Analog Modulation. Amplitude modulation F. Dellsperger

Transcription

1 Analog Modulaion Apliude odulaion AM -8 F. Dellsperger

2 Conen. Analog odulaion ehniques Apliude odulaion Conenional apliude odulaion Double Sideband Modulaion DSB and Single Sideband Modulaion SSB Independen Sideband ISB Vesigial sideband odulaion VSB Quadraure AM QAM AM odulaors AM deodulaors Disurbane and noise behaior o AM Reerenes F. Dellsperger

3 Fig. -: Varians o apliude odulaions Fig. -: AM- signal in ie doain Fig. -3: AM- signal in requeny doain (speru) Fig. -4: AM signal in phase diagra (Phasor) Fig. -5: AM- signals wih odulaion index o.,.5 and Fig. -6: Modulaion index.5 (Oerodulaion)... 4 Fig. -7: Oerodulaion wihou phase inersion... 4 Fig. -8: Speru o AM-signal wih single sinusoidal odulaion signal... 4 Fig. -9: AM-Speru o arbirary odulaion signals... 4 Fig. -: Baseband wih sinusoidal odulaion signals... 4 Fig. -: AM Speru o baseband wih sinusoidal odulaion signals Fig. -: AM Bandwidh Fig. -3: AM-Power or -Tone-Modulaion wih = khz and = Fig. -4: DSB signals wih redued and suppressed arrier in ie doain Fig. -5: Speru and phasor o DSB signals wih redued and suppressed arrier Fig. -6: SSB Signals or redued and suppressed arrier, ie doain Fig. -7: Speru and phasor o SSB signals wih redued and suppressed arrier, Fig. -8: Enelope or SSB, ull arrier, = Fig. -9: Suary o apliude odulaed signals Fig. -: Transier and reeier iler or esigial sideband odulaion... 5 Fig. -: QAM Transier... 5 Fig. -: QAM Reeier... 5 Fig. -3: Blok diagra o addiie AM odulaor Fig. -4: Cirui diagra o a diode AM odulaor Fig. -5: Diode AM odulaor, a) Diode IV ure, b) Speru o oupu signal Fig. -6: Blok diagra o ulipliaie AM odulaors Fig. -7: AM odulaor Fig. -8: High power AM odulaors Fig. -9: Double sideband odulaor wih suppressed arrier Fig. -3: Double balaned ring ixer, a) Cirui diagra, b) Modulaion signal, ) Swihing signal (Carrier), d) Oupu signal in ie doain, e) Oupu speru Fig. -3: Double balaned ringixer, speru o odulaion signal, arrier and oupu signal Fig. -3: SSB-Modulaor, iler ehod Fig. -33: SSB-Modulaor, phase ehod Fig. -34: Enelope deeor, irui and waeors Fig. -35: Deeor oupu olage or dieren ie onsan RC Fig. -36: Coheren AM deodulaor, produ deodulaor... 6 Fig. -37: Blok diagra or noise analysis... 6 Fig. -38: Threshold ee o enelope deeor F. Dellsperger

4 . Analog odulaion ehniques. Apliude odulaion Wih regard o apliude odulaion, dieren arians ay our: Apliude Modulaion AM DSB SSB ISB VSB LSB and USB, Carrier LSB and USB, Redued or suppressed arrier LSB or USB, Full, redued or suppressed arrier LSB and USB independen, Full, redued or suppressed arrier LSB or USB wih Nyquis slope DSB: Double Sideband USB: Upper Sideband SSB: Single Sideband LSB: Lower Sideband ISB: VSB: Independen Sideband Vesigial Sideband Fig. -: Varians o apliude odulaions In addiion, ehods wih a redued or suppressed arrier are oon or DSB, SSB and ISB. The Inernaional Teleouniaion Union (ITU) designaed he arious ypes o apliude odulaion as ollows: Designaion A3E H3E R3E J3E B8E C3F Desripion Basi AM, Double sideband, ull arrier SSB, Single sideband, ull arrier SSB, Single sideband, redued arrier SSB, Single sideband, suppressed arrier ISB, Independen sideband VSB, Vesigial sideband Table -: ITU Designaions or apliude odulaion.. Conenional apliude odulaion The apliude o a haroni arrier is inluened by he odulaion signal. Carrier: Modulaion Signal: AM-Signal: ˆ V os os AM The apliude o an AM signal is subje o ie and a union o he odulaion olage () : AM ( ()) (.) (.) This union is also designaed as Enelope. The requeny o he arrier does no hange. -8 F. Dellsperger 36

5 Wihin he onex o onenional AM, he enelope siply orresponds o he su o he unodulaed arrier apliude ˆV and he odulaion signal () : AM Vˆ () (.3) Wih a sinusoidal odulaion olage ˆ V os (.4) he enelope will be ˆ ˆ ˆ V () V V os (.5) AM As he arrier apliude ˆV is onsan, he shape o he enelope orresponds o he odulaion signal. Thereore, wih and he appliaion o he rigonoeri relaion osaos b osa b osa b he apliude-odulaed signal is: AM os ˆ ˆ AM V V os os ˆV AM Vˆ os os os Carrier Lower Sideband Upper Sideband (.6) (.7) V ˆ V ˆ V ˆ ax () T T Enelope ˆV V ˆ V ˆ V ˆ in Enelope Fig. -: AM- signal in ie doain V() ˆV ˆV / - + Fig. -3: AM- signal in requeny doain (speru) -8 F. Dellsperger 37

6 The hree requeny oponens o an AM wae wih a sinusoidal odulaion an also be drawn in he phase diagra as phasors roaing wih angular eloiy. Q I Fig. -4: AM signal in phase diagra (Phasor) Reerring o he arrier requeny, he phasor o he signal o he lower sideband ( ) roaes slower by, i.e. lokwise, he phasor o he signal o he upper sideband ( ) roaes aser by, i.e. ani-lokwise. The resul o he hree phasors is a phasor wih a arying apliude and roaion wih he arrier requeny, i.e. an apliude-odulaed signal. Modulaion index In he equaion (.6) or he AM signal, he arrier apliude ˆV is aored ou: ˆV AM() os( ˆ ) V os( ) ˆV Modulaionindex os( ) Vˆ os( ) (.8) The odulaion index is an indiaor or he degree o he apliude odulaion and is soeies indiaed in peren. Aer he deodulaion, he apliude o he deodulaed signal is proporional o he odulaion index. ˆV ( ) (.9) ˆV The apliude-odulaed arrier reahes a axiu alue o Vˆ ax Vˆ Vˆ ˆ V iniu alue o Vˆ Vˆ Vˆ Vˆ. in and a -8 F. Dellsperger 38

7 The odulaion index an hereore be alulaed ro he axiu and iniu alues o he enelope: Vˆ ˆ ax V V ˆ V ˆ ax in in (.) AM signals wih dieren odulaion index =. =.5 = Modulaion Signal ( ) s ( ) s ( ) s Enelope AM ( ) s AM ( ) s AM ( ) s AM Signal AM ( ).5.5 s AM ( ).5.5 s AM ( ).5.5 s Fig. -5: AM- signals wih odulaion index o.,.5 and -8 F. Dellsperger 39

8 Oerodulaion ( > ): In he ase o V ˆ ˆ V, he odulaion index will be >; his is alled oerodulaion. The enelopes ross he zero line. Due o his, phase jups resul, he enelope does no orrespond o he odulaion signal anyore and he enelope deodulaion generaes a disored signal. AM ( ) AM ( ) 3 AM ( ) Fig. -6: Modulaion index.5 (Oerodulaion) s Howeer, AM odulaors are oen no able o inluene he phase so ha he apliude reains zero unil he nex phase inersion. AM ( ) Fig. -7: Oerodulaion wihou phase inersion s -8 F. Dellsperger 4

9 Apliude speru o an AM signal Wih he Fourier ransor or by expanding and onering he equaion (.8) o he sinusoidal odulaed AM signal, he indiidual oponens o he speru an easily be alulaed: () os( ) Vˆ os( ) AM Lower Sideband Vˆ os( ˆ ˆ ) V os( ) V os( ) Carrier Upper Sideband (.) V ˆV ˆV - + Fig. -8: Speru o AM-signal wih single sinusoidal odulaion signal The apliude speru onsiss o he ollowing oponens: unodulaed arrier wo sideband requenies wih a disane o he odulaion requeny ro he arrier. -8 F. Dellsperger 4

10 AM speru or rando odulaion signals Non-sinusoidal odulaion signals oupy a baseband in a requeny range in o ax. In an AM signal, wo sidebands are generaed, whih exaly orrespond o he baseband, and are irrored o he arrier requeny. V() V Baseband in ax in ax V() V Lower Sideband Carrier Upper Sideband - ax ax Fig. -9: AM-Speru o arbirary odulaion signals In he lower sideband, he higher odulaion requeny ax lies below he lower odulaion requeny in. This is alled an inered sideband. In he upper sideband howeer, he relaions are noral (non-inered sideband). Eah o he sidebands respeiely onains he oplee inoraion o he baseband. Here, i is eiden ha due o he apliude odulaion, he double-sided baseband speru is shied o he arrier requeny. In he siples ase, a non-sinusoidal baseband signal onsiss o wo sinusoidal oponens and : u () Uˆ ˆ os( ) U os( ) V () Baseband - - Fig. -: Baseband wih sinusoidal odulaion signals -8 F. Dellsperger 4

11 Hene, he AM signal will be: () Vˆ Vˆ os( ) Vˆ os( ) os( ) AM Vˆ os( ) Vˆ os( ) os( ) Vˆ os( ) os( ) Expanded and onered: () Vˆ os( ) AM ˆV ˆV ˆV ˆV os ( ) os ( ) os ( ) os ( ) (.) V() Carrier Lower Sideband Upper Sideband Fig. -: AM Speru o baseband wih sinusoidal odulaion signals -8 F. Dellsperger 43

12 Bandwidh o AM signals An AM signal oupies a bandwidh, whih orresponds o he axiu baseband requeny uliplied by wo: B AM ax ax = axiu baseband requeny (.3) V() Carrier LSB USB ax ax AM-Bandwidh Fig. -: AM Bandwidh A reeier iler or AM has o hae a leas a pass bandwidh orresponding o he AM bandwidh. I he bandwidh is oo sall, high odulaion requenies are u o. Power o AM signals The eeie power realized in a resisor R is P ˆV R For AM, seeral power deiniions are used: Carrier power = power o a unodulaed arrier AM power (ean power) = su o he powers o all requeny oponens. PAM P PUSB POSB T/ PAM li AM d T T T/ For a sinusoidal odulaion signal (-one-odulaion), his resuls in: PAM P P P ˆV R (.4) (.5) (.6) -8 F. Dellsperger 44

13 Peak Enelope Power PEP = power o a arrier period wih axiu enelope apliude. For a sinusoidal odulaion signal, he ollowing applies: PEP P (.7) In a bes-ase senario wih =, he ean power o an AM ransier is.5 ies he arrier power P. /3 o he power are loaed in he arrier, whih does no onain any inoraion, and only /3 o he power is loaed in he wo sidebands arrying inoraion. For he axiu alues o he enelope, he ransier us be able o generae a power ha is our ies he arrier power. This eans high deands or he lineariy o he power apliier. 5 PEP = 4P P P AM 4 3 Insananeous Power PEP P ins ( ) AM-Power =.5P Carrier Power = P.5.5 s Fig. -3: AM-Power or -Tone-Modulaion wih = khz and =.. Double Sideband Modulaion DSB and Single Sideband Modulaion SSB Conenional AM signals are quie ineiien wih regard o heir power as well as heir bandwidh. Aually, in a bes-ase senario ( = ), /3 o he power are loaed in he unodulaed arrier and only /3 o he power is loaed in he sidebands arrying he inoraion. Thereore, i sands o reason ha he arrier should a leas be signiianly redued or een oied. This leads us o double sideband odulaion wih a redued arrier (DSB-RC, double sideband redued arrier) or wih a suppressed arrier (DSB-SC, double sideband suppressed arrier). In a, DSB-SC does iproe he power eiieny, howeer, i sill has he sae bandwidh as onenional AM. As he inoraion is opleely onained in eah o he sidebands, i would aually be suiien o ransi one single sideband, whih resuls in a single sideband odulaion (SSB, single sideband). Varians: USB: upper sideband LSB: lower sideband Bu in addiion o he adanages in onneion wih hese ypes o odulaion, here is also a signiianly higher irui oplexiy a ransier and reeier. Deodulaion wih a siple enelope deodulaor is no possible. In he pas, reeiing o SSB and DSB-SC signals was a ery oplex proess and praially only possible or experiened users. In onras o his, onenional AM oers ery easy deodulaion possibiliies and reepion is also possible or inexperiened users. Today, hese probles are no ery iporan anyore. The a ha up o now, onenional AM has no been replaed by ehods ha are ore eiien is howeer basially a quesion o oninuiy and he opaibiliy o syses. -8 F. Dellsperger 45

14 Double Sideband Modulaion DSB DSB-RC DSB-SC DSB() Vˆ k os( ) os( ) ˆ ˆ DSBSC () V os( ) V os( ) Exaples wih sinusoidal odulaion signal: =, arrier redued o % =, arrier suppressed ˆ ˆ () V. os( ) os( ) DSB () V os( ) os( ) DSB SC DSB ( ) DS B ( ).5.5 DS B ( ) s DSB ( ) DS B ( ).5.5 DS B ( ) s Fig. -4: DSB signals wih redued and suppressed arrier in ie doain V() V() Q Q I I Fig. -5: Speru and phasor o DSB signals wih redued and suppressed arrier In addiion o apliude ariaions, double sideband signals also show phase jups. In he ase o he double sideband AM wih a redued or suppressed arrier, a reersal o he odulaion signal resuls in a phase inersion o he odulaed signal and he proess is no a ere apliude odulaion anyore. The or o he enelope does no orrespond o he odulaion signal anyore. -8 F. Dellsperger 46

15 The power o he DSB-SC signal is alulaed as ollows: T/ T/ T/ ˆ ˆ os T T/ T T/ T T/ ˆV T/ T/ li d li os d T T T/ T T T/ PDSB SC li AM d li V os d li V d T T T As () is a low-pass signal and is requenies are signiianly lower han li os d applies and hereore T/ T/ T T Vˆ Vˆ P li d P T T/ DSBSC T/ T P power o he odulaion signal, Single sideband odulaion SSB Exaples wih sinusoidal odulaion signal: LSB, =, arrier redued o 5% ˆ LSB() V.5 os( ) os( )) LSB, =, arrier suppressed LSB() Vˆ os( )).5.5 LSB ( ) LSB ( ) s s Fig. -6: SSB Signals or redued and suppressed arrier, ie doain V() V() - - Q Q I I Fig. -7: Speru and phasor o SSB signals wih redued and suppressed arrier, -8 F. Dellsperger 47

16 In he ase o a single sideband signal wih arrier (ay be redued), here are also phase ariaions. In he ase o an SSB signal wih arrier or redued arrier, he odulaion signal an sill be deeed in he enelope. Howeer, he enelope has a disored shape in oparison o he odulaion signal. For he enelope o an SSB signal wih arrier, he ollowing applies: ˆ () V os( ) (.8) E SSB FC Exaple wih =.7 (7%) and ull arrier:.5 ESSB ( ) Fig. -8: Enelope or SSB, ull arrier, =.7 s For SSB wihou arrier and sinusoidal odulaion signal, he enelope is onsan. There is no apparen odulaion. -8 F. Dellsperger 48

17 Suary ˆ V os AM AM ( ) Carrier Double Sideband Lower Sideband ˆV os os Upper Sideband Single (lower) Sideband () Vˆ os( ) Vˆ os( )) LSB LSB ( ).5.5 Wih Carrier V.5.5 s V().5.5 s ˆV ˆV Bandwidh: - + B ax ˆV Power: PAM P R ˆV DSBSC os os Lower Sideband Upper Sideband Bandwidh: - B ax Power: ˆV PSSBRC P R () V ˆ os( )) LSB Suppressed Carrier DSB ( ) DS B ( ) V().5.5 DS B ( ) s LSB ( ) V() s Bandwidh: Power: P DSB SC - + B ax ˆV 4 R Bandwidh: Power: P SSB - B ax ˆV R Fig. -9: Suary o apliude odulaed signals -8 F. Dellsperger 49

18 ..3 Independen Sideband ISB The wo sidebands an also be odulaed wih dieren inoraion, e.g. wih he le and he righ hannel o a sereo signal. The praial ipleenaion is realized by addiion o an LSB and an USB signal...4 Vesigial sideband odulaion VSB In ase he baseband onains low requenies down o Hz, SSB anno or hardly be ipleened (ery seep ilers, e.). In his ase, esigial sideband odulaion (VSB, esigial sideband) an help, or whih a sall par o he unwaned sideband is inluded in he ransission. In order o aoid errors, a speial iler wih a so-alled Nyquis slope (poin syeri) has o be onneed ahead o he VSB deodulaion on he reeier side. The pars, whih are u o ro one o he sidebands, are opleed by a orresponding par o he oher sideband. Vesigial sideband Carrier Transier iler Nyquis slope Carrier Reeier iler LSB USB LSB USB Transier Reeier Fig. -: Transier and reeier iler or esigial sideband odulaion The esigial sideband odulaion is or exaple used in analog, erresrial TV iage ransission. -8 F. Dellsperger 5

19 ..5 Quadraure AM QAM Two arriers, whih are phase-shied agains eah oher by 9, an be odulaed wih one independen signal eah and be ransied ogeher. This proedure is alled quadraure apliude odulaion (QAM). The odulaor aording o Fig. - generaes he ollowing signal a he oupu ˆ ˆ s s V os s V sin (.9) QAM s Mod. Signal s Mod. Signal ˆV os o 9 ˆV sin ˆ V os Carrier sqam Fig. -: QAM Transier I his signal is ransied o a deodulaor aording o Fig. - oer an ideal hannel, he odulaion signals s are reoered wih he exepion o a onsan apliude s and aor. On he reeiing side, he arrier has o be reonsrued o he exa phase wih an addiional irui. Taking ino aoun he rigonoeri ideniies, he signals sin x osx os x osx sinxosx sinx sa and sb ˆ ˆ ˆ ˆ sa sqam V os s V os s V sin V os ˆ ˆ s V os s V sin os Vˆ Vˆ Vˆ s s os s sin reoe wih lowpass iler ˆ ˆ ˆ ˆ sb sqam V sin s V os s V sin V sin ˆ ˆ s V os sin s V sin Vˆ Vˆ Vˆ s s sin s os reoe wih lowpass iler in he deodulaor will be -8 F. Dellsperger 5

20 Wih he lowpass iler, all signals a r r s s s s ˆV ˆV Thus, he deodulaed signals are reoed. s o he ransier, wih he exepion o he onsan sr and sr orrespond o he odulaions signals s ˆV. and sa Low-pass sr ˆV os sqam o 9 ˆV sin ˆ V os Carrier sb Low-pass sr Fig. -: QAM Reeier An appliaion o he quadraure-am an be ound a he ARI and RDS sereo broadas. -8 F. Dellsperger 5

21 ..6 AM odulaors On priniple, apliude odulaion an be realized by eans o adding he arrier and odulaion signal and heir ransission oer a non-linear wopor or by eans o uliplying he arrier and odulaion signal. Boh ehods are suiable or odulaors wih sall signals. Addiie ehod Nonlinear Twopor Band-pass AM ˆ V os Fig. -3: Blok diagra o addiie AM odulaor Ideally, he non-lineariy should hae a purely square haraerisi ure. The square haraerisi ure i k s is, or a sinusoidal odulaion signal, onrolled by he signal () V () () V Vˆ os( ) Vˆ os( ) s The urren ˆ ˆ i() k V V os( ) V os( ) aongs ohers onains he desired requeny oponens, and. For a diode odulaor, he (non-linear) diode is onrolled by he su o () and () in an operaing poin deined by V. Thus, a non-linear urren will low in he irui, whih indues a olage in he load resisor, and he speru o his olage also onains he desired AM signal in addiion o seeral unwaned signals. This signal an pass he band-pass iler. V + Nonlineariy (Diode, BJT, JFET) () Band-pass iler () R R () AM () Fig. -4: Cirui diagra o a diode AM odulaor -8 F. Dellsperger 53

22 I D V R () Bias poin V a) b) V D - + V AM () Fig. -5: Diode AM odulaor, a) Diode IV ure, b) Speru o oupu signal A diode only has an approxiaely square haraerisi ure. Aually, he PN junion o a diode has an exponenial ure: D VT i Is e Volage I S = Reerse Curren, V T = Teperaure Volage (a. 5V), D = Diode The exponenial union an also be represened as a power series expansion: 3 n x x x x x e!! 3! n! Besides seeral oher poenials, he square eleen whih is neessary or he AM odulaor is also onained here. All eleens o a higher order ause disurbanes. They an generae unwaned requeny oponens, whih lie wihin he AM band and an hereore no be reoed by he bandpass iler. The haraerisi ure o a JFET has a square union, hereore, AM odulaors an be realized wih alos no disorion using JFET. Mulipliaie ehod Wih he equaion (.6) os Vˆ os os Vˆ os wo blok diagras or he realizaion resul. ˆ AM V os AM AM ˆ os V os AM AM AM ˆV Vˆ os os Vˆ os Fig. -6: Blok diagra o ulipliaie AM odulaors The blok diagra on he righ-hand side shows a DSB-SC odulaor, where he arrier is added again. This odulaor an be realized by eans o he irui in Fig F. Dellsperger 54

23 AM Powersplier db Aenuaor ˆ V os Powerobiner Carrier Generaor Fig. -7: AM odulaor AM odulaors or ransiers wih high power In he ase o power ransiers, he apliude odulaion is oen ipleened in he oupu power apliier (ube or ransisor). A his poin, he apliiaion o he oupu apliier is inluened by he odulaion signal. In praie, he eeie supply olage o he oupu apliier is usually onrolled by he odulaion signal. This an or exaple be realized wih as swihing power supply unis or, as shown in he exaple below, by eans o a odulaion ransorer. The required audio requeny power lies wihin he range o he arrier power, as he audio signal us praially delier he sideband power. On he oher side he power apliier an be nonlinear lass C wih high eiieny. The resuling haronis are ilered wih he olleor uned irui. V CC () Power Supply Conrol Volage () C C L AM () C 3 AM () () Power Apliier () Fig. -8: High power AM odulaors -8 F. Dellsperger 55

24 DSB odulaors I he odulaion signal is uliplied wih he arrier, a double side band signal wihou a arrier will resul (DSB-SC). As ulipliaors, ring ixers aording o Fig. -3: an be used: DSBSC ˆ V os Fig. -9: Double sideband odulaor wih suppressed arrier VV ˆ ˆ DSBSC V os( ) V os( ) os( ) os( ) ˆ ˆ () D D4 () a () b) D3 D () a) () ) V a () a () e) d) Fig. -3: Double balaned ring ixer, a) Cirui diagra, b) Modulaion signal, ) Swihing signal (Carrier), d) Oupu signal in ie doain, e) Oupu speru The 4 diodes swih he polariy o he odulaion signals aording o he arrier pulses. They an also be replaed by oher swihing eleens, e.g. JFET or MOSFET. The os popular doublebalaned ixer used in RFIC designs is he Gilber Cell ixer. The arrier signal is usually a high apliude sinusoidal signal and ay be onsidered as a square wae signal beause o he apliude liiaion by he diodes. The diodes operae as a swih. In he posiie hal yle o he arrier, he diodes D and D are onduie. Thus he oupu signal is. a In he negaie hal yle o he arrier, he diodes D3 and D4 are onduie. Thus he oupu signal is. a -8 F. Dellsperger 56

25 The Fourier series o he square wae is: 4 os os3 os and he speru V The onoluion o he arrier speru he speru o he oupu signal Va : V Va V V 3 V V wih he odulaion signal speru V resuls in Va V V V C V a Lower Sideband Upper Sideband Fig. -3: Double balaned ringixer, speru o odulaion signal, arrier and oupu signal Wih a low-pass iler he signal oponens a 3 and higher an be reoed. -8 F. Dellsperger 57

26 SSB odulaors Single sideband odulaors aording o he iler priniple: Aer he AM odulaor (ideally a DSB-SC odulaor wih suppressed arrier), he unwaned sideband is reoed wih a narrowband bandpass iler. Modulaion signal DSB- Modulaor Band-pass iler SSB-signal Filer aenuaion Lower Sideband Upper Sideband Carrier - u + u Fig. -3: SSB-Modulaor, iler ehod In order o reah he required iler slope, quarz ilers are required in os appliaions. The SSB odulaor aording o he phase ehod is based on he priniple o he anellaion o signals in phase opposiion. A he oupus o he ixers, here are boh o he sidebands, howeer wih dieren phase posiions. I or exaple, he wo upper sidebands are in phase opposiion, hey will anel eah oher ou during he subsequen adding, while he wo inphase lower sidebands are added. Fro his, an USB signal resuls. sa s Mod. Signal Broadband o 9 ˆV os ˆV sin o 9 ˆ V os Carrier sssb sb Fig. -33: SSB-Modulaor, phase ehod Wih analog irui ehnology, he neessary broadband phase shiers an hardly be realized, so ha he phase ehod was rarely used in he pas. Today, wih digial signal proessing, he required irui bloks an howeer be reaed wihou any probles. A broadband 9 o -phaseshier wih alos ideal properies an be realized wih a Hilber ransoraion using digial signal proessing in a DSP or FPGA. -8 F. Dellsperger 58

27 ..7 AM deodulaors Inoheren deodulaion The enelope deodulaor as he siples deodulaor irui only needs a iniu nuber o oponens. I onsiss o a peak deeor and a subsequen low-pass (RC eleen). This is alled an inoheren deodulaion as his irui does no require arrier reoery. T T C R C Fig. -34: Enelope deeor, irui and waeors An iporan aor is he seleion o he ie onsan o he RC eleen. I ay no be oo sall or oo large. For is u-o requeny g, he ollowing requireen applies: R C u g u : Carrier requeny u : Highes odulaion requeny As in os ases, he arrier requeny is uh higher han he highes odulaion requeny, he seleion o he ie onsan is no riial. oo sall ideal oo large Fig. -35: Deeor oupu olage or dieren ie onsan RC R C The apaior C seres or DC-deoupling. Togeher wih he load resisor o he deodulaor, i ors a high-pass irui. The u-o requeny o he high-pass should be signiianly lower han he lowes odulaion requeny. -8 F. Dellsperger 59

28 Coheren AM deodulaors The os oplex bu bes ehod or AM deodulaion is he produ or synhronous deodulaor. The reeied AM signal is uliplied wih a reonsrued arrier signal, i.e. he sidebands are shied (ixed) o heir original posiion wihin he baseband. Aer bandpass ilering, he original odulaion signal is resored. AM AM signal Synhronisaion, Carrier reoery Muliplier Reonsrued arrier R Band-pass iler k os Deodulaed signal RX Fig. -36: Coheren AM deodulaor, produ deodulaor Analysis o he irui: A he inpu o he deodulaor, an AM signal is applied Vˆ os Inside he uliplier, he AM signal ˆ D D AM AM is uliplied wih he reonsrued arrier V os. Here, is he phase shi beween he arrier o he inpu signal and he reonsrued arrier. ˆ ˆ AM D V os V os D ˆV D ˆV os os Vˆ Vˆ Vˆ ˆV RX os D Wih he exepion o he aor signal o he ransier. D os os os D D ˆV D reoed by band-pass iler os ˆV os, he deodulaed signal orresponds o he odulaion In ase he phase o he arrier reonsruion deiaes ro he phase o he ransied arrier o, apliude disorions will resul. A 9, he deodulaed signal will be zero. In order o ailiae a phase synhronous arrier reonsruion on he reeier side, i is beer o ransi a redued arrier. I here is a arrier or residual arrier wihin he odulaed signal, he original arrier an be reonsrued quie well. A phase dierene wih respe o he original arrier resuls in a DC oponen. Thereore, a bandpass iler is neessary on he oupu. The produ deeor is suiable or all AM ypes (DSB, SSB, e.). For he reoery o he arrier (synhronizaion), a narrowband bandpass iler or a PLL (Phase Loked Loop) an be used. -8 F. Dellsperger 6

29 I he odulaion signal onains ery low requenies, he arrier reoery will be diiul wih hese ehods. For exaple, in he ase o a FM sereo signal, a pilo-one is ransied wih i and ro his piloone, he arrier or he deodulaion an be reoered...8 Disurbane and noise behaior o AM In he ase o AM signals, he inoraion is arried in he ariaions o he apliude. This requires linear signal proessing. Non-lineariies in he syse hain resul in non-linear disorions o he deodulaed signals. Disurbanes osly resul in apliude luuaions. These are hereore siilar o AM and an hardly be disinguished ro he desired apliude ariaions. During he deodulaion, he dieren bandwidhs and power raes resul in odiied signal-o-noise raios. Here, he behaior o he odulaion ehods wih regard o noise is o be exained. The noise (AWGN Addiie whie Gaussian noise) is added o he waned signal wihin he syse. By eans o a bandpass iler, a narrowband noise is generaed, whih has a noise power speral densiy wihin a sall bandwidh around a ener requeny. This noise is oen alled bandpass noise. I has haraerisis whih orrespond o a real ransission syse wih a narrowband reeier. Channel Deodulaor Modulaor AM DSB SSB AWGN Band-pass smod s n BRF B MOD PS P N Deeor Enelope or Synhro Low-pass B ax PS PN smod sam,sdsbsc,sssb n : Band-pass noise Fig. -37: Blok diagra or noise analysis The narrowband noise an be desribed wih he ollowing equaion: n an os ni os nq sin (.) wih a n n and n I Q The rando ariables ni and nq nq an ni orrelaed. For he square ean alues, he ollowing applies: I Q are saisially independen ro one anoher and no n n n (.) For he analysis, he signal-o-noise raio a he inpu o he deodulaor will be S P N P S N And a he oupu o he deodulaor S P N P S N (.) (.3) -8 F. Dellsperger 6

30 I will be analyzed or AM, DSB-SC and SSB. For AM, he enelope deeor will be analyzed in addiion o he synhronous deeor. Wih he odulaion signal AM AM s he ollowing applies o s s S s os AM (.4) s S s os DSB-SC (.5) DSBSC DSBSC sssb SSSB s os s sin x x S Peak apliude o s A he inpu o he deodulaor in Fig. -37 he signal s s n AM AM AM AM SSB (.6) is applied o AM s S s os n (.7) This resuls in he ollowing signal, arrier, AM and noise power a he inpu o he deodulaor PS SAM s (.8) P SAM (.9) PAM SAM s (.3) N P n G B (.3) Here, G is he noise power speral densiy, B is he bandwidh o he baseband signal and B is he required RF bandwidh. Enelope deeor: The enelope deeor onsiues he enelope o he ie union s SAM s ni nq For a large signal-o-noise raio (low noise olage), he ers o seond and higher order an be disregarded: AM I s sam : an be expanded ino a power series and (.3) s S s n (.33) A he oupu o he deodulaor, signal and noise power will be: S AM P S s (.34) N I P n n G B (.35) Wih he equaions (.8), (.3), (.34) and (.35), we an now alulae he signal-o-noise raios a he inpu and oupu: S AM s s S PS P N P G B G B N S AM P N S P S s s s P N P G B G B G B (.36) (.37) -8 F. Dellsperger 6

31 S Oupu in db N Thereore, he ollowing applies: S S N N This eans ha he signal-o-noise raio or sall noise signals is ies or 3 db beer a he oupu o he deodulaor han a he inpu o he deodulaor. I he oerall AM power is used or he deiniion o he signal-o-noise raio a he inpu o he deodulaor, he ollowing will apply: P S AM s S AM N P G B ' N (.38) (.39) N AM S PS S s N P G B S s S N s N ' (.4) (.4) For he analysis o he enelope deeor wih a sall signal-o-noise raio (high noise olage), he ollowing equaion resuls ro a slighly dieren power series expansion o (.3) a he oupu o he deodulaor: s a S s os (.4) ' n AM The seond er o he equaion an hardly be disinguished ro he noise deodulaor does no generae a suiable oupu signal. an and he In he ase o a sall signal-o-noise raio, he waned signal is linked by ulipliaion o he disurbane ariable os S / N raio a he and wih an inrease o he noise olage, he deodulaor oupu disproporionaely dereases. This is deined as he hreshold o he enelope deodulaor Synhron deeor - Inpu Enelope deeor S in db N Fig. -38: Threshold ee o enelope deeor The ransiion akes plae in a range o S / N db and is hereore irrelean or os appliaions as signals wih S/N<dB are no o suiien qualiy and anno be used. Furher onsideraions an be ound in Li. [], [] and [5]. -8 F. Dellsperger 63

32 Synhronous deeor: In he ase o he synhronous deeor, he inpu signal o he deeor arrier ˆV os. The power a he oupu equals sam is uliplied wih he P S SAM s (.43) 4 PN n G B G B (.44) 4 4 The power raios a he inpu are he sae as or he enelope deeor. S AM s S PS N P G B N S P AM S 4 N PN G B S s Thereore, he ollowing applies: S S N N Wih he exepion o he issing hreshold, he signal-o-noise raios orrespond o hose o he enelope deeor. For DSB-SC and SSB, he sae analyzes an be arried ou. The resuls are suarized in Table -. (.45) (.46) (.47) P S P AM P N G AM Enelope de. S AM s S AM s P S AM P N G B S / N S / N AM Synh.de. S AM s B G S s AM S s B G S AM s 4 DSB-SC S DSB SC s SSB S SSB s B G B G B G B G B RF-Bandwidh B RF B B B B Table -: Signal- and Noise-power or AM, DSB-SC and SSB For DSB-SC, he iproeen o he signal-o-noise raio o in oparison o or SSB is neuralized by he double noise power a he inpu due o he double bandwidh. -8 F. Dellsperger 64

33 ..9 Reerenes [] Taub, H., Shilling, D.L.: Priniples o ouniaion syses. MGraw-Hill, nd Ediion 986 [] Kaeyer, K.D. : Nahrihenüberragung. Vieweg+Teubner, 4. Aulage 8 [3] Roppel, C.: Grundlagen der digialen Kounikaionsehnik. Carl Hanser Verlag, 6 [4] Oh, J-R., Lüke, H.D.:Signalüberragung. Springer Verlag Berlin,. Aulage 7 [5] Shwarz, M.: Inoraion, Transission, Modulaion, and Noise. MGraw-Hill, 98 [6] Zinke, O., Brunswig, H.: Hohrequenzehnik, Springer Verlag Berlin, 5. Aulage 999 [7] Supers, F.L.M.H.: Theory o requeny odulaion noise. Pro. Ins. Radio Engrs. 36, 948, 8-9 [8] Rie, S.O. : Saisial properies o a sine wae plus rando noise. Bell Sys. Tehn.J. 7, 948, 9-57 [9] on Grünigen, D.Ch.: Digiale Signalerarbeiung i einer Einührung in die koninuierlihen Signale und Sysee. Carl Hanser Verlag, 5. Aulage 4 [] on Grünigen, D.Ch.: Digiale Signalerarbeiung: Bauseine, Sysee, Anwendungen. Fooroar Prin und Media, 8 [] Dellsperger, F.: Passie Filer der Hohrequenz- und Nahrihenehnik. Leure Srip, -8 F. Dellsperger 65