Figure: Co reeiver The requeny o he lol oillor i djued o be he e he rrier requeny. The deeor in he upper ph i reerred o he in-phe oheren deeor or I- hnnel, nd h in he lower ph i reerred o he qudrure-phe oheren deeor or Q-hnnel. Thee wo deeor re oupled ogeher o or negive eed bk ye deigned in uh wy o inin he lol oillor ynhronou wih he rrier wve. Suppoe he lol oillor ignl i o he e phe he rrier wve ued o genere he inoing DSBSC wve. Then we ind h he I-hnnel oupu onin he deired deoduled ignl, where he Q- hnnel oupu i zero due o qudrure null ee o he Q-hnnel. Suppoe h he lol oillor phe dri ro i proper vlue by ll ngle rdiion. The I- hnnel oupu will rein eenilly unhnged, bu here will be oe ignl ppering he Q-hnnel oupu, whih i proporionl o in or ll. Thi Q-hnnel oupu will hve e polriy he I-hnnel oupu or one direion o lol oillor phe dri nd oppoie polriy or he oppoie direion o lol oillor phe dri. Thu by obining he I-hnnel nd Q-hnnel oupu in phe diriinor whih oni o uliplier ollowed by LF, d onrol ignl i obined h uoilly orre or he lol phe error in he volge-onrolled oillor. o 5