Angle Modulation (Ch.6 in Textbook)
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- Mildred Cobb
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1 Objeves: gle Mdula (Ch.6 Texbk T sudy requey dula (FM T sudy phase dula (PM T sudy he sruure dular ad dedular plude dula (M: The aplude he arrer vares ardae wh he essage sgal (. gle dula (FM, PM: The agle he arrer s vared ardae wh he essage sgal whle he aplude he arrer s sa. a s M FM, PM 144
2 plude Mdula vs. gle Mdula plude Mdula: -- The speru he dulaed sgal s shed/saled vers he essage sgal speru. -- Trasss badwdh Message badwdh -- SNR u a be reased ly reasg he rased sgal pwer. gle Mdula: -- The speru he dulaed sgal s NOT sply relaed essage sgal speru. -- Trasss badwdh >>Message badwdh. -- Iprvee SNR u whu reasg he rased sgal pwer 145
3 gle Mdulaed Sgal s s Phasr Represea: Sgal s represeed by a rag ver plex plae. Re : phasr agude j j e e Re : saaeus phase agle (deeres he ps rag ver a e relaed essage sgal 146
4 gular vely: (requey 1 = s de average requey r dura daes hw as/slw agle hages de l l d d saeus requey a e als kw as agular vely d d d d vared wh essage sgal Reall X=v X=dsae, v=vely, = e gle: d 147
5 ( Phase Mdula (PM Phase Mdular PM s geer r s k p k p : phase deva sa s Isaeus agle Isaeus requey k p d d k p d d Phase ( PM ax k p ax Maxu (peak phase deva 148
6 Frequey Mdula (FM s geer r ( Frequey Mdular s FM s k d k : requey deva sa Isaeus agle Isaeus requey k d d k Frequey ( d ax k ax Maxu (peak requey deva FM 149
7 Exaple FM ad PM sgals Phase hages Phase hages Frequey hages 15
8 PM FM Rela bewee FM ad PM Sgals (I s k p s k d ( Phase Mdular PM s ( Derear d ( d Frequey Mdular PM s 151
9 PM FM Rela bewee FM ad PM Sgals (II s k p s k d ( Frequey Mdular FM s ( Iegrar d Phase Mdular FM s 15
10 Narrwbad FM (NBFM s s s s s s a b sasb s asb NBFM assup s 1 s 1 s s NBFM sgal 153
11 ssue Case Sudy: NBFM Sgle Te Mdula a s s k d Isaeus requey d d Sgle Te Mdula k ak s s ak k ax Peak requey deva Isaeus agle k d ak s d de a k ak s Mdula dex FM sgal 154
12 Case Sudy: NBFM Sgle Te Mdula (C d as s k d s s s s s s s s s a b sasb s asb s s 1 1 s 1 s s s NBFM s s s NBFM sgal r sgle e dula 155
13 Case Sudy: NBFM Sgle Te Mdula (C d s s s Rearragg as k s k a 1 1 s s 1 1 s s a s dulaes he aplude he evelpe suers dsr, uless β s very sall 156
14 Case Sudy: NBFM Sgle Te Mdula (C d The ls β r NBFM apprxa 1 1 s s a s a 1 s d s? d 1 s s s s 1 s 1 s 1 s s reasable bud r he arrwbad apprxa 157
15 Wdebad FM (WBFM Fr a geeral FM sgal, s pssble evaluae he Furer rasr. Here, we aga us sgle e dula. as s k d s ak s d s s ak Hw a we wre he abve express ers s?, 1,,
16 s s Re WBFM (C d j e s j Ree x x j s e x X e j X T / 1 j T x T / e d X X T / 1 j s j T e T / e d 1 j s T e d Varable hage Ths egral a be evaluaed uerally ers he paraeers ad β ad abulaed exesvely. I s deed by J (β ad alled Bessel u he rs kd. They are real-valued. 159
17 WBFM (C d x j s j e J e X where J de 1 j s e d j Ree x j s Re e Ф (= Φ j j Re e J e [(] J s s s J s J 16
18 Bas Prperes Bessel Fus J 1 J J J J,, s s eve dd 1 Fr J 1 J 1 J r J 1 161
19 Pls Bessel u he rs kd J J 1 1 J r
20 WBFM Sgal J s Hw a we ba NBFM sgal r WBFM express? Fr 1 J r J J s s 1 J s 1 J 1 J 1 J 1 s s s 163
21 Badwdh FM Sgals J s Φ J ( as a arrer pe ad a e se sde requees laed syerally eher sde arrer requey (.e. ±ω. These requees are eger ulples ω, deed as hars. = =1 J =-1 = J 1 J1 J =- J Φ = =-1 J =1 =- J 1 J1 J = J I geeral, Fr 1 B rad depeds de sga sdebads B rad, ly =,±1 ers exs. 164
22 Sga Sdebads De r Badwdh FM Sgals Hw ay sdebads are pra he FM rasss a sgal? Ths depeds he eded appla requrees ad essage sgal. rule ly adped s ha a sdebad s sga s agude s equal r exeeds 1% he udulaed arrer,.e. J. 1 J (β dshes rapdly ad he ra /β 1 as β bees large. β>>1 J. 1 J. 1 Therere, he badwdh r large β a be apprxaed as B rad Reall ak 165
23 Cars s Rule r Badwdh FM Sgals B rad 1 rad B Fr very sall, Brad 1 Fr very large, B rad 1 a be egleed a be egleed Cars s Rule agrees wh ur prevus bservas r lg ases, baed r he speal ase dulag sgal he r a susdal. Cars s Rule als hlds r geeral dulag sgals ha are bad-led ad have e pwer. Cars s Rule gves less badwdh ha ur de sga sdebads. ( rue r he lg ases 166
24 verage Pwer FM Sgals s s P lerave represea ( ers Bessel u J s Tal average pwer J J Φ 4 1 J d S P =1 J S Pwer speral desy Tal average pwer 167
25 FM Sgal Uder NB assups Geera NBFM Sgals s s s s s k ( = a k s( s( egrar + s( _ + ( NBFM -9 phase sh Iegrar pu Iegrar upu k (= a k s( = s( (/ s( = s( s( 168
26 Geera WBFM Sgals Idre Mehd ( Narrwbad Freq. Mdular Frequey Mulpler Frequey Cverer NBFM sgal WBFM sgal Frequey Mulpler Frequey Cverer Nlear Deve Badpass Fler s 1 Badpass Fler 169
27 Idre Mehd (C d Frequey Mulpler (x Nlear Deve Badpass Nlear deve desged ulply he k requees he pu sgal by a gve ar. eu ke ssue NBFM has d. dex β ad desred WBFM has d. dex β We eed use = Ipu Oupu e e s s u s s s s k 1 1 s s s e u e e s Reved by he ler 1 Ca be adjused by he ler ga Mulpled by 17
28 Idre Mehd (C d Csderg he requrees, requey ulpler gh eed be pleeed usg ulple seps. The upu he requey ulpler: s s + addal ers B 1 1 B BPF Lg d ( verlappg B 1 B B 1 B 171
29 Frequey ulpler upu: Idre Mehd (C d s s Frequey ulpler reases he dula dex by a ar as desred. Ths als resuls a rease he arrer requey, whh gh be sue ay ases. The arrer requey eeds be shed he desred requey by requey verer. Frequey Cverer Badpass Fler Frequey verer s used sh he speru he sgal by a gve au. I des hage s speral e. s 1 Oe he upu ers shuld gve desred requey ad he her wll be reved by he prper he BPF
30 Geera WBFM Sgals Dre Mehd Vlage-rlled sllar (VCO s ay sllar whse requey s rlled by he dulag-sgal vlage. Osllar C L Oslla requey Vlage-varable apaae C C k 1 LC k 1 LC 1 k / C LC C Reall: 1 x 1/ 1 x / The requey s prpral he essage sgal (. The lg-er requey-sably s as gd as he dre ehd. 173
31 k FM FM dfm d Dedula FM Sgals Dre Mehd: Dsrar Derear s k d k s k d Evelpe Deer The abve express has he r DSB-LC sgal. Evelpe he sgal a he upu k 1 derear There s a slgh vara he requey. Hwever, he evelpe deer a be sll used dee he (. The deal derear a be apprxaed by ay deve whse agude raser u s reasably lear wh he rage requees eres. 174
32 Exaple 6.1: Sple Derear v C R v u v s s H V V u V R jrc R 1 j C 1 j RC RC 1 H jrc v h RC d d Reall: V=IR R: ressr dv u RC RC 1 s s s d V=I(1/jwC C: apar V=I(jwL L: dur evelpe 175
33 Idre Mehd: Phase Lked Lp (PLL LPF Lp ler v u Phase parar r Vlage rlled sllar Ipu sgal s s k d The vlage-rlled sllar (VCO prdues a saaeus requey whh s prpral v u r r u k v d ssue VCO upu as r r s kr vu d r s r 176
34 PLL ( d Lw pass ler upu r r r s s Oly hs er passes he ler r Fr sall s r r r r I he learzed reg, hs shee a be used as a phase parar LPF 177
35 PLL ( d --- Whe he pu sgal s appled, phase pars wh VCO geeraes errr vlage. I ur, hs res VCO syhrze sel he pu requey. --- I he lk ps (.e. VCO s syhrzed VCO requey bees deal pu requey. --- s he pu requey vares slwly wh he essage sgal, PLL s able rak pu requey hrugh hages errr vlage. r k d k r v u d v u 178
36 Exaple 6.: 1MHz sgal s requey-dulaed by a susdal sgal suh ha he peak requey deva s 5kHz. Deere he badwdh he FM sgal he requey he dulag susd s a 5kHz b 5 Hz 1kHz. a 51 1 MHz Narrwbad sgal B B MHz. 1 b Wdebad sgal B 1 khz B 1 11 khz B B 1 1 khz khz Usg de sga sdebads 179
37 Exaple 6.3 Carrer sgal 1s Message sgal s The essage s used requey dulae he arrer wh k =1π. Fd he express r he dulaed sgal ad deere hw ay hars shuld be seleed a 99% he dulaed sgal pwer. 1s k d s 1s 5s 1 J 5s P 5 k k J 5 J J 5 J k 1 By ral ad errr, k=6 18
38 5 Exaple 6.4 NBFM s 1 5 x d 8 3 WBFM s x d ax 1 x Frequey ulpler a be pleeed wh e sep! NBFM Mulpler 5 6 Mulpler 6 BPF 8 8 s 1 WBFM Frs ulpla Sed ulpla Carrer requey eeds be adjused. 181
39 Sgal--Nse Ra (SNR Frequey Dsrar ( + Fr-ed ler aplude ler derear (+( s( -( (+ ( Evelpe deer LPF s (+ ( w( Ipu BPF: (1 ( s[ k d ] ( w( s whe se wh PSD S (ω w η/ r - ω. S w ( / whe se Oupu sgalr BPF, whse badwdh equals he badwdh ( B (1 N hage ( w( (, whse PSD S. η /, r -B ω B (ω., herwse. S ( / : Bad-led se 18
40 SNR Frequey Dsrar ( d ( + Fr-ed ler plude ler Derear (+( s( -( (+ ( Evelpe deer LPF s (+ ( w( plude Ler reves ay udesred evelpe vara (.e.keepg sa ( ( Derear upu d d k s k d Evelpe deer' s upu(aer revghe er Sgaler s ( k ( wh pwer S s ( k ( 183
41 SNR Frequey Dsrar ( d Hw d The bad- led se ( s( ω he speral desy ( he s( ω se press? presee ( s( ω a udulaed ( s( ω ( s( ω s( s( ω r ( s[ ω ( ] aplude se phase se s arrer s( ω : Se r he 1 ( a s( ( dealg ( wh phase- se: ( requey dula, 1 s( a ( d ( 1 d s( d d s ( gre aplude- se r( a S 1 s( (? s ( s( bu us 184
42 SNR Frequey Dsrar ( d S s ( he LPF's S ( N Derear ( ( H s upu: S S s ( ( S ( S ( ( S LPF ( s LPF d See leure es se 3 h( 3 1 d d 1 H j S S ( S s - ( - / ( PSD s squarelaw depedee 185
43 ( pwer wh ( Sgaler k ( s S k ( s pwer wh er Nse N ( 3 3 ( 3 3 ( k k N S SNR Frequey Dsrar ( d 3 a k N S a a 3 ( ( s ( I 3 3 B rad Fr wdebad FM, SNR reases wh reasg badwdh hrugh k depedee. ω s prpral k 186
44 Cpars Bewee FM & DSB-LC Csder DSB-LC wh arrer sgal s ad essage sgal a s FM N S a 3 s ( essage sgal Fr he LC DSB d N ( LC DSB a N S ssue uy dula dex, =1,.e. =a. Ths s he s avrable ds r DSB-LC ers pwer requrees. FM N LC DSB FM N S a N S 3 LC DSB FM N S N S wll I LC DSB FM N S N S 3 187
45 Cpars Bewee FM & M The prevus argue hlds r he pars bewee FM ad DSB-LC. We have earler dsussed ha DSB-LC ad SSB has he deal upu SNR he presee whe se. S N FM 3 S N M B 1 FM prves he SNR a he s reased badwdh. The exhage badwdh r SNR FM a NOT be ued deely. The se pwer reases wh he reased badwdh ad resuls very pr syse perrae. Ths s kw as hreshld ee ad he abve aalyss des hld ayre. 188
46 s s s ω ω ω ( ω ( ( ω r ω ( ω ( ω ( ω ω ( s( s( s( s( The,. respe wh sa as ed apprxa are ad Suppse ] ( s[ ( s( s( s( s( prevusly deled as: was s( arrer d udulae a presee he se Bad- led se phase se aplude FM s Phase-Nse s Threshld Ee (Sreler Chaper 6.9 b b b s b s b b b B B B C ω C ω B ω B ω B ω s s a, s a, B where s( s( s( s( s( s( s(
47 wll ex us : a 1 FM s Phase-Nse s Threshld Ee ( d s requey dula ers prarly he requey/ phase, he aalyss Bs( b Bs( b 1 1 Bs( a b Bs( b a be uerall y evaluaed. ad s are parable, apprxas d b Ne /B a be regarded as a vlage sgal--se ra. B s 3dB Mea-square phase se reases rapdly whe he ra /B s saller ha abu 3dB. Ths s kw as hreshld ee. 19
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