4 Analogtodigital converter 华科Word格式.docx

4 Analogtodigital converter 华科Word格式.docx

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Thevaluesareusuallystoredelectronicallyinbinaryform,sotheresolutionisusuallyexpressedinbits.thenumberofdiscretevaluesavailable,or"

levels"

isusuallyapoweroftwo.

Forexample,anADCwitharesolutionof8bitscanencodeananaloginputtoonein256differentlevels,since28=256.Thevaluescanrepresenttherangesfrom0to255（i.e.unsignedinteger）orfrom-128to127（i.e.signedinteger）,dependingontheapplication.

（分辨率也可以用电压单位伏特来表示）Resolutioncanalsobedefinedelectrically,andexpressedinvolts.ThevoltageresolutionofanADCisequaltoitsoverallvoltagemeasurementrangedividedbythenumberofdiscreteintervalsasintheformula:

Where:

Q：

resolutioninvoltsperstep（voltsperoutputcode）,

EFSR：

thefullscalevoltagerange=VRefHi−VRefLo,

M：

theADC'

sresolutioninbits,and

N：

thenumberofintervals,givenbythenumberofavailablelevels（outputcodes）,whichis:

N=2M

下面具3个例子：

Someexamplesmayhelp:

Example1

Fullscalemeasurementrange=0to10volts

ADCresolutionis12bits:

212=4096quantizationlevels（codes）

ADCvoltageresolutionis:

（10V-0V）/4096codes=10V/4096codes

0.00244volts/code

2.44mV/code

Example2

Fullscalemeasurementrange=-10to+10volts

ADCresolutionis14bits:

214=16384quantizationlevels（codes）

（10V-（-10V））/16384codes=20V/16384codes

0.00122volts/code

1.22mV/cod

Example3

Fullscalemeasurementrange=0to8volts

ADCresolutionis3bits:

23=8quantizationlevels（codes）

（8V−0V）/8codes=8V/8codes=1volts/code=1000mV/code

ThistypeofADCcanbemodeledmathematicallyas:

（实际系统中，AD分辨率由性噪比决定）

Inpractice,theusefulresolutionofaconverterislimitedbythebestsignal-to-noiseratiothatcanbeachievedforadigitizedsignal.AnADCcanresolveasignaltoonlyacertainnumberofbitsofresolution,calledthe"

effectivenumberofbits"

（ENOB）.Oneeffectivebitofresolutionchangesthesignal-to-noiseratioofthedigitizedsignalby6dB,

（如果分辨率被AD限制，那么前置运放的信噪比将起很大作用）iftheresolutionislimitedbytheADC.IfapreamplifierhasbeenusedpriortoA/Dconversion,thenoiseintroducedbytheamplifiercanbeanimportantcontributingfactortowardstheoverallSNR.

1.2Responsetype（线型非线性）

1.2.1LinearADCs

MostADCsareofatypeknownaslinear,

althoughanalog-to-digitalconversionisaninherentlynon-linearprocess（sincethemappingofacontinuousspacetoadiscretespaceisapiecewise-constantandthereforenon-linearoperation）.Thetermlinearasusedheremeansthattherangeoftheinputvaluesthatmaptoeachoutputvaluehasalinearrelationshipwiththeoutputvalue.

1.2.2Non-linearADCs

Iftheprobabilitydensityfunctionofasignalbeingdigitizedisuniform,thenthesignal-to-noiseratiorelativetothequantizationnoiseisthebestpossible.

Becausethisisoftennotthecase,it'

susualtopassthesignalthroughitscumulativedistributionfunction（CDF）beforethequantization.Thisisgoodbecausetheregionsthataremoreimportantgetquantizedwithabetterresolution.Inthedequantizationprocess,theinverseCDFisneeded.

Thisisthesameprinciplebehindthecompandersusedinsometape-recordersandothercommunicationsystems,andisrelatedtoentropymaximization.（Neverconfusecompanderswithcompressors!

）

Forexample,avoicesignalhasaLaplaciandistribution.Thismeansthattheregionaroundthelowestlevels,near0,carriesmoreinformationthantheregionswithhigheramplitudes.Becauseofthis,logarithmicADCsareverycommoninvoicecommunicationsystemstoincreasethedynamicrangeoftherepresentablevalueswhileretainingfine-granularfidelityinthelow-amplituderegion.

Aneight-bita-lawortheμ-lawlogarithmicADCcoversthewidedynamicrangeandhasahighresolutioninthecriticallow-amplituderegion,thatwouldotherwiserequirea12-bitlinearADC.

1.3Samplingrate（如何确定采样频率）

Theanalogsignaliscontinuousintimeanditisnecessarytoconvertthistoaflowofdigitalvalues.Itisthereforerequiredtodefinetherateatwhichnewdigitalvaluesaresampledfromtheanalogsignal.Therateofnewvaluesiscalledthesamplingrateorsamplingfrequencyoftheconverter.

Acontinuouslyvaryingbandlimitedsignalcanbesampled（thatis,thesignalvaluesatintervalsoftimeT,thesamplingtime,aremeasuredandstored）andthentheoriginalsignalcanbeexactlyreproducedfromthediscrete-timevaluesbyaninterpolationformula.

Theaccuracyislimitedbyquantizationerror.

However,thisfaithfulreproductionisonlypossibleifthesamplingrateishigherthantwicethehighestfrequencyofthesignal.ThisisessentiallywhatisembodiedintheShannon-Nyquistsamplingtheorem.（奈奎斯特采样定理）

SinceapracticalADCcannotmakeaninstantaneousconversion,theinputvaluemustnecessarilybeheldconstantduringthetimethattheconverterperformsaconversion（calledtheconversiontime）.Aninputcircuitcalledasampleandholdperformsthistask—inmostcasesbyusingacapacitortostoretheanalogvoltageattheinput,andusinganelectronicswitchorgatetodisconnectthecapacitorfromtheinput.ManyADCintegratedcircuitsincludethesampleandholdsubsysteminternally.（采样保持电路）

1.3.1Aliasing

Forexample,a2 

kHzsinewavebeingsampledat1.5 

kHzwouldbereconstructedasa500 

Hzsinewave.Thisproblemiscalledaliasing.

Matlab演示：

second_nyqst.mdl。

Toavoidaliasing,theinputtoanADCmustbelow-passfilteredtoremovefrequenciesabovehalfthesamplingrate.Thisfilteriscalledananti-aliasingfilter,andisessentialforapracticalADCsystemthatisappliedtoanalogsignalswithhigherfrequencycontent.

（可以用作下变频或带通采样）Althoughaliasinginmostsystemsisunwanted,itshouldalsobenotedthatitcanbeexploitedtoprovidesimultaneousdown-mixingofaband-limitedhighfrequencysignal。

1.3.2IF/RF（bandpass）sampling

（信号有正频率，和负频率，采样是按照采样频率将它们在频谱上进行搬移）RealsignalshaveFourierspectrawithsymmetryaboutzero.Thatis,theyhaveanegative-frequencyspectrumthatisamirrorimageofthepositive-frequencyspectrum.Samplingeffectivelyshiftsbothsidesofthespectrumbymultiplesofthesamplingfrequency.Thecriteriontoavoidaliasingisthatnoneoftheseshiftedcopiesofthespectrumoverlap.

画图解释采样是将被采样信号进行频谱周期搬移。

Inthecaseofabandpass（non-baseband）signal,

withlowandhighbandlimitsfLandfHrespectively,theconditionforanacceptablesamplerateisthatshiftsofthebandsfromfLtofHandfrom–fHto–fLmustnotoverlapwhenshiftedbyallintegermultiplesofsamplingratefs.Thisconditionreducestotheconstraint:

forsomensatisfying:

Thehighestnforwhichtheconditionissatisfiedleadstothelowestpossiblesamplingrates.（n最大的时候采样率最低）

Importantsignalsofthissortincludearadio'

sintermediate-frequency（IF）orradio-frequency（RF）signal.（中频或射频采用这个）

Ifn>

1,thentheconditionsresultinwhatissometimesreferredtoasundersampling,bandpasssampling,orusingasamplingratelessthantheNyquistrate2fHobtainedfromtheupperboundofthespectrum.（n>

1的时候，就不满足普通的奈奎斯特频率要求了）

Alternatively,forthecaseofagivensamplingfrequency,simplerformulaefortheconstraintsonthesignal'

sspectralbandaregivenbelow.（举个容易理解的例子）

Example:

ConsiderFMradiotoillustratetheideaofundersampling.

IntheUS,FMradiooperatesonthefrequencybandfromfL=88MHztofH=108MHz.Thebandwidthisgivenby

Thesamplingconditionsaresatisfiedfor

Therefore,ncanbe1,2,3,4,or5.

Thevaluen=5givesthelowestsamplingfrequenciesinterval

andthisisascenarioofundersampling.

Inthiscase,thesignalspectrumfitsbetweenand2and2.5timesthesamplingrate（higherthan86.4–88MHzbutlowerthan108–110MHz）.（被采样信号，卡在2到2.5倍采样频率之间）

Alowervalueofnwillalsoleadtoausefulsamplingrate.Forexample,usingn=4,theFMbandspectrumfitseasilybetween1.5and2.0timesthesamplingrate,forasamplingratenear56MHz（multiplesoftheNyquistfrequencybeing28,56,84,112,etc.）.

Whenundersamplingareal-worldsignal,thesamplingcircuitmustbefastenoughtocapturethehighestsignalfrequencyofinterest.（信号采集频率应该快到采集最高频的信号）

Theoretically,eachsampleshouldbetakenduringaninfinitesimallyshortinterval,butthisisnotpracticallyfeasible.（每次采集时间应该无限短，不过不实际）

Instead,thesamplingofthesignalshouldbemadeinashortenoughintervalthatitcanrepresenttheinstantaneousvalueofthesignalwiththehighestfrequency.（实际上，足够短就行，不需要无限短）

ThismeansthatintheFMradioexampleabove,thesamplingcircuitmustbeabletocaptureasignalwithafrequencyof108MHz,not43.2MHz.Thus,thesamplingfrequencymaybeonlyalittlebitgreaterthan43.2MHz,buttheinputbandwidthofthesystemmustbeatleast108MHz.Similarly,theaccuracyofthesamplingtiming,orapertur