Couniaion Syses (Theory) Chaper pliude Modulaion Objeive Upon opleion of his haper you will be able o: Undersand he proess of pliude Modulaion. Undersand differen ypes of pliude Modulaion. Design differen odulaors for pliude Modulaion. Undersand he differen deodulaion ehniques. Inroduion Baseband er is used o designae he band of frequenies of he signal delivered by he soure. In elephony, baseband is he audio band i.e. 0 3.5 KHz. Baseband Signals are ransied wihou odulaion as hey have suffiien power a low frequenies so hey anno be ransied a radio frequenies bu by eans of o-axial ables and opial fibers. Long haul ouniaion over radio links requires odulaion o shif he speru o higher frequenies in order o enable effiien power radiaion using anennas of reasonable diensions. Modulaion is a proess by whih soe haraerisis of he arrier signal like is pliude, Frequeny or Phase are varied in proporion o essage signal. pliude Modulaion refers o he proess in whih apliude of he arrier wave is varied wih he essage signal. The proess of odulaion i.e. shifing he signal speru o a higher frequeny is illusraed below by an exaple, If signal and is Fourier Transfor is x X j j By Frequeny Shifing Propery, x e X and x e X y x os Suppose, y x e j e j y X X F.T. Hene, x os f X f f X f f The speru of x() and y() are shown below, o o Krearyx. ll Righs Reserved. www.krearyx.o
Couniaion Syses (Theory) In he figures shown above, M(0) represens he agniude of speru a 0 frequeny. s an be seen fro he above figures, ha speru of baseband speru is shifed o higher arrier frequeny by ulipliaion wih sinusoidal arrier signal. This is he basi proess of apliude odulaion. Furher, we will see differen ypes of pliude Modulaion. DSB-FC (Double Side Band Full Carrier) This is also known as ordinary pliude Modulaion. The following ers are generally used in regards o pliude Modulaion, Baseband signal essage signal () Carrier signal () Modulaed signal s() Here, apliude of arrier is hanging aording o essage signal. ssuing, os s os os os F.T. f f f f os If we wrie he speru in ers of f hen we have o divide by π Krearyx. ll Righs Reserved. www.krearyx.o
Couniaion Syses (Theory) Speru of Modulaed Signal, S f f f f f M f f M f f The seond er has been derived fro Mulipliaion Theore of Fourier Transfor. Speru of Baseband signal is shown below, Bandwidh = f Speru of Modulaed Signal looks like as shown below, Sine, he speru onsiss of ipulses a arrier frequeny and wo side bands naely USB i.e. Upper Side Band and LSB i.e. Lower Side Band so i is alled as Double Side Band Full Carrier. B.W. f f f f f H z I eans bandwidh of M signal is wie he bandwidh of essage signal. Noe: If essage signal () is non sinusoidal, and onains frequenies f,f,f 3 and so on and frequeny of arrier () is f ; frequenies in odulaed signal will be, s f f,f f,f f 3 e. Krearyx. ll Righs Reserved. 3 www.krearyx.o
Couniaion Syses (Theory) Solved Exaples Proble: If a 60kHz arrier is apliude odulaed by a speeh band of 300kHz 3kHz. Wha is range of frequeny for USB and LSB? Soluion: Carrier Frequeny, f 60kHz Message Frequeny, f 300Hz 3kHz The lower frequeny is apped o The upper frequeny is apped o 60 0.3 60 3 khz khz ssuing a speru of essage signal, he apliude odulaed speru is shown below, Band pass signal B.W. 59.7 57 63 60.3 5.4kHz B.W. 3 0.3.7kHz Proble: MHz sinusoidal signal is apliude odulaed by a syerial square wave of 00μs, whih of he frequeny will no be presen in oupu? a) 00kHz b) 00kHz ) 030kHz d) 990kHz Soluion: If signal is non sinusoidal and is eiher square, riangular or saw ooh, hen by half wave syery i will onain only add haronis. f MHz T 00s Fundaenal Frequeny, f 0 4 Hz Frequeny in square wave: f,3f,5f,7f Frequeny in Modulaed Signal, f f 990kHz, 00kHz f 3f 030kHz, 970kHz ns: 00 khz Krearyx. ll Righs Reserved. 4 www.krearyx.o
Couniaion Syses (Theory) Proble: 000kHz arrier is siulaneously odulaed wih 300Hz and khz audio sine wave. Whih of he frequenies are no presen in oupu? a) 998kHz b) 000.3kHz ) 999.7kHz d)700khz Soluion: Carrier Frequeny, f 000kHz Modulaing Signal Frequeny, f 0.3kHz Frequenies presen in oupu, 00kHz f f 998kHz ns: 700kHz f khz 999.7kHz f f 000.3kHz Modulaion Index Modulaion Index is defined as he raio of peak of essage signal o he peak of arrier signal. Modulaed Signal, s os Modulaion Index, ax a for sinusoidal signal ax os so, a If ; ; a under odulaion If ; ; a over odulaion If ; ; riial odulaion a Tie doain represenaion of odulaed signal for sinusoidal signal Under-odulaion s os a Krearyx. ll Righs Reserved. 5 www.krearyx.o
Couniaion Syses (Theory) Fro he above figure i an be observed ha shape of essage signal reains ina as he envelope of arrier signal and hene i an easily be deeed. Criial Modulaion a In his ase, envelope deeor is no an ideal soluion beause inforaion will be los a ouhing poins i.e. he poins where he wo envelopes ee eah oher. Over Modulaion a No inforaion is seen a CRO beause posiive and negaive porion will anel effe of eah oher. Envelope deeor anno be used in his ase. The rossing over of posiive and negaive envelopes is shown in he figure below, Krearyx. ll Righs Reserved. 6 www.krearyx.o
Couniaion Syses (Theory) Calulaion of M.I. fro odulaed wavefor Modulaion Index, a a ax in a ax in So, axiu and iniu apliude, ax C a in C a For eg. if 0, 5 ax in 0 5 Modulaion Index, a 0 5 3 Frequeny Doain represenaion of odulaed signal for sinusoidal signal Modulaed Signal, os le s os s os os s os os os Krearyx. ll Righs Reserved. 7 www.krearyx.o
Couniaion Syses (Theory) s os os os Taking Fourier Transfor of he odulaed signal, S Calulaion of power for pliude Modulaion Modulaed Signal, Power in os s os os os an be alulaed in ers of Fourier Series Coeffiiens os e e Power = k j j e e j j Power in Modulaed Signal, P T k, Here, represens ean value of os Le os Krearyx. ll Righs Reserved. 8 www.krearyx.o
Couniaion Syses (Theory) Hene, P T 4 P a where T a P P a T This is valid only if essage signal is sinusoidal. P of R If R Power in Carrier Signal, P R P P a T Sine, P I I I a T a Power in Modulaed Signal, P P a P T Here, a P represens oal sideband power. Sine, sideband onsiss of Upper Sideband and Lower sideband P a P LSB 4 P a P USB 4 Krearyx. ll Righs Reserved. 9 www.krearyx.o
Couniaion Syses (Theory) P P verage sideband power USB LSB a P 4 If essage signal is no given, i is assued o be sinusoidal. In praial essage signal is never sinusoidal as sinusoidal signals are deerinisi so no inforaion is onained in i. Solved Exaples Proble: If () and a() are used o generae an M signal wih Modulaion Index (M.I.)=0.5, Wha is he raio of oal sideband power o arrier power? Soluion: Toal Sideband Power, Toal Sideband power arrier power 8 a P P 8 Proble: If equaion for M is sideband power? Soluion: Message Signal, sin f Modulaed Signal, Modulaion Index, 0.5 a 00 Carrier Power, P 50 s 0 0.5sinf osf, wha is value of average s 0 5sinf osf verage sideband power a 50 P 50 = 3.5 wa 4 6 6 Peak oupu power ax R R Iporan Forulas Maxiu pliude, ax Carrier power P R Krearyx. ll Righs Reserved. 0 www.krearyx.o
Couniaion Syses (Theory) Toal sideband power verage sideband power Peak oupu power P P P.P USB LSB 4 R Solved Exaples Proble: given M broadasing saion ransier has a oal power of 5W. If arrier is odulaed by a sinusoidal signal of 0.707. a Calulae (i) verage sideband power (ii) Peak oupu power In boh ases, assue ha anenna is replaed by a 50 Soluion: Transied Power, P P a T P 5 Carrier Power, P T 4W a 4 verage sideband power a P 4 = 0.5W 4 8 Sine, P R 4 50 400 0 Modulaion Index a C 0 0 0 Peak oupu power.65w R 50 resisane. Krearyx. ll Righs Reserved. www.krearyx.o
Couniaion Syses (Theory) Proble: If odulaion index of is hanged fro 0 o, hen ransied power will, (a) Inrease by 50% (b) Derease by 50% () Inrease by 60% (d) Derease by 60% Soluion: If 0 ; P P a T If ; P a P P.5P a T hange in power.5 P 00= 50% P Hene, Transied Power inreases by 50% Proble: If a arrier has peak apliude of 0V a a frequeny MHz. If sinusoidal signal of frequeny khz odulaes beween 7.5 and.5. Then alulae, (i) Modulaion index (ii) Peak oupu power (iii) verage sideband power ssue ha anenna used has a resisane of 50. Soluion: Given.5 7.5 ax in.5 7.5 5 Modulaion Index, ax in a.5 7.5 0 4 ax in 00 verage sideband power a 4 R 4 6 50 W 0.0565W 64 a Peak oupu power 00 0.5.5 =.565W R R 50 Transission effiieny in ase of M Transied Power, P T Sideband Power, P SB Transission effiieny For sinusoidal signal P a SB 4 P SB P T Krearyx. ll Righs Reserved. www.krearyx.o
Couniaion Syses (Theory) P C Effiieny, 4 a a 4 Maxiu ransission effiieny: 00 33.33% ax 3 a Only 33.33% power will be uilized while 66.67% power is wased. Noe: Main disadvanage is ha 66.6% power is wased. Bu a he sae ie, reeiver has inforaion abou arrier frequeny, so here will be no need o use exra synhronizing irui, for knowing arrier suh as Cosas Reeiver in ase of suppressed arrier odulaion. Proble: If a essage signal is given by a arrier of frequeny in%? os sin. If () is odulaed wih o generae s os, hen wha is he value of Soluion: Message Signal os sin os 4 Hene, a Modulaion Index, a a 00% 00% 00% 0% 5 a Krearyx. ll Righs Reserved. 3 www.krearyx.o
Couniaion Syses (Theory) Proble: For a given M signal, if oupu is of he for: s os 400 Bos 380 Bos 40. If P 00w and 40% wha are values of and B? Soluion: Modulaed Signal an also be expressed as, s os 400 Bos 400 os0 Bos0 os400 Coparing wih sandard equaion, Carrier Power, P 00 Carrier pliude, 0 a Transission Effiieny, 0.4 a a a Modulaion Index, a 3 B a 3 B 0 3 s os os Proble: If s 4os 800 0os 000 4os 00 Calulae (a) a (b) Toal power P T () (d) Bandwidh Soluion: Cobining he firs and hird er in odulaed signal, s 0 8os00 os000 8 Modulaion Index, 0.8 a 0 00 0.64 P 50.3 66.0 W T Transied Power, 0.64 800 Transission Effiieny, 00 4.%.64 33 Sine, odulaed signal requires wie he bandwidh as opared o essage signal, 400 Bandwidh B.W. f 00Hz Krearyx. ll Righs Reserved. 4 www.krearyx.o
Couniaion Syses (Theory) pliude odulaion in ase of Non Sinusoidal Signals Transied Power, P T Here, value an be opued as, d T T is ean square value of essage signal (). For a periodi essage signal his Where, T is ie period of essage signal () Solved Exaples Proble: If (i) Toal power os P T and essage signal is shown, hen alulae (ii) Effiieny T T d d T T 0 T Soluion: Mean Square Value of Message Signal, T T 4 4 =4 T 4 () 4 4 P 4 T () % 00% 00% 50% P 4 T Proble: Solve he previous proble if square wave of essage signal is replaed by sawooh wavefor shown below, Krearyx. ll Righs Reserved. 5 www.krearyx.o
Couniaion Syses (Theory) Soluion: Equaion of () in T T, 6 T T/ T/ d d T T T T/ T/ T 3 3 3 T 3 3 3 3 Sine, arrier signal is sae so arrier power reains sae. 4 3 Transied Power, P 3.5w T Effiieny, 3 00 4.85% 3.5 Proble: Calulae oal power and effiieny arrier signal is given as, odulaion index is 0.5 a. The essage signal wavefor is shown below, os and () ax k Soluion: Modulaion Index, 0.5 a Hene, K= Krearyx. ll Righs Reserved. 6 www.krearyx.o
Couniaion Syses (Theory) K Mean Square Value of Message Signal, Toal Power, P T 4 P.67W T 6 0.6 Transission Effiieny, 00% 7.9%.6 3 3 Proble: Figure shows posiive envelope of.m. wave, alulae and. a Soluion: Modulaion Index, ax in a ax in Carrier pliude, 45 5 ax in 30 30 0.5 60 Peak of odulaing Signal, 30 0.5 5 ax C a 5 Mean Square Value of Message Signal, 75 Toal Power, P T 900 75 P 487.5 W T Transission Effiieny, 37.5 00% 7.69% 487.5 3 Krearyx. ll Righs Reserved. 7 www.krearyx.o
Couniaion Syses (Theory) Trapezoidal Mehod If he odulaed signal is ploed in X-Y ode on a CRO hen he shape of a rapezoid appears as shown below, L L a L L I is generally used for non periodi signals. Here, L represens he iniu apliude and L represens axiu apliude. Solved Exaples Proble: If M wave paern for non periodi, signal in CRO is shown, wha is value of Modulaion Index? Soluion: Fro he figure, iniu apliude L 0 L L Modulaion Index, a L L Proble: In rapezoidal ehod, if raio of shor heigh o long heigh is 0.65, wha is value of odulaion index? Soluion: Raio of shor heigh o long heigh is, L L Modulaion Index, a L L L L L L L L 0.65 0.35 0. 0.65.65 Muli-one Message Signal Muli-one essage signals are hose whih have uliple frequeny oponens. s for an Krearyx. ll Righs Reserved. 8 www.krearyx.o
Couniaion Syses (Theory) exaple any periodi signal an be resolved ino Fourier Series and so i an be reaed as Muli-one Signal. Le os os os... 3 3 Modulaed Signal, s os s() os os... os s() os os... os s os os... os a a Here, ai represens odulaion index for i h one Modulaion Index,... a a a a3 B.W. ax,,,... 3 B.W. ax,,,... 3 Frequeny speru The frequeny speru for odulaed uli-one signal is as shown below, Solved Exaples Proble: If equaion of M wave is given as: s 0 5os0 3 os 40 3 os0 6 Calulae, (i) (ii) P (iii) Bandwidh a T Soluion: Modulaion Index for differen ones presen in he signal are, Krearyx. ll Righs Reserved. 9 www.krearyx.o
Couniaion Syses (Theory) 5 0.5 and 0. a 0 a 0 Modulaion Index, 0.5 0. 0.9 0.5385 a 0.5385 Power Transied, P a 50 = 57.5W T Bandwidh, B.W. ax 0 3, 0 3 4kHz Transission Effiieny, 50 0.5385 00%.66% 57.5 Low Level and High Level Modulaion The firs figure below shows he blok diagra of low level odulaion and seond figure shows blok diagra shows blok diagra for high level odulaion In ase of low level, generaion of M akes plae in iniial sage only and his generaed M is odified by using a linear devie whih ay be a lass or lass B aplifier. In high level, odulaion akes plae in final sage of aplifier and odulaion iruiry has o handle high value of power. These are wo basi ehniques o ipleen pliude Modulaion. The differenes in boh ypes of odulaion ehniques are lised below, Krearyx. ll Righs Reserved. 0 www.krearyx.o
Couniaion Syses (Theory) Low Level Modulaion Modulaion ours is iniial sage of aplifier Modulaion irui handles low power Siple irui Low Power udio plifier is required Class aplifier is used Low effiieny Low Disorion High Level Modulaion Modulaion ours is final sage of aplifier Modulaion irui handles high power Coplex Cirui High Power udio plifier is required Class C aplifier is used High Effiieny High Disorion Generaion of M There are wo basi ehods for generaion of pliude Modulaed Wave, Swihing Modulaor Non-Linear Devie Swihing Modulaor The inpu volage o he irui is su of essage and arrier signal. During posiive half yle of inpu, Diode is ON V V o i The praial and ideal haraerisis of Diode are shown Below, Praial haraerisis are non-linear due o knee volage. If knee volage is negleed he haraerisis beoe linear. This diode swihing operaion an also be assued as ulipliaion of inpu signal by an infinie square pulse shown below, Krearyx. ll Righs Reserved. www.krearyx.o
Couniaion Syses (Theory) Here, he swihing pulse is during he posiive half yle so ha inpu and oupu are sae and swihing pulse is 0 during negaive half yle as Diode is OFF so oupu beoes zero. Posiive and negaive yles are assued based on osine funion whih is he arrier wave. The ie period of square wave, T p Sine, i is a periodi funion, i an be represened in ers of Fourier Series p() os os3... 3 The oupu of swihing odulaor is hen, V os os os3... o 3 V os os os... o Desired oponens are (I) and (IV) ou of all he oponens presen afer ulipliaion. If one seles a LPF wih u-off frequeny hen firs and fourh oponen an be exraed bu in ha ase nd oponen is also presen a he oupu whih is undesired. Hene, one has o ake a BPF beween and Here, is axiu frequeny of essage signal. Modulaed Signal is he oupu of filer, s os os 4 os 4 k apliude sensiiviy a Krearyx. ll Righs Reserved. www.krearyx.o
Couniaion Syses (Theory) Modulaion Index,.k a ax a Using Non-Linear Devie Suppose, Non-Linear Devie has he inpu-oupu relaion as, V a v a v o i i Inpu Volage, V os i V a os a os o V a a os a a os a os o Ou of hese ers he desired ers are seond and fourh er. The band of Filer is,, In order o reove he hird er fro he oupu of band pass filer, he neessary ondiion is, where fer passing hrough a BPF, is frequeny of hird er a V a os a os a os o a a Modulaion Index, M.I.. a ax Krearyx. ll Righs Reserved. 3 www.krearyx.o
Couniaion Syses (Theory) Solved Exaples Proble: Wha is Modulaion Index of generaed.m. wave where V V 0.V i i and inpu volage is V 4 os00 os000? i Soluion: Inpu Volage, V 4 os00 os000 i V 4 os 00 os 000 0. 4 os 00 os 000 V 4 os00 os000.6os 00 0.4 os 000.6os00 os000 Here, seond and fifh er are of ineres in pliude Modulaion. So, we apply a filer of band pass frequeny,.6os00os000 = 0.8os00 os800 Range of BPF : w w w w 000 00 000 00 800 00 he oupu of filer we have, V os000.6os00 os000 0.8os00 os000 a Modulaion Index, 0.8 a Proble: non linear devie wih ransfer haraerisis i 0 V 0.V is i i applied wih a arrier of V apliude and a sinusoidal signal of 0.5V in series. If oupu of only frequeny oponens of pliude Modulaed wave is onsidered, han wha is he deph of odulaion? Soluion: Deph of Modulaion or Modulaion Index, 0. 0.5 0. a a a a ax Deeion ehod of pliude Modulaion The following hree ehods are used for deodulaion of pliude Modulaion, (i) By use of non linear devie/square law ehod. (ii) By use of synhronous deeions. (iii) By use of envelope deeor. Krearyx. ll Righs Reserved. 4 www.krearyx.o
Couniaion Syses (Theory) The inpu o reeiver is he pliude Modulaed Wave, s k os a By use of Non Linear devie Inpu of Deodulaor, s os k os a ssue he inpu-oupu relaion of deodulaor is, V a V a V i i V a os k os a os k os a a V a os a k os a os a a k os a k os a a Sine, os os This expression an be expressed as, V a os a k os a a k k os k os k os a a a a The desired oupu is he signal proporional o essage signal, a Desired oupu k a To exra his er we will Use a LPF wih u off frequeny, followed by a apaior. Due o presene of negleing haroni disorion, k a k a k a oponen, here ay be haroni disorion in oupu. For I eans his ehod is no suiable for large apliude essage signal, I is generally preferred if essage signal apliude is less han vol. Krearyx. ll Righs Reserved. 5 www.krearyx.o
Couniaion Syses (Theory) Solved Exaples Proble: Wha is a value of axiu Haroni Disorion possible in non linear devie oupu? Soluion: Le os k y k os k os a a a os k os a k k % Haroni Disorion a 00% a 00% 5 k k 4 a Maxiu Haroni Disorion = 5% a ax k a Proble: sserion: Square Law Deeor are no pariularly saisfaory for deeion if odulaing signal base apliude is greaer han V. Reason: square deeor H.D. is as high as 5% for opleely odulaed signal. Soluion: Boh sserion and Reason are orre bu reason is no orre explanaion of asserion. Reason will be ha is auses haroni disraion for high apliude ( will be denoinaing). Synhronous Deeion Modulaed Signal, s k os a Here, synhronizaion eans frequeny of arrier and frequeny of loal osillaor are in synhronizaion. V s k os ' os a a a V ' k os k os ' V k os k os a a Krearyx. ll Righs Reserved. 6 www.krearyx.o
Couniaion Syses (Theory) ' ' Oupu of LPF: k a Oupu of apaior: ' k a The apaior bloks DC Volage and so he oupu is proporional o essage signal. So, here is no disorion in oupu. Envelope Deeor For he ase of under-odulaion, he odulaed wave and is envelope are shown below, Here, if we are able o exra he envelope hen essage signal an be exraed fro he odulaed wavefor wihou he loss of any inforaion. When odulaion index is i.e. he ase of riial odulaion he odulaed wavefor and is envelope are shown below, Bu he inforaion is los when he odulaed wavefor ouhes he axis so essage signal anno be opleely reovered. Krearyx. ll Righs Reserved. 7 www.krearyx.o
Couniaion Syses (Theory) In he figure shown above, he odulaion index is greaer han and so i is a ase of Over- Modulaion. Inforaion is los due o overlapping of posiive and negaive envelope so envelope deeion will no yield he essage signal. Hene, Envelope deeor will work effiienly only when odulaion index is less han. Basi Operaion In posiive half, diode will be ON and apaior sars hanging hrough resisane R. s The ie onsan for harging of apaior is, RC. s Here apaior will harge fas upo peak value and hene should be sall. RC s f If ie onsan is sall, apaior harging will be fas. In negaive half, diode beoes off and sar disharging hrough R L beoes very iporan.. In his ase, RC L If RC is very sall, hen here will be fluuaion in he oupu and high value of ripple L will be presen. Due o his here ay be soe ripples a he oupu. These spikes/ripples fluuaions will degrades he perforane of oupu. R C L f If RC L is very high; iniially apaior will be harged upo peak and due o high value of RC. Le volage disharge upo soe value in negaive half yle (during period when L diode is off). Nex peak a inpu having high value will harged apaior o higher volage. During negaive half yle, apaior disharges very slowly and anno reah he level of nex peak. If having very sall value, volage is no suffiien o ake diode ON and so, i will Krearyx. ll Righs Reserved. 8 www.krearyx.o
Couniaion Syses (Theory) iss ha peak; so an aoun of inforaion will be los (sall peaks) due o large disharge ie his is alled as Diagonal lipping. The apaior shall be able o disharge by he nex peak arrives so ha no inforaion is issed and hene, R C T L f R C {for saisfaory operaion} f L f Solved Exaples Proble: n.m. signal is deeed using an envelope deeor arrier frequeny are MHz and khz, hen wha is value of ie onsan for envelope deeor? (a) 500 s () s (b) 0 s (d) 0. s Soluion: For saisfaory deeion of essage signal, RC 0 0 s RC 500s 6 3 Opiu Tie Consan Opiu value of RC o avoid diagonal lipping in a single one sinusoidal signal is given by, RC a. a To avoid diagonal lipping, rae of disharge of apaior volage should be greaer han rae of derease of odulaing volage. Krearyx. ll Righs Reserved. 9 www.krearyx.o
Couniaion Syses (Theory) Modulaed Wavefor, s os os a Envelope of Modulaed Signal is, V os envelope a When he apaior disharges, he apaior volage is given by, V V e RC V envelope envelope RC Capaior should disharge before nex peak arrives so no inforaion is los. Hene, dv d dv envelope d dv d V envelope RC dv envelope sin sin d a a V envelope sin RC a os Thus, a RC RC sin a os a sin a for axiu value of RC so ha ie is no diagonal lipping differeniae w.r.. ; sin. sin os os a a a a sin os os a a os a RC os a sin a a a a Krearyx. ll Righs Reserved. 30 www.krearyx.o
Couniaion Syses (Theory) RC ax a a Noe: This is valid for single one sinusoidal signal only. Here value of ie onsan depends upon ax odulaion frequeny and odulaion index. a Envelope deeor is an synhronous deeor (sine no osillaor is used). Solved Exaples 6 Proble: If s 0 0.5os 500 os 0 and deodulaed by envelope deeor, han wha is axiu value ie onsan o avoid diagonal lipping? 0.5 Soluion: RC a 0.55 ax. 0.5 500 a dvanages and Disadvanages of DSB-FC The bigges disadvanage is ha ransied power is wased and effiieny is iniu. One of he advanages is ha i has siple odulaion and deodulaion ehod. DSB SC (Double Side Band - Suppressed Carrier) pliude Modulaed signal wih DSB-FC is, s os os If we suppress he arrier i.e. arrier is no presen in he oupu signal. Then, i is known as Double Side Band wih Suppressed Carrier. s os Due o arrier er reoved he power in Transied Signal is, P P a T Hene, enire power belongs o essage signal and no energy is wased in ransiing he arrier. So, ransission effiieny % 00% Krearyx. ll Righs Reserved. 3 www.krearyx.o
Couniaion Syses (Theory) Solved Exaples Proble: In DSB FC, if a, wha is % saving in ransied power if: a) Only arrier is suppressed b) Carrier and one side band is suppressed. Soluion: For 00% Modulaion Index, he ransied power is 3 P P a P P T If arrier is suppressed hen, ransied power beoes, P T P 3 P P % saving = 66.67% 3 P Now, if one sideband as well as arrier is suppressed he ransied power beoes half P T P 4 3 P P 4 % saving 00% = 83.33% 3 P Proble: Repea previous quesion for 0.5 a Soluion: IN DSB-FC ransied power is, 0.5 P P a P.5P T Wih suppressed arrier he ransied power beoes, 0.5 P P a P 0.5P T.5 0.5 % saving 00% 88.89%.5 Krearyx. ll Righs Reserved. 3 www.krearyx.o
Couniaion Syses (Theory) If one sideband is also suppressed, P T 0.5 P 4.0.65 0.065 % saving 00% 94.44%.065 So, in order o save ore ransied power: (i) Carrier should be suppressed (ii) One sideband should be suppressed. (iii) Modulaion Index should be sall DSB SC ie doain represenaion In DSB-SC, whenever essage signal rosses zero level i.e. i beoes negaive fro posiive or vie versa hen odulaed signal also hanges polariy. This an be alled as 80 0 phase shif in he sinusoidal arrier wave. When () is negaive. Suppose, () = -g() Then, odulaed signal beoes, s os g os 0 s g os 80 DSB SC Frequeny Doain Represenaion Krearyx. ll Righs Reserved. 33 www.krearyx.o
Couniaion Syses (Theory) Suppression of arrier eans firs generae DSB FC and hen suppress he arrier. s os The speru of Modulaed Signal is, S w M M Fro, he speru of odulaed wave, Bandwidh, BW rad se Generaion of DSB-SC Signal There are wo eans of generaing a DSB-SC signal, Non-Linear Devie Linear Devie Non Linear Devie The oupu of Non-Linear Devie is, V a V a V i i The inpu o Non-Linear Devie is su of essage and arrier signal, V os i The oupu of Non-Linear Devie is, V a a os a os os To generae DSB SC, Make a 0 so ha non linear devie will be siply square law devie. Then we an use a Band Pass Filer of frequeny o Then, a he oupu seond and fourh ers are presen whih eans DSB-FC is generaed. The arrier is hen suppressed o generae DSB-SC signal. Krearyx. ll Righs Reserved. 34 www.krearyx.o
Couniaion Syses (Theory) By use of Linear Devie Balaned/Produ Modulaor The wo signals generaed in his odulaor are, s os s os The oupu of odulaor is, s s os The oupu of Balaned Modulaor is produ of Message and Carrier Signal. Ring Modulaor The inpu o Ring Modulaor is he essage signal. The arrier signal onrols he swihing of Diodes o ransfer he inpu signal o oupu. (i) For () = 0 and D,D ON and D,D OFF 3 4 The oupu is zero. Krearyx. ll Righs Reserved. 35 www.krearyx.o
Couniaion Syses (Theory) (ii) For () = 0 and D,D ON and D,D OFF 3 4 The oupu is zero. (iii) For 0 and D,D ON and D,D OFF 3 4 Message Signal is ransferred o oupu by eans of wo ransforers wih sae polariy. So, oupu is sae as essage signal. (iv) for 0 and D,D ON and D,D OFF 3 4 Message Signal is onneed o oupu as shown below, Message Signal is ransferred o oupu wih opposie polariy due o ross onneion. Krearyx. ll Righs Reserved. 36 www.krearyx.o
Couniaion Syses (Theory) Sine odulaed wave beoes zero when () beoes zero and here is phase reversal also a () = 0 as shown by irled poins in oupu wave; hene i is DSB SC. In ring odulaor, if one frequeny is f f and f f f and oher is and no oher frequeny will be presen. f, oupu will have frequeny Mulipliaion in ie doain = onvoluion in frequeny doain and by onvoluion he signal ges ranslaed o new frequeny so frequeny shifs whih is happening by his ehod. Hene, boh ehods are generaing DSB SC only. Deeion of DSB SC The following ehods an be used for deeion of essage signal fro DSB-SC Modulaed Signal. Swihing Modulaor The operaion of diode an be replaed by swihing wavefor shown below, The Fourier Series of he swihing wavefor an be expressed as, p() os os3... 3 The oupu of diode is, V V.p o i V os os os3... o 3 Krearyx. ll Righs Reserved. 37 www.krearyx.o
Couniaion Syses (Theory) os V os os o 3 V os os... o To ge essage signal, one an design a LPF of u off frequeny praially, i an be aken as Synhronous Deeion/Coheren Deeion Synhronizaion beween odulaing signal and arrier signal, The arrier uliplied o essage signal and he one used for deodulaion needs o have sae frequeny and hene synhronized o eah oher. V os os If we use a LPF for deeion hen he oupu is, V o os os os Quadraure Null Effe If i.e. he deodulaing arrier signal is in quadraure o odulaed signal, hen V os sin sin fer filering wih a Low Pass Filer, here is no essage signal reovery a he oupu. This effe is alled as Quadraure Null Effe. If 0, hen V os os os fer filering wih a Low Pass Filer, here is oplee essage signal reovery a he oupu. Krearyx. ll Righs Reserved. 38 www.krearyx.o
Couniaion Syses (Theory) V o In his ase, he deodulaing signal is in perfe synhronizaion wih he odulaing signal. General Error in ase of Synhronous Deeion In general, he signal used for deodulaion ay have slighly differen frequeny han he odulaed signal. Then, ' os ' V os ' os os os i fer passing hrough he LPF, oupu is ' y os Case : 0 and 0 No disorion, no aenuaion y Case : 0 and 0 Only aenuaion as apliude is hanged. y os Case 3: 0 and 0 ' y os Here, aenuaion as well as disorion is presen in he oupu. Case 4: 0 and 0 Only Disorion is presen due o ie dependen er in he oupu. y os Krearyx. ll Righs Reserved. 39 www.krearyx.o
Couniaion Syses (Theory) Cosas Reeiver Cosas Loop is a phase loked loop used for reovery of arrier signal fro DSB-SC Modulaed Signal. Modulaed Signal, s os The oupu y and y will be, y os os os os y os os 90 sin sin When boh hese signals are passed hrough LPF hen he oupus are, s os s sin For sall value of ; os and sin s s Phase disriinaor is a devie whih generaes DC volage orresponding o phase differene Φ. This DC volage will odify phase in value suh ha VCO phase and inpu phase are sae so, by Cosas Reeiver, he reeiver irui will beoe oplex and his is for only low phase errors. Solved Exaples Proble: essage signal band liied o frequeny 'f ' of oupu shown in figure? has power 'P ', wha is power Krearyx. ll Righs Reserved. 40 www.krearyx.o
Couniaion Syses (Theory) Soluion: The power onen in he signal os P Oupu of uliplier is, X os os The oupu of Low Pass Filer beoes, y os Power os 4 P Power of Oupu os 4 os os Proble: Deerine he oupu of he syse shown below, ssue sin, os 00 and n sin 98 Soluion: Oupu of Muliplier is, X sin os 00 Oupu of dder is, X n 0 Frequeny of oupu, f 0Hz sin0 sin98 sin0 sin98 sin98 sin0 Krearyx. ll Righs Reserved. 4 www.krearyx.o
Couniaion Syses (Theory) Sine, u-off frequeny f Hz y 0 whih eans no signal will pass hrough LPF. is less han he frequeny of essage signal. Hene, Proble: If he inpu o a oheren deeor is DSB SC signal plus noise, han wha is value of noise a oupu? ssue n n os n sin I Q and n I : In-phase oponen of Noise n Q : Quadraure oponen of Noise os Soluion: The inpu o uliplier is, s n os n os n sin I Q The oupu of uliplier is, X os n os n os sin I Q n n n X I I os Q sin The oupu of LPF is, y n I Hene, in-phase oponen of noise is presen a he oupu of syse. Types of Envelope There are hree ypes of envelope, Pre Envelope n analyi signal is a oplex signal reaed by adding a signal wih is Hilber Transfor in Quadraure. I is also known as pre-envelope of a signal. ˆ x x jx p Here, ˆx is he Hilber Transfor of x() Krearyx. ll Righs Reserved. 4 www.krearyx.o
Couniaion Syses (Theory) By aking he pre-envelope he negaive frequeny oponens are disarded and he real signal an be easily reovered fro oplex signal by disarding he iaginary par. Naural Envelope The agniude of pre-envelope of a signal is known as naural envelope of a signal. Naural Envelope: x p Coplex Envelope nalyi Signals are ofen shifed in frequeny or down onvered o 0Hz. I possibly reaes negaive frequeny oponens. This helps in reduing he axiu frequeny so ha sapling rae also redues. Coplex Envelope is given by, j x x e p Solved Exaples Proble: odulaed signal is given by a s e os u where and are posiive onsans, alulae: (i) Pre envelope (ii) Coplex envelope (iii) Naural envelope Soluion: Pre-envelope, s s jsˆ p a s e os u jsin e a p This happens beause Hilber ransfor of osine signal is sine signal. j a s e u e p j e a e u j j j s s e e e u e p Coplex Envelope, a j s e a e u Naural Envelope, s e a e u e a u p j Krearyx. ll Righs Reserved. 43 www.krearyx.o
Couniaion Syses (Theory) Noe: In quesions, if only envelope is asked, hen envelope aken is naural envelope. If s s os s sin I Q Naural envelope: s s s s p I Q Proble: If a odulaed signal is given as, x os envelope of he signal. Soluion: Mehod- Pre-Envelope, x os jsin p j x os jsin p e Naural Envelope, x p. Deerine naural Mehod- x os os sin sin Naural Envelope x p I Q os sin I Q Proble: For he syse shown below, sin99 Deerine he oupu if, n, Soluion: Oupu of firs uliplier, X sin 0 sin 98 sin0 sin98 sin99 n Oupu of seond uliplier, sinn and os00 Krearyx. ll Righs Reserved. 44 www.krearyx.o
Couniaion Syses (Theory) sin0. os 00 sin99 os 00 sin98 os00 n n sin 40 sin sin399 sin sin398 sin Frequeny oponens presen in he oupu, 40 f 0Hz f Hz 399 f 99.5Hz 3 f 0.5Hz 4 398 f 99Hz 5 Hene, a he oupu of LPF only Hz and 0.5 Hz oponens are presen. y sin sin Proble: Consider a syse shown in figure. Le X(f) and Y(f) denoe Fourier Transfor of x() and y() respeively. If ideal HPF has u off frequeny of 0kHz. Then posiive frequenies where Y(f) will have speral peaks are? Krearyx. ll Righs Reserved. 45 www.krearyx.o
Couniaion Syses (Theory) Soluion: The speru of he signal oupu of firs uliplier is, The oupu of High Pass Filer will look like, The oupu of seond uliplier will be, So, he posiive frequeny peaks lie in he speru a khz and 4kHz. lernaively, we an direly solve by observing ha inpu has peaks a -khz and khz, so afer firs uliplier peaks will lie a 9kHz and khz. fer High Pass Filer, only khz and - khz peak passes and afer seond uliplier -khz is shifed o khz and khz is shifed o 4kHz. Proble: DSB SC signal is o be generaed wih arrier frequeny / f =MHz using a non linear devie wih inpu-oupu haraerisis V a V a V 3 o i i where a and a o are onsans. The oupu of non linear devie an be filered by an appropriae BPF. Le V os f i where () is essage signal. Then value of f in MHz is? Krearyx. ll Righs Reserved. 46 www.krearyx.o
Couniaion Syses (Theory) Soluion: The inpu-oupu relaion of Non-Linear Devie is, V a V a V 3 o o i i 3 3 3 3 V a osf a osf o o V a osf a os f a o o 3a os f 3a osf This an also be expressed as, 3 3 3 V a osf a os f a o o os 4f 3a 3a os f Desired oponen for DSB-SC generaion, y 3a os 4f The DSB-SC for a arrier frequeny of osf ' On oparing wih generaed DSB-SC, 4f f ' f ' MHz f.5mhz 50kHz f ' us be, Proble: 00MHz arrier of V apliude and MHz odulaing square of V apliude are fed o a odulaor. If oupu of odulaor is passed hrough a HPF wih u off frequeny of 00MHz and oupu of filer is added o 00MHz signal of V ap. nd phase shif as shown in figure, han wha is resulan of envelope of he signal? 0 90 Krearyx. ll Righs Reserved. 47 www.krearyx.o
Couniaion Syses (Theory) Soluion: The inpu o he odulaor is, V os 00 0 6 i The oupu of odulaor is, V os 00 0 6 6. os 0 = os 0 0 6 os 99 0 6 When i is passed hrough a HPF, he oupu is V os 0 0 6 fer he adder he oupu is, = 8 6 os 0 0 y os 0 8 0 6 sin 0 6 y os 0 8 os 0 6 sin 0 8 sin 0 6 sin 0 6 y os 0 6 os sin 0 6 sin The naural envelope of he signal is, y os0 6 sin0 6 os sin sin 4 4 Here, 0 6 rad / se 5 y sin 0 6 4 Quadraure pliude Modulaion (QM) QM is a odulaion shee by whih we an ransi wo essage signal by pliude Modulaion of wo arrier waves whih are in phase quadraure o eah oher. Boh he signals are hen sued and ransied ogeher. The odulaed signal by QM is of he for, s s s os sin oivaion for he use of quadraure apliude odulaion oes fro he fa ha a sraigh apliude odulaed signal, i.e. double sideband even wih a suppressed arrier oupies wie he bandwidh of he odulaing signal. This is very waseful of he available frequeny speru. QM resores he balane by plaing wo independen double sideband suppressed arrier signals in he sae speru as one ordinary double sideband suppressed arrier signal. Krearyx. ll Righs Reserved. 48 www.krearyx.o
Couniaion Syses (Theory) Generaion of QM By 90 0 phase shif we generae a seond arrier arrier signal os sin in phase quadraure wih he Deeion of Message Signal in QM The oupu of firs uliplier is, y s. os os sin os os y sin By he use of LPF, he oupu is, y 0 Krearyx. ll Righs Reserved. 49 www.krearyx.o
Couniaion Syses (Theory) The oupu of seond uliplier is, y s. sin sin os sin os y sin By he use of LPF, he oupu is, y 0 In QM, we ransi wo signals using he sae Bandwidh and so i leads o effiien uilizaion of Bandwidh. Review of Hilber Transfor Fourier Transfor hanges ie doain signal o frequeny doain bu Hilber ransfor hanges ie doain o ie doain signal only bu phase is hanged. 0 90 V 0 90 0 V 0 Frequeny Doain Represenaion of his signal is, F.D. H j e, 0 j e, 0 j, 0 j, 0 jsgn The ie doain represenaion of his signal is, FT jsgnw Sine h 0 for every value of, hene h 0 for < 0; hene i is non asual syse. Hilber Transfor of a signal is orhogonal o is Hilber Transfor. x() and lso, d d ˆx are orhogonal o eah oher. H.T. d d x xˆ Krearyx. ll Righs Reserved. 50 www.krearyx.o
Couniaion Syses (Theory) Solved Exaples Proble: Wha is Hilber Transfor of x sin o? Soluion: The speru of signal x() is, X j o o Fourier Transfor of Hilber Transfor is, H jsgn o o Y X H sgn Y Taking Inverse Fourier Transfor, y os o o o Single Side Band Modulaion Suppressed Carrier (SSB - SC) The speru of differen odulaion shees is shown below, When we use only one of he sidebands insead of wo sidebands i is known as Single Sideband. Krearyx. ll Righs Reserved. 5 www.krearyx.o
Couniaion Syses (Theory) In he above speru, we have only onsidered Upper Sideband for SSB Modulaion. In he above speru we have onsidered he lower sideband ou of he wo sidebands. SSB SC requires iniu value of Bandwidh and iniu value of ransied power. Sine, inforaion is arried ou by sidebands and hey are iages of eah oher, hene hey arry sae inforaion. Bandwidh is noise filering haraerisis of he syse, eans as Bandwidh inreases he effe of Noise inreases. The power speral densiy of Noise is onsan so he higher he Bandwidh ore is he Power onained in Noise and so ore is he effe of Noise. For one o any ouniaion, we will prefer eiher DSB SC or DSB FC sine design for reeiver needed is siple for one o one ouniaion, we will use SSB SC odulaion. SSB an be effeively used for FDM and generally used in poin o poin ouniaion and obile ouniaion. Generaion of SSB SC To generae SSB-SC, we firs reae DSB-FC and suppress he arrier in order o generae DSB-SC and hen eiher upper or lower sideband is suppressed o reae SSB-SC. Le os and DSB-FC odulaed signal is, os os os os s os If he arrier is suppressed, s os os s os os os os The firs er has higher frequeny and seond one has lower frequeny. So, firs one is alled as Upper Sideband and seond er is alled as Lower Sideband Krearyx. ll Righs Reserved. 5 www.krearyx.o
Couniaion Syses (Theory) For Upper Sideband, ˆ y USB os os sin sin os sin Here, ˆ is Hilber Transfor of () If ˆ os and sin For Lower Sideband, y LSB os os sin sin ˆ os sin Generaion of SSB SC There are hree ehods used for generaion of SSB-SC signal, () Frequeny disriinaor () Phase disriinaor (3) Weaver disriinaor Frequeny Disriinaor or Filer Mehod This ehod firs generae DSB SC and a filer is used o reove unwaned sidebands. This filer ay be RC, LC or ehanial filer depending on arrier frequeny. This filer ay have fla pass band and exreely highly aenion ouside he pass band. The frequeny generaed by his filer ay be very low whih will be ranslaed o a higher frequeny by use of loal osillaor. This d filer ay be used upo a frequeny of 00kHz and is bulky in size whih an reae a proble. Hene ehanial filer will be preferred and due o his reason, ehanial filer are preferred. dvanages This ehod gives side suppression raio upo 90 db whih is quie adequae. Side band filer also help o aenuae arrier if presen in Balaned Modulaor. In his ase, Pass Band is suffiienly fla and wide. Krearyx. ll Righs Reserved. 53 www.krearyx.o
Couniaion Syses (Theory) Disadvanages They anno generae SSB a every frequeny. They are bulky in size. lower audio frequeny, design beoes expensive. The speru a various seps of his odulaor is shown below, Sep-: Oupu of Muliplier or Balaned Modulaor is DSB-SC signal Sep-: Filer Speru is as shown below, The oupu of he filer will have he speru, Sep-3: This speru us be ranslaed o higher arrier frequeny by he use of Loal Osillaor. The oupu will have a speru of, Krearyx. ll Righs Reserved. 54 www.krearyx.o
Couniaion Syses (Theory) By his ehod, we an generae SSB-SC in whih only upper sideband is presen. Siilarly, by hanging he signal pass band we an generae he Lower Sideband signal. Phase shif/phase Disriinaor/Harley Modulaion Mehod Here, BM represens Balaned Modulaor whih uliples essage signal wih arrier signal. H.T. represens Hilber Transfor. The oupus of Balaned Modulaors are, S os os S sin sin These signals an also be represened as, S os os S os os The oupu of suer will be eiher upper sideband or lower sideband based on wheher signals are added or subraed. ddiion: Subraion: y S S os LSB y S S os USB dvanages Bulky filer are replaed by sall filer. I an generae SSB a any frequeny. Low audio frequeny ay be used for odulaion. There is easy swihing fro one sideband o oher side band. To generae SSB a high frequeny up onversion and repeiive ixing is no required. Krearyx. ll Righs Reserved. 55 www.krearyx.o
Couniaion Syses (Theory) Disadvanages I requires a oplex audio frequeny phase shif nework beause i has o work for low frequeny range. Sideband suppression depends on phase relaionship beween wo phase shifers else sideband ay no be suessfully suppressed. Oupu of balaned odulaors us be exaly sae oherwise orrelaion is no oplee and desired frequeny oponen is no ahieved. Solved Exaples Proble: In following shee, if speru M(f) of () is shown in he figure, hen speru Y(f) of y() will be? Soluion: This is a phase disriinaion ehod of generaion of SSB-SC and due o addiion of boh signals, LSB will be generaed. The DSB-SC speru will be as shown below, When LSB is reaed he speru looks like as shown below, Krearyx. ll Righs Reserved. 56 www.krearyx.o
Couniaion Syses (Theory) Weaver Mehod In Weaver Mehod, he band of ineres is firs ranslaed o zero by odulaing wih a arrier wave of frequeny lying a he ener of band, B f This pair of signals is passed hrough LPF o reove sidebands ha is no enered a zero. Then i is odulaed o desired arrier frequeny by a pair of quadraure ixers. ssue osf The oupu of firs osillaor is, v osf Due o 90 0 phase shif, v sinf fer he uliplier or Balaned Modulaor he oupu is, v os f os f os f f os f f 3 v os f sin f sin f f sin f f 4 fer he LPF only he low frequeny oponen is passed hrough, v os f f 5 v sin f f 6 The oupu of seond osillaor is, and v sinf v os f 7 8 Krearyx. ll Righs Reserved. 57 www.krearyx.o
Couniaion Syses (Theory) The oupu of seond se of Balaned Modulaors is, v os f f os f 9 v os f f f os f f f 9 4 Siilarly, v sin f f sin f 0 v os f f f os f f f 0 4 The oupu of Weaver Modulaor is, y os f f f If B B f and f f Then, y os f f C Sideband signal an be generaed. whih is he Upper Sideband signal and siilarly Lower Coparison of Tehniques Paraeer Filer Phase Shif Weaver 90 0 phase shif No Required Required Required SSB Generaion No for all frequeny ll Frequenies ll Frequenies Up-onversion Required No Required No Required Coplexiy Less Moderae Highes Design spe Size, Weigh and Phase Shif of 90 0 Syery of B.M. Frequeny Swihing Capaiy No Possible Easy Easy Deeion of SSB SC Synhronous Deeion Krearyx. ll Righs Reserved. 58 www.krearyx.o
Couniaion Syses (Theory) SSB Modulaed Signal is, ˆ s os sin The oupu of Balaned Modulaor is, ˆ y os ˆ sin os os sin fer Passing hrough LPF, y Phase Synhronizaion proble SSB Modulaed Signal is, ˆ s os sin If he arrier inpu o Balaned Modulaor has a phase shif wih respe o odulaed signal, ˆ ˆ os y os os sin os y os os sin sin fer passing hrough LPF, ˆ y os sin If 0, y ˆ ; y I eans here is no Quadraure Null Effe proble in he SSB SC due o phase error. Pilo arrier in SSB Krearyx. ll Righs Reserved. 59 www.krearyx.o
Couniaion Syses (Theory) Due o absene of arrier and one side band, ransied power and Bandwidh are redued bu a sae ie due o absene arrier, reeiver will beoe oplex. In order o redue his proble, a sall power arrier signal is direly ransied fro he ransier so ha hese will be synhronizaion in frequeny of loal osillaor and odulaed signal. Sae funion is served by osar reeiver in DSB SC. Iporan poins abou SSB SC () Due o absene of arrier, a lile hange in frequeny wih haper qualiy of ransied and reeived signal hene i anno be used for ransission of good qualiy signal suh as usi bu an be used for speeh ouniaion. () Bandwidh and ransied power is redued in SSB SC and here is no Quadraure Null effe. Vesigial side band odulaion (VSB - SC) Krearyx. ll Righs Reserved. 60 www.krearyx.o
Couniaion Syses (Theory) The firs wavefor shows he speru of DSB-SC odulaed signal. The seond and hird wavefors represen Upper Sideband and Lower Sideband variaion of VSB signal. B.W. f f b Major advanage of SSB is ha i redued bandwidh equal o half as opared o M or DSB FC bu SSB signal are very differen o generae beause i is diffiul o desired side band and eliinae undesired sideband. For his purpose, filer us have a very sharp u off frequeny and in ase inforaion onains low frequeny signal, hen generaion of SSB be diffiul. This diffiuly is generae by a shee beause VSB SC whih is a oproise b/w DSB SC and SSB SC. Maheaial explanaion of VSB SC (Design of VSB filer) Oupu of Muliplier, y osf Oupu, y y h osf h y y h y hd y h osf d y os f h os f d sinf h sinf d We an break he oupu ino wo oponens one in-phase oponen and oher is Quadraure Coponen. s h osf d hosf I Taking Fourier Transfor, S f M f. H f f f f f I M f. H f f H f f Krearyx. ll Righs Reserved. 6 www.krearyx.o
Couniaion Syses (Theory) For design of VSB SC filer, H f f H f f, Thus, S f Mf I f W and s I Quadraure oponen of oupu is, s Q h sin f d h sin f S f M f. H f f H f f Q j s Q Q Thus, he oupu of VSB odulaor is, ˆ s os Q sin VSB Krearyx. ll Righs Reserved. 6 www.krearyx.o
Couniaion Syses (Theory) Generaion and Deeion of VSB Generaion: S M M.H I Deeion: M H H Y w S S Here, we have negleed H o H H I I Y Y.H M o o Hene, y o oponens = M(w) I I Calulaion of Envelope in ase of SSB SC DSB-FC Modulaed Signal is represened as, s os Coparing his o SSB signal, he in-phase and quadraure oponen of signal are, s I and Naural Envelope SSB SC ˆ s os sin s 0 Q Krearyx. ll Righs Reserved. 63 www.krearyx.o
Couniaion Syses (Theory) For USB Signal, s os s os os sin sin The in-phase and quadraure oponen are, s os s sin I Q Envelope So, envelope of SSB SC is onsan. So, envelope deeor anno be used. SSB FC s os os s os os sin sin The in-phase and quadraure oponen are, s os s sin I Q Envelope os os sin 4 4 Envelope os 4 Envelope os 4 os 4 Envelope of SSB SC is onsan and independen of essage. In ase of SSB FC, envelope is funion of essage hene i an be deeed by envelope deeor. Krearyx. ll Righs Reserved. 64 www.krearyx.o
Couniaion Syses (Theory) ISB (Independen side banding) In his ase, differen side bands are arrying differen inforaion and ha is why very useful for poin o poin ouniaion. Figure o Meri (FOM) F.O.M. SNR o SNR o SNR Defined as raio of average power of deodulaed signal o average power of noise boh easured a reeiver oupu. SNR Defined as raio of average power of odulaing signal o average power of noise boh easured a reeiver inpu. FOM for DSB SC P SNR o 4 N o Here, = onsan = Carrier power P SNR 4 N o P = power of essage signal = essage signal Bandwidh N o = Power speral densiy of whie noise FOM for DSB SC = FOM for SSB SC = In ase of SSB SC, a he oupu power is jus half of DSB SC, Bu F.O.M. will reain sae. F.O.M. in boh ases is sae as ransission effiieny. Krearyx. ll Righs Reserved. 65 www.krearyx.o
Couniaion Syses (Theory) FOM for DSB FC/M K P SNR a 0 N o k P a SNR N o k P Figure of Meri, F.O.M. a where P k P a FOM a a If ; F.O.M. whih is sae as Transission Effiieny a 3 Tehnial naes of pliude Modulaion ehods DSB FC 3E DSB SC R3E SSB FC H3E SSB SC J3E VSB C3F ISB B8E Krearyx. ll Righs Reserved. 66 www.krearyx.o