Extinction Ratio and Power Penalty
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1 Application Not: HFAN-.. Rv.; 4/8 Extinction Ratio and ow nalty AVALABLE
2 Backgound Extinction atio is an impotant paamt includd in th spcifications of most fib-optic tanscivs. h pupos of this application not is to show how th optical xtinction atio is dfind and to dmonstat how vaiations in xtinction atio affct th pfomanc of digital optical communication systms. Dfinitions Extinction Ratio and ow nalty n an idal tansmitt, would b zo and thus would b infinit. n most pactical optical tansmitts, howv, th las must b biasd so that is in th vicinity of th las thshold, maning that a finit amount of optical pow is mittd at th low lvl and thus, >. n many cass it is usful to talk in tms of th avag optical pow,, and in ths instancs th following lationships a usful: n gnal, digital optical communication systms tansmit binay data using two lvls of optical pow, wh th high pow lvl psnts a binay and th low pow lvl psnts a binay. hs two pow lvls can b psntd as and, wh > and th units of pow a watts. n optical tansmitts, lctical cunt is convtd to optical pow (lctical to optical convsion, o E/O), and, in optical civs, optical pow is convtd back to lctical cunt (optical to lctical convsion, o O/E). h lctical cunts and a popotional to th cosponding optical pow lvls. h sponsivity, ρ, of th civ is th constant of popotionality btwn th civd optical pow lvl and th cunt with units of amps p watt. h sponsivity can b usd to dmonstat th following: ρ and ρ () ρ ( ) () (3) h atio btwn th on lvl and th zo lvl, shown in Equation 3, is dfind as th xtinction atio, and is psntd by th symbol. (Not that xtinction atio is dfind in som litatu as th cipocal of Equation 3.) (4) (5) (6) 3 Eo obability in Digital Communication Systms h civ in a digital communication systm must mak two dcisions: () whn to sampl th civd data and () whth th sampld valu psnts a binay o. n od to undstand th ffcts of xtinction atio on systm pfomanc, th following analysis focuss on th scond dcision. 3. Dcisions about th Rcivd Signal h dcision cicuit in a basic civ simply compas th sampld voltag, v(t), to a fnc valu, γ, calld th dcision thshold. f v(t) is gat than γ, thn it dcids that a binay was snt; whas if v(t) is lss than γ, thn a binay must hav bn snt. A majo obstacl to making th coct dcision is nois in th civd data. f w assum that additiv whit Gaussian nois (AWGN) is th dominant caus of onous Application Not HFAN-.. (Rv.; 4/8) Maxim ntgatd ag of 5
3 dcisions, thn w can calculat th statistical pobability of making an incoct dcision. h pobability dnsity function fo v(t) with AWGN can b wittn mathmatically as: v s v( t) ROB [ v( t)] (7) π wh v S is th voltag snt by th tansmitt (th man valu of th dnsity function), v(t) is th sampld voltag valu in th civ at tim t, and is th standad dviation of th nois. Equation 7 is illustatd in Figu. ROB[v(t)] Figu. AWGN pobability dnsity function n binay signaling, v S can tak on on of two voltag lvls, which w will call v S and v S, and th pobability of making an onous dcision in th civ is as follows: [ε] [v(t) > γ v S v S ] [v S ] [v(t) < γ v S v S ] [v S ] (8) wh [ε] psnts th pobability of o and [x y] psnts th pobability of x givn y. f w assum an qual pobability of snding v S vsus v S (5% mak dnsity), thn [v S ] [v S ].5. Also, in od to simplify th xampl at this point, w will assum that th sam nois affcts ith voltag lvl (i.., ), which mans that [v(t) > γ v S v S ] [v(t) < γ v S v S ]. Using ths assumptions, Equation 8 can b ducd to: [ε] [v(t) > γ v S v S ] [v(t) < γ v S v S ] ROB [ v( t)] dt (9) γ wh ROB[v(t)] is dfind in Equation 7. his sult is illustatd in Figu. Application Not HFAN-.. (Rv.; 4/8) v S v(t) ROB[v(t)] [v(t) v S v S ] [v(t) v S v S ] Fom Figu and Equations 8 and 9, w can s that th pobability of o is qual to th aa und th tails of th dnsity functions that xtnd byond th thshold, γ. his aa and thus th bit-o atio (BER) a dtmind by two factos: () th standad dviations of th nois ( and ) and () th distanc btwn v S and v S. (Not: his is basd on th assumption that γ (v s,-v s )/, which is valid only fo.) 3. h Q Facto h conclusion of th discussion abov is that th BER is dtmind by th standad dviation (RMS avag) of th nois and th distanc btwn th signal lvls. his conclusion can b phasd in tms of th optical signal-to-nois atio at th input to th optical civ, which is dfind (in units of cunt) as th pak-to-pak signal cunt dividd by th RMS nois cunt. (Not: h optical civ convts optical pow to lctical cunt. his cunt is lat convtd to a voltag bfo it is applid to th civ dcision cicuit.) his fom of th signal-to-nois atio has bn givn th nam Q o Q-facto in th litatu and can b wittn mathmatically as: v S γ v S [v(t) < γ v S v S ] [v(t) > γ v S v S ] Figu. obability of o fo binay signaling Q () v(t) h sult in th dnominato of Equation is basd on th assumption that and a uncolatd (i.., ), so that ( ). Maxim ntgatd ag 3 of 5
4 h BER can b wittn mathmatically in tms of Q as follows: Q BER fc () wh fc( ) is th complmntay o function, dfind as 3 : fc( x) π x y dy 4 h ow nalty () As notd in Sction, is idally qual to zo, making th optimum xtinction atio infinit. Whn th xtinction atio is not optimum, howv, th tansmittd pow must b incasd in od to maintain th sam BER. his incas in tansmittd pow du to non-idal valus of xtinction atio is calld th pow pnalty. n od to div a mathmatical xpssion fo th pow pnalty, w can stat by noting that, fom Equations and, if th Q-facto is hld constant, thn th BER will main constant. n od to simplify th analysis, w will assum that thmal nois is dominant and qual fo both th and pow lvls, and thus, and (wh is th standad dviation of th thmal nois). Using th following algba, w can wit an xpssion fo th Q-facto in tms of th xtinction atio, : Q (Equation ) ρ( ) (using Equation ) ρ ρ Q (using Equations 5 and 6) (3) Nxt, w can aang Equation 3 in od to xpss as a function of : Q ( ) ρ (4) Fom Equation 4, w can mak th following impotant obsvation: As th xtinction atio is dgadd blow its idal valu of infinity, th avag pow must b incasd in od to maintain a constant valu of Q and hnc a constant BER. h pow pnalty is dfind as th atio of th avag pow quid fo a givn valu of to th avag pow quid fo th idal cas of. his can b dfind mathmatically as: ( ) ( ) δ ( ) (5) ( ) ( ) wh δ is th pow pnalty and ( ) is dfind in Equation 4. h pow pnalty as a function of xtinction atio is gaphd and tabulatd blow fo both lina and logaithmic (db) atios. Application Not HFAN-.. (Rv.; 4/8) Maxim ntgatd ag 4 of 5
5 ow nalty Extinction Ratio abl. Extinction Ratio and ow nalty Extinction Ratio ow nalty (db) δ δ (db) Figu 3. ow pnalty vs. xtinction atio (lina atios) 5 Conclusion ow nalty (db) Extinction Ratio (db) Smingly small changs in xtinction atio can mak a lativly lag diffnc in th pow quid to maintain a constant BER. his ffct is spcially acut fo xtinction atios lss than svn, wh a chang of on in xtinction atio tanslats to an appoximat % chang in quid avag pow. his additional quid pow is aptly tmd th pow pnalty, as nothing is gaind by this incas in pow oth than th unncssay pivilg of opating at a ducd xtinction atio. Also, th DC offst associatd with a low xtinction atio can caus ovload poblms in th civ.. J. M. Snio, Optical Fib Communications: incipls and actic, Htfodshi (UK): ntic Hall ntnational (UK) Ltd, pp , 99.. N. S. Bgano, F. W. Kfoot, and C. R. Davidson, "Magin Masumnts in Optical Amplifi Systms," in EEE hotonics chnology Ltts, vol. 5, no. 3, pp , Ma Figu 4. ow pnalty vs. xtinction atio (db atios) 3. G. Agawal, Fib-Optic Communication Systms, Nw Yok, N.Y.: John Wily & Sons, pp. 7, 997. Application Not HFAN-.. (Rv.; 4/8) Maxim ntgatd ag 5 of 5
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