Inerediae Frequeny IF Iage frequeny p. II-33
Apliude Modulaion: SSB DSB odulaion: By ixing wih a inuoidal arrier a rad/e, half of hi peral deniy i ranlaed up in frequeny and enered abou and half i ranlaed down o -. Doubling of he bandwidh of a given ignal Sine eah half onain all he inforaion abou he ignal, he original ignal an be reovered again fro eiher he upper or lower pair of ideband by an appropriae frequeny ranlaion. So only he upper or he lower pair of ideband i required o rani. Suh kind of odulaion i alled ingle-ideband SSB odulaion. I i effiien beaue i require no ore bandwidh han ha of he original ignal and only half of he orreponding DSB ignal. p. II-34
Apliude Modulaion: SSB SSB: SSB: p. II-35
Apliude Modulaion: SSB Generaion of SSB Signal -fir generae a DSB ignal, hen uppre one of he ideband by filering. p. II-36
Apliude Modulaion: SSB Generaion of SSB: Phae-Shif Mehod x e Conider he odulaing ignal x i j and le he arrier ignal be e. Muliplying, we ge x e j e j e j j I{ e j } j I{ e } Taking he real par, we have Re{ e j e j } Re{ e j }Re{ e j } I{ e j }I{ e o o in in I{Re[ Beaue hi repreen he upper ideband, we wrie e SSB+ o o in in x e j j Siilarly, by uing, he lower ideband i SSB o o + in in } I{ e - j e j e j j } ]} + + In general, we an wrie SSB x o ± xˆ in where xˆ frequeny. i ha ignal obained by hifing he phae of x by 9 a eah p. II-37
Apliude Modulaion: SSB Generaion of SSB Signal : Phae-Shif Mehod p. II-38
Apliude Modulaion: SSB Deodulaion of SSB Signal The ynhronou deeor will properly deodulae SSB-SC ignal p. II-39
Apliude Modulaion: SSB Given ha he inoing SSB-SC ignal i SSB x o ± xˆ in Le he loally generaed arrier ignal be o[ + + θ ], where i he frequeny error and θ i he phae error. SSB [ x o 1 2 1 2 x {o[ xˆ {in[ ± xˆ in ]o[ + + θ ] + θ ] + o[2 + + θ ] in[2 + + θ ]} + θ ]} Afer paing hrough a low-pa filer, he oupu x o beoe 1 x 1 x o[ + θ ] xˆ in[ + θ o ] Diored! 2 2 1 If and θ, hen x o x 2 p. II-4
Apliude Modulaion: SSB Exaple: When an SSB upper/lower-ideband i reeived and fed ino he following deodulaor: SSB± IF Ap LPF x o SSB-SC a 2 MHz 1.-1.3 MHz o2π f o2π f d Upper ideband SSB-SC -f -f +f d +f d 3kHz f 3.3MHz -2 MHz 2 MHz 1.3 MHz 1 MHz Freq. f d 1.3MHz Lower ideband SSB-SC -f -f +f d +f d 3kHz f 3.MHz -2 MHz 2 MHz 1.3 MHz 1 MHz Freq. f d 1.MHz p. II-41
Apliude Modulaion: SSB Single Sideband-Large Carrier SSB-LC Signal An expreion for an SSB-LC ignal i A o + x o xˆ in The original ignal x an alway be reovered fro uing ynhronou deeion. If he arrier i large, however, envelope deeion an alo be ued. The envelope an be wrien a x x r [ A + x ] + 2 2 2 2 2 + [ xˆ ] A 1+ + 2 2 A A A If he arrier i uh larger han he SSB-SC envelope, we have 2x x r A 1 + A 1 + A + x. A A Thu afer diarding he d er inrodued by arrier, he SSB-LC ignal an hen be deodulaed orrely uing an envelope deeor. xˆ p. II-42
Apliude Modulaion: VSB Veigial ideband VSB odulaion i a oproie beween DSB and SSB. In VSB odulaion, one paband i paed alo opleely wherea only a reidual porion of he oher ideband i reained in uh a way ha he deodulaion proe an ill reprodue he original ignal. S DSB S VSB The parial uppreion of one ideband redue he required bandwidh fro ha required for DSB bu doe no ah he peru effiieny of SSB. If a large arrier i alo ranied, he deired ignal an be reovered uing an envelope deeor. If no arrier i en, he ignal an be reovered uing a ynhronou deeor or he injeed arrier ehod. p. II-43
Apliude Modulaion: VSB Generaion of VSB Signal S VSB 2 2 + 1 [ 1 X + X ] H The filering operaion an be repreened by a filer H f ha pae oe of he lower or upper ideband and o of he upper or lower ideband. p. II-44
Apliude Modulaion: VSB Deodulaion of VSB Signal VSB LPF x o o Synhronou Deodulaion The peral deniy of he reeived veigial-ideband ignal i S VSB 2 2 + 1 [ 1 X + X ] H The oupu of he ynhronou deeor i X x [ o ] o o 1 4 1 4 VSB X X LP 1 [ H + ] + X [ H ] LP 4 [ H + + H ] LP For faihful reproduion of x, we require ha [ H + H + ] LP onan,. LP p. II-45
Apliude Modulaion: VSB [ H + H + ] LP onan,. By leing he onan be 2H : [ H + H + ] LP 2 H, Thu, H exhibi odd yery around he arrier frequeny. The u of he value of H a any wo frequenie equally diplaed above and below i uniy. p. II-46
Apliude Modulaion: VSB Synhronou Deodulaion of VSB Signal Reeived VSB ignal S VSB Afer ixer X d 2 2 Afer LPF X o p. II-47
Apliude Modulaion: VSB Exaple of VSB Signal: Televiion ignal Televiion piure ignal ha noinal bandwidh of 4.5MHz If DSB odulaion i ued, i require a lea 9MHz for eah TV hannel. So, VSB odulaion i ued o ha he whole TV ignal i onfined o abou 6MHz. p. II-48
Angle Modulaion A oninuou-wave CW inuoidal ignal an be varied by hanging i apliude and i phae angle. Apliude odulaion: A o[ + φ ] To arry a eage ignal x: Keep θ onan and varie A proporionally o x. [ ] A o + φo where A x Angle odulaion: Keep A onan and varie [ +φ] proporionally o x. [ + φ ] where [ + φ ] x Ao p. II-49
Angle Modulaion Phaor Repreenaion The phaor repreenaion of a onan-apliude inuoid i hown a follow θ i A: agniude of he phaor θ: phae angle θ + φ + θ i : inananeou angular rae dθ i + d o dφ d θ i τ dτ + θ p. II-5
Angle Modulaion If he phae φ i varied linearly wih he inpu ignal x, we have θ + k x + θ p i.e. φ x where, k p, θ are onan. A he phae i linearly relaed o x, hi ype of angle odulaion i alled phae odulaion PM wih PM A o[ + k p x + θ o ] and, φ i alled inananeou phae deviaion. dθ dφ i + ipm + k d d p dx d p. II-51
Angle Modulaion If he inananeou frequeny i proporional o he inpu ignal, we have dφ + k x x dθ dφ i FM f Q i + d d d θ where, k f are onan. A he frequeny i linearly relaed o x, hi ype of angular odulaion i alled frequeny odulaion FM, wih dφ + k f x τ dτ + θ o FM A o[ + k f x τ dτ + θ o ] and; i alled inananeou frequeny deviaion. d p. II-52
Angle Modulaion Phae Modulaion PM Frequeny Modulaion FM Inananeou angular rae ipm dx d + k p i FM + k f x Modulaed ignal PM A o[ + k p x + θ o ] FM A o[ + k f x τ dτ + θ o ] Proporionaliy φ x dφ d x p. II-53
Angle Modulaion FM and PM Wavefor p. II-54
p. II-55 Angle Modulaion: Fourier pera [ ] [ ] { } { } o j j j e e A e A φ φ φ A Re Re + + Conider an angle-odulaed ignal Expand e jφ in a power erie, give + + + + + L L L A n j j A e n n j φ φ φ φ φ φ in 3! o 2! in o! 2! 1 Re 3 2 2 The ignal oni of an unodulaed arrier plu variou apliudeodulaed er, uh a φin, φ 2 o, φ 3 in,, e. Hene he Fourier peru oni of an unodulaed arrier plu pera ideband of φ, φ 2, φ 3,, e., enered a.
p. II-56 Angle Modulaion: Narrowband If φ ax << 1, hen, by negleing he higher-power er of φ in he, give A A φ in o whih i alled he narrowband NB angle-odulaed ignal. d x k A A x k A A f NBFM p NBPM τ τ in o in o
Angle Modulaion: NBFM Sinuoid Narrowband FM NBFM Conider For FM, x i a o + k + a f k x f o where k f i he frequeny odulaion onan; ypial uni are in radian per eond per vol. Define a new onan alled he peak axiu frequeny deviaion, hu, we have a k f i + o p. II-57
Angle Modulaion: NBFM Sinuoid The phae of hi FM ignal i θ τ dτ + θ + in + + β in i [ + o τ ] dτ + θ where Thu, he reuling FM ignal i FM Re A A jθ { A e } o + β in θ i e o zero for onveniene. β o o β in A in in β in For narrowband FM NBFM, β i very all o ha Thu, o β in NBFM 1, A o in β in β in A β in in The paraeer β i alled he odulaion index of he FM ignal. p. II-58
Angle Modulaion: NBPM Sinuoid Narrowband PM NBPM Conider x a in The phae of hi PM ignal i θ + k x + θ + k a + β in p p in The reuling PM ignal i PM Re A A jθ { Ae } o + k + a in o o β in A o β in For narrowband PM NBPM, β i very all, Thu, NBPM p 1, A o θ i e o zero for onveniene. β k a p in in β in in β in β in A β in in p. II-59
Angle Modulaion: NB Sinuoid In uary, if he eage ignal x i a pure inuoid, ha i, x a a in o for PM for FM Then, φ β in where β k k f a p a for PM for FM : peak frequeny deviaion Noe ha β i known a odulaion index for angle odulaion and i he axiu value of phae deviaion for boh PM and FM. I i only defined for inuoidal odulaion. If φ ha a bandwidh of W B, he NB angle-odulaed ignal will have a bandwidh of 2W B. p. II-6