Transimpedance Considerations for High-Speed Operational ...

1 ApplicationReportSBOA122 , gain , ,providesa setofdetaileddesignequations,explainstho seequations, (10pFSourceCapacitance).. November2009 TransimpedanceConsiderationsforHigh-Spee dAmplifiersSubmitDocumentationFeedbackCo pyright 2009,TexasInstrumentsIncorporated-VBlA(s )VOCFCCMCDCDIFFRFIDV-C = C + C+ CSDCMDIFFV = V A(s)O--A(s) =As +wwOLAA VIOD=-ZF1 +1 +ZZFGA(s) transimpedancecircuitis toconvertaninputcurrentfroma currentsource(typicallyaphotodiode) tousea ,theachievablegainusingthismethodis ; ; closed-loopapproach,usinganoperationalam plifier,is typicalcircuitwithallnecessarycomponents forthisanalysisis shownin Figure1. Inthiscircuit,thegeneratoris a photodiode,whoseroleis toconvertthephotonsintoa thenamplifiedbythefeedbackresistorRF.

2 Workingwithanidealamplifierfornow,wecans eethatbecausenobiascurrentis present,allthesignalgeneratedbythephotod iodeis notofinteresthere;it is lowimpedance,allowinga goingtobea functionofthesourcecapacitance(CS), thefeedbackcapacitance(CF), (CS) is thesumofthephotodiodecapacitance(CD), thecommon-modecapacitanceoftheamplifier( CCM), andthedifferentialcapacitanceoftheamplif ier(CDIFF). therestofthisapplicationreportis a singlepoleop-ampmodel,asshownin Equation1. Thismodelallowsustoanalyzetheresultingtr ansimpedancedesignasasecond-order,closed -looptransferfunction.(1)ExpressingtheLa placetransferfunctionin Bodeanalysisformyieldsthefollowingequati on.(2)2 TransimpedanceConsiderationsforHigh-Spee dAmplifiersSBOA122 November2009 SubmitDocumentationFeedbackCopyright 2009,TexasInstrumentsIncorporatedZ = R ||FF1s CF =1 RCFF 1 CFs +Z =G1s CS 1 +ZZFGwp2AZ1P1F0 FCGain BandwidthProduct (GBP)Log Frequency (Hz)NoiseGainLog gain (dB)0dB20log (A )OLOp AmpOpen-Loop GainCCSF1 +((20logZ =112 R (C + C )pFSFHzP =112 R CpFFHzF =0 ZGBP1 F =CCCSF1 +((GBP1 + :(3)(4)Atdc,andif theopen-loopgainoftheamplifieris infinite,theamplifiergainis = 0 in Equation3 andpluggingtheresultintoEquation2 whilesettingA(s)=.))))

3 Is thedifferencebetweentheopen-loopgain(AOL ) plottedin Figure2 alongsidethesinglepole, ,thegainis indeedtheexpectedtransimpedancegainRF, whileathighfrequency,it is. Notethatonlythefeedbackcapacitor(CF) andthesourcecapacitance(CS) areusedforstability;consequently,it canbenotedthata unity-gainstableamplifieris ,it is recommendedtousea decompensatedamplifierinstead, easilyillustratedbytwofamiliesofdevices: theOPA842/3/6/7andtheOPA656/7. TheOPA842is stableforgainsgreaterthan3V/Vandhasa voltagenoiseof2nV/ stableforgainsgreaterthan7V/Vandhasa ,theOPA847hasa Hzandis stableforgainsgreaterthan12 ,theOPA656providesunity-gainstabilitywit ha 7nV/ Hzinputvoltagenoise;theOPA657hasa Hzvoltagenoise,butisstableforgainsgreate rthan7 functionof oandQ.

4 GiveninEquation5 withEquation6 andEquation7 expressing oandQ withphysicalelementsofthecircuit yieldsthefollowingresults:3 SBOA122 November2009 TransimpedanceConsiderationsforHigh-Spee dAmplifiersSubmitDocumentationFeedbackCo pyright 2009,TexasInstrumentsIncorporatedVIOD= RF AA + 1 OLOLwo2 woQs + s+wo22 wp= 2F =o0 (A + 1)wOLA R(C + C )FSF (A + 1)wOLA R(C + C )FSF Q =wA 1 + A+OL CC + CFSF1R (C + CFSF) ((Z =11R (C + CFSF) A2wpOLA GBP =1 + AOL AOLCC + CFSFCC + CFSF((F = ZGBP01 Q =FZ01C+ FF = ZGBP01 Q =PF10P =112 R CpF F (5)(6)(7)Setting, andrecognizingthatthegainbandwidthproduc t(GBP)is equaltoandusingthefollowingalgebraicsimp lifications: CS>> CFtosimplifyZ1 (AOL+ 1) A@AOL A= 2 GBP Leadstothefollowing:(8)(9)Furthersimplif icationonQ leadstotheseeasier-to-useequations:(10)w ith:(11)4 TransimpedanceConsiderationsforHigh-Spee dAmplifiersSBOA122 November2009 SubmitDocumentationFeedbackCopyright 2009,TexasInstrumentsIncorporatedGBP = 2FR Cp-3dBFS 2300250200150100500 Maximum AchievableFlat Frequency Response (MHz)125102050100200500 1000 Maximum Transimpedance gain (k ) ButterworthresponsewithQ = aninterestingpointbecausethisis alsoequivalenttosayingthatthe 3dBbandwidthis equaltoF0, andallowsustoderivea designequationthatprovesveryusefulforamp lifierselection.))))

5 (12)Notethatthe 3dBbandwidthandthetransimpedancegainared esiredparametersandthesourcecapacitancei s ,Equation12allowsyoutodothefollowing: Knowingthebandwidthrequiredbytheapplicat ion,thephotodiodecapacitance,andthetrans impedancegainspecification,calculatethem inimumGBPrequirementfortheamplifier Knowingtheamplifier,thetransimpedancegai n,andthephotodiodecapacitance,calculatet hemaximumachievablebandwidthWecanusethis lastpointtocalculatethemaximumachievable bandwidthfora a a 800 MHzGBPdevicewitha2nV/ OPA847,OPA846andOPA843 ,theOPA657is a ,theOPA657is a showsanexampleofachievablebandwidthversu stransimpedancegainfora (10pFSourceCapacitance)Therelativeperfor manceforeachamplifieris thisexampleconsiderstheamplifierparasiti c, forexample,forRF= 20k , f 3dB= 10 MHz ,usinga November2009 TransimpedanceConsiderationsforHigh-Spee dAmplifiersSubmitDocumentationFeedbackCo pyright 2009,TexasInstrumentsIncorporatedeNeORF4 kTRFVFBOp AmpIBNCSi=EQ++eRNF224kTRFiB+2(eN2 FC ) transimpedanceamplifiermakesthefollowing assumptions: Thisevaluationis anintegratednoiseanalysisthatusesspotnoi seoverfrequency,andis notintendedtobeusedasa spotnoiseequationfornarrowbandapplicatio ns.

6 Theapplicationis dc-coupled,pulse-orientedwheretheintegra tednoiseis ofinterest. Thefinalsignalbandwidthforboththetransim pedancedesignandanypost-filteringis greaterthan10timesthe1 Thetransimpedancebandwidthis setgreaterthanthepost-filtering. Thecurrentnoisetermonthenoninvertingis ,thenoisetermsofinterestareshownin providedinEquation13.(13)where: IB= invertinginputspotcurrentnoise 4kT= 16 10 21J at290degreesKelvin RF= feedbackresistor eN= noninvertinginputspotvoltagenoise CS= invertinginputtotalcapacitance F = noiseintegrationfrequencylimitAllthesepa rametersexceptthenoiseintegrationfrequen cylimitcanbefoundin (F)representstheequivalentbrick-wallfilt erofa theOPA846andtheOPA657 ,itis preferabletousebipolartechnologytoachiev elowernoise,whileabovethethresholdit is ,wewillconsiderthatthenoiseintegrationfr equencylimitis expressedin November2009 SubmitDocumentationFeedbackCopyright 2009,TexasInstrumentsIncorporatedi+B (BIP)2++(e2FC)3pN(BIP)S(BIP) 24kTRFeRN(BIP)F((2i+B (FET)2++(e2FC)3pN(FET)S(FET) 24kTRFeRN(FET)F((2=RF=eeN (FET)N (BIP)))))

7 -22+2F3p iiB (BIP)B (FET)-22 (CeCe)-S(BIP)(BIP)S(FET)(FET)NN 22+ (14)ThesolutionforRFis shownin Equation15.(15)Forexample,witha band-limitfilterbandwidthsetat10 MHzanda 10pFdiodecapacitance,allotherparametersa resetaccordingtoTable1 (takenfromtheOPA657andOPA846productdatas heets). (FET)= HzOPA657IB(FET)= HzCS(FET)= 10pF+ (BIP)= HzOPA846IB(BIP)= HzCS(BIP)= 10pF+ thatfora resistorlowerthan2k , thebipolaramplifieroffersa noiseadvantage;wecanthereforeconcludetha teventhoughthevoltagenoiseoftheOPA657is high ,thetotalinput-referrednoisegenerate dbytheOPA657 FETamplifierwillbelowerthanthatoftheOPA8 46bipolaramplifierforanytransimpedancega ingreaterthan2k . If a largerpost-amplifierfilterbandwidthis necessary,thebipolaramplifier(suchastheO PA846) (andfroma noiseperspective),FETinputamplifierssuch astheOPA657arebestforlargeorverylargetra nsimpedancegainwithlow-to-mediumbandwidt hbecauseofthepost-amplifierfilterlimitat ions, , themaximumachievablebandwidthversustrans impedancegain,it is ,firstconsiderthefollowingapplicationcir cuit(Figure5).

8 TransimpedanceGainwith200pFSourceCapacit anceCircuit7 SBOA122 November2009 TransimpedanceConsiderationsforHigh-Spee dAmplifiersSubmitDocumentationFeedbackCo pyright 2009,TexasInstrumentsIncorporated3002502 00150100500 Maximum AchievableFlat Frequency Response (MHz)125102050100200500 1000 Maximum Transimpedance gain (k ) ,usingEquation12, , ,theOPA657yieldsa 5pA/ Hzequivalentinputnoisecurrentif weassumethenoisepowerbandwidthlimitis ,whichis ,whichhasa muchlowervoltagenoisebutmuchhighercurren tnoise,actuallyyieldeda lowerequivalentinputnoisecurrentof3pA/ theOPA846notusedin thisapplication?6DC-ParametersConsiderat ionTheinputbiascurrentoftheOPA846,19 A,generatesanoutputoffsetvoltagewiththef eedbackresistorof310k operatingona 5 Vpowersupply, 310k , showsthemaximumachievablebandwidthasa functionofthetransimpedancegainfora ,suchastheOPA657,arecapableofhighertrans impedance, dcparameterfora transimpedanceapplications,thelimitin performanceisalwayslimitedbythetransimpe dancegain,thebandwidth, November2009 SubmitDocumentationFeedbackCopyright 2009,TexasInstrumentsIncorporatedIMPORTA NTNOTICET exasInstrumentsIncorporatedanditssubsidi aries(TI)

9 Reservetherighttomakecorrections,modific ations,enhancements,improvements, , , ,eitherexpressorimplied,isgrantedunderan yTIpatentright,copyright,maskworkright,o rotherTIintellectualpropertyrightrelatin gtoanycombination,machine, , ,conditions,limitations, (suchaslifesupport)whereafailureoftheTIp roductwouldreasonablybeexpectedtocausese verepersonalinjuryordeath, ,andacknowledgeandagreethattheyaresolely responsibleforalllegal,regulatoryandsafe ty-relatedrequirementsconcerningtheirpro ductsandanyuseofTIproductsinsuchsafety-c riticalapplications, , "enhancedplastic." 'srisk, ,iftheyuseanynon-designatedproductsinaut omotiveapplications, :TexasInstruments,PostOfficeBox655303,Da llas,Texas75265 Copyright 2009,TexasInstrumentsIncorporat