ANALYSIS OF SIGNAL IN ANALOG MODULATION

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Esmond Sims
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1 NLYSIS OF SIGNL IN NLOG MODULTION Sandro drano Fasolo and Luano Leonel Mendes bsra Today, he a lo o noraon s reorded n dgal ora The bes way o rans hs dgal noraon s usng a dgal ounaon syse In hs senaro, he analog odulaon aears o be no oran anyore However, any analog ounaon syses wll be n use or a long e (e, and M Broadasng The ones nvolved n he odulaon and deodulaon are no very sle and s neessary o use soe ddaal ool o nrease he eeny o he eahng roess o hs ssue The an a o hs aer s o resen an eduaonal aroah o analyze he deren ehods o analog odulaon (M, M-SC, and PM dedaed ouaonal ool was develoed on C++Bulder laor o rodue and analyze he odulaor and arrer sgnals n he e and requeny doans Index Ters analog ounaon, a odulaon, odulaon INTRODUCTION Ths aer resens an eduaonal aroah or he sudy abou generaon o sgnals odulaed n alude, requeny and hase Ths aroah s realzed usng a sulaon rogra develoed wh C++Bulder laor, whh allows he user o dene he alude, requeny, waveor and oher sgnals s araeers o he odulaor The sulaor allows o user o grahally analyze he sgnals n e and requeny doans The sulaor o ounaon syse s general There are hundred o unons wh akes easy o sulaed any ounaon syse In he begnnng, he suden don know wh value has been used The an objeves hs work s o ge an een and raed laor where suden an hange he value beween he nu and he axu allowed value For eah hange, he rogra auoaally udaes he grahs alos n real e The aer oulne s as ollows Frs, n he nex seon, a bre revew o alude odulaon s realzed Then, he angle odulaon (requeny and hase s overvewed Nex, he sulaon rogra s desrbed er ha, one exale o sulaon are shown Fnally, n he las seon, he onluson s resened MODULTION Modulaon s he roess where a roery or a araeer o a sgnal s vared n rooron o a seond sgnal The equaon o a general snusodal sgnal an be wren as ( θ ( ( ( os ( where ( s he e-varyng alude and θ ( s he e-varyng angle I s onvenen o wre θ ( + ( ( so ha ( ( os( + ( (3 where ( s alled he enveloe o sgnal (, s alled he arrer requeny, ( s he hase varaon o ( We assue ha ( and θ ( varyng slowly oared o MPLITUDE MODULTION In alude odulaon (M, he alude o a snusodal sgnal (denonae arrer s vared rooronally o a gven sgnal, whose requeny and hase are xed The alude odulaon rodues a sh n he requeny oonens o he a gven sgnal, ranslang s requeny oonens o hgh requenes Ths rnle s used n he suerheerodyne reever, where he nong RF sgnal s shed o a neredary requeny lude Modulaon Suressed Carrer - MSC In he alude odulaon, he er ( n (3 s zero or onsan and he enveloe s ade rooronal o he gven sgnal ( Thus, he equaon or MSC s MSC ( ( ( os (4 The blok dagra o he odulaor s shown n Fgure (a The er ( n (4 s alled he odulang sgnal, as showed n Fgures (b(, and he er os ( s alled arrer sgnal, showed n Fgures (d(e The ullaon o he snals os ( by ( resuls n MSC(, alled he odulaed sgnal, as ndaed n Fgures ((g Ulzng he Euler s denes Sandro drano Fasolo, INTEL, v João de Caargo, 5, 3754-, Sana Ra do Sauaí, MG, Brazl, sandroasolo@naelbr Luano Leonel Mendes, INTEL, v João de Caargo, 5, 3754-, Sana Ra do Sauaí, MG, Brazl, luanol@naelbr

2 n (4, leads o ex( j + ex( j os( (5 MSC ( [ ( ex( j + ( ex( j ] (6 Denng he Fourer ar ransor ( F( (7 MSC ( Φ MSC ( (8 and alyng he odulaon roery o he Fourer ransor n (6, lead o j e F ( (9 ( Φ F( + + F( ( MSC ( Fro Fgure, an be seen ha boh osve and negave requeny onan he sgnal ro now on only he osve requeny wll be dslayed Ths les ha he bandwdh o ranssson sgnal, (, s we he bandwdh o he sgnal ( Beore he odulaon roess, he unodulaed sgnal ( oues a bandwdh o The odulaed sgnal oues a bandwdh o The seru enered around s oosed o wo ars, one oron les above ha s know as he uer sde band, and he oher oron les below ha s know as he lower sde band Slarly, he seru enered around has uer and lower sde bands The MSC rovdes a een ehod o ranslae he seru o a sgnal, enered n he requeny x, o anoher requeny Ths s erored usng a sle ullaon o he sgnal arrer wh requeny OL, alled sgnal o loal osllaor ( ( (a ( (b (d MSC ( ( ( os ( ( os P( ( π F( ( F( (e lude Modulaon -Large Carrer The dsadvanage o MSC s ha requres a arly olaed rury a he reever o aqure and anan he hase synhronzaon I s oran o reeber ha exs one ranser and llon o reever To allow he use o nexensve reevers, s oran o avod he need o arrer n he reeon Ths an be done by ransng a large arrer wh he odulaed sgnal The equaon or M s resen ro he MSC sgnal lus a arrer Thus M ( os( + ( os( ( [ + ( ] os( The blok dagra o odulaor s show n Fgure (a The er os ( n ( s alled lo o The seral densy o M ( s Φ M ( F( + ( + F + πδ ( + + πδ ( ( Φ MSC ( F( (g FIGURE SIGNLS IN MPLITUDE MODULTION SUPPRESSED-CRRIER SYSTEM The seral densy o M (, s he sae ro he MSC, wh addon o ulses n ±, as ndaed n Fgure (e I s onvenen o dene a odulaon erenage or a MSC sgnal wh snusodal odulaon as E (3 E

3 (a ( + ( (b os( [ + ( ] os( F( ( F( I θ ( Re (d M ( FIGURE 3 GENERL PHSOR REPRESENTTION However, he angular rae s no onsan, he relaon beween he nsananeous angular rae ( and θ ( s gven by π Φ M ( F( π (e FIGURE SIGNLS IN MPLITUDE MODULTION SYSTEM where E s he Peak Volage o odulaon sgnal, E os(, and E s he Peak Volage o sgnal odulaed, E os( ly hs denon on ( M ( os E E ( + ( os( os( + E os( os( [ + os( ] os( NGLE MODULTION (4 The angle o a snusodal sgnal s desrbed n ers o a requeny and/or a hase angle The resely one o requeny o a snusod wll be exlan hrough a hasor reresenaon, as ndaed n Fgure 3 snusod wh a onsan angular rae,, eans ha s requeny s radans er seond The angle θ( nreases lnearly wh e ( θ ( θ( ( dτ Takng he dervave o boh sdes o (5, lead o (5 dθ ( ( (6 d We onlude ha he nsananeous requeny o a snusodal sgnal s gven by he e dervave o s hase Ths one o nsananeous requeny ers are o desrbe wo knds o angle odulaon PHSE MODULTION The hase odulaon s obaned when he hase, θ (, lnearly vares as unon o he nu sgnal, ( The nsananeous value or he hase angle s where rad / V θ ( + k ( (7 and The nsananeous value o he requeny s k are onsans The uny o he er k s dθ ( d ( ( + k (8 d d FREQUENCY MODULTION noher ye o odulaon s obaned by akng he nsananeous requeny rooronal o he nu sgnal ( k ( (9 +

4 where and k are onsans The er k s gven by rad / s / V The nsananeous value or he hase angle s ( τ dτ + θ ( k ( τ dτ ( In resue, he equaon or he odulaed sgnal n requeny s desrbe by os j( + k ( τ dτ { e } ( Re ( + k ( τ dτ ( and, o equaon or he odulang sgnal n hase s gven by ( Re os j( + k ( { e } ( + k ( SPECTRUM OF SIGNL MODULTED IN NGLE ( I s no ossble o evaluae he Fourer ransor o a general waveor Bu he resuls o he analyss o odulaed sgnal n requeny by a snusod wll er us o draw soe general onlusons I he odulang sgnal s gven by hen, or a, ( a os( (3 ( + k a os( + os( (4 The er ak s he axu requeny sh o sgnal odulaed Ths value s dre rooronal o alude o snusod and he araeer k The angle o hs sgnal s θ( ( τ dτ + sn( + β sn( (5 where he er β s he odulaon ndex s gven by β (6 Usng olex noaon s ossble o show ha j ( + β ( Re sn( e (7 { } The seond exonenal n (5 s erod unon o e Exandng n a Fourer Seres we have he nal resul resened ( Re e n n j J n n ( β e jn J ( β os( + n (8 The seru o he odulaed sgnal s oosed by a nne nuber o sdebands, where he alude o eah seral oonen s gven by he value o he Bessel unon o he rs knd o order n and arguen β, as shown n Fgure 4,,9 J( β,8,7 J( β,6 J( β,5 J 3 ( β J,4 4 ( β J5 ( β J6 ( β J7 ( β J8( β,3,,, -, -, -,3 -, FIGURE 4 BESSEL FUNCTION OF THE FIRST KIND, J n (β THE SIMULTION PLTFORM Fgure 5 shows he sulaon rogra The haraerss o hs rogra are: Tyes o odulaon: MSC, M, and PM lude o arrer: V E V M odulaon ndex: a odulaon ndex: k 3rad / s / V PM odulaon ndex: k 3rad / V Frequeny o sgnal odulang: Hz Frequeny o arrer: Hz β

Knds o odulang sgnal: snusod, rangle and square waveors Plos n e doan: odulang sgnal and odulaed Plo n requeny doan: odulaed sgnal CKNOWLEDGMENT The auhors would lke o hank INTEL or he nanal suor

5 Knds o odulang sgnal: snusod, rangle and square waveors Plos n e doan: odulang sgnal and odulaed Plo n requeny doan: odulaed sgnal CKNOWLEDGMENT The auhors would lke o hank INTEL or he nanal suor resened an een soluon o suden o sel-learn he ones abou hs ssue REFERENCES [] Sreeler, F, G, Inroduon o Counaon Syses, ddson- Wesley,99 [] Lah, B, P, Counaon Syses, John Wley & Sons, In, 968 [3] Hsu, H, nalog and Dgal Counaons, Shau s Oulne Seres, MGraw Hll, 3 CONCLUSIONS Ths aer has resened a dda sulaor o analyze sgnals o analog odulaon The laor o sulaon has FIGURE 5 INTERFCE OF PLTFORM OF SIMULTION

Sklar: Sections (4.4.2 is not covered).

Sklar: Sections (4.4.2 is not covered). COSC 44: Dgal Councaons Insrucor: Dr. Ar Asf Deparen of Copuer Scence and Engneerng York Unversy Handou # 6: Bandpass Modulaon opcs:. Phasor Represenaon. Dgal Modulaon Schees: PSK FSK ASK APK ASK/FSK)