光纖通信(第5版)課后習題答案要點

#10(b)SCconnectorseachrequireaspaceof1.5cmby1cm.Therecanbeanarraythatcontains10connectorsalongthe10cmlengthand13connectorsalong(he20cmlength(since20/1.5=13.3).Thetotalarraycontains10x13=130connectors*8-20Panel:JO20JO20BodyofSFFConnector:0.50cm0,75cni0,75cniInthelongdirectionwecanfit:20/0.75=26connectorsInthenarrowdirectionwecanfii：10/0.05=20connectorsThus,wccanfitatotalof:20(26)=520connectors8-21Assemblytimes:Quicksplicetimetq=60sConventionalsplicetime-5minules144fibersneediobespliced,QuickspiiccTotaltime二144xGO-19,280s=144minutes=2horsand24minutesConventionalSpliceTotaltime-144x5=720minutes二12hoursCHAPTER9DISTRIBUTIONNETWORKSAIWOFIBERCOMPONENTSP才P3=4,Pj=+P±soP3=0t2PiandP2=°-8PiLjhp=-10logP?/P]=0.97dBLTAp--10logpy?!=&99dBP24九

=-10log~p~-=OdBLd亠?】01隅P#Pi=dB9-2(a)GivenP2/P3^4,"=2dB,=40dB,.-…卩2+P：J.—Lj?弓*10log"~p_=2dB內(nèi)+P(4■0.63】P“P2=0.5048PbP嚴P/471262P1Ld--IQfogP4/p!tP4=0.0001?!(b)Lthp=-10logP3ZP1-2.97dBLj^p—-10logPj/Pj=&99dB(c>ThetotalpoweremergingfromalloftheoutputportsisPq=P?+Pj十P4=0百3IPjThe]ossisthen-10logPoTj=2dB=Le,asexpected.9-3Ly=R"+L/pjjp++Lp+L^'+Ly^p+=Lp—0S=LTHP+L1AP.A3-dBcouplerisdefinedbyLyHp373dBForanidealcoupler*"hp=3dBimpliesIhatLtap=3(113Thisisconfirmedbyatableinthetextonidealdirectionalcouplercharacteristics.Thus,by=3+3=6dB*9-4L丁刖=LThp+L”=?dB+L5dB—4.5dBLrAp-L'jap+=3dB+J.>dB=4.5tlB匸0.8(1B,Lp=4dB.L”『~Ltfip亠Ljap++5Lt=17.8dB(b)FromTerminalToTerminalTransmissionLoss12L=2=2(3)+3=9dB13L二3Lthp十Lt^f=3(3)+3=12dB1斗Lw斗Lthf+Ltaf二4($)+3=15dBt5L=(NJ)“HP+Ltap~4(3)+3—15dB9-6FromTable9-hfora10-dBcoupler

Ltap=WciB,Lyjjp—0,4^OB.FromterminalItoterminal:2;L=2Lthp%Ltap~10.92dB3+L—3Lj^hp+Ltap=11”38dB4:L=4Lthp+LtaP=11.84dB5:L—4Lthp+=11.84dBThe"best"couplerdependsontheapplication.Theminimumlossbetweenanytwoadjacentterminalsexcluding1and5is20,92dB.Lp=(35dB/km)(0+1km/section)=3.5dB/section■L^=0,8dB,Lg=0*2dBLthp=L'THp+LE=3+15LtaP=L't十°E='十1.5u4,5dBLossfromterminal1toterminal:2:L=2Lthp+^tap+2Lc十3L號+Lp—19.2dB3:L=3Lthp+LtaP扌+5Lg■+2Lp—27,6dB4;L=4L^hp+LtaP+2Lc十7Ly+3Lp=36dB5:L=4L^hp+S'ap+2L(2+8Lg+4Lp=39*7dB

―SFUCE?giWECTK廉L=-10log(l/N)+LE+2L<-h2Lf―SFUCE?giWECTK廉Le=L<=Lf=OL=401og(0J)=6.99dBStarlossis:j=6.99dB(fromproblcni9'8)LE-2dBbL<-0.8dB,Ls=02dBLp=(33dB/km)(0.1km/sEction)=3.5dB/seciionUp=(35dB/km)(0.02kirL'sculion)=0.7dB<sectionLossfromT]loR”Rj,R3,orR4：L=LST十Le+2L^+2LS；2Lp17.99dBLossfromTjtoR5:L=L§丁+Le十2L^+2Lg+Lp+L'p-15.2dB9J0L=Lst+Le+21<=J0log(l/N)+3+2(0.8)=-IOhg(l/N)+4.6No.ofLossTerminals(dB)39.3761238914.141416.06】837452017.61a2ds&1012uisisioofItemiiulE9-11

a2ds&1012uisisioofItemiiulEBytrialanderror,w巳canfindthatd-23.1pmsatisfiesthisequation.9-12Sincethebeamdiameterhasbeenincreasedoverthebcanndiameterinproblem9-11byafactorof10,thetoleranceisincreasedbyafacLurof10,L=10(23」pm)=231pm9-13華Forexample;Amnitiplexcr/dcmultiplexersuchasdescribedinCh.9.9-13華Forexample;Amnitiplexcr/dcmultiplexersuchasdescribedinCh.9.9-14Lossfromterminal2toterminal:1:L=3(3dB)=9dB3:L=4(3dB)=l2dB4:L=5(3dB)=15dB5:L=5(3dB)-15dB9-15Lossfromterminal2toterminal:I:￡=31^^)^3(10)=30dB3:L==+2Lthp=2(10)+2(0.46)亠20,92dB4:L=2Ltap+3Lq=2(10)+3(046)=2138dB5:L—+3L/pHp=2(10}+3(0*46)=21.38dB9-16Tocompletelyinterconnect6terminalsbypoint-to-pointlinksrequires:6(5)=30transmittersUsingamultifibcrbundlerequiresjust1transmitterforeachteiminul*Inthiscasejust6transmitters.9-1725km.4dBFresnelreflectionLDTheFresnelreflectionattheendofthefiberreflects4%ofthelight(determinedinChapter3).ThereturnbeamlossindBis:L=-10log0.04=14dBSummingthefiberattenuation(bothdirections)withthereflectionlossyieldsatotallossofLT=14<4+4=22dB<3-18Anisolatorreducesthepowerreflectedinproblem9-17byafactorof50.Thus,theisolatorintroducesadditionallossofthereturningbeam(ML=10log50=17dB

<)-19TRANSMTHHiCONNECTOR<)-19TRANSMTHHi口IOAiPTherearetwoglass^io-airinterfaces.Eachreflects4%.Thereflectedpoweris8%ofthattransmitted.Thereturnisthus;L=10log0.0$=J0.97dB.Sinceonly96%ofthelightistransmittedacrosseachinterface,thetotalreflectedlightismoreaccuratelygivenby0,0440.04(0.96產(chǎn)=0,07686or-1L14dB.9-20Faradayrotalionisolator.Therotationanglemustbe45°(ti/4radians).ItisgivenbyEq.(9-14),8=VHLV=4.68x!0*6r/AL=100mH=0/VL二(n/4}/(4.68x10_6x100)=1.678x103A/mL=1mH=1.678x12A/m9-21FromEq.(9-11)P2/Pj=cos2(ApL)Pj/Pj=sin2(ApL)PlP2兔PaAdding:P2/Pl+P3/Pt=cos2(A|3L)+sin2(郵PlP2兔PaThusP2+P3=P|andalltheinputpoweremergesfromports2and3*⑻Pg+P廣pl0785mm.P2/P3=cos2(ApL)=0.50785mm.ApL=0.785radians,L=0585/1(b)P/P3-10,P2+P3=PiThusPz+0.1P2=PlPlTJP?pyPi=o?09Pj-T^cos2(A3L)-0.909ApL=0306radiansI_=0.306mm9-23AtIf丄2radians/mmandP3/P1=1Pj/Pj=sin2(A|J|L)=1forXj△卩]L=3n/2L=3兀/4=2,355mmP；/PL=cos2(Ap2L)=1fora2九卩=nA|32=陽2355=1,33radians/mmFor乃,thecouplinglength,fromEq.(9-12)is:Lq2=皿2郵21^2=3?t/8=1.178mm9-24TransmissionFiber\12Xjsnd9-24TransmissionFiber\12Xjsnd入2434WDM9-25TransmissionFiberXiJ12Ar]?43WDM9-26ISOLATOR9-27filter4drops"gfilter3dropsandfilter2drops心9-28Filters2t3tand4addwavelengthsasindicatedonlhefigure-9-29NORMALOPERATIONNODE2NODE2NODE2NODE29-30C-band:1530-1565runBandwidth:35nmUsek=1550nminthecalculationsChannelspacing;Af=25GHzDeterminetheequivalentAZthemaximumnumbercfC-bandchannels,

Xc/幾Xc/幾A；=(L55xlO-)-25xio9=2xiy10ffl3x10sA/l=0.2xl0_9mA/l=0t2hwThemaximumnumberofchannelsthmlcanbefittedbyDWDMis:N-—175channels029-31N=175chunnclsR=10Gb/sperchannelTatalfibercapacity:Ry=NxR=175x10=1750Gb/s=1.75Tb/s9-32S-band:1460-1530nmBandwidth:70nmUseX=1500nminthecalculationsChannelspacing:Af-50GHzDeterminetheequivalentAXandthemaximumnumberofS-bandchannels.…加(L5X1C)2?in.“Vin-ioA2=—Af-50x10=3.75x10mc3x10A2=0.375nmThemaximumnumberofchannelsthatcanbefinedbyDWDMis:N-—'—=186.7-186channels0.3759-33Thesourcespectralwidthis:AX=2nm

TheratelengthproductofthesystemwillbedominatedbytheinaLerialdispersionai820nm.UsemaierialdispersionM=100ps/(nmxkm)ThenA(r/L)=A/AA=2x100=200pslkmForNRZcoding：A(r/A)200x10-12A(r/A)200x10-12=3*5x13b/sxktn7?xA-3.5GbisxkmThelengthofthesystemwillbepowerLimitedbytliclosssd820ruilUsingatypicallossof3dB/kmal820nmandalossbudgetof50dB,wegelamaximumsystemlengthof;Length=50/3=16.67kmThechannelat1300nmhasanunlimitedratelengthproductifweassumezerodispersion.Thechannelat1550runhasdispersionofabout20ps/(nrnxkm).Thisis5timessmallerthanthedispersionatS320nm,soitscapacityis5limesgreater:/?xi=5x3+5=17.5Gb/s^ktn9-34Ajhdk.AX<■—召H爲一AA石］=s易十△兄&j_=AX石一為=AA血=1600加《Af=12,5GHz

^4護^4護gig加皿％AZ=0.1067nm人-1600-0.1067=1599,8933nm入=1600nm-1600+0.1067=1600J067nrnTheoutputwavelengthsduetofour-wavemixingare:A=入+2—入，Thewavelengthsgeneratedbyfour-wavemixingaretabulatedbelow:□fl▲「I<r伽）I爲入一AZ1599787rr人A+A41jI+AZ1600入右+人一人召—2AA1599.787AA人+人-入人+2A21600.21341A易+入—易—AA1600易+Aj—人+A216002134Thereisonlycrosstalkfromchannels1and3intochannel2.Thereisnocrosstalkinchannels1and3.9-35BragggratingResananlwavelength:1550nmGratingperiodtuning:0.1%perUCGratingperiodA二幾/2=】550/2=775nmBut,Lmustbemeasuredinth亡core.Assumelhecoreindexofrefractionis1.5.A=—=匕里=1033nmn1.5-?A=>1/2-1033/2=516.7nmThisistheactualgratingperiodTuning0.1%^=0,001/°CThechangeinresonantwavelength(asmeasuredinthecore)is;0,01x516.7=0.5167nm/^CTheequivalentchangeinresonantfrequencyasmeasuredinfreespaceis:0.5167xn=0.5167x1.5—0.775nnV°CComputethechangeinfrequencycorrespondingtoachangeinwavelengthof0.775nmat1550nm.Af=—弘⑷」、(0775xl0_9)=9.677x10IDHzJ(1.55x!0^)2紉=96*77GHzThetuningisthus:9&力GBz^C9-363x3router工1545nmk*=1550nnikjx=1555nmwherexrepresentsthechannelindicator.

SYSTEM]1?A22—?33入11,Z-2hgXu,IzJjX33Xib心，k陽入31,h'2,kuMl,&,59-37MsilicaglasswaveguidesAL=pathdiflerenceXo~1550nmWaveguides;ALPhaseshift:?=kz=^/8whenz―ALI11US：△0=k&L=jt/8沁旦z?8A￡=^/16Lettingkbethewavelengthinthewaveguide：2n;i=1.5Then:*r入1550—oAZ=—=64583肋16/i16(1.5)Ingeneral:久A)—2祁*5)心s193.75爐△0=——\_(64.583)=——AwhereZoisinrumXo(nm)緲(radians)15480.12516兀15490.12508k15500.12006n15510.124918k15520J24838k9*38AWGCrosstalk=30dBZ=1550nniPK=0JmW*P廠00】mWPowerfromfiberxtofiberyisfoundfrom:P.-lOlog*^—30Pxp“=0.1xl0'3=10^mWPowerfromfiberytofiberxistbundftom:-lOlog^-30P-^=10-3P.p=0.01xl0_3=10^mWInfiberx,thecrosstalklevelis:p01CT=lOlog亠=lOlogy^=40dBPy^Infibery,thecrosstalklevelis:CT=10log—=101og^|=20dB尸Iu

9-399-409-41MEMsNxNswitch2to1000portsN-numberofportsM-numberofmirrorsFura2Dswitch;AnNxNswitchrequiresN2mirrors.M=N2Fora3Dswitch:AnNxNswitchruqnires2Nmirrors.M=2NNM(2D)M(3D)2斗一410100|20WO10,0002001000To5..」200Q20004x10°40009-42,4SWITCHES

CHAPTER1010-11iIH（皿）10-11iIH（皿）tn'=Igp/loc1=+〕SPCOS(x)ti!N-50+30cos(2nx40x106t)9)nV=30/50=0.6T=1JI=1/(10xlO^z25xiO59)T=1JI=1/(10xlO^z25xiO5￡3-曲=l/27TTbt=l/(2n=l/(2nx80x106)-L9x10*^s<a=2兀f二2x(40x106)=25133x106rad/sPsp-〒?凹丄盟，=(UK旳一一一=2,68mWd】+⑷評￥1+(2.51x10*xL9x10'y)ZPnc=引切匚三(01)(30)=5mWP=P°CfPgpcosqHP-5.0+2.683cos(2nx40x1061)(mW)心卅DC=2.683/5.0=0.537(b)mT=h30/50=0.6JO-2For80MHzt(c)w=2nf(b)mT=h30/50=0.6JO-2For80MHztt-L9x10'^s(fromproblem10J)psp=引加_kOJxJQ==2.2,12mWV1+(wtPV1+(5-02x10sx19x10'9hP°c=打‘D(?二(O’1)(50)—5mWP=^5.0+2.12cos(2ttx80x106t)(<1)in匸Pgp/Pocm2J2/5?O=0.424(c)w=2nf=753.98x106rad/s1=l,9x10^sP<^P=1.66mW(b)m*二hp/IxPdc=5mW(b)m*二hp/IxP=5+1.66cos[2tt(120x106)t]m-P^p/Poc=166/50—03310-3(a)R^RbR10-3(a)R^RbRa+Rb=2kf2RcRc={[0M?Vo)/Q?RM】邛尸迢&O(b)ie=tcAtvCE=0,k=(10-0^8)/Rt=95mA.AttheQpoint,ic-lc.VCE=Vpc_vd'~3MVCE=Vpc_vd'~3Mv(c)[sp=92-50-42mA104FromEq.(10-10),P~PdC+幻F+珂1sina)t-0.5a??cos2s【、▼7THD=(opticTHD=(opticpoweri口fundamental)50dB=-10logTHD,a]=0.05,1=250^-10log(0.25x4xa2/0.05)sa2=01X)0158mW/(mA)210-5‘‘DC=VLED+【cR=VCE，k10-5‘‘DC=VLED+【cR=VCE，k=Vd，^led-~R】04上=―60—1<7w96.67mA,Ijj匸956?，~50=I93mABandLightRadio0-1600KHzSourceRtcaivBr(Tun^r)mierRaii學Bandwidth=1600*540+10=1070kHz=1,07MHzThisyields107stationswith10kHzbandwidtheach.Thaiis;10x107=1070kHz=1.07MHz10-7Stationanalogbandwidth二5kHzSampleai10kHzrate(twice[hehighestfrequency).Usean8bitcode.Thus,foreachstationweneed10x8-80kbps

For10stations,weneed10x80=800kbpsUsingtheRZcode?the3-dBelectricalbandwidthequdlsthechidr址匕.Thus,bandwidth?800kHt10-SSamediagramasinproblem106,withtheFMbandreplacinglheAMbandBandwidth=107.9-8K1+02-20MHs107.9kHz±100KHz107.9kHz±100KHz881KHz±lOOkHz10-9ThefrequencyallocationfortheVHFTVchannelsi￡shownonrhefollowingtable:CHANNELNUMBERSFREQUENCYRANGE(MHz)2f3?454-725,676-887,8,%i0T11,12,13174-216

Eachofthe12channelsisallowed6MHz.ThebandwidLhis216-54=162MH厶butonly12x6=72MHzareused.Thesubcarrierfrequencies(Cq)areindicatedonthefigure*

10*10Sampleattwicethe6MHzupperfrequencyandencodeusing8bjtspersample.ChannelBW=6x2x8=96MbpsFor12channels,thesystemdatarateis:R=12x96Mbps=1152Mbps-LI52GbpsThisisabouttherequiredsv'stembandwidth.Ctum&lLD24AnalogtoDigitalCbnvfenessMax哼dFqn畐WDMSYSTEMD/A2——Ctum&lLD24AnalogtoDigitalCbnvfenessMax哼dFqn畐WDMSYSTEMD/A2——2TfAnsmissiOtfiDEMULTIPLEXERDigiultoAnalogCcrfiv&nefs—13PD=phtodetector10-11GivenafrequencydivtSLonmultipkxingsystemwithTHDj^=25dBand=50mA,m=0,5(50%AMmodulationh100%intaisitymoduktioti.SubcarriersareatfgCj=]MHz,$C2=2MHz,andtheinformationsignalisalfrequency編=100Hz+THDdB10logTHD=25.Thi^THD=(1.00316P=Pdc+十a(chǎn)2J3'dit]=°slopeofth<?characteristiccurveal蘭5mW/1OOmA=al^2=yxVTTHI5=?月址2)70*00)16=0.112i蘭Ig[(1+mcost)cose置]l十(1+mcosco^20x(cos①肚”]+1。【°=50mA,ii)mi-①應~2ttfnVwscl,2=2北^clt2ip’昨十65)+(1+0?5“iptak=100mAandthusIs=16,7mAi皿廠h+【妄(亠5-1-5)=0i=(16.7mA{[]+0.5ccs(2hx1x10^t)]cos(1x10^x2m)十[I+0.5cos(2zx10001)]cos(2x10^x2rtt)}Po=aj1^=(0.05)(0.05)=0.0025W=25mWps=引Is=(0.05)(0.0167)=0.000835W=0.835mWP=P0-hPs[(l+0,5cos(0mit)cosg昭]t+(1+0,5cost)xcosReceivedcurrent:=pP,p=0.5iR=0.5{2.5+0.835[1<0.5coswmlt]cos+0.835[1+0.5cos①泌t]coswsclt}(mA)SPECTRUM：.417mA,417mA>L25wA.104mA|t,104fnA,104mA(ttk.104mAt1護?1000斑lb2x1^*10001MI&nAlOOOHsIxlO^+lOCOTheproblemmayberedonetoincludelhesecondharmonicterm.Inthiscase,

p=p0+a1is+a2ij,whereis=i-laisthesignalcurrent10-12100111000101MIZRZMANCHESTERBIPOLAR□ir~n「MIZRZMANCHESTERBIPOLARn,,nnn,■■ni-Ti^jmJULTLTLTTUKL_JHj.r±11n10*13Let:Leveli:I=01=0-Level2:1=73mA,ij>1.6mA,<2~0Level3:1=146mA,i]>L6mA,i2>16mAI=id+ic2>VDC=5VIxvel2:LoadJineequations:VDC=vd+iclR+vCElVpC=vd+QR+VCE2.Vdc?咒.AtvCEl=VCE2=JcJ二_R=lc25-1.4Set昭]竺ic2=80mA,R=~qg=45￡1Aticl=iC2-o,vCE|=vCE2=VDC-vd=5-1+4=3*6V

Fromthetransistorcharacteristicscurve,ifig>mA,then冷土75mA.AtsaturationVDC-vd-VCE(sat)"1.4*0,3“°ici=亍"=—45—二亦AThus,atleveltwowehave:i]>L6mA,i2=0icl=93mA,IC2-U1=ici十心=73mAAtleveltlireewehave,i】>L6mA*i?>1*6mAI二咕十i(，2=146mA10-14FromEq,(10-9)P=Pdc+a1is+a2i§ThesignalcurrentissimilartothegivenbyEq.(10-20),butwithtwosubcarriersandtwomodulationfrequencies--lSi(1+mjcoswinit)cosSscit+【S2(1+m2cos①沁UcosOSC2tLetI$i=02=【S航m!=m2=mis=ls(1+mcoscos3?t+Is(1+nicoscosto?1ThenP=Pdc+引[1$(1+mcosa)mlt)cosG>scltils(l+mcoscos￡0SC2t]+a2[ls(l+mcoso)m|t)cos+ls(l+mcosw^t)cosExpandingthea?termonly:a?[11(1十mcos2cos2(OgcU+【§(i+mcosa?mt)2cos2<oSC212S2111

2S2111

fL+mcos(1+nicoscos⑴比Jcos^scptMultiplyoutailsinusoidaltermstocompletethesolutionThedetectedcurrentisproportionaltotheopticalpower.Thefrequenciespresentinthedelected￡廿rrenlarc:FrequencyU3SCI^SC2?SC1xwml網(wǎng)C2-ft)m23t0SCl2u)sc2吋⑻m22咗口士叫nl2郵o士23血2wSC2土<°ni22SC2土加也^SC2+⑴SCI十十叫也WSC2+Jl)SCl+mml+仍m2WSC2+WSC1+roml+wm2ffiSC2+^SCl+wml亠％i2

Tominimizethecrosstalk,wecan:ReducethenonlinearitycoefficientSpread(hesubcarrierssolhereisnooverlap(crosstalk).Inthisease,set<03^2>2esci10-15R=10GbpsRZcodeT-1/R=1/10】°=10dO$tpulsedurationk=1550nmf=c/Z=3k應/1.55kIO_6=L935xiOl4Hz\/f=0.5Hx1CT"secondspercycle.Thenumberofoscillationsisthen:777；=芝丄。―\7=0.9677x104=9677oscillations1"0,517xlOd410-16Totalfibercapacityis:R=8xW=80Gbps=80x109bpsTherequirementis64,000bitspersecondpervoicechannel.Thetotalnumberofvoicechannelsallowedisthen:80x10勺64,000=1.25x10&-1.25millionvoicemessages.10-17Increasingthedatarateto80Gbpsrequireslheelecironicsworkatthisrate,greatlyincreasingelectronicscomplexityandcost.10-18Theavailablecapacityis80Gbps.Assumingacompressedvideorateof5Mbpspervideochannel,theallowednumberofchannelsis:80x1()9/(5x106)=1.6x104=16,000videosignals10-19WehaveanOTDMsystemwithtvn40Gb/schannelsTotalsystemdataraicandcapacity:R=10x40=400Gb/sMaximumallowablepulsewidth：=2.5xl0_:3sT-2.5ps10-20WecancombineOTDMandDWDMtoincreasethetotalcapacityofasinglefiber.ForthedescribedOTDM/DWDMsystem,thetotalcapacitywouldbe:R^35x4x1011=14x1012b/s=14Tb/s10-2]Typesofpossiblemodulators:Externalmodulators^ElectroopticandElcctroabsorption.10-22When:=0,Wg=0.9473eV.SlatetTransmission.=-2.Wg=0.9458eVSate2.Absorption,X=1310lunThephotonenergy31thiswavelengthis;^=1^=0.94656eV

Aphotonistransmitttxfwheniisenergyislessthanthebarxigapenergy,Thaiis:聲<吧ThisistrueinstateLAphotoni&absorbedwhenitsenergyisgreaterthanthebandgapenergy,lhalis：Thisistrueinstate2.10-23Electroabsorptionmoduiaior10-23L=150-0.015cma-75cm1Extinctionratio:ZCT=30=101og?^30=lQlogeOOMu心=嚴他In105=6,908=Q.03AuA(2=230.2cm~x<7+A^-75+230,2=305.251424ER=ExtinctionRatioER=TransmissionStatePower-2txLAbsortionStatePower1424ER=ExtinctionRatioER=TransmissionStatePower-2txLAbsortionStatePower2"3'Q*j￡rUER=eInsertionloss:^er=]°l°咅呂門⑴；凸亦也s=I0】og嚴-10血対心2沁二LiffAid即卵o二LiffAid即卵o町-Lili.Tmnswssion)CHAPTER11NOISEANDDETECTIONT=35°C=308KRLCHAPTER11NOISEANDDETECTIONT=35°C=308KRL-50fl10%R￡^50kQk二138xIO-23J/KSt三創(chuàng)器二2.04x10q5A2iNT(RMS)-7f^=45.2nAvNT(RMS)二ixr(RMS)Rl=2.26rVP^T=iRiRl=L02sIO'13WdkTAjf■rT=2.O4x10J8A2ih'T(RMS)-*i；T_L43nA(RMS)-iN'T(RMS)R￡=7L4pVPNT=Sil=110*13W

AssumeIp=0.Af=6x10^Hz,e=1.6xlO'1^Cis=10'9ARL=50QiRMS=右石=“2詁瓦-43.8pAvc=icRt=J*iTN=Rt=50nVbRMS^RMSLLvSNrms=iRM$Rl=2.2nVS/N二i§Rl/2eAfisRL=521二27.2dBS/N=i|Rl/(2eAfisRL+4kTAl)=503x10^=-33dB11-3PNS=2cAFRl(p?+怙)SetpP=切5xIO-9……P=bzP=o；5=WdU11-4Given;p-0.5A/W?1^,=2x1o"A,Rj_=2000Q,Af=50xIO6HzTT=313K7k=1.38xIO'23J/K.PNS=2eAf(pP十ID)RL=32x10'9(05P+2x10^)PNT=4kTAf=864x1013.SetPks=PNT?P=54nWPe5=(pPopt)2Rl=?5x54xW6)22000=1*46pWS/N==￡n*_=844xio3-59.3dBP骯+卩幡2Pnt(C)PNS=PNT=864xmWPNS=2eA?pP+TD)RLM2-2(1.6x1Q19)50xIO6(O.5P+2xIO'9)(100)22x】滬=3.2x10_s(104)(OJP+2x10'9)Pns=3,2x10'4(0.5P+2x2)PNT=4kTAf=4(138x10-23)5x107=S.G4jc10-13WSeiPns=pNT3.2x10^(0.5P+2xIO_9)=8.65xW13O.5P+2x10_9=2.7x10'9O,5P=07xIO-9p=t4XIO'9=1.4nW(05x1.4x10'9x102)22x1(?Ppq=9.SxIO'12S/N=98X1Q^T^5.672(8-64x1O'B)SAN=754dBPns-Pnt=8.64x10qjW

1i-6Receivedpower:P=1p-W,p=0.5A/W,Iq=4nA,T=27QC=300K,Af=500MHz,^=500￡2,￡=1,6x1019CS/N=(pP*RL/[2eRLAf(JD+pF)+4kTAf]-1.51=)59dBlb)(c)(d)(n)t=(PP)‘RL/4kTAf^E51=1.79dB伶)S=(pP)?R[々ERgf(l])+pP)=3l25=34.9dBWant(S/NJds=30dBthenS/N=1000.S/NPeePns+Pkt/M，Pes1/m2=(s/n)pnt￡ns

P帖T=0.001031.25jc4x1汕_=0.00103IO3(8.28xIO12)'8.28x10-12M=3L211-7(a)“2巳IpAf+(4kTAff/RLpifZfJ320x10訂】十｛.66xIO^/Rl(b)Rl=50Q,NEP=6.07x10_11Pmin=NEP(Af)1/2=607nWRl-5000Q,NEP=6.07xIO"12Pmin=NEP(Af)1/2=60.7nWRl=50,000QtNEP二1,93x10'12Pmin=NEP(0f)"2=M3nw]1-8GivenAf=10x!0“Hztp=0.5A/W,=1x]0'^A,m=0.4,M=0(S/N=50dB=10,000,T=300K,RL=50Q.(m2/2)(MpP)2%S/N耳=Mn2eRLAf(ID+pP)+4kTAf(042/2)泄總巴?上02(1.6x10-J9)(50)(10x106X10-9+0.5P)+4(138x10*2\300)(107)P-133gW11-9Given:ID=2nA,p=05A/W,T=27T=300K,Rl二100Q,IF=500MHz,Ps=5nW,e=1.6xIO-19C,k=1.38x10"，'J/K,p=rje/nfQuantumLimit:S/N=qP/hfAf=(p/e)(Ps/Af)=3L3,S/N=15dBWewant:S/N=15-1-14dB,S/N=25Forheterodynedetection:￡2P‘RRP|.25N2eRLAf[ID十pPJI+P打J]+4kTAfPl=4mWDirectDetection:S_SPsFRlN2eRLAf[lD+pPs]+4kTAfAf-250MHzPs=2ThissystemisthennaI-noiselimited.11-10erf(x)-1-e_x/(xnl/2).forx>3.Kerf(x)3.01-2.32(10'5)=0.9999767913.51-7.71(10'7)=0.9999992284.01-1.59(IO-8)=0.99999998414.509999999997995.00999999999998435.5(1999999999999992526.00.9999999999999999782U-ilGivenBER=iO'9,RL=50,T=30()K,R=500Mbps,n=0.9,Z=L3x10*6m7e=L6x10J9CFromthefigureofprobabilityoferrorforthermalnoiselimitedsystems,S/N=21.5dBP二(h"切)"住ff=5J36pWi)p-P/hfRnp=$136k】0切(5天108x6.63x10'34x3xWS/l.3xIO*6)rip=6.7xIO4photons/bLt11-12GivenZ-L3xP^-1.6xIO-9(a)FromihetabicofPCMerrorratesforthecaseofnn=0,(a)%=20,7=r%=20,7=r(PVhf=(6.626xIO34)(3x10Byi.3xIO6P=L76tiW(b)rip=ns/Tj=20.7/0,9=23photons/bjtTheshot-noise-litniledsystemrequiredconsiderablylessopticalpoweratthereceiverthanthethermd-noise-limitedsystemtoachievethesamedataanderrorrates.UsinganAPDwillenablethesystemtoapproachthequantumlimit.11-13Given:Gain=8,noisefigureF^g=3dB,p=0.5Rl=100Q,Ps=0.5pW.T-300K,Af=1XfHz,k=1.38x1O'23J/KPfs=^Li|=Rl(PPQ，=63x1012WP0UT=GPes=8P￡S=5x10*11WPNT=4kTAf=L6610_,4WSince卩曲=lOlo^F,F^2and(PNT)Oirr=FGPnt-2x8xPnt=2.65x10'13WTc=T+TA,TA=Te-T-600-300=500K-

PN=4kTeAf=2.65xi0_13/8=033xIO13W6.25X10_，2……mS/N=Pes^NT二]石6x10"4=377=2585x10-11S/N=Pout*Pnt)out=265x10$=188=22.7dB11-14(a)C=Cj+CT=3x10'12+6x1012=9xIO'12Ff=1/2tiRC二n-=MHz佃2n(2000)(9xIO'12)035“(b)片-=39.6nsr亦1M5(a)1/R=L/Rt+I/Rja]=2/2000,R=1000QsC=9x10J2FfjdB-1/2ttRC=17.68MHz(b)0.35=19.8ns11-16ReceiverCircuitR|andR2biasthetransistor.VgreversebiasesthePINphotodiode.Thelightsignalisamplifiedbyrjs?<r￡T_0+?QRjanduse^t0^iastheFET.isusedtobiastheFET,isusedtoreversebiasthephotodiode.11-lSGiven：Rp—10kQ,Cp-0.2pF,Cj-5xKfF,pz0.5A/W,Ps=0.5pW,k=13SxIO'23J/K,e=L6x10*l9C(a)%=igRfpP$Rf=mW(切也曠云冷=人9張J4kTAfiNT=FRf7=11-5nAis-pPg=025S/N=2eAfRpis+4kFTAfF-10FdB，W=100"1=2,51=L85x102=22.7dBThissystemisnearlythermallimited.11-19ProveEq.(11-40)(SOUT專闔INp^otrr11-19ProveEq.(11-40)(SOUT專闔INp^otrrPN,CUTAxttplifi*rProof:PgOUT=GPs」nSignalPowerwhereGisthepowerpin.FromEq,1139,Pn,OUT二FGPWjNMoisePowerIS]^Ps.out_GP5iqut^丄〔N」outPnqutFGFkiwF\nH]1-20FromEq.(11-40)Indecibels亂"「g亂「gFOUTJB'Nbu丁0H■N'L.dH11-21N=10amplificni-3dB,amplifiernoisefigure,Fj=2%dB=32dB=10loga,oq二0.00063Fractionalfiberlossbetweenamplifiers0^-63x10'4AmplifiergainGj=10^—30dBThena,G；=6.3x10"^x10^—0.63Now,inEq.⑴-43)F=(F/di)〔1十血心于1/(爲3)2++口aG『+l/f^Gi)5十l/^Gj)6+l/(ajGj)7+11otjGj)8+1@心)牛F=(2/63x10"*)[1+1/.63+1/.633+1A633+1A634+1/.635+1A636+1/.637+1/.638+1A639]F=3174.6(I+1.59彳2.51十4+6.35+10+16+25.4+40+64]F=3174.6x171=542,380=542x105=573dBThus:侖)三倍)?Fob'N^OLT,dedB=80-573^22.7dB

11-22RIN=-1351GHz,PR=20pWFromEq.(11-46)P^LP^L=RINP5AfOr,usingEq.(11-47):RLNdaHz=10RLNdaHz=10logAf.-135=10log\(20XlO^FX1O9J-135=10log\(20XlO^FX1O9J=10logPnl=0.4(3,16X10_l4)-J.2xW14(a)Pnl=L.12冥Pnl=0.4(3,16X10_l4)-J.2xW14(a)Pnl=L.12冥10^0.112mW(b)=0.3(0.112)=0.034pALaserNoisePowerNoisecurreniThesignatcuncntisis=03(20)=6^iA11-23FromEq*(13-24)foranalogmodulation(m2/2)(MT)eP/hf)2Rr工~~―—?——一Mn2eRfAf(ID+r^P/hf)+4kTAfTheaddednoiseduetoRINis:MnRIN(pP)2AfRLThus,lettingp=r|g/hf(m2/2)(MpP)2AfRtS/N=Mn2eRLAaiD+pP)4-4kTAf+MnRIN(pP)2AfRb]1-24M=100Excessnoi$efactor=Mn'2=5lOtf1-2=5I00nx(100)'2=5100i1/]0+4=510011-5kW4l02n=5x104log102n=lo￡5xIO42n=4.7n-23511-25Problem(11-6}considersaPCMsysiem.TheSNRisgivenbyEq.(11-14)(MpP『R住JILT_J'Mn2eRLAf(Id+pP)+4kTAfP=W6W,p=0.5pA/'mW,T=300K,Af=500MHzR|_=50fl,】d=4nATheexcessnoisefactoris:M11-2=M2-35~2Thus:Mft=M,p2M2=M035M2Now護護50_M0J5M22(1.6x10'19)50(5x108)(4xIO"9+.5xIO-6)+4(L38xIO'33x300x5kl0B>M’1.25耳10」~4.03xIO-15M2M035■+8.2Sx)0i2

MS/N11,511.781013621.3506502S.IdB10055927.7dB20048i26.8dB500350254dB100027624.4dB1000012320,9dB4063028dB6065128」dB.5565428JdBM1Thisquancumlimitis;S/fJ=3101=34.9dB11-26Attheiransmitter,the^milledspectrumandpuh^looklike：RandomamplitudesoftheemiltedspectrumThepulsesemittedatthethreewavelengthalsohaverandomajnplitudes:WavelengthXi_Wavelength心WavelengthWavelengthk、Thetotalpulseaniplitud?hasnormalizedintcnsiiyof10,asidundbyaddingtheintensitiesoflhethreewavelengthsineachT/8secondintervalatihe(ransmitter.Atthereceiver,theIhreepulsesaredelayedbyT/Ssecondswithrespectioeachother.Thetableofintensitiesatlhereceiverisgivenby:T/8T/43T/8T/25T/B3T/47T/8Tr9T/85323253300Xt03552325200022355325569to7131011?145SUM

INPUTOUTPUT154-INPUTOUTPUT154-0TMT/23T/4TEDFAReceiverFiber10dB>Pg'Pr*「11-271II.II__J__k_|~L10—5耳=3億p=0?5川叭/廠4曲"=2廠C=300KMr=500MH乙7?￡=5OQ101昭生=10PrPr=iop尺s_IpPrYRl何#■2胡丄"(打+P3)+4刃&S(0.5x105)250W=2x1.6x10w(50)5x10*(4x10^+O,5xlo-S)+(4)138x10^(300)5x10s—=150Nc(-)^=2L77^

型、「（昭(b)VNt~4kT^f已產(chǎn)旦斗5輛(b)Nt8?28燈0七=21/79曲ThisisthethermallimitedSNR.s,9緯?（初廠2叫他+譏）需“,250曲=44.9dB(d)Wewant:韋)”40曲2三10ooo=]0"NS__PP梅譏M沁+仞譏SolvingforM：~PQ士^S^gxiO-71丄=(^S^gxiO-71M2104A/2=97.465M=9.8711-28EDFAReceiverFibertOdBF=5dBPr=\pWp=Q.5A/iVtID=4nAyT=27=300K=500Af//z,Rl=5OQ,^=IO/zfFAsnotedinSection11-4,foralhennallimitedsystem,theSNR(inUB)isreducedbylheamplifier'snoisefigure(alsoindB),Thus,inparts(a)and(b)ofproblem11-26,wenowhave:c(^)^=21.8-5=16.8CHAPTER12SYSTEMDESIGNTheproblemsinthischapterareopen-ended.Thereforetheyhavenouniquesolutions.Afewsamplesolutionsfollow.12-1Systemspecifications:Analogmodulatedvideosignal,tJW=4.5MHz,S/N=48dB,L=10km.ComponentSpecifications:Laserdiode:Pavc=10mW,"=1ns,AZ.=5nm?X=L3屮msjwimetricalbeampatternwithfullhalf-powerbeamwidthof44,4"MuilimodeGRINfiberNA-0,24,jpxL=500MHzxkmInGaAsPINphotodiode:p=0.6A/Wt1^=5nA,Cj=5pFRcceiv亡r:Assume100%modulation