Digitalsignalprocessing

Digitalsignalprocessing(DSP)isconcernedwiththerepresentationof

\o"Signal(electronics)"

signals

byasequenceofnumbersorsymbolsandtheprocessingofthesesignals.Digitalsignalprocessingand

\o"Analogsignalprocessing"

analogsignalprocessing

aresubfieldsof

\o"Signalprocessing"

signalprocessing

.DSPincludessubfieldslike:

\o"Audiosignalprocessing"

audio

and

\o"Speechsignalprocessing"

speechsignalprocessing

,sonarandradarsignalprocessing,sensorarrayprocessing,spectralestimation,statisticalsignalprocessing,

\o"Digitalimageprocessing"

digitalimageprocessing

,signalprocessingforcommunications,controlofsystems,biomedicalsignalprocessing,seismicdataprocessing,etc.

ThegoalofDSPisusuallytomeasure,filterand/orcompresscontinuousreal-worldanalogsignals.Thefirststepisusuallytoconvertthesignalfromananalogtoadigitalform,bysamplingitusingan

\o"Analog-to-digitalconverter"

analog-to-digitalconverter

(ADC),whichturnstheanalogsignalintoastreamofnumbers.However,often,therequiredoutputsignalisanotheranalogoutputsignal,whichrequiresa

\o"Digital-to-analogconverter"

digital-to-analogconverter

(DAC).Evenifthisprocessismorecomplexthananalogprocessingandhasa

\o"Discretesignal"

discretevaluerange

,theapplicationofcomputationalpowertodigitalsignalprocessingallowsformanyadvantagesoveranalogprocessinginmanyapplications,suchas

\o"Errordetection"

errordetectionandcorrection

intransmissionaswellas

\o"Datacompression"

datacompression

.

DSP

\o"Algorithm"

algorithms

havelongbeenrunonstandardcomputers,onspecializedprocessorscalled

\o"Digitalsignalprocessor"

digitalsignalprocessors

(DSPs),oronpurpose-builthardwaresuchas

\o"Application-specificintegratedcircuit"

application-specificintegratedcircuit

(ASICs).Todaythereareadditionaltechnologiesusedfordigitalsignalprocessingincludingmorepowerfulgeneralpurpose

\o"Microprocessor"

microprocessors

,

\o"Field-programmablegatearray"

field-programmablegatearrays

(FPGAs),

\o"DigitalSignalController"

digitalsignalcontrollers

(mostlyforindustrialappssuchasmotorcontrol),and

\o"Streamprocessing"

streamprocessors

,amongothers.

OperationalAmplifierCircuits

Wehavebuiltvoltageandcurrentamplifiersusingtransistors.Circuitsofthiskindwithniceproperties(highgainandhighinputimpedance,forexample),packagedasintegratedcircuits(ICs),arecalledoperationalamplifiersoropamps.Theyarecalled``operational''amplifiers,becausetheycanbeusedtoperformarithmeticoperations(addition,subtraction,multiplication)withsignals.Infact,opampscanalsobeusedtointegrate(calculatetheareasunder)anddifferentiate(calculatetheslopesof)signals.

Figure1:Acircuitmodelofanoperationalamplifier(opamp)withgainandinputandoutputresistancesand.

AcircuitmodelofanoperationalamplifierisshowninFigure

1

.Theoutputvoltageoftheopampislinearlyproportionaltothevoltagedifferencebetweentheinputterminalsbyafactorofthegain.However,theoutputvoltageislimitedtotherange,whereisthesupplyvoltagespecifiedbythedesigneroftheopamp.Therangeisoftencalledthelinearregionoftheamplifier,andwhentheoutputswingstoor,theopampissaidtobesaturated.TheoutputrangesoftheamplifierswebuiltaspartofLab

3

weresimilarlylimitedbythesupplyvoltage.

Anidealopamphasinfinitegain(),infiniteinputresistance(),andzerooutputresistance().Youshouldusethesetwoassumptionstoanalyzetheopampcircuitscoveredintheassignmentsbelow.Aconsequenceoftheassumptionofinfinitegainisthat,iftheoutputvoltageiswithinthefinitelinearregion,wemusthave.Arealopamphasagainontherange-(dependingonthetype),andhenceactuallymaintainsaverysmalldifferenceininputterminalvoltageswhenoperatinginitslinearregion.Formostapplications,wecangetawaywithassuming.

Figure2:(a)Schematicsymbolforanopamp.

(b)ConnectiondiagramfortheLM741andLF4118pindualinlinepackages(DIPs).

Wewillnotmakeuseofthenull(LM741)/balance(LF411)pins.PinslabeledNCarenotconnectedtotheintegratedcircuit.

Wewillusetwooperationalamplifiersinourlaboratoryexercises,theLM741,ageneralpurposebipolarjunctiontransistor(BJT)basedamplifierwithatypicalinputresistanceof2

M,andtheLF411,withfieldeffecttransistors(FETs)attheinputsgivingamuchlargerinputresistance().DetaileddatasheetsforthesedevicesareavailablefordowloadattheNationalSemicondictorwebsite(Ofthetwo,theLF411comesclosesttosatisfyingourtwoassumptionsassociatedwithidealopampbehavior.ItcostsmorethantheLM741(awhopping$0.61vs.$0.23asofspring2001).Theschematicsymbolforanopampandtheconnectiondiagramforthechips,calleddualinlinepackages(DIPs),wewillbeusingareshowninFigure

2.

InvertingAmplifier

Figure24:Invertingamplifiercircuit

AninvertingamplifiercircuitisshowninFigure

24

.

Showthatthegainoftheamplifieris

NoninvertingAmplifier

Figure25:Noninvertingamplifiercircuit.

AnoninvertingamplifiercircuitisshowninFigure

25

.

Showthatthegainof