Angle Modulation: NB (Sinusoid)

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1 gle Moulaio: NB Siuoi I uay, i he eage igal i a pue iuoi, ha i, a a i o o PM o FM The, i whee a p a o PM o FM : pea equey eviaio Noe ha i ow a oulaio ie o agle oulaio a i he aiu value o phae eviaio o boh PM a FM. I i oly eie o iuoial oulaio. I ha a bawih o W B, he NB agle-oulae igal will have a bawih o W B. ERG30-II p. II-60

2 ERG30-II p. II-6 gle Moulaio: Siuoi { } e e i Re i o The epoeial i a peioi uio o ie wih a uaeal equey o a/e. I a be epae i a Fouie eie. e e i e i whee e e i i y y e Seig y, he whee i he Beel uio o he i i o oe a ague. e e e o Re Re

3 gle Moulaio: Siuoi Beel uio o he i i o oe a ague :. ERG30-II p. II-6

4 ERG30-II p. II-63 gle Moulaio: Siuoi LL 3 o 3 o o o o o o o o eve Spea

5 gle Moulaio: Siuoi o Whe a all ohe ae zeo Oly he aie o oulaio, o ieba The peu oi o aie-equey opoe plu a iiie ube o ieba opoe a equeie ±,,3,. The elaive apliue o he peal lie epe o he value o, a he value o beoe vey all o lage value o. The ube o igiia peal lie ha i, havig appeiable elaive apliue i a uio o he oulaio ie. Wih <<, oly 0 a ae igiia, o he peu will oi o aie a wo ieba lie. Bu i >>, hee will be ay ieba lie. ERG30-II p. II-64

6 ERG30-II p. II-65 gle Moulaio: Siuoi Coie he aveage powe o o o o o Q Thu he aveage powe iipae by he agle-oulae igal ove a -oh eio i P

7 gle Moulaio: Bawih o The bawih o he agle-oulae igal wih iuoial oulaio epe o a. I piiple, he ube o ieba i iiie he equie bawih o eopa uh a igal i alo iiie. I paie, lage poio o he oal powe i oie o a iie ube o ieba iie bawih o eiou ioio o he igal eul i he ieba ouie hi bawih ae lo. Epeie how ha a log a oe ha 98% o he oal igal powe i eaie wihi a eai bawih ae a ile/hael, he ioio i oleable. ERG30-II p. II-66

8 ERG30-II p. II-67 gle Moulaio: Bawih [ ] L Sigle uelie: >70% powe oie; ouble uelie: >98% powe oie Table o Beel uio

9 gle Moulaio: Bawih FM o WB Naowba FM Fo all << oly 0 a ae igiia, o he peu will oi o aie a wo ieba lie. WB M M Fo, he peu, whih oie >98% o oal powe, will oi o aie a oe ieba lie, o he able o Beel uio, we obeve > 98 % Thu, o W B Fo vey lage >>, WB o Thu, Wieba FM WB ERG30-II p. II-68

10 gle Moulaio: Bawih FM,PM Reall: a p a o PM o FM FM PM << WB WB WB WB >> WB WB Coie a oa, o hage o PM o FM ; W B o PM lighly o o hage o FM ERG30-II p. II-69

11 gle Moulaio: Lie Spea o FM o Coa Coa ERG30-II p. II-70

12 gle Moulaio: biay The oulaio ie i oly eie o iuoial eage igal Fo abiay eage igal, whih i baliie o M, we eie D pea equey eviaio bawih o M Bawih W B D M I D<<, he WB M I D>>, he W B ERG30-II p. II-7

13 gle Moulaio: Eaple Eaple: Coie a agle-oulae igal 0o[0 8 5i0 3 ]. Fi he aiu phae eviaio a aiu equey eviaio. Soluio: a 8 3 θ 0 5i 0 5i 0 ' o 0 3 Thu, aiu phae eviaio i a 5 a; aiu equey eviaio i a 50 3 a/ 0 4 a/ o 5Hz ERG30-II p. II-7

14 gle Moulaio: Eaple Eaple: Coie a agle-oulae igal 0o 3i ]. ue PM a Hz, PM o[ p ] 0 o 3i Wih a i PM 0 o pa i Thu, he oulaio ie p a 3 a bawih Whe i ouble, Hz, 3, a hu bawih W B 36Hz Whe i halve, 0.5Hz, 3, a hu bawih W B 30.54Hz ue FM a Hz, FM o[ τ τ ] 0 o 3i 0 a Wih a o FM 0 o i p Thu, he oulaio ie a 3 a bawih WB 8Hz Whe i ouble, Hz, 3/, a hu bawih W B 3/0Hz W B 8 Whe i halve, 0.5Hz, 6, a hu bawih W B 60.57Hz Hz ERG30-II p. II-73

15 gle Moulaio: Geeaio Geeaio o aowba agle-oulae igal: NBPM: NBFM: NBPM o i -/ NBFM o p p i 0 - NBPM o τ τ i i -/ - o NBFM ERG30-II p. II-74

16 gle Moulaio: Geeaio Geeaio o wieba agle-oulae igal: Iie Meho: - poue a aowba agle-oulae igal i; - ove o wieba igal by uig equey uliplie NB o[ ] Fequey uliplie WB o[ ] Fo eaple, he ipu-oupu haaeii o a ieal quae-law evie i vo av. I he ipu igal i he FM igal, v o i, i i he oupu i v o a o / a i / a o i equey ouble igal Siilaly, ue o a h law evie ollowe by a ile yiel a aie a a oulaio ie ha have bee ieae by a ao o. ERG30-II p. II-75

17 gle Moulaio: Geeaio Ue o equey ulipliaio ieae he aie o he FM igal a well a he oulaio ie vey high aie equeie To avoi hi, equey ovee i eeay o hi ow he aie equey. NBFM igal WBFM igal NBFM, Fequey uliplie, BPF ERG30-II p. II-76

18 gle Moulaio: Geeaio Eaple: Coie a NBFM igal pae hough a equey uliplie. o i Wih <0.5 a 00Hz. Le age o 50Hz o 5Hz, a le he aiu equey eviaio a he oupu be 75Hz. Fi he equie equey ulipliaio a he aiu allowe equey eviaio a he ipu. Soluio: Uig, hu i a I 0.5, whee i he ipu, he he equie equey ulipliaio i a 500 a The aiu allowe equey eviaio a he ipu, eoe, i Hz 3000 ERG30-II p. II-77

19 gle Moulaio: Geeaio Die Meho: - he oulaig eage igal iely ool he aie equey oo eho ue i o vay he iuae o apaiae o a ue eleoi oillao, e.g. Volage-oolle Oillao VCO. Coie a LC iui, i L o a C o ae he iiial iuae a apaiae, epeively wihou ay applie igal, he equey o oillaio i L C I he apaiae C i vaie aoig o he eage igal, The C C ; a o o o LoC Lo[ Co ] LoCo C o C o ERG30-II vaage: lage equey eviaio poible Diavaage: aie equey will i ee equey abilizaio iui p. II-78

20 gle Moulaio: Deoulaio Deoulaio: To povie a oupu igal whoe apliue i liealy popoioal o he iaaeou equey o he ipu agle-oulae igal. Die Meho: To ue a ye ha ha a liea equey-o-volage ae haaeii. Suh a ye i alle a equey iiiao. Coepually, ieeiao wih a liea apliue veu equey haaeii a be ue a equey iiiao. Oupu volage Ipu equey ERG30-II equey iiiao Ieal iiiao haaeii p. II-79

21 gle Moulaio: Deoulaio Fo a geeal FM igal: FM o τ τ 0 uig ha i a oa, we have e [ ]i τ τ 0 I <<, i aeble o a M igal whoe evelope i D a whoe iaaeou agula equey i The eulig M igal a be eee by a evelope eeo a he ligh vaiaio i he aie equey woul o be eeable by he evelope eeo a log a <<. ERG30-II p. II-80

22 gle Moulaio: Deoulaio Eaple: FM igal,, i applie o a RC iui a how: C R v Tae epoe o he RC iui: Fo << ; he RC Fo he oupu v H RC h H R R C RC RC V S H S RC Reall he popey o Fouie ao: F Thu, v RC [ ] So, he uio o hi iui a a a ieeiao a he evelope o he oupu i popoioal o he eage igal eoulae. ERG30-II p. II-8

23 gle Moulaio: Deoulaio RC iui a ieeiao ERG30-II p. II-8

24 ERG30-II p. II-83 gle Moulaio: Deoulaio FM Deoulaio by Phae-Loe Loop PLL Loop ile h Volageoolle oillao e v [ ] 0 o τ τ whee [ ] v 0 i τ τ whee [ ] [ ] ile oupu i i e [ ] { } [ ] { } * ] i h v whee [ o all h * h * H V Φ Tae Fouie ao o boh ie,

25 ERG30-II p. II-84 gle Moulaio: Deoulaio v 0 τ τ V V Φ Φ Φ Φ H V Φ Tae Fouie ao o boh ie, Subiue io give H L L L V H V H H V V Φ Φ Φ o v

26 ERG30-II p. II-85 gle Moulaio: Deoulaio >> Φ Φ L o V H L L L V o v Tae ivee Fouie ao o boh ie, So, he PLL a a a ieeiao a he oupu v i popoioal o he eage igal. v 0 τ τ Q

27 ERG30-II p. II-86 gle Moulaio: Deoulaio FM Deoulaio by zeo-oig eeo o o 0 FM θ τ τ Le a > eoe he ie aoiae wih wo aae zeo oig o uh ha 0 Thu, τ τ θ θ τ τ Wih ] [

28 ERG30-II p. II-87 gle Moulaio: Deoulaio Le N eoe he ube o zeo oig o i ie T a,, 3, eoe he ie o zeo-oig wih T -, T 3 -,. Thu, T T T T N Uig he eul i i T N T N N T N i T,,3,..., T o give M T T << < M : Bawih o eue hee ae zeo oig wihi ie T eue o eeive aveagig o oohig o

29 gle Moulaio: FM Reeive I i iila o he M upeheeoye eeive wih he eepio o he aiio o a iiiao a poibly a liie. Coeial FM aio 75Hz ERG30-II p. II-88

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