EE (082) Chapter IV: Amplitude Mod. Lecture 14 Dr. Wajih Abu-Al-Saud

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1 EE (08 hapter IV: Ampltude Md Leture 14 Dr Wajh Abu-Al-Saud arrer Aqustn In the dfferent AM mdulatn methds where a arrer s nt transmtted (DSBS, SSB, et, we assumed that the arrer that was used n the transmtter s als avalable at the reever Ths s a bg assumptn sne t may be easy t generate a sne wave, hwever, t s dffult t get a sne wave wth the SAME FREQUENY and PHASE as the sne wave that was used n the transmtter Therefre, the nept f arrer aqustn s mprtant fr these types f mdulatn arrer Aqustn n DSBS Sne at the nput f a DSBS demdulatr system, nly the transmtted sgnal (and randm nse s avalable, the demdulatr must have sme methd t extrat the arrer frm the reeved sgnal It s knwn that the arrer frequeny s lated at the mddle f the DSBS sgnal as shwn belw In thery, a flter wth an extremely narrwband (few Hz that s entered at the arrer frequeny ω wuld be able t extrat a sgnal that represents the arrer frequeny Hwever, ths assumes that the message sgnal has a D mpnent that when mdulated ths D mpnent mves t the arrer frequeny Havng a D mpnent n the message sgnal that wll be mdulated usng DSBS s nt neessarly the ase In fat, t s generally nt the ase Take fr example an aud sgnal Aud sgnals d nt ntan D sne and aud sgnal travels thrugh the ar mleules n the frm f varatns n the ar pressure arund the atmspher pressure A mrphne reeves these varatns n the ar pressure and generates an eletr sgnal wth n D Als, dgtal data n the frm f bnary numbers s generally represented by 1 s and 0 s that have vltages f +5 V and 5 V, respetvely Suh a sgnal generally has n D S, n prate, the message sgnals that are mdulated usng DSBS (r ther mdulatn tehnques d nt have a D mpnent as shwn n the fllwng fgure When ths sgnal s DSBS mdulated, we get the fllwng sgnal

2 EE (08 hapter IV: Ampltude Md Leture 14 Dr Wajh Abu-Al-Saud learly, n ths ase, the use f a narrwband BPF t extrat the arrer frequeny frm the mdulated sgnal s nt pssble beause n mpnents n the mdulated sgnal fall at the arrer frequeny Therefre, anther methd must be used n general Sgnal Squarng Methd The blk dagram f ths system fr extratng a arrer frm the reeved DSBS sgnal s shwn bellw Narrwband s( x( y( Phase Lked z( :1 r( ( BPF Lp Frequeny (PLL Dvder F = As mentned earler, mst message sgnals ntan n D mpnents and therefre ther DSBS mdulated sgnals ntan n mpnents at the arrer frequeny Hwever, passng suh a DSBS mdulated sgnal thrugh a squarng deve as shwn n the blk dagram abve wll gve a sgnal x( that s gven by x( = m ( m ( m ( [ s( ω ] = m ( s ( ω = [ 1+ s(ω ] = + s(ω Ths sgnal ntans a frm f the square f the message sgnal (ths s a baseband sgnal and the mdulatn f ths sgnal arund twe the arrer frequeny Althugh may have n D mpnent, m ( wll ALWAYS ntan D sne t s always pstve

3 EE (08 hapter IV: Ampltude Md Leture 14 Dr Wajh Abu-Al-Saud Nte that F{m (} s NOT EQUAL TO M (ω but s equal t the M(ω*M(ω S, t has twe the bandwdth f M(ω and ntans a D mpnent S, the spetrum f x( wll be Passng ths sgnal thrugh a narrwband BPF wth enter frequeny f ω wll pass the snusd at that frequeny a small part f m (s(ω arund that frequeny S, the utput f the BPF wll lk lke the fllwng Y T purfy the snusd wth twe the arrer frequeny frm the remanng part f m (s(ω, we feed ths sgnal t a phase lked lp (PLL, whh prdues a snusd wth the same frequeny and phase as that f the snusd at the nput but rejets the addtnal sgnal that represents a dstrtn (dsussn abut PLLs wll be nex S, the utput f the PLL wll have the fllwng spetrum Ths s a snusd wth twe the arrer frequeny Passng ths sgnal thrugh a deve that dvdes the frequeny f ts nput sgnal by tw wll gve a snusd wth the arrer frequeny (the desred sgnal

4 EE (08 hapter IV: Ampltude Md Leture 14 Dr Wajh Abu-Al-Saud Phase Lked Lp (PLL In the blk dagram shwn abve, ne f the blks was a phase lked lp (PLL The PLL s nstruted as shwn belw Vltage ntrlled Osllatr (VO: s a deve that prdues a sne wave wth a frequeny that s lnearly prprtnal t the value f the nput sgnal (when the nput nreases, the frequeny f the utput nreases and ve versa The frequeny f the utput f the VO when the nput s zer s alled the Free Runnng Frequeny (FRF Assumng that the nput sgnal t the PLL s A sn(ω t+, ths sgnal s multpled by the utput f the PLL Let us assume that the utput f the PLL was at sme nstant equal t B s(ω t+ Therefre, bth the nput and utput have the same frequeny but dfferent phases The sgnal x( bemes AB x = AB sn( ω t + s( ωt + = + [ sn( + sn(ω t + ] ( The frst term n x( s a baseband sgnal sne the sne des nt ntan the arrer frequeny The send mpnent s a hgh frequeny mpnent at twe the arrer frequeny Therefre, the LPF passes the frst mpnent and blks the send mpnent S, y( s AB y( = sn( Nw lkng at ths sgnal arefully, we see that t s zer when the tw angles and are equal S, assumng that and were equal at sme tme ( =, whh means that the sgnal z( s B s(ω t+, the sgnal nput t the VO wll be zer Wth ths, the utput f the VO wll be the same sgnal as what t has been utputtng befre (e, B sn(ω t+ Nw assume that the phase f the nput t the PLL started t nrease (r started t derease slwly suh that s slghtly greater than (r s slghtly less than The sgnal z( wll be a small pstve (r negatve value Ths sgnal wll fre the VO t speed up (r slw dwn and therefre prdue a sne wave wth an

5 EE (08 hapter IV: Ampltude Md Leture 14 Dr Wajh Abu-Al-Saud nreasng (r dereasng phase untl the phase f the utput f the VO bemes equal t the phase f the nput sgnal At ths mment, the sgnal z( wll be zer and ths wll nfrm the VO that t has the same phase as the phase f the nput sgnal s t t stp speedng up (r slwng dwn and ntnue at that frequeny and phase haratersts f a PLL PLL have several haratersts that are summarzed as fllws: 1 APTURE Range f a PLL: every PLL s bult t perate n a spef range f frequenes If the nput sgnal has a frequeny n ths range, the PLL wll be able t apture the phase and frequeny f the nput sgnal and start t prdue a sne wth that frequeny and phase LOK Range f a PLL: ne the PLL has been able t apture a sgnal and attah ts frequeny and phase t t, the frequeny and phase f the nput sgnal an hange and the PLL wll stll be able t trak these hanges The LOK range f a PLL s always LARGER THAN the APTURE range 3 Nse flterng: f the nput t the PLL ntans sme lw pwer nse r sme lw pwer dstrtn that makes the nput sgnal a nn pure snusd, PLLs an n general purfy the nput sgnal frm the nse r dstrtng sgnal and prdue a very lean snusd (S, n the sgnal squarng methd dsussed abve, nputtng the snusd wth the dstrtn sgnal t the PLL prdues a pure snusd wth the same frequeny and phase as the nput snusd stas Lp Ths s anther methd fr extratng the arrer frm the reeved sgnal n a DSBS reever The blk dagram f the stas lp s gven belw The sgnals x 1 ( and x 1 ( n the blk dagram abve are smply btaned by multplyng the reeved DSBS mdulated sgnal respetvely by s(ω t+ and sn(ω t+, whh s btaned by shftng s(ω t+ by π/ S,

6 EE (08 hapter IV: Ampltude Md Leture 14 Dr Wajh Abu-Al-Saud x 1( = s( ωt + s( ωt + = s(ω t s( arund ω arund 0 x = + + = ( s( ωt sn( ωt sn(ω t sn( arund ω arund 0 Sne bth f these sgnals has a mpnent arund ω and a mpnent arund 0 frequeny, the hgh frequeny mpnents f these flters wll be rejeted by the LPF and nly the lw frequeny mpnents wll pass S, y1( = s( y ( = sn( These tw sgnals are multpled t prdue the sgnal z(, whh s gven by z( = s( sn( = m ( = 8 m ( = sn 8 { sn(0 + sn[ ( ]} [ ( ] m ( s( sn( 4 The sgnal z( s a baseband sgnal It s zer nly f = When ths s the ase, the utput sgnal w( f the fllwng Narrwband LPF wll be zer, and therefre, the nput t the VO s zer Ths zer sgnal tells the VO t just stay at ts urrent frequeny and phase beause they are the rret values Assumng that we started wth = but eventually the arrer f the reeved sgnal started t speed up (r slw dwn a lttle s ( beame a small pstve (r negatve value, the sgnal z( wll beme the pstve (r negatve square f the message sgnal Ths sgnal ntans a pstve (r negatve D value sne t s the square f the message sgnal Therefre, usng a narrwband LPF that s desgned t extrat nly the D value f ths sgnal wll prdue a pstve (r negatve number that s prprtnal t ( S, the sgnal w( wll be D w( = sn[ ( ], 8 Where D s the D value f m ( Assumng the dfferene ( s small, the value f w( wll be a small pstve number when ( > and a small negatve number when ( < Ths sgnal wll ether fre the VO t speed up t ath up wth the advanng phase f the reeved sgnal r slw dwn t allw the reeved sgnal t ath up wth t

7 EE (08 hapter IV: Ampltude Md Leture 14 Dr Wajh Abu-Al-Saud Nte that the utput f ths system ardng t yur bk s the sgnal y 1 ( Ths s n fat the demdulated utput sgnal Hwever, f yu nly needed t extrat the arrer sgnal frm the reeved mdulated sgnal, then the sgnal yu are nterested n s r( arrer Aqustn n SSB The abve tehnques d nt wrk fr SSB (try usng the sgnal squarng methd fr a SSB sgnal Therefre, the press f btanng the arrer f the transmtted sgnal at the reever when usng SSB requres sme help frm the transmtter by transmttng a arrer wth a very small amunt f pwer mpared t the message sgnal The purpse f ths arrer s dfferent frm the arrer n Full AM The ampltude f the arrer n Full AM s t smplfy the demdulatr by usng an envelpe detetr Ths arrer n fat ntans mst f the pwer f the transmtted sgnal Transmttng the lw pwer arrer n SSB allws the reever t knw the frequeny and phase f the arrer used n the mdulatn Ths s dne by usng a narrwband BPF at the frequeny f the arrer t extrat that lw pwer sgnal and then amplfyng t The pwer f that arrer sgnal s just a small fratn f the pwer f the transmtted sgnal (1/0 the pwer f the transmtted sgnal fr example