UNIT-6 ANGLE MODULATION (FM) II

Transcription

1 UNI-6 ANGLE MODULAION FM II opis: Demodulaion o FM waes, Phase Loed Loop, Non-linear Model o he phase loed loop, Linear model o he phase loed loop, FM sereo muliplexing, Nonlinear ees in FM sysems, and FM sysems. Frequeny demodulaion is he proess ha enables us o reoer he original modulaing signal rom a requeny modulaed signal. Frequeny Demodulaor produes an oupu signal wih ampliude direly proporional o he insananeous requeny o FM wae. Frequeny demodulaors are broadly lassiied ino wo aegories: i Dire mehod examples: requeny disriminaors and zero rossing deeors. ii Indire mehod example: phase loed loop. he dire mehods use he dire appliaion o he deiniion o insananeous requeny. he indire mehod depends on he use o eed ba o ra ariaions in he insananeous requeny o he inpu signal. Slope Cirui: his is a irui in whih he oupu olage is proporional o he inpu requeny. An example is a diereniaor. he oupu o he diereniaor, x ds/d and he ranser union, H jπ. Fig: 6. A simple diereniaor wih ranser union.

2 Slope deeor: A slope deeor irui onsiss o wo unis: a slope irui and an enelope deeor. he slope irui oners he requeny ariaions in he FM signal ino a olage signal, whih resembles an AM signal. he enelope irui obains he oupu signal proporional o he message signal. s slope s enelope s o irui deeor FM FVC AM AM demodulaor Fig: 6. lo diagram o a Slope deeor. Consider an FM signal as deined below: equaion 6. s A os π π m τ dτ, where i m 6. Le he slope irui be simply diereniaor: s A m sin m d π π π π τ τ so A π π m he oupu o he slope irui is hus proporional o he message signal, m. A simple slope deeor irui is shown i ig-6.3, onsiss o slope irui and an enelope irui. Fig: 6.3 A simple Slope deeor irui.

3 alaned Frequeny Disriminaor: he requeny disriminaor onsiss o slope iruis and enelope deeors. An ideal slope irui is haraerized by he ranser union ha is purely imaginary, arying linearly wih requeny inside a presribed requeny ineral. he ranser union deined by he equaion 6. and is shown in igure 6.4a. Fig: 6.4 a Frequeny response o ideal slope irui, H. b Frequeny response o omplex low pass iler equialen Frequeny response o ideal slope irui omplemenary o para. 6. oherwise,,, a j a j H π π

4 Consider an FM signal s haing sperum rom / o / and zero ouside his range. Le s be he oupu o he slope irui. Any slope irui an be onsidered as an equialen low pass iler drien wih he omplex enelope o inpu, FM wae. Le H ~ is omplex ranser union o he slope irui. his union is relaed o H by Using equaions 6. and 6.3, we ge his is depied in he igure 6.4b. Le s be he FM wae, deined in equaion6. and is omplex enelope be s ~ gien by: Le s ~ be he omplex enelope o he response o he slope irui deined by ig-6.4a. he Fourier ransorm o s ~ is Using he diereniaion in ime domain propery o Fourier ransorm; oherwise,, ~ a j H π...6.3, ~ > or H H 6.5 exp ~ omplex enelope o d m j A s s π 6.6 oherwise,, ~ ~ ~ ~ S a j S H S π 6.7 exp ~ ~ ~ d m j m aa j s j d ds a s π π π

5 hereore he response o he slope irui is deined as 6.8: s Re π [ ~ s exp jπ ] aa m os π π m d π 6.8 he signal, s is a hybrid modulaed wae in whih boh he ampliude and requeny o he arrier wae ary he message signal, m. I m < or all, resuling oupu ~ s π aa m o enelope 6.9 deeor is he bias erm π a A is proporional o he slope a o he ranser union o he slope irui. he bias may be remoed by subraing rom he enelope deeor oupu rom he oupu o a seond enelope deeor preeded by a omplemenary slope irui wih a ranser union H as desribed in ig:6.4. ~ ~ H H 6. Le s be he oupu o he omplemenary slope irui wae s. he enelope o he irui is ~ s π aa m produed by he inoming FM 6. he dierene beween he wo enelopes in equaions 6.9 and 6. is s ~ ~ s s 4π aa m 6. hus an ideal requeny disriminaor an be modelled as a pair o slope iruis ollowed by enelope deeors and a summer as shown in ig-6.5 whih is alled balaned requeny disriminaor.

6 Fig: 6.5 Idealized model o alaned requeny disriminaor. he idealized model an be losely realized using he irui shown in ig-6.6 whih onsiss o wo resonan iruis. he upper and lower resonan ilers are uned o requenies aboe and below he un-modulaed arrier requeny,. he ampliude responses o he uned ilers and he oal response are shown in he ig-6.7. Fig: 6.6 alaned requeny disriminaor. he oerall perormane o he balaned requeny disriminaor will be good only when boh he ilers hae high Q-aor and a proper requeny separaion beween he uning requenies o he wo ilers. Howeer here will be disorions presen in he oupu due o he ollowing aors:. Sperum o FM wae is no exaly zero or he requenies ouside he range.. uned ilers are no srily band-limied 3. RC ilers in he enelope deeor inrodue disorions 4. uned iler haraerisis are no linear oer he whole requeny band.

7 Fig: 6.7 Frequeny response. Zero Crossing Deeor: his deeor irui explois he propery ha he insananeous requeny o an FM wae is approximaely gien by dθi π d i 6.3 where is he ime dierene beween he adjaen zero rossings o he FM wae. Le n be he number o zero rossings inside an ineral and hen express he ime is gien by n and i n 6.4 hus he insananeous requeny is linearly relaed o he message signal m; i an be reoered rom he nowledge o n. A simpliied blo diagram o a zero rossing deeor based on he aboe priniple is shown in he ig-6.8. he basi blos are Limier, Pulse generaor and Inegraor. he Limier produes a square wae ersion o he inpu FM wae. he Pulse generaor produes pulses a he posiie going edges and negaie going edges o he limier oupu. he Inegraor perorms he aeraging oer he ineral and hene produes he message signal.

8 Phase-Loed Loop PLL: he PLL is a negaie eedba sysem ha onsiss o hree major omponens: a muliplier, a loop iler and a olage onrolled osillaor VCO onneed in he orm o a loop as shown in he ig-6.9. he VCO is a sine wae generaor whose requeny is deermined by he olage applied o i. Fig: 6.9 Phase Loed Loop Iniially he VCO is adjused suh ha onrol olage is zero, wo ondiions are saisied:. Frequeny o VCO is se preisely a he arrier requeny, and. VCO oupu has a 9 o phase shi w.r.. o he un-modulaed arrier wae. Le he inpu signal applied o he PLL be s: s A where sin [ π φ ] φ π m d

9 Le he VCO oupu be r: r A where os [ π φ ] φ π d where is he requeny sensiiiy o VCO in Hz/ol. Inoming FM signal and VCO oupu are applied o he muliplier. he Muliplier oupu e m s r, produes wo omponens: where m muliplier gain in ol -. A high requeny omponen: m A A sin[ 4π ϕ ϕ ]. A low requeny omponen: m A A sin[ ϕ - ϕ ] he high requeny omponen is eliminaed by he loop iler low pass ype and VCO. hen he inpu o he Loop iler is: e m A A sin[ ϕ - ϕ ] 6.8 e m A A sin [ φ ] e he Phase error : φ e φ φ φ π d he loop iler operaes on he inpu e o produe he oupu: e * h; where h is impulse response o he loop iler. e τ h τ dτ Diereniaing he equaion 6.; we ge dφ e dφ π d d

10 Using 6. and 6.9; and rearranging dφe d where dφ π K sin d K A A : loop m [ φ τ ] h τ dτ e - gain parameer he equaion 6. represens a Non-linear model o a phase loed loop and is shown in ig-6.. he nonlinear model resembles he basi PLL sruure. he Muliplier is replaed by a subraor and a sinusoidal nonlineariy, and he VCO by an inegraor. u he nonlinear model is ery diiul o analyze. Fig: 6. Non-linear model o a Phase Loed Loop Linear Model o Phase-Loed Loop : he nonlinear model is a ompliaed model and is diiul o analyze. Hene a simpler ersion o his model alled a linear model is obained. An assumpion ha phase error, ϕ e is small leads o an approximaion: sin[ ϕ e ] ϕ e 6.3 and subsiuing in 6.9; we ge e m A A ϕ e. 6.4 hus he nonlinear model in ig-6. an be wrien in a simpliied orm as shown in ig:6..

11 Fig: 6. Linear model o a Phase Loed Loop Subsiuing equaion 6.3 in 6. leads o dφe dφ π K d d [ φ τ ] e h τ dτ dφe d π K dφ d [ φ * h ] e Applying Fourier ransorm o equaion 6.5; jπ ϕ e π K ϕ e H jπ ϕ j Φe Φ j K H Le L be open-loop ranser union o PLL. L K H j hen ϕ e an be wrien as Φe Φ L he oupu o he linear model in ig 6., an be deined as

12 K Φ e * h Applying Fourier ransorm and using 6.7 we ge u sin g V 6.8 K V H Φ j e L Φ L j. L Φ... e 6.3 As he loop ranser union, L approahes large alue, ϕ e approahes zero. he phase o VCO beomes asympoially equal o he phase o he inoming wae and phase-lo is esablished. j For L >>, V Φ Applying inerse Fourier ransorm o he aboe equaion: dφ π d Subsiuing or ϕ rom 6.5 m hus he oupu o he linearized model is proporional o he message signal.

13 FM Sereo Muliplexing: Sereo muliplexing is a orm o requeny diision muliplexing designed o ransmi wo separae signals ia he same arrier. I is widely used in he FM radio broadasing o send wo dieren elemens o a program. For example he dieren elemens an be seions o orhesra, a oalis and an aompanis. his gies a spaial dimension o is perepion or he lisener a he reeiing end. he wo imporan aors ha inluene he FM sereo ransmission are:. he ransmission has o operae wihin he alloaed FM broadas hannels.. I has o ompaible wih he monophoni reeiers. he FM sereo ransmier onsiss o a muliplexing sysem. he blo diagram o he muliplexer is shown in ig-6.. Fig: 6. Muliplexer sysem in ransmier o FM sereo. Le m l and m r denoe he wo signals rom he wo dieren mirophones a he ransmier end o he sysem. hey are applied o a marixer ha generaes he sum signal and he dierene signal. he sum signal [m l m r ] is used in he base band orm only. he dierene signal [m l - m r ] along wih a 38 Hz sub-arrier are applied o a produ modulaor o generae a DSSC modulaed wae. he sub- arrier is generaed rom a requeny doubler using 9 Hz osillaor. he hree signals: sum signal, dierene signal and a pilo arrier signal o requeny 9 Hz are ombined/added o obain he muliplexed signal. he muliplexed signal an be deined as:

14 m [ m l m r ] [ m l - m r ] os4π K osπ where 9 Hz and K is a onsan, hosen o mainain he pilo beween 8% and % o he pea requeny deiaion. he sperum o he muliplexed signal is shown in he ig6.3. Fig: Sperum o Sereo muliplexed signal, m. he muliplexed signal is used as a modulaing signal or he FM modulaor o produe an FM signal or ransmission. he FM sereo reeier onsiss o demodulaor and de-muliplexer. he de-muliplexer is shown in ig.6.4. he de-muliplexer onsiss o hree ilers: a low pass iler and wo band pass ilers. he base band low pass iler reoers he sum signal in he band -5 Hz, he band pass iler reoers he modulaed dierene signal in he band 3-53 Hz and a narrow band pass iler is used o reoer he pilo arrier 9 Hz. he sub-arrier signal o requeny 38 Hz is obained by requeny doubling he pilo arrier. he dierene signal is hen obained rom sub-arrier and modulaed dierene signal using a oheren deeor. he marixer add/subraor reonsrus he le signal, m l and he righ signal, m r. Fig: 6.4 : De-muliplexer sysem in reeier o FM sereo.

15 Non-linear Ees in FM Sysems: Nonlineariies are presen in all elerial newors in one orm or he oher. he wo basi orms o nonlineariies are: Srong non-lineariy and wea non-lineariy.. he Srong non-lineariy is inrodued inenionally and in a onrolled manner or some speii appliaion. Ex: Mulipliers. Square-law Modulaors, Limiers, and Frequeny. he Wea non-lineariy is o parasii naure whih arises due o impereions. he ee o his is o limi he useul signal leels in a sysem. In his seion he ees o hannel on FM signal is onsidered. Le i be an FM signal; i A Cos[ π ϕ ] 6.34 Consider a ommuniaion hannel whose ranser haraerisi are deined by he non-liner inpu oupu relaion: i be he inpu and o be he oupu o he hannel o a i a i a 3 3 i o a A Cos[ π ϕ] a A Cos [ π ϕ] a 3 A 3 Cos 3 [ π ϕ] Expanding and simpliying, we ge a A a a A A os 3 4 a 3 A 3 os [ π φ ] 4 3 [ 4π φ ] a A os[ 6π 3φ ] he irs erm represens he DC omponen, he remaining hree erms represen he requeny modulaed signals wih arrier requenies, and 3. o exra he FM signal rom he hannel oupu, i is neessary o separae he FM signal wih arrier rom he loses omponen o arrier requeny. Le denoe he requeny deiaion and W denoe he highes requeny omponen o message signal, m. he hannel oupu o will hae he highes omponen rom irs FM as W and he lowes omponen rom he seond FM is W. Hene he neessary ondiion required o separae he FM signal is:

16 W > W hereore > 3 W hus by using a band pass iler o mid requeny and bandwidh W he hannel oupu is redued o 3 3 a A a3 A os φ W w 4 [ π ] hereore he ee o passing an FM signal hrough a hannel wih ampliude nonlineariies, ollowed by appropriae ilering, is simply o modiy is ampliude. Hene unlie AM, FM signals are less aeed by he hannel disorions. he FM signal is sensiie o phase nonlineariies. Phase nonlineariies are enounered in Mirowae radio sysems, whih is due o he phase haraerisis o repeaers or ampliiers used in he sysem. hus he FM signal is less sensiie o ampliude nonlineariies and more sensiie o phase nonlineariies. FM Sysem: A FM sysem onsiss o wo basi unis: FM ransmier and FM reeier. A lile inormaion is added in his seion abou boh ransmier and reeier. FM ransmier he basi blo diagram o FM ransmier is shown in ig.6.5. he audio inpu signal is irs pre-proessed using pre-emphasis irui o minimize he ariaion in SNR signal-onoise raio a he reeier. he narrow band modulaor is generaed and hen passed hrough requeny mulipliers o ge wide band FM. he wide band FM signal is ed o drier and hen o a power ampliier whih inreases he signal srengh beore ransmission. Pre-emphasis: Mos ommon analog signals hae high requeny omponens ha are relaiely low in ampliude han low requeny ones. Ambien elerial noise is uniormly disribued. hereore, he SNR or high requeny omponens is lower ompared o low

17 requeny omponens. o orre his problem, inpu signal is pre-emphasized beore requeny modulaion. In FM broadasing, he high requeny omponens are boosed by passing he modulaing signal hrough a HPF wih a 75 ms ime onsan beore modulaion. his opi is disussed in deail in noise analysis o FM sysems. Fig: 6.5: A simple FM ransmier FM Reeier: A reeier based on super heerodyne priniple is shown in he ig.6.6. he RF ampliier booss he signal srengh o reeied wea signal. he mixer and loal osillaor ogeher perorms he down onersion o FM signal o IF range. he disriminaor irui perorms he demodulaion proess o dee he message signal. Fig: 6.6: A simple FM reeier

18 Ampliude Limier: An FM wae ges disored when i is ransmied hrough he hannel. he FM wae a he inpu o he reeier will no hae onsan ampliude beause o he hannel impereions. Hene a he reeier i is neessary o remoe he ampliude ariaions prior o he demodulaion. his is arried ou by an ampliude limier irui in he reeier. An ampliude limier irui onsiss o a hard limier and a band pass iler. he hard limier will oner disored FM wae ino an FM square wae. he band pass iler will blo all he harmonis in FM square wae o obain an undisored FM wae. De-emphasis: A he FM reeier, he signal aer demodulaion mus be de-emphasized by a iler wih omplemenary haraerisis as he pre-emphasis iler o resore he relaie ampliudes o he modulaing signal. he de-emphasis newor is a simple R-C newor similar o a low pass iler. Summary: In his haper arious demodulaion shemes suh requeny disriminaor, PLL based demodulaors are disussed. In addiion o ha he FM sereo muliplexing mehod is explained. During he ransmission FM signal he hannel will indue disorions due o he nonlineariies. o minimize hese proper hoie o ilers are essenial. In he end, a disussion is done on he FM ransmier and FM reeiers.