Optical Modulation Amplitude (OMA) and Extinction Ratio

Transcription

1 Application Not: HFAN-.. Rv; 4/8 Optical Modulation Amplitud (OMA) and Extinction Ratio AVAILABLE

2 Optical Modulation Amplitud (OMA) and Extinction Ratio Introduction Th optical modulation amplitud (OMA) of a signal is an important paramtr that is usd in spcifying th prformanc of optical links usd in digital communication systms. Th OMA dictly influncs th systm bit rror ratio (BER). With an appropriat point of fnc (such as avrag powr), OMA can b dictly latd to xtinction ratio. Th purpos of this application not is to dfin OMA and how it lats to othr paramtrs such as xtinction ratio and avrag powr. Furthr, this application not will clarify th trad-offs btwn spcifying OMA vrsus xtinction ratio and xplo appropriat spcification rangs for ach. Dfinitions and Rlationships For bi-lvl optical signaling schms, such as nonturn-to-zro (NRZ), only two disct optical powr lvls a usd. Th highr lvl psnts a binary on, and th lowr lvl psnts a zro. W will us th symbol to psnt th high powr lvl and th symbol to psnt th low powr lvl. Using ths symbols w can mathmatically dfin a numbr of usful trms and lationships. OMA is dfind as th diffnc btwn th high and low lvls, which can b writtn mathmatically as: OMA = () Avrag powr is simply th avrag of th two powr lvls, i.., + = () W will us r to psnt th xtinction ratio, which is th ratio btwn th high and low powr lvls: Application Not HFAN-.. (Rv.; 4/8) r = (3) Through algbraic manipulation of quations,, and 3, w can driv th following lationships: OMA = (4) + OMA r = + (5) r = + OMA = (6) + = OMA = (7) + 3 Absolut Vrsus Rlativ Spcs OMA and xtinction ratio by thmslvs a lativ quantitis, sinc thy only spcify th diffnc or ratio of th powr lvls. In ordr to driv an absolut quantity from th OMA or xtinction ratio, w must hav an additional point of fnc, such as,, or. Th lationships of quations 4-7 all dpnd on on of ths absolut points of fnc. For xampl, an OMA of W can corspond to an infinit numbr of possibl valus for,, or : could b W with qual to W, or could b 5W with qual to 5W, or could b mw with qual to 99.9mW, tc., tc. In th altrnat cas of xtinction ratio, a similar xampl using r = can corspond to an infinit numbr of possibl valus for,, or : could b W with qual to W, or could b 5W with qual to 5W, or could b mw with qual to mw, tc., tc. ag of 5

3 If, in addition to th OMA or xtinction ratio, w spcify a fnc point of = W, for xampl, thn th ambiguity is gon. With an OMA of W and = W, can only b 5W and can only b 5W. If th xtinction ratio is and = W, thn can only b 8W and can only b 8.W. 4 Optical Attnuation Up to this point in th discussion, it may sm appant that OMA and xtinction ratio a basically quivalnt. Eithr can b computd with knowldg of th othr and on fnc point. Both can b quantifid whn th valus of and a known, tc. Th a diffncs, howvr, and on of ths is how OMA and xtinction ratio chang as th signal propagats through an optical systm. Assuming a systm with linar attnuation btwn two points, th xtinction ratio will stay constant vn though th signal is attnuatd, whil th OMA will chang by a factor qual to th attnuation. For xampl, ovr km of optical fibr with an attnuation of.3db/km, th total attnuation ovr th lngth of th fibr is 3dB, which is quivalnt to a factor of. If w transmit a signal through th fibr that starts with = mw and =.mw, thn r = /. = and OMA =. =.9mW at th fibr input. Aftr passing through th fibr th signal lvls a ducd by a factor of, so =.5mW and =.5mW. Thfo, at th fibr output, r =.5/.5 = (th sam as at th input r ) and OMA =.5.5 =.45mW (half of th input OMA). From this xampl w s that onc th xtinction ratio is known, a simpl avrag powr masumnt anywh in th systm will yild nough information to calculat,, and vn OMA. On th othr hand, if w hav knowldg of th OMA at on point in th systm, w cannot dtrmin it s valu aftr attnuation without knowing th magnitud of th attnuation or ls masuring additional paramtrs (such as,, or ). 5 owr-lvl Effcts on Transmittrs and Rcivrs In thory, th systm bit rror ratio (BER) is dtrmind ntily by th optical signal-to-nois ratio, which is commonly calld th Q-factor (s Maxim application not HFAN-9.. Optical Signal-to-Nois Ratio and th Q-Factor in Fibr- Application Not HFAN-.. (Rv.; 4/8) Optic Communication Systms ). Th Q-factor is dfind as th OMA dividd by th sum of th rms nois on th high and low optical lvls, i.., Q = (8) σ + σ Basd on quation 8 (and assuming that th nois is a fixd quantity) it is clar that th systm BER prformanc is dictly controlld by th OMA. Thfo, in ordr to optimiz BER prformanc, th OMA should b as larg as possibl. Also, quation 8 says nothing about, implying that w will gt th sam BER prformanc whthr and a mw and mw or mw and mw. In al systms, th a practical uppr and lowr practical limits on and thfo OMA. From th optical civr point of viw, th is an uppr limit on th optical powr that can b civd calld th ovrload lvl. Whn th powr xcds this lvl, saturation ffcts dgrad prformanc. This mans that for optimum civr BER prformanc, th OMA should b as larg as possibl whil avoiding ovrload, which occurs whn = and is just blow th ovrload lvl. In this cas, OMA= OVERLOAD,.5 OVERLOAD and r =. If >, thn th OMA must b ducd to avoid ovrloading th civr. From th optical transmittr point of viw, it is vry difficult to duc to zro. Whn th lasr is quickly switchd from th compltly off stat to th on stat it causs ngativ ffcts such as turn-on dlay and laxation oscillation. If th lasr is biasd abov its thshold lvl thn it is always slightly on, and problms with turn-on dlay and laxation oscillation dcas as th bias lvl is incasd. For this ason, practical transmittrs mit som optical powr at. A complicating factor is that th lasr thshold changs significantly with tmpratu, so, if th diffnc btwn th bias and thshold is to main constant, th bias curnt must b adjustd as th tmpratu changs. cis control of th bias curnt ovr a larg tmpratu rang adds significant complxity and cost to th transmittr. Whn w considr both th optical transmittr and th civr, it is appant that should b kpt as low as possibl without gtting so low that it causs ag 3 of 5

4 problms with th lasr. If is incasd much byond this point, powr is wastd and civr prformanc is potntially dgradd. Using ths argumnts w can dfin uppr and lowr practical limits for. 6 ractical owr Limits As notd in th pvious sction, it is gnrally not practical to achiv th idal lvl of low powr, i.., =. Whn is raisd abov th idal, howvr, th avrag powr must b incasd with no corsponding incas in systm BER prformanc. Th ratio btwn th avrag powr transmittd by a particular al optical systm and th avrag powr that would b quid in th idal cas (to achiv th sam BER) is calld th powr pnalty. Whn spcifying th OMA of an optical communication systm, it is important to considr th potntial powr pnalty du to th diffnc btwn and. Whil this diffnc can b spcifid dictly, it is mo usful to spcify as a ratio to th OMA. This is bcaus th ability to control to a givn lvl of pcision is latd to th magnitud of th OMA. Also, it is mo informativ to think of th powr pnalty in trms of a ratio btwn th OMA and. For xampl, if th OMA is spcifid to b vry larg (.g., mw), thn controlling to within a vry small fraction of th OMA (.g., W abov zro) achivs vry littl bnfit and is vry difficult. Also, th powr pnalty associatd with a W variation in would b insignificant lativ to an avrag powr on th ordr of OMA/ = 5mW. For ths asons, should b spcifid as a ratio to th OMA, and a convnint way to do this is th OMA to ratio. Thus, if = 8W and = W, th OMA = 8 = 6W and th OMA to ratio is 6W/W = 8. This corsponds to an xtinction ratio of r = 8W/W = 9. Th gnral lationship btwn xtinction ratio and th OMA to ratio can b drivd through manipulation of quation (5) as: OMA r o = = (9) wh r o psnts th OMA to ratio. For th idal cas (wh = ), r o = and r =. As mntiond abov, th ratio btwn th actual avrag powr transmittd by an optical systm and Application Not HFAN-.. (Rv.; 4/8) th avrag powr that would b quid in th idal cas (to achiv th sam BER) is calld th powr pnalty. This can b writtn as: ( r ) = (actual r ) r = + o o δ o o () ( ro = ) ro wh o (r o ) psnts th powr pnalty in trms of th OMA to ratio. Altrnatly, (actual ) + δ ( ) = = () ( r = ) r wh (r ) psnts th powr pnalty in trms of xtinction ratio. As an xampl of powr pnalty calculation, w can us th valus from th pvious xampl (wh = 8µW, = µw, OMA = 6µW, r o = 8, and r = 9). In this cas, th powr pnalty in trms of r o is δ o (r o ) = (8+)/8 =.5 or, in trms of r, δ (r ) = (9+)/(9-) =.5. This mans that th actual powr transmittd is.5 tims gatr than it would b in th idal cas wh = and r o = r =. Maxim application not HFAN-..: Extinction Ratio and owr nalty, includs th following graph of xtinction ratio vrsus powr pnalty. () owr nalty Extinction Ratio / Figu. owr nalty Vrsus Extinction Ratio ag 4 of 5

5 Through th nd of this sction w will nglct fnc to th OMA to ratio, mmbring that it is quivalnt to th xtinction ratio minus on. From Figu and quations () and (), w can mak som important conclusions about th practical limits on xtinction ratio. First, w call from th pvious sction that vry high xtinction ratios caus many problms for th transmittr. In gnral, th practical limit on xtinction ratio for a transmittr is in th rang of to. From quation () w not that th powr pnalty for r = is. and for r = it is.8. Whil th incasd complxity and xpns of th transmittr is usually quit significant to achiv r = vrsus (spcially ovr a larg tmpratu rang), th savings in powr is 4%. If w limit th powr pnalty and xtinction ratio numbrs to on dcimal plac (masumnt of ths quantitis to mo pcision than this is difficult and unliabl) w s that th powr pnalty mains at a constant. for xtinction ratios btwn 9. and 4.4. If w allow a % dgradation to a powr pnalty of.3 (roundd to on dcimal plac), thn th corsponding rang of xtinction ratio is 6.7 to 9.. This lationship btwn rangs of xtinction ratio and powr pnalty roundd to on dcimal plac is tabulatd in th following tabl: TABLE. Extinction Ratio Rangs Vrsus owr nalty Roundd to On Dcimal lac r r (db) δ (r ) From Figu and Tabl w can s that th practical lowr limit on powr pnalty is approximatly., which corsponds to an xtinction ratio in th 9 to 4 rang. If w can accpt a % dgradation in powr pnalty from th. lvl, thn any xtinction ratio gatr than 6.6 (8.dB) will do. As far as th lowr practical limit on xtinction ratio, w s that, for xtinction ratios blow 6.6 (8. db), Application Not HFAN-.. (Rv.; 4/8) th powr pnalty incass by at last % for an xtinction ratio chang of on. Whn th xtinction ratio is 3, th powr pnalty is. (maning w a wasting half of th powr). Whn th xtinction ratio is lss than 3, th powr pnalty incass dramatically, thus th xtinction ratio should always b kpt abov 3. 7 Summary. Optical Modulation Amplitud (OMA) is an important quantity that is dictly latd to th systm Bit Error Ratio (BER).. OMA and xtinction ratio a lativ quantitis that can b mathmatically latd to ach othr only if w hav an absolut point of fnc, such as or avrag powr. 3. Extinction ratio dos not chang as th optical signal is linarly attnuatd. Attnuation dos chang th OMA by a factor qual to th attnuation. 4. In an idal systm, th zro-lvl optical powr is zro (i.., = ). This sults in optimum powr fficincy and systm BER. 5. In a lasr-basd transmittr, it is not practical to st =. Stting too clos to zro causs turn-on dlay, laxation oscillation, tc. Constructing a transmittr that maintains vry clos to zro ovr a larg tmpratu rang can b vry difficult and xpnsiv. 6. Eithr th OMA to ratio or th xtinction ratio can b usd in spcifying th transmittr prformanc lativ to th = lvl. Ths two paramtrs a ssntially quivalnt. 7. Th practical uppr limit on xtinction ratio is in th rang of to, which corsponds to an OMA to ratio of 9 to. Transmittr complxity (and thfo cost) can b gatly ducd if th xtinction ratio quimnt is ducd. Th tradoff is incasd optical powr quimnts for th sam BER prformanc. Rducing th xtinction ratio quimnt from th to rang to a minimum of 6.6 (8.dB) sults in an optical powr incas of approximatly %. 8. Th absolut lowr practical limit on xtinction ratio is approximatly 3, which corsponds to an OMA to ratio of. At this lvl on-half of th optical powr is wastd. Blow this lvl th powr pnalty incass tmndously. ag 5 of 5