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Event-Based Compression Circuits for Neural Recording

Permanent Link: http://ufdc.ufl.edu/UFE0042492/00001

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Title: Event-Based Compression Circuits for Neural Recording
Physical Description: 1 online resource (153 p.)
Language: english
Creator: XU,JIE
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2011

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Subjects / Keywords: Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Wireless neural recording devices are necessary for Brain Machine Interfaces (BMIs) because implantable devices reduce the risk of infection and provide subjects unrestrained movability. An implanted neural recording system must satisfy stringent constraints of low power, low noise, compact size, limited bandwidth and robustness. This dissertation developed low-noise, low-power, low-bandwidth neural recording systems and investigated the event-based compression methods suitable for implantable neural recording systems. A low-power low-noise variable-gain variable-bandwidth amplifier is presented to boost weak neural signals to the voltage level that can be processed by data encoders. A novel current-mode circuit design approach to implement the event-based asynchronous Integrate-and-Fire (IF) encoder is proposed to decrease power consumption and design complexity. This research shows that the IF encoder in current-mode implementation for data conversion is a promising alternative to conventional voltage-based and synchronous analog-to-digital converter (ADC) based approaches. The IF has proven to reduce the data rate in neural recording applications, but is sensitive to DC offset and motion artifacts. This research proposes another novel event-based asynchronous time-derivative (TD) encoder to overcome the offset and artifact issues. The TD encoder concentrates its output events in the regions of high change while the IF encoder generates output events in the regions of high magnitude. The reconstruction algorithm can perfectly recover the input signal if certain Nyquist constraints are met. The CMOS implementation is presented and measurement results show that the TD encoder is suitable for implantable neural recording applications.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by JIE XU.
Thesis: Thesis (Ph.D.)--University of Florida, 2011.
Local: Adviser: Harris, John G.

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Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2011
System ID: UFE0042492:00001

Permanent Link: http://ufdc.ufl.edu/UFE0042492/00001

Material Information

Title: Event-Based Compression Circuits for Neural Recording
Physical Description: 1 online resource (153 p.)
Language: english
Creator: XU,JIE
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2011

Subjects

Subjects / Keywords: Electrical and Computer Engineering -- Dissertations, Academic -- UF
Genre: Electrical and Computer Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract: Wireless neural recording devices are necessary for Brain Machine Interfaces (BMIs) because implantable devices reduce the risk of infection and provide subjects unrestrained movability. An implanted neural recording system must satisfy stringent constraints of low power, low noise, compact size, limited bandwidth and robustness. This dissertation developed low-noise, low-power, low-bandwidth neural recording systems and investigated the event-based compression methods suitable for implantable neural recording systems. A low-power low-noise variable-gain variable-bandwidth amplifier is presented to boost weak neural signals to the voltage level that can be processed by data encoders. A novel current-mode circuit design approach to implement the event-based asynchronous Integrate-and-Fire (IF) encoder is proposed to decrease power consumption and design complexity. This research shows that the IF encoder in current-mode implementation for data conversion is a promising alternative to conventional voltage-based and synchronous analog-to-digital converter (ADC) based approaches. The IF has proven to reduce the data rate in neural recording applications, but is sensitive to DC offset and motion artifacts. This research proposes another novel event-based asynchronous time-derivative (TD) encoder to overcome the offset and artifact issues. The TD encoder concentrates its output events in the regions of high change while the IF encoder generates output events in the regions of high magnitude. The reconstruction algorithm can perfectly recover the input signal if certain Nyquist constraints are met. The CMOS implementation is presented and measurement results show that the TD encoder is suitable for implantable neural recording applications.
General Note: In the series University of Florida Digital Collections.
General Note: Includes vita.
Bibliography: Includes bibliographical references.
Source of Description: Description based on online resource; title from PDF title page.
Source of Description: This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility: by JIE XU.
Thesis: Thesis (Ph.D.)--University of Florida, 2011.
Local: Adviser: Harris, John G.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2011
System ID: UFE0042492:00001


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EVENT-BASEDCOMPRESSIONCIRCUITSFORNEURALRECORDINGByJIEXUADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHYUNIVERSITYOFFLORIDA2011

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c2011JieXu 2

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ACKNOWLEDGMENTS IwouldliketothankthepeoplewhohavehelpedmeinvariouswaysduringmytimeattheUniversityofFlorida.Iamfortunatetobewithsuchanintellectualgroup.Firstandforemost,IwanttoextendmysincerestgratitudetoDr.Harris,fortheopportunitytoworkonthewirelessimplantablerecordingelectrodeprojectthroughoutmygraduatestudies.Noneoftheseworkscouldbepossiblewithouthissupportiveadvice,guidanceandpatience.SinceIjoinedthelab,IhavebeenencouragedbyDr.Harristothink,analyzeandsolveproblemsfrombothdeeperandbroaderperspectives.Dr.Harrishasbeenbothaveryhelpfuladvisorandagoodfriendofmine.Iamalsogratefultohimforgivingmetheopportunitytoworkonaninternshipwhiledoingmydissertationresearch.Iwouldliketoacknowledgetheinspirationalinstructionandguidanceofmycommitteemembers,Dr.JosePrincipe,Dr.RobertFox,Dr.MingzhouDing,andtheformercommitteememberDr.JustinSanchez.Theirhelpfulinsights,commentsandsuggestionssignicantlyshapedmyresearchwork.MyformerCNELlabmates,YuanLi,ChristySheandDuChendeservemythanksfortheirpatienceandhelpwhenIwasnewtoneuralrecordingdesign.IamalsothankfultomycurrentCNELlabmates,especiallyManuRastogi,VaibhavGarg,SteveYenandRaviShekharforcontributingtoalloftheresearchdiscussionsinthelab.Manyideaswereinspiredfromourdiscussions.IthankAlexanderSingh-Alvaradoforhishelpinsignalprocessing.Furthermore,Iwouldliketothanktherestofmylabmatesforcreatingadelightfulandfriendlyatmospherewhichmademyworkpossible.Finally,Iwouldliketothankmyparentsfortheirencouragementandconsistentsupport.AspecialthankstomybelovedhusbandNianweiLin,whomImetandmarriedinthissmallmagicaltownofGainesville.Hefulllsmylifeandmakeseverythingmeaningfultome. 3

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 3 LISTOFTABLES ...................................... 7 LISTOFFIGURES ..................................... 8 ABSTRACT ......................................... 12 CHAPTER 1INTRODUCTION ................................... 14 1.1Signicance ................................... 14 1.2TheNatureofNeuralSignals ......................... 14 1.3ImplantedNeuralRecordingSystemOverviewandConstraints ...... 16 1.4ResearchGoalandDissertationStructure .................. 19 2LOW-NOISENEURALSIGNALAMPLIFIERDESIGN .............. 21 2.1Introduction ................................... 21 2.2AmplierCircuitDesign ............................ 22 2.2.1First-StageAmplier .......................... 22 2.2.1.1Circuitdesignandfrequencyresponse .......... 22 2.2.1.2Noiseperformance ..................... 24 2.2.2Second-StageAmplier ........................ 28 2.2.2.1Circuitdesign ......................... 28 2.2.2.2Frequencyresponse ..................... 29 2.2.2.3Noiseperformance ..................... 31 2.3MeasurementResults ............................. 33 2.3.1Bench-TopTestResults ........................ 33 2.3.2InVivoTestResults .......................... 38 2.4Summary .................................... 39 3CURRENT-MODECIRCUITIMPLEMENTATIONOFINTEGRATE-AND-FIREENCODING ...................................... 40 3.1Introduction ................................... 40 3.1.1Integrate-and-FireEncodingOverview ................ 41 3.1.2Voltage-ModeImplementationoftheIFEncoder .......... 43 3.2Electrolyte-ElectrodeInterfaceElectricalModel ............... 45 3.3Current-ModeImplementationoftheIFEncoder .............. 46 3.3.1CurrentConveyorOverview ...................... 49 3.3.2BidirectionalCurrentConveyorIFCircuit ............... 52 3.3.2.1Class-ABbidirectionalcurrentconveyor .......... 52 3.3.2.2Class-ABcurrentconveyorIFcircuit ............ 54 4

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3.3.3CurrentAmplierandFeedbackLoop ................ 56 3.3.3.1Currentamplier ....................... 57 3.3.3.2Low-passlterfeedbackloop ................ 58 3.3.3.3Frequencyresponse ..................... 61 3.3.4Current-ModeImplementationoftheIFwithAmplication ..... 66 3.3.4.1Current-modeIFcircuit ................... 66 3.3.4.2Noiseperformance ..................... 69 3.3.4.3Circuitsimulation ....................... 73 3.3.4.4Chipmeasurement ..................... 74 3.4ComparisonofCurrent-ModeandVoltage-ModeIFImplementation .... 76 3.5Summary .................................... 77 4THETIME-DERIVATIVEENCODINGANDITSCIRCUITIMPLEMENTATION 79 4.1Introduction ................................... 79 4.2TheTime-DerivativeEncodingModel .................... 80 4.3ReconstructionAlgorithm ........................... 82 4.4CircuitImplementationoftheTime-DerivativeConverter .......... 84 4.4.1Time-DerivativeConverterCircuit ................... 84 4.4.2LinearTransconductor ......................... 86 4.5NonidealEffects ................................ 90 4.5.1FiniteTimeConstantRCLeakyEffect ................ 90 4.5.1.1First-orderRCleakyequation ................ 91 4.5.1.2Leakytime-derivativeencoding ............... 92 4.5.1.3SERdegradationduetoleakyeffect ............ 94 4.5.1.4Leakytime-derivativereconstruction ............ 95 4.5.2OffsetVoltages ............................. 97 4.5.2.1SERdegradationduetooffset ............... 97 4.5.2.2Offsetcorrectioninreconstruction ............. 100 4.5.3SignalDependentThresholdVariationoftheComparator ..... 100 4.5.4MOSFETSwitches ........................... 100 4.5.5TimingJitteroftheTimeQuantizer .................. 101 4.6MatlabSimulationResults ........................... 102 4.6.1SimulationwithSyntheticSignalasInputSignal ........... 102 4.6.2ComparisonBetweentheTDandtheIFConverters ........ 107 4.6.3SimulationwithNeuralActionPotentialSignalasInputSignal ... 109 4.6.4ComparisonoftheTDandIFConvertersonEncodingNeuralSignals 111 4.6.5ComparisonoftheTDConverterwithSynchronousADCs ..... 113 4.7CircuitSimulationResults ........................... 114 4.7.1SimulationoftheLinearTransconductor ............... 114 4.7.2SimulationoftheTDConverterCircuit ................ 116 4.8Bench-TopMeasurementResults ....................... 118 4.8.1MeasurementwithNon-NeuralSignalsasInputSignals ...... 118 4.8.2MeasurementwithNeuralSimulatorSignalasInputSignal ..... 121 4.9Summary .................................... 123 5

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5NEURALSIGNALENCODINGMETHODS .................... 124 5.1Introduction ................................... 124 5.2NeuralSignalEncodingwithSynchronousADC ............... 124 5.3NeuralSignalEncodingwithAsynchronousADC .............. 125 5.3.1AsynchronousLevel-CrossingEncoding ............... 126 5.3.2AsynchronousDeltaSigmaEncoding ................. 128 5.3.3AsynchronousDeltaEncoding ..................... 131 5.3.4TheIntegrate-and-FireEncoding ................... 133 5.3.5TheTime-DerivativeEncoding .................... 135 5.4NeuralSignalEncodingwithNon-LinearTransformation .......... 137 5.5Summary .................................... 142 6CONCLUSION .................................... 144 REFERENCES ....................................... 147 BIOGRAPHICALSKETCH ................................ 153 6

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LISTOFTABLES Table page 1-1Existingneuralrecordingsystemsoverview .................... 18 2-1Capacitorvaluesusedintheamplierdesign ................... 33 2-2Measuredcharacteristicsoftheamplier ..................... 38 3-1ThesimulatedperformancesoftheIFcircuitsinvoltageandcurrentmodes .. 77 3-2Theperformancesoftheamplierinvoltageandcurrentmodes ........ 78 4-1PerformancecomparisonoftheTDconverterandthesynchronousADCs ... 113 4-2SimulatedcharacteristicsofGm .......................... 114 4-3GmtransconductancevariationandTHD ..................... 115 4-4PowerconsumptionoftheTDconverter ...................... 117 7

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LISTOFFIGURES Figure page 1-1Neuralsignalcharacteristics ............................ 15 1-2Blockdiagramofanimplantedneuralrecordingsystem ............. 17 2-1Schematicoftherst-stageamplier ........................ 22 2-2SchematicoftheOTAintherst-stageamplier ................. 26 2-3Schematicofthesecondstageamplier ...................... 29 2-4SchematicoftheOPA ................................ 31 2-5Measuredfrequencyresponseoftherst-stageamplier ............ 34 2-6Measuredinput-referrednoisevoltagespectrumoftherst-stageamplier .. 34 2-7Measuredfrequencyresponseofthetwo-stageamplierwithvaryinggaincontrolbitsg<2:0> ................................ 35 2-8Measuredfrequencyresponseofthetwo-stageamplierwithvaryingR1 .... 35 2-9Neuralsimulatorsignalmeasurements ....................... 37 2-10Measuredinput-referrednoiseofthetwo-stageamplier ............. 38 2-11Invivomeasurementresultfromtherat ...................... 39 3-1BiphasicIFencodermodel ............................. 41 3-2Integrated-circuitvoltage-modeimplementationoftheIFconverter ....... 43 3-3ThedriftissueoftheIFencoderobservedinbench-topmeasurements .... 44 3-4Equivalentcircuitoftheelectrode-electrolyteinterface .............. 45 3-5Electrode-IFcircuitdiagram ............................. 47 3-6Currentconveyorcircuitwithvoltagesourceinput ................. 48 3-7Blackboxrepresentationofthecurrentconveyor ................. 49 3-8Negativesecond-generationcurrentconveyor ................... 50 3-9BidirectionalpositivecurrentconveyorCCII+ ................... 51 3-10SimulationofinputandoutputcurrentofbidirectionalCCII+ ........... 51 3-11Class-ABbidirectionalcurrentconveyor ...................... 53 3-12ThansfercharacteristicoftheClassABbi-directionalcurrentconveyor ..... 53 8

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3-13SchematicoftheClass-ABcurrentconveyorIFcircuit .............. 54 3-14CadencesimulationoftheClass-ABcurrentconveyorIFcircuit ......... 55 3-15ReconstructionresultoftheClass-ABcurrentconveyorIFcircuit ........ 56 3-16Currentconveyoramplier .............................. 57 3-17Continuous-timeresetbiasnetwork ........................ 58 3-18Currentconveyoramplierswithbiasnetwork ................... 61 3-19Frequencyresponse ................................. 65 3-20Currentconveyorintegrate-and-recircuitimplementation ............ 66 3-21Two-stageoperationalamplier ........................... 67 3-22Simulatedfrequencyresponseofcurrentamplier ................ 73 3-23Measurementresultsfromthecurrent-modeIFchip ............... 75 3-24Reconstructedsignalandoriginalsignals ..................... 75 4-1TheTime-Derivativeencodingmodel ........................ 80 4-2IllustrativeexampleofthespiketimesoftheIFandtheTDneurons ....... 81 4-3Circuitimplementationoftime-derivativeconverter ................ 84 4-4LinearGmschematic ................................ 86 4-5TheideaofthelinearGmdesign .......................... 87 4-6First-orderRCsystem ................................ 91 4-7Small-signalequivalentcircuitoftheTDconverterduringtheintegrationphase 93 4-8SERdependencyonresistanceR ......................... 96 4-9SERdependencyontheinputoffsetvoltageoftheGM ............. 99 4-10SERdependencyontheoffsetvoltageofthecomparators ............ 99 4-11SERvsClockperiod ................................. 102 4-12OneexampleoftestedsyntheticsignalanditsmagnitudeofFFT ....... 103 4-13TransientsimulationoftheTDencoder ....................... 103 4-14SimulationoftheTDencodingsyntheticsignalandreconstructionresults ... 104 4-15SERvsPulserate .................................. 105 9

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4-16Refractoryperiodeffect ............................... 106 4-17SimulationresultsoftheTDandtheIFencoding100randomsyntheticsignals 107 4-18InputsignalwithDCvariation ............................ 108 4-19ResultsoftheTDandtheIFencodingthesignalwithDCvariation ....... 108 4-20ReconstructionresultoftherecordedextracellularneuralsignalduringthesurgeryencodedbytheTDconverter ....................... 110 4-21ReconstructionresultoftherecordedextracellularneuralsignalafterthesurgeryencodedbytheTDconverter ............................ 110 4-22ReconstructionresultoftherecordedextracellularneuralsignalduringthesurgeryencodedbytheIFconverter ........................ 112 4-23ReconstructionresultoftherecordedextracellularneuralsignalafterthesurgeryencodedbytheIFconverter ............................. 112 4-24ComparisonoftheTDandIFconverteraccuracyperformanceonneuralspikes 113 4-25TransconductanceofGmincadencesimulation .................. 115 4-26ACresponseofGm ................................. 115 4-27CadencesimulationsoftheTDconvertercircuit .................. 116 4-28ReconstructionresultfromtheTDconverterpulseoutputincadencesimulation 117 4-29Bench-toptestoftheTDconverterchip ...................... 118 4-32ReconstructionresultfromtheTDconverterchipoutputinbench-toptest ... 120 4-33TheTDconverterbench-topmeasurementwiththeneuralsimulatorsignalasinput .......................................... 122 5-1Generalarchitectureofasynchronousanalog-to-digitalconverter ........ 125 5-2Waveformsoftheasynchronouslevel-crossingconverter ............ 127 5-3ArchitectureoftheasynchronousM-bitlevel-crossingconverter ......... 127 5-4Architectureofthe1storder1-bitasynchronousdelta-sigmaconverter ..... 129 5-5Architectureofthe2ndorderM-bitasynchronousdelta-sigmaconverter .... 130 5-6Waveformsofthe1storder1-bitasynchronousdelta-sigmaconverter ..... 131 5-7Architectureoftheasynchronousdeltaconverter ................. 132 5-8Waveformsoftheasynchronousdeltaconverter ................. 132 10

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5-9Architectureoftheintegrate-and-reconverter .................. 134 5-10Waveformsoftheintegrate-and-reconverter ................... 134 5-11Architectureofthetime-derivativeconverter .................... 135 5-12Waveformsofthetime-derivativeconverter .................... 136 5-13Nonlineartransferfunctions ............................. 137 5-14Signalcompressioncoefcientoflogarithmoperation .............. 139 5-15TheIFconversionwithnonlinearoperation .................... 140 5-16ReconstructionresultsoftheIFconversionwithnonlinearoperation ...... 141 5-17AccuracyversuspulserateperformanceoftheIFconverterwithlogarithmicnonlineartransformation ............................... 142 11

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AbstractofDissertationPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofDoctorofPhilosophyEVENT-BASEDCOMPRESSIONCIRCUITSFORNEURALRECORDINGByJieXuMay2011Chair:JohnG.HarrisMajor:ElectricalandComputerEngineering WirelessneuralrecordingdevicesarenecessaryforBrainMachineInterfaces(BMIs)becauseimplantabledevicesreducetheriskofinfectionandprovidesubjectsunrestrainedmovability.Animplantedneuralrecordingsystemmustsatisfystringentconstraintsoflowpower,lownoise,compactsize,limitedbandwidthandrobustness.Thisdissertationdevelopedlow-noise,low-power,low-bandwidthneuralrecordingsystemsandinvestigatedtheevent-basedcompressionmethodssuitableforimplantableneuralrecordingsystems.Alow-powerlow-noisevariable-gainvariable-bandwidthamplierispresentedtoboostweakneuralsignalstothevoltagelevelthatcanbeprocessedbydataencoders.Anovelcurrent-modecircuitdesignapproachtoimplementtheevent-basedasynchronousIntegrate-and-Fire(IF)encoderisproposedtodecreasepowerconsumptionanddesigncomplexity.ThisresearchshowsthattheIFencoderincurrent-modeimplementationfordataconversionisapromisingalternativetoconventionalvoltage-basedandsynchronousanalog-to-digitalconverter(ADC)basedapproaches. TheIFhasproventoreducethedatarateinneuralrecordingapplications,butissensitivetoDCoffsetandmotionartifacts.Thisresearchproposesanothernovelevent-basedasynchronoustime-derivative(TD)encodertoovercometheoffsetandartifactissues.TheTDencoderconcentratesitsoutputeventsintheregionsofhighchangewhiletheIFencodergeneratesoutputeventsintheregionsofhighmagnitude. 12

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ThereconstructionalgorithmcanperfectlyrecovertheinputsignalifcertainNyquistconstraintsaremet.TheCMOSimplementationispresentedandmeasurementresultsshowthattheTDencoderissuitableforimplantableneuralrecordingapplications. 13

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CHAPTER1INTRODUCTION 1.1Signicance Thehumanbrainisanextremelycomplicatedsystemthatcontainsabout1011neuronsandeachneuronconnectswithapproximately103otherneurons[ 1 ].Inspiteofrecenttechnologicaladvances,biologicalsystems,includingthehumanbrain,surpassinanimatemachinesintermsofperceptionandcognitiveabilities.SinceFetzrstdemonstratedthecorrelationbetweenneuronactivityandtheassociatedsubjectbehavior[ 2 ],manyexperimentaltechniquesandanalyticaltoolshavebeendevelopedtoextractinformationfromthebrain.Furthermore,theextractedinformationtranslatedintoreal-timecommandsforcontrollingsoftwareormechanicalinterfaces[ 3 ],contributingtothegrowingeldofbrainmachineinterfaces(BMIs).TheultimategoalofBMIresearchistoimprovethelivesofpatientssufferingfromamputationorparalysis. Todiscovertheunderlyingmechanismsofneuralinformationprocessing,afundamentalstepistoobservethesimultaneousactivitiesofmultipleneuronsinthebrain.Thepatternoftheseactivitiesenableneuroscientiststoobtainvaluableinformationinordertointerpretintentionalstatesofthebrain.Neuralrecording,therefore,hasbeenanactiveareaofresearchintheeldsofneuroscienceandengineeringsincetheearlytwentiethcentury.Althoughthereareseveralcommercialmulti-electrodearraysavailable,theyareusuallyconnectedtoexternalinstrumentsbytranscutaneousconnectorsandwirebundles,whichlimittheactivityofthesubjectsandincreasetheriskofinfection.Toavoidthesedisadvantages,afullyimplantedmulti-channelneuralrecordingsystemwithwirelesstransmissionishighlypreferred. 1.2TheNatureofNeuralSignals Ingeneral,neuralsignalscanbesplitintotwocategoriesbasedontheirrecordinglocations:theneareldsignalsandthefareldsignals.TheElectrocorticogram(EcoG)andelectroencephalogram(EEG)aretwoexamplesoffareldsignals.Forimplanted 14

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Figure1-1. Neuralsignalcharacteristics neuralrecordingsystems,theneuralsignalsrepresenttheneareldsignalsthatareprobedinsideoraroundneurons.Theintracellularactionpotentialismeasuredbypenetratingasharpmicroelectrodetipintoasingleneuron.Themeasuredsignalmightbeaslargeas100mV,relativetotheextracellularuid.Atypicalneuronproduces10to150spikespersecond,andthedurationofeachspikeisabout1v2ms[ 4 ].Theextracellularactionpotentialmeasuredbyamulti-electrodearrayneartheneuronsispreferredtotheintracellularactionpotentialinchronicrecordings.Dependingonthesizeofthemicroelectrodetipandthelocationbetweentheneuronsandthemicroelectrodes,theamplitudeandtheshapeoftheextracellularactionpotentialseenbytheelectrodesareanattenuatedandlteredversionoftheintracellularactionpotentials.Figure 1-1 depictsatypicalextracellularneuralsignal.Itisreportedthattheamplitudeoftheextracellularpotentialfromthepyramidalneuronsofahippocampalratisgreaterthan60Vifthemicroelectrodeisplacedwithin50mdistanceofthecellbody[ 5 ].Typically,theactionpotential,alsocalledaspike,hasapeak-to-peakamplitudefrom50Vto500V[ 6 ]withafrequencyrangeof300Hzto5KHz[ 7 ]whenrecordedextracellularly.Besidestheactionpotentials,thesynchronousactivitiesoflargegroupsofneuronsinoneregionofthebrainalsoprovidesneuroscientistswithusefulinformationthathelpsuncoverhowthebrainfunctions.Agroupofneurons 15

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generatesactionpotentialssynchronously,leadingtoalowfrequencyoscillationknownasthelocaleldpotential(LFP).TheLFPcanbeashighas5mVwithfrequenciesrangingfromlessthan1Hzto200Hz[ 8 ].Theactionpotentialsandthelocaleldpotentialsarecoherentintheneuralactivities,andtheseparationofthesecanbeaccomplishedbylteringthesignalintheappropriatefrequencyrange. Practically,therecordedactionpotentialisalwaysmixedwiththebiologicalnoisesoriginatingfromfareldneuronsandelectricalnoisesfromtheelectrodesandtherecordingsystem.Thenoiseoorcanbeashighas20Vrms.Duetothedifferentpotentialsbetweentherecordingelectrodeandthereferenceelectrodeintermsoftheelectrochemicaleffectsattheinterfacebetweentheelectrodetipandthetissue,theneuralsignalhasalargeDCoffset,typically1v2V[ 9 ].Ifoneoftheelectrodesinanelectrolytemovesrelativetotheotherelectrodes,thedifferenceofthepotentialwillvaryandleadtomotionartifacts. Inshort,severalpropertiesoftheextracellularneuralsignalsmustbetakenintoaccountfordesigningimplantedneuralrecordingsystems.First,theamplitudeofthesignalsissmall,usually50Vto500V.Second,thefrequencyrangesofthelocaleldpotentialsandtheactionpotentialsarefrom1Hzto200Hzandfrom300Hzto5KHz,respectively.Third,theDCoffsetoftheextracellularneuralsignalscanbeashighas1Vto2V.Finally,andperhapsmostimportantly,theneuralsignalsarequietmostofthetimeandonlyproducelargerpotentialssporadically.Itisbelievedthatmostoftheinformationinthebrainisencodedinthespikes. 1.3ImplantedNeuralRecordingSystemOverviewandConstraints Figure 1-2 showsablockdiagramofagenericimplantedneuralrecordingsystem,whichcontainsanimplantedfront-endandaback-endoutsidethebody.Thefront-endunitconsistsofmicroelectrodes,ampliersandlters,dataconversionandreductioncircuitry,aswellasawirelesstransmitter.Electrodesareinvasivelyinsertedintothebraintomeasuretheneuralsignals.Theweakneuralsignalsmustbeboostedrst 16

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Figure1-2. Blockdiagramofanimplantedneuralrecordingsystem byampliersforfurtherprocessingandtheampliersmustbeplacedclosetotheelectrodestoreducethenoise.Inafullyimplantedunit,thedatamustbewirelesslytransmittedoutofthebody,sincewiredconnectionstoadeviceoutsidethebodycancauseinfectionandrestricttheactivityofthesubject.Beforewirelesslytransmittingthesignals,themulti-channelanalogneuralsignalsmustbedigitizedandserializedintoasingleserialdatastreambyanalog-to-digitalconverters(ADCs)andreadoutcircuitry.Thentheserialdatastreamisrelayedoutofthebodythroughthewirelesslink.Comparedtothefront-end,theback-endoutsidethebodyhaslessstringentconstraintsonpowerandsize.Theserialdatastreamiscapturedbythereceiverandisconditionedincludingdemodulationandde-serializationforfurtherprocessing,suchassignalreconstructionandspikesorting. Thedesignofsuchafullyimplanteddevicemustsatisfyseveralconstraints.Sincetheneuralsignalsareweakandsensitive,thesignalsmustbeboostedbyalow-noiseamplierforfurtherprocessing.Toremovethetetherstoexternalinstrumentsandtoavoidinfection,theinformationcanonlybetransmittedoutthroughawirelesstelemetrylinkthathaslimitedbandwidth.Someresearchresultsshowthatonly80mW=cm2heatuxcanresultinnecrosisinmuscletissue[ 10 ].Assuminga100channelsystemwith1cm2size,eachchannelcannotconsumemorethan800W;otherwisethesurrounding 17

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Table1-1. Existingneuralrecordingsystemsoverview SamplingRateADCRes.Tx.BWMonitorModeSpikeDet.Mode Michigan[ 11 ]62.5Ks/s8bit2Mb/s2Ch.64Ch.Utah[ 12 ]15.7Ks/s10bit345.6Kb/s1Ch.100Ch.Duke[ 13 ]31.25Ks/s12bit-1Ch.96Ch.Brown[ 14 ]31)]TJ /F5 11.955 Tf 11.95 0 Td[(40Ks/s12bitUpto10Gb/s16Ch.tissuewillbedamagedbytheheat.Thus,theimplantedmulti-channelneuralrecordingdeviceincludingtheamplier,thedataconverterandthetelemetrymustbelowpower,lownoise,lowbandwidthandcompactinsize. Thankstotheadventofintegratedcircuittechnologyandthedevelopmentofmodernsurgicalprocedures,thesimultaneousneuralsignalrecordingofmultiplechannelsisfeasible.Thebottleneckofthemulti-channelrecordingsystemisthewirelesstransmissionofalargebandwidthdatastream.Constrainedbythenitewirelesstransmissionbandwidth,itisnotpossibletotransfertherawsignalsfromhundredsofchannelssimultaneously. ThechallengeofbuildingafullyimplantablewirelessneuralrecordingsystemforBMIhasbeenundertakenbyseveraluniversities,suchastheUniversityofMichigan[ 11 ],theUniversityofUtah[ 12 ],DukeUniversity[ 13 ]andBrownUniversity[ 14 ].Eachsystemhastheirrespectiveadvantagesanddisadvantagesdependingonthesiteofimplantation,targetedsignalacquisition,power/bandwidthtradeoffs,implantsize,andfabricationtechnology.AbriefoverviewoftheimplantableneuralrecordingsystemsdevelopedbytheseuniversitiesisshowninTable 1-1 .AllofthemuseconventionalsynchronousADCs.TheMichiganimplantable64-Channelwirelessmicrosystemconsistsofasiliconmicroprobearray,preamplier,neuraldataprocessingunitandwirelesstransmission[ 11 ].Theampliedneuralsignalisdigitizedbythe8-bitconventionalsynchronousADCsatspeedof62.5Ksample/s.Sincethetransmissionbandwidthis2Mb/s,themicrosystemcantransmitonlyfullwaveformson2channels 18

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oronlyspikeoccurrenceanditssiteoforiginon64channels.SimilartotheMichiganapproach,theUtahandDukemulti-channelneuralrecordingsystems[ 12 ],[ 13 ]alsodigitizesignalsbythesynchronousADCsandcanonlytransmitthefullwaveformononechannel.Toefcientlyusethebandwidth,theUtahimplantableneuralrecordingsystemperformsspikedetectionandtransmitsonlythespiketimings.However,transmittingspikedetectionresultslimitstheabilitytoreferenceactionpotentialswiththebackgroundactivity,sincethereisnoaccesstotheoriginalsignal.ThelimitedbandwidthconstraintisavoidedbytheapproachtakenbyBrownUniversity,whichtransmitsthedigitizedneuralsignalsthroughtheskinbyinfraredlightusingalaserdiode[ 14 ].Theinfraredapproachachievesabandwidthofupto10Gbps.However,theinfraredtelemetryconsumes12mW.Suchhighpowerconsumptionpreventstheimplantableneuralrecordingdevicefrombeingusedincloseproximitytobraintissue. Thus,evenifthetransmissionbandwidthcansatisfytherequirementoftransmittingdigitizedrawsignalsofallchannels,thehighpowerconsumptionatsuchhighdataratewillbeaconcern.Afeasiblesolutionovercomingthebandwidthandpowerconstraintsistoreducethedatarateofthesystem,ortoreducethenumberofrecordingchannels,orthedatarateofeachchannel.Somesystemsusespikedetectionschemestotransmittheeventsofactionpotentialsorthewaveformsofactionpotentialsinsteadoftheentireneuralsignals[ 11 13 ].However,neuroscientistsprefertheentiresignalsandnotjustthespikedetectionresults,sincetheentiresignalsprovidetremendouspossibilitiestoexplorecharacteristicsoftheneuralsignals.Alsoifonlyspiketimesaretransmitted,thenitisimpossibletospikesortandclassifymultipleneuronsoneachchannel. 1.4ResearchGoalandDissertationStructure Thegoalofthisresearchistondsolutionstothetrade-offbetweentheacquisitionaccuracyandthelimitedtransmissionbandwidthinneuralsignalrecordingapplications.Therearetwotypesofsituations.Therstsituationistoreconstructtheentirecontinuoussignal.Inordertofurtherreducethedatarate,thesecondsituationisto 19

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reconstructsparsesignals,suchasthespikeregionsinneuralsignals.Thedissertationproposeslow-power,low-noise,low-bandwidthimplantableneuralrecordingsystemsusingtheasynchronousevent-baseddatacompressionschemes,specicallytheintegrate-and-re(IF)andthetime-derivative(TD)encoders.BysimplychangingtheparametersoftheIFandtheTDencoders,suchasthethresholds,therecordingcanbeswitchedbetweenthetwosituationseasilytosatisfydifferentrecordingapplicationrequirements. Theorganizationofthedissertationisasfollows: Chapter2describesatwo-stagelow-powerlow-noiseamplierdesign.Therst-stageisalow-noisexed-gainxed-bandwidthamplierandthesecond-stageisavariable-gainvariable-bandwidthamplier.Bench-topmeasurementandinvivoexperimentresultsarepresented. Chapter3overviewstheIntegrate-and-Fire(IF)encodingschemeanditscircuitryinvoltage-modedesignatrst.SincetheinputtotheIFisintheformofacurrent,thisresearchproposesdifferentcircuitimplementationsoftheIFincurrent-modedesignalongwithanalysis.Simulationandbench-topmeasurementresultsarealsoprovided. InChapter4,anotherasynchronousevent-basedencodingscheme,theTime-Derivative(TD),isintroduced.TheTDreconstructionalgorithmisdevelopedtorecovertheinputsignal.AnalysisandsimulationresultssuggestthattheTDencodingissuperiortotheIFencodingandtheconventionalsynchronousanalog-to-digitalconverters(ADCs).TheCMOSimplementationoftheTDencoderisproposedandbench-topmeasurementresultsarepresented. InChapter5,theperformancesofasynchronousADC,vedifferentasynchronousADCs,aswellastheencoderwithnon-lineartransformationareanalyzedandcomparedtondoutthemostefcientdataconversionandcompressionschemeforneuralrecordingapplications.Finally,theconclusionsaregiveninChapter6. 20

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CHAPTER2LOW-NOISENEURALSIGNALAMPLIFIERDESIGN 2.1Introduction Theamplitudesofextracellularneuralsignalsvaryfrom50Vto500V[ 6 ]aroundamuchlargerDCvalueoftypically1v2V[ 9 ].Thecomponentsofextracellularneuralsignalsrangingfrom1Hzto200Hzareusuallyconsideredlocaleldpotentialsandthecomponentsofneuralsignalsrangingfrom300Hzto5KHzareactionpotentials.Theneuralsignalneedstobeampliedandlteredbeforesuchalowamplitudesignalcanbefurtherprocessed,i.e.,analog-to-digitalconvertedandtransmitted.Agoodamplierintheimplantableneuralrecordingunitmustsatisfythefollowingrequirements: 1. Lowinput-referrednoisetoavoidcorruptingsuchsmallamplitudesignals 2. Lowpowerconsumptiontopreventheatingdamage 3. RejectionoftheDCoffsettoavoidthesaturationofthedevice 4. Sufcientandappropriategaintoamplifythesignalsofinterest 5. Compactsiliconareawithnooff-chipcomponents 6. Highimpedancetosurpasstheimpedanceduetotheelectrode-tissueinterface 7. Highimmunitytotheinterferencefrom60Hzpowerlinenoise 8. Highpowersupplyrejectionratio 9. Highcommon-moderejectionratio Oneofthechallengesintheneuralsignalamplierdesignisthetrade-offbetweenpowerconsumptionandnoise.Thelimitedsizeandthelargetime-constantoftheamplier,forlteringtheinterestedsignalandrejectingthedcoffset,posemoredifculty.Sincetheneuralsignals,sometimesareasweakas10V,andsometimesareasstrongas500V,duetotheactivitiesoftheneuronsandtherelativepositionsoftheelectrodestotheneurons,theamplierwithaprogrammablegaincansufcientlyamplifytheweaksignalswithoutclampingtheampliedstrongsignals.Dependingon 21

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thedifferentapplications,theactionpotentialsorthelocaleldpotentialsneedtobecaptured.Atunablebandwidthprovidesthefreedomofmonitoringdifferentcomponentsofthesignalsduringrecoding. Thischapterdescribesthedesignoftheamplierscomposedofalow-noiseamplierattherststageandthevariablegainwithtunablebandwidthamplieratthesecondstage.Bench-topmeasurementresultsandtheinvivotestresultswillbepresentedattheend. 2.2AmplierCircuitDesign Theneuralsignalamplierpresentedherecontainstwostagesinsteadofasinglestagebecauseofthelimitedgain-bandwidth-product.Therststageisalow-noisepreamplierwithareasonablegain,anditcoversthefrequencyrangeoftheentireextracellularsignalsandrejectsthedcoffset.Thesecondstageamplierisavariable-gaintunable-bandwidthlterthatbooststheneuralsignalsintheappropriatefrequencyrangetotheexpectedlevel. 2.2.1First-StageAmplier 2.2.1.1Circuitdesignandfrequencyresponse Figure2-1. Schematicoftherst-stageamplier 22

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Alow-powerlow-noisebio-amplierwasproposedbyHarrison[ 15 ]andhasbeenwidelyusedinmanyneuralrecordingsystems.Figure 2-1 showstheschematicoftherst-stageamplierthatfollowsthestructureofHarrison'samplierwiththeadditionalfast-settletransistors.TheinputsignalisACcoupledtotheinputsoftheOperationalTransconductanceAmplier(OTA)throughC1toremovetheoffset.C1shouldbeassmallaspossibletoincreasetheinputimpedanceandtopreventsignalattenuationduetotheimpedanceoftheelectrode.C1andC2formthecapacitivefeedbacknetworkandsettheclosed-loopgain.Thediode-connectedtransistorsinthefeedbackloopactasresistors,denotedbyR,toprovidetheoperatingpointoftheOTAandsetthelow-cutofffrequencywithC2together.CListhecapacitiveloadandthetransconductancevalueoftheOTAisGm.AssumingC1C2,CLC2andGmRC1 C2,thetransferfunctionofthepreamplierH1(s)canbederivedandsimpliedas: H1(s)=RC1C2s2+(C1)]TJ /F3 11.955 Tf 11.95 0 Td[(GmRC1)s R(C1C2+C1CL+C2CL)s2+(C1+GmRC2+CL)s+Gm)]TJ /F3 11.955 Tf 23.11 8.09 Td[(C1 C2s(1)]TJ /F3 11.955 Tf 11.96 0 Td[(sC2 Gm) 1 C2R+s+s2C1CL C2Gm=)]TJ /F3 11.955 Tf 10.49 8.08 Td[(C1 C2s(1)]TJ /F3 11.955 Tf 11.95 0 Td[(sC2 Gm) 1 C2R(1+sC2R)(1+sC1CL GmC2)=AMs(1)]TJ /F8 7.97 Tf 17.35 4.71 Td[(s !z2) (1+s !p1)(1+s !p2)1 C2R(2) AM=)]TJ /F3 11.955 Tf 10.49 8.08 Td[(C1 C2 (2) !z1=0,!z2=Gm C2 (2) !p1=1 C2R,!p2=C2Gm C1CL (2) Thustherst-stageamplierisaband-passlterwiththemid-bandgainC1 C2andthelowandhighcutofffrequenciesat1 C2RandC2Gm C1CL,respectively.AzerolocatedattheoriginremovestheDCoffset,andtheotherzerolocatedatveryhighfrequencybarelyaffectstheamplieroperation. 23

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Theextracellularsignalscontainaverylowfrequencycomponent,i.e.1Hzor300Hz,sothetime-constantC2Rmustbelargeenoughtocovertheentirefrequencyrangeofthesignals.IfC2is200fF,theresistorRhastobe2.65Gtoachievea300Hzlowcutofffrequency.Usingaphysicalresistorintheintegratedcircuitsisnotfeasibletoobtainsuchlargevalueresistance.Usingalargevalueoff-chipresistoralsorequiresalargearea,andincreasesthepackagecomplexityoftheimplantableunit.AsshowninFigure 2-1 ,thediode-connectedtransistorprovidesanareasavingmethodofrealizingthelargevalueresistor.ThetransistoreitheractsasadiodewhenVGSisnegativeoractsasaparasiticpnpbipolarjunctiontransistorwhenVGSispositive[ 16 ].WhenVGSofthetransistorissmall,theequivalentresistanceofthediode-connectedtransistorisextremelylarge.ForjVGSj<0.2V,theequivalentresistanceismorethan1011[ 15 ].Twodiode-connectedtransistorsinaseriesprovidesalargervoltagerangeacrossthem,whichincreasestheoutputvoltagerangeoftheamplier. Duetothelargetime-constant,theamplierrecoversveryslowlyfromlargetransients.Duringtherecoveryphase,theneuralsignalmaybelostifthelargetransientcausestheampliertogointosaturation.Thefastsettlingswitchesareaddedinparallelwiththediode-connectedtransistorstospeeduptherecoveryandtoquicklyresettheoperationpointoftheamplier. 2.2.1.2Noiseperformance Thenoiseoftherst-stageamplierplaysanimportantroleintheneuralsignalamplierperformance.ThethermalnoisesoftheOTAandthediode-connectedtransistorscontributetothetotalnoise.Theinput-referrednoiseoftheOTAwithtransconductanceGmusingadifferentialpairattheinputstageismodeledsimplyasavoltagesourcev2ni,OTA(f)=16kT 3Gm.Thenoiseofthediode-connectedtransistorsinseriesasaresistiveelementRcanalsobemodeledasavoltagesourcev2n,R(f)=4kTR.The 24

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outputnoiseoftheamplierduetothethermalnoisesoftheOTAandRisgivenby v2no,amp1(f)=v2ni,OTA(C1+C2+Cin C2)2+v2n,R1 (2fC2R)2(2) whereCinisthetotalparasiticcapacitorsattheinputnodeoftheOTA. Theinput-referrednoisespectraldensityv2ni,amp1(f)canbeobtainedbydividingtheoutputnoisebythegain. v2ni,amp1(f)=v2ni,OTA(C1+C2+Cin C1)2+v2n,R1 (2fC1R)2(2) Aboveaparticularfrequency,thenoiseisdominatedbytheOTAandbelowthatfrequency,thenoiseisdominatedbytheresistorR.Denethisparticularfrequencyascornerfrequencyfcorner.AssumeC1C2+Cinand,fcornerisapproximatelygivenby fcorner1 2s 3Gm 4C21R=1 2r 3CL 4C1!p1!p2(2) Tominimizethenoisecontributionbythediode-connectedtransistors,thecornerfrequencyshouldbesetatamuchsmallerfrequencythanthelow-cornerfrequencyoftheamplier!p1,byselectingCL C14 3!p2 !p1.However,theickernoiseoftheOTAalsocontributestothetotalnoiseatlowfrequency.Inpractice,theickernoiseoftheOTAmaydominateoverthenoisecontributionfromthediode-connectedtransistors,andfcornerisdeterminedbythecornerfrequencyoftheOTA. Ifthenoisecontributionofthediode-connectedtransistorsisnegligible,thenoiseoftheamplierismostlydeterminedbythenoiseoftheOTA.Thus,todesignalow-noiseamplier,thenoiseoftheOTAmustbeminimized.Figure 2-2 showstheschematicoftheOTA.Theinput-referrednoisespectraldensityoftheOTAincludingthermalnoise 25

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Figure2-2. SchematicoftheOTAintherst-stageampliershowninFigure 2-1 andickernoiseisequalto v2ni,OPA(f)=2(v2P1(f)+2v2N1(f)g2mN1 g2mP1+v2P3(f)g2mP3 g2mP1)=16kT 3gmP1(1+2gmN1 gmP1+gmP3 gmP1)+2KP WP1LP1Coxf(1+2KN KP WN1LN1 WP1LP1g2mN1 g2mP1+1 WP3LP3 WP1LP1g2mP3 g2mP1)(2) wheregm~isthetransconductanceofthetransistor~andW~,L~arethewidthandthelengthofthetransistor~.kistheBoltzmannconstantandTistheabsolutetemperature.KPandKNarethetechnology-dependentconstants.UsuallyKPismuchlessthanKNwhenjVGSjisnotmuchhigherthanthethresholdvoltage[ 17 ]. PMOStransistorsareusedattheinputstageinsteadofNMOStodecreasetheickernoiseandthetransistorsaremadeaslargeaspossibletominimizetheickernoise.ThethermalnoiseisminimizedbyincreasinggmP1anddecreasinggmN1andgmP3asmuchaspossible,equivalentlybyincreasingWP1 LP1anddecreasingWN1 LN1andWP3 LP3.Followingtherulesofsizingtransistorsresultsshowthattheinputdifferentialpairworksinthesubthresholdregionandtheothertransistorsoperateinthedeepsaturationregion.However,gmN1andgmP3cannotbemadearbitrarilylowbecausethepolesassociatedwithtransistorsN1sN4,P3andP4hastobeseveraltimeslarger 26

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thanthedominantpolegmP1 CLtoguaranteethestabilityoftheOTA.IncreasinggmP1helpsreducethenoiseoftheOPA,butmaynotreducethenoiseoftheoverallamplierbecauseincreasingthesizeoftheinputtransistorsalsoincreasesCin.AsEq. 2 shows,increasingCinresultsinincreasingtheinput-referrednoiseoftheamplier.TheoptimalsizeoftheinputtransistorsP1andP2canbeobtainedbyminimizingtheoverallnoiseoftheamplier. Therootmeansquare(rms)input-referrednoiseoftherst-stageamplierv2ni,rms1iscalculatedastheintegrationoftheinput-referrednoisespectradensityv2ni,OPA(f)overtheentirefrequency.Ignoringtheickernoise, v2ni,rms1=Z10v2ni,amp(f)df=(C1+C2+Cin C1)216kT 3gmP1(1+gmN1 gmP1+gmP3 gmP1)f(2) wherefisthenoisebandwidth.Thenoisebandwidthofalow-passlterwithasinglepoleis 2f3dB,wheref3dBisthe3dBbandwidthofthelter[ 18 ].Since!p1isverylow,thenoisebandwidthfofthepreamplierapproximatelyis 2fp2=!p2 4.AssumingC1C2andgmP1gmN1,gmP3,thermsinput-referrednoisecanbesimpliedas v2ni,rms1=16kT 3gmP1f4kT 3CLjAMj(2) Theaboveequationshowsthattheintegratedrmsinput-referrednoiseisirrelevanttothebandwidthoftheamplier,butisinverseproportionaltothemid-bandgainandtheloadcapacitor.Themid-bandgainislimitedbytheopen-loopgainoftheOTAandthesiliconarea.Theloadcapacitorisalsorelatedtothesiliconarea.Thus,thenoiseandthesiliconareaisatradeoffintheimplantedneuralsignalamplierdesign. Anothertradeoffoftherst-stageamplierdesignisamongpowerdissipation,bandwidthandnoise.TheNoiseEfciencyFactor(NEF)wasintroducedtoevaluatethistradeoff[ 19 ]: NEF=Vni,rms1r 2Itotal UT4kTBW(2) 27

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whereUTisthethermalvoltagekT=q,Itotalisthetotalsupplycurrent,andBWisthebandwidthoftheamplierinunitsofHz. Replacingvni,rms1withEq. 2 andnoticingthatthecurrentIDP1owingthroughtransistorP1isonequarterofthetotalcurrent,theNEFreducesto NEF=s 16 3UTIDP1 gmP1(2) Thus,theNEFisminimizedbypushingtransistorsP1andP2intotheweakinversionregiontoachievethemaximalgm IDvalue. 2.2.2Second-StageAmplier 2.2.2.1Circuitdesign Theneuralsignalsarepre-ampliedbythelow-noiserst-stageamplierasdescribedinSection 2.2.1 .Duetothegain-bandwidthproductionlimitation,thegainoftherst-stageampliercannotbeverylarge.Forsmallamplitudeneuralsignals,asecondstageamplierisnecessarytofurtherboostthesignal.Forexample,therst-stageamplierwith40dBgainampliestheneuralsignaltypicallywithamplitudesintherangeof10Vto500Vtotherangeof1mVto50mV,andextragainof6dBto40dBmayberequiredbythesuccessivedataconverters.Inordertoreducethe60Hznoiseandimprovethesignal-to-noiseratiooftheampliedactionpotentials,theentireampliershouldbeaband-passltertoonlypassthesignalinthefrequencyrangeofinterestandsuppressthenoiseoutsidethebandwidth.Sincetherst-stageamplierisalow-passlter,thesecondstageamplierisdesignedtobeahigh-passlter. Duetothehighgainrequirement,themulti-feedbacktopologyofthehigh-passlterispreferredoverthesallen-keytopology.TheschematicofthesecondstageamplierisshowninFigure 2-3 .ThegatevoltagecontrolledtransistorM1andthediode-connectedtransistorsM2,M3actastworesistorsR1andR2,respectively.Usingtransistorsinsteadofphysicalresistorscanachievelargeresistancevalueswithminimumareacost.Asmentionedpreviously,R2isintherangeofGwhenthevoltageacrossM2,M3isless 28

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Figure2-3. Schematicofthesecondstageamplier than0.2V.Whenthegate-sourcevoltageofM1,jVGSM1j,islargerthanthethresholdvoltageVthM1,M1isindeeptrioderegionandR1equals R1=1 pCox(W L)M1(jVGSM1j)]TJ /F3 11.955 Tf 17.94 0 Td[(VthM1)(2) wherepisthemobilityofholes,Coxisthegatecapacitanceand(W L)M1isthedimensionoftransistorM1.ResistorR1istunablebyadjustingthegatevoltageofthetransistor.DuetotheparasiticcapacitorsassociatedwithtransistorsM1,M2andM3,theimpedancesofR1andR2degradeathighfrequency. 2.2.2.2Frequencyresponse Theoperationalamplier(OPA)showninFigure 2-3 canbesimplymodeledasarst-orderlow-passlterwithDCgainA0andadominantpoleat!pa.WithreasonableassumptionsofA01,A0!pa1,A0!paC5R11andC4R2C3R1,thetransferfunctionofthemulti-feedbackhigh-passlterH2(s)canbederivedandsimpliedas H2(s)=)]TJ /F3 11.955 Tf 124.82 8.09 Td[(C3C4R1R2s2+C3C24R1R22s3 1+C4R2s+C4(C3+C4+2C5)R1R2s2+C24C5R1R22s3+C24(C3+C5)R1R22 A0!pas4(2) H2(s)showsthatthesecondstageamplierisafourthordersystemwithtwozerosattheorigin.Thethirdzeroislocatedatlowfrequency1 C4R2,whichiscanceledbyapole 29

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atthesamelocation.Forthefrequencyrangehigherthan1 C4R2,H2(s)canbewrittenas H2(s))]TJ /F3 11.955 Tf 138.88 8.08 Td[(C3C4R1R2s3 s+(C3+C4+2C5)R1s2+C4C5R1R2s3+C4(C3+C5)R1R2 A0!pas4=AMs2 !2L 1+s QL!L+s2 !2L+s3 !2L!H(2) where AM=)]TJ /F3 11.955 Tf 10.5 8.09 Td[(C3 C5 (2) !L=1 p C4C5R1R2 (2) QL=1 C3+C4+2C5r C4C5R2 R1 (2) !H=C5A0!pa C3+C5 (2) Themid-bandgainisdeterminedbytheratiobetweenC3andC5.Thecutofffrequencyofthemulti-feedbackhigh-passlterdependsonC4,C5,R1andR2.Inthesecondstageamplierdesign,C3isselectedbythreebits(notshownintheschematic)toprogramthegainwithoutaffectingthecutofffrequency.Thecut-offfrequencyisvariedbytuningthegatevoltageofM1tochangeR1withoutaffectingthegain. Althoughthehigh-passlterstructureisadopted,thesecondstageamplierbehavesasaband-passlterandtheroll-offathighfrequencyisduetothenitebandwidthoftheOPA.Thehigh-cornerfrequencyoftheentireamplierisdeterminedbythesmallervalueofhigh-cornerfrequenciesofboththerst-stageamplierandthesecond-stageamplier,!p2inEq. 2 and!HinEq. 2 .Generally,!p2islowerthan!H. Aclassictwo-stageOPAshowninFigure 2-4 isusedinthesecondstageamplier.TheinputstageisaP-typedifferentialpairloadedwithanN-typecurrentmirrorandthesecondstageisanN-typecommon-sourcestagewhichhasanactiveload.Thegainof 30

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Figure2-4. SchematicoftheOPA theOPAA0is A0=gmP1(roN2jjroP2)gmN3(roN3jjroB3jjZL)(2) wheregmP1isthetransconductanceofthedifferentialinputpairP1,P2,andgmN3isthetransconductanceofthecommon-sourcetransistorN3.roistheoutputimpedanceoftransistorsandZListheoutputloadimpedance. Thedominantpole!paisequalto !pa=gmP1 A0Ccomp=1 CcompgmN3(roN3jjroB3jjZL)(roN2jjroP2)(2) ThecompensationcapacitorCcompandtheleadresistorRleadarecarefullychosentoguaranteesufcientphasemarginandthestabilityoftheOPA[ 18 ]. Thecommon-modeinputrangeandtheoutputswingthatensuretheappropriateoperatingregionofeverytransistorisgivenby VGSN1)]TJ /F3 11.955 Tf 11.96 0 Td[(VthP1VinVdd)]TJ /F5 11.955 Tf 11.96 0 Td[((jVGSB1j)-223(jVthB1j))-222(jVGSP1jVGSN3)]TJ /F3 11.955 Tf 11.96 0 Td[(VthN3VoutVdd)]TJ /F5 11.955 Tf 11.96 0 Td[((jVGSB3j)-222(jVthB3j)(2) 2.2.2.3Noiseperformance Thenoiseperformanceofthesecond-stageamplierislesscriticalthantherst-stageamplierbutitstillneedsattention.SincetherststageoftheOPAhasalargegain,thesecondstageoftheOPAhaslittlenoisecontributiontotheinput-referred 31

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noiseandwillbeneglectedinthenoiseanalysis.Theinput-referrednoiseoftheOPAis v2ni,OPA2(f)=16kT 3gmP1(1+gmN1 gmP1)+2KP WP1LP1Coxf(1+KN KP WN1LN1 WP1LP1g2mN1 g2mP1)(2) Toreducethethermalinput-referrednoise,thetransconductanceoftheinputpairgmP1mustbemaximizedandthetransconductanceoftheNMOScurrentmirrortransistorsgmN1shouldbeassmallaspossible.Thiscanbeachievedbyincreasing(W L)P1,2anddecreasing(W L)N1,2.However,thesizesandthetransconductanceofN1,2arerelatedtothenon-dominantpolebygmN1=CN1,whereCN1isthetotalcapacitanceseenbythegateofN1,2.ReducingthegmN1willpushthenon-dominantpoleclosetotheoriginandmayintroducestabilityproblems.Sincetheickernoiseisinverselyproportionaltothedimensionofthetransistors,decreasingtheickernoiseimpliesincreasingthesizeoftransistors.However,increasingthesizeofthetransistorincreasestheparasiticcapacitance,thereforepossiblyintroducinginstabilityconcerns. TheresistivecomponentsM1,M2andM3alsocontributetotheinput-referrednoiseoftheamplier.Thenoiseofthesetransistorscanbesimplymodeledbytheresistorthermalnoisesincetheyactasresistors. v2n,R1(f)=4KTR1v2n,R2(f)=4KTR2(2) Ideally,thecapacitorsarenoisefree.Thus,thetotalinput-referrednoiseofthesecondstageampliercanbederivedas v2ni,amp2(f)=v2ni,OPA2(f)[1+[(C3+C4+C5)R1+C4R2](2f)+C4C5R1R2(2f)2 C4C5R1R2(2f)2]2+v2n,R1(f)[C4R2(2f) C4C5R1R2(2f)2]2+v2n,R2(f)[1+(C3+C4+C5)R1(2f) C4C5R1R2(2f)2]2(2) Fromtheaboveequation,wecanseethatatlowfrequency,theOPA,resistorsR1andR2contributetothenoisetogetherwhileatmidandhighfrequency,theOPAdominatesthenoise.Thustominimizethenoiseoftheamplier,thenoiseofthe 32

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Table2-1. Capacitorvaluesusedintheamplierdesign C1C2CL1C3C4C5Ccomp 20pF200fF6pF800fF+1.2pF+2.4pF+4pF7.2pF400fF2pF OPAmustbeminimizedasmuchaspossibleandthevalueoftheresistorsshouldbeaslargeaspossiblewithoutharmingthestability,bandwidth,gain,andconsumingsufcientlylowpower. 2.3MeasurementResults Thegainofthedesignedrst-stageamplieris40dBandthemaximumgainofthesecond-stageamplieris26dB.Allcapacitorsarefabricatedusingpoly-to-polystructuresandthecapacitorvaluesarelistedinTable 2-1 .ThevalueofC3isacombinationofseveralcapacitorsdependingontheprogrammablegaincontrolbitsg<0:2>.TheentireamplierincludingthetwostagesasdescribedinSection 2.2 hasbeendesignedandfabricatedinAMI0.5mthree-metal,two-polyprocess.Itoccupies520mby652mdieareaandthreequartersofthedieareaisconsumedbythecapacitors. 2.3.1Bench-TopTestResults Thefabricatedtwo-stageamplierhasbeenmeasuredusingtheStanfordResearchSystemSR785SpectrumAnalyzer. Figure 2-5 showsthefrequencyresponseoftherst-stageamplier.Themeasuredmid-bandgainis40.5dBandthe3dBbandwidthfrequencyislocatedat5.7KHz.Themeasuredlowcornerfrequencyisat20mHzwhichmeanstheequivalentresistanceofthediode-connectedtransistorsRishigherthan1013.Thenoiseperformanceismeasuredattheoutputoftherst-stageamplierwiththeinputandthereferencenodesoftherst-stageamplierconnectingtoVss.Figure 2-6 showstheinput-referrednoisevoltagespectraldensity(VSD)oftherst-stageamplier,whichiscalculatedbydividingthemeasuredoutputnoiseVSDbythegainoftherst-stageamplier.Thebluesolidlineistheinput-referrednoiseVSDandthegreendashedlineistheinput-referred 33

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Figure2-5. Measuredfrequencyresponseoftherst-stageamplier Figure2-6. Measuredinput-referrednoisevoltagespectrumoftherst-stageamplier 34

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instrumentationnoiseVSD.Integratingtheareaunderthebluesolidlinefrom10Hzto25.6KHzyieldstheinput-referrednoise3.75Vrms.OthermeasuredcharacteristicsarelistedinTable 2-2 Figure2-7. Measuredfrequencyresponseofthetwo-stageamplierwithvaryinggaincontrolbitsg<2:0> Figure2-8. Measuredfrequencyresponseofthetwo-stageamplierwithvaryingR1 Thesecondstageamplierhasbeenmeasuredtogetherwiththerst-stageampliertoobtaintheperformanceoftheentireamplier.Thegainofthesecondstage 35

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amplierisrelatedtoC3 C5andthedesignedcircuitcontainsthreebitstoselectoneof8differentC3values.Figure 2-7 showsthemeasuredfrequencyresponseoftheentireamplierwithdifferentcontrolbitswhichhasthegainfrom47dBto64dB.Anotherprogrammableabilityoftheamplieristhelow-cornerfrequencywhichisachievedbytuningthegatevoltageofM1notedasVr1tovaryR1.ThemeasuredfrequencyresponseoftheentireamplierwithvaryingVr1isshowninFigure 2-8 .Thegaincontrolbitsaresettothehighesttogetmaximumgain.TheresultsshowthatwhenVr1ischangedfrom0.6Vto0.7V,thelow-cornerfrequencyisvariedfrom107Hzto770Hz.Thefallingofthefrequencyresponseisdeterminedbytherst-stageamplier,whichisnotaffectedbythesecondstageamplieraslongasthebandwidthoftheOPAinthesecondstageishigherthanthehigh-cornerfrequencyoftherst-stageamplier.Whenthelow-cornerfrequencyispushedtowardhigh-cornerfrequency,thebandwidthoftheamplierbecomesnarrower,andthegainstartstodegrade.WhenVr1ishighenough,transistorM1isturnedoffandR1becomesverylarge,thelow-cornerfrequencydecreasestoaverylowvaluethatissuitableforthelocaleldpotentialrecording. Thedesignedamplierhasbeentestedwiththeneuralsimulatorsignal.Eachsimulatorchannelgeneratesthreedifferentactionpotentialsrepeatedly,withamplitudesof200,250and300V.Eachactionpotentiallastsabout1ms.Whenburstactivityoccurs,theneuronresevery10ms.Thedifferentialsignalbetweentwochannelsisthecombinationofthethreeactionpotentialsandtheippedthreeactionpotentials.Figure 2-9 showstheamplieroutputwiththeneuralsimulatorsignalasinputsignal.Thewaveformsattherstrowarethedifferentialneuralsimulatorsignalsduringburstingperiod,onwhicharetheinputsignalstotheamplier.Theactionpotentialsareredevery5msandthesixdifferentactionpotentialsrepeatevery30ms.Theneuralsimulatoroutputhashighfrequencynoiseandthenoiseoor(peak-to-peak)isabout200V.Thewaveformsonthesecondrowaretheampliedsignalby40dBrecordedattherst-stageamplieroutput.Theactionpotentialsareboostedtoanamplitudeof20, 36

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Figure2-9. Neuralsimulatorsignalmeasurements:rstrowshowstheinputsignalsfromneuralsimulator;secondrowplotstheoutputsoftherst-stage40dBgainamplier;thirdrowplotstheoutputsofthesecond-stageamplierwithdifferentgain.Firstcolumn,g2g1g0=000,gain=200V/V;secondcolumn:g2g1g0=110,gain=670V/V;thirdcolumn,g2g1g0=111,gain=1270V/V. 25and30mV.Thenoiseoorisaround8mV.Thethirdrowplotstheampliedsignalsattheoutputofthesecond-stageamplierwithdifferentgaincontrolsettings.Fromlefttoright,thegainoftheentireamplierare200,760and1270V/V,respectively.Thenoiseoorsoftherecordedsignalsare15,40and50mV,respectively.Duetothenoiseoftheoscilloscopeinthemeasurement,asampliergainincreases,thesignal-to-noiseratioofthesignalshownontheoscilloscopeincreases. Thenoiseoftheamplierismeasuredwhenthegainis63dB,thelow-cornerfrequencyis752Hzandthehigh-cornerfrequencyis7.4KHzbysettingthegaincontrolbitsto<111>andVr1to0.6V.Figure 2-10A showsthemeasuredinput-referred 37

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ANoisespectrumdensity BTransientnoise Figure2-10. Measuredinput-referrednoiseofthetwo-stageamplier Table2-2. Measuredcharacteristicsoftheamplier Parameter1st-stageamplier2nd-stageamplierEntireamplier Supplyvoltage3.3V3.3V3.3VSupplycurrent14.7A11.5A26.2APowerconsumption48.5W38W86.5WGain40dB724dB4764dBLow-cornerfrequency0.02Hz0.02700Hz0.02700HzHigh-cornerfrequency5.7KHz-5.7KHzInput-referrednoise3.75V-2.32VCMRR80dB-80dBPSRR78dB-52dBArea(in0.5mCMOS)--0.34mm2 VSD.Theintegratedinput-referrednoiseis2.32Vrms.Figure 2-10B istherecordedtransientoutputnoisedividedbythegainwhosermsvalueis2.28Vrms.Theresultisconsistentwiththeintegratedinput-referrednoiseoverthefrequencyrangeoftheamplierbandwidth. Thesummarizedcharacteristicsoftheentireampliercontainingtherst-stageamplierandthesecond-stageamplierarelistedinTable 2-2 2.3.2InVivoTestResults An8-channelrst-stageamplierchiphasbeenip-bondedwiththeexiblepolyimidemicro-electrodearraybyDr.NishidaandErinPatrick.Theexiblemicroelectrode-amplier 38

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Figure2-11. Invivomeasurementresultfromtherat:therecordedsignalattheoutputofthepreamplierwith40dBgain. devicehasbeenimplantedintoanadultmaleSprague-DawleyratbyDr.SanchezandapprovedbytheUniversityofFloridaIACUC.TheelectroderowwasimplantedintheforelimbregionofM1(primarymotorcortex)at3.6mmdepthwhichcorrespondstoanareainthecorpuscallosum.Theampliedneuralsignalisdigitizedwithasamplingfrequencyat12KHzandstoredbyacommercialsignalprocessingproductfromTucker-DavisTechnologies.Figure 2-11 showstheampliedrat'sneuralsignalrecordedattheoutputoftherst-stageamplierwith40dBgain.Thepeak-to-peakamplitudeoftheobservedinput-referredactionpotentialisabout15Vandthenoiselevelis4V.Thedurationofspikesisaround1.52ms. 2.4Summary Thischapterpresentsatwo-stageamplierforneuralsignalrecording.Theconstraintsofsuchanimplantedneuralsignalamplierarenoise,powerandsize.TheamplierhasbeendesignedandfabricatedintheAMI0.5mCMOStechnology.Bench-topmeasurementresultsofthefabricatedchipprovethatthedesignedneuralsignalampliersatisesalltheconstraints.Thefunctionalityoftherst-stageamplieralsohasbeenveriedbyaninvivotestonaratwiththeexiblepolyimideelectrode. 39

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CHAPTER3CURRENT-MODECIRCUITIMPLEMENTATIONOFINTEGRATE-AND-FIREENCODING 3.1Introduction Itisstraightforwardtotransmitananalogsignalusingwires,butthisissusceptibletonoiseandtetheringthechipsandequipmentstogetherexcludesthepropertiesofportabilityandimplantation.Differentfromanalogsignals,digitalsignalsareeitherhighorlow.Thus,digitalsignalscanbearmorenoisethananalogsignals.Digitalsignalsaremorerobusttobetransmittedthroughwiresorwireless.TheconventionalcodingmethodusessynchronousAnalog-to-DigitalConverters(ADCs)togenerateuniformlyspacedseriesofdigitalbinaryoutputvalues.ThesynchronousADCsdigitizeanalogsignalsatxeddatarates,independentofsignalproperties,whichisnotoptimalfortransferringneuralsignalsfromtheperspectiveofbandwidth.ComparedtosynchronousADCs,event-basedconverterscanreducedatarateswhenencodingsignalswithsparseinformation,becausetheevent-basedconverterscompresssignalsbasedonthepropertiesofthesignalsandtheinternalstates. TheIntegrate-and-Fire(IF)encoderisoneoftheevent-basedconverterswhichtakesadvantageoflowinformationregionsoftheneuralsignals,i.e.,betweenspikes,totremendouslyreducethedatarate.TheIFhasbeenanalyzedandimplementedbyWei,ChenandLiduringtheirPh.DstudiesattheUniversityofFlorida[ 20 ],[ 21 ]and[ 22 ]. Thechapterisorganizedasfollows.ThebackgroundoftheIntegrate-and-Fire(IF)techniquefordataconversionisdescribedrstandfollowedbyareviewofthevoltage-modeimplementationandtheanalysisofitsdrawbacks.Next,weproposedifferentimplementationsoftheIFincurrent-modewhichprovidetheinputcurrenttobeintegratedbyconveyingandamplifyingthecurrentfromthephysicalneuroneldtothehardwarecircuitry.Finallythecadencesimulationandbench-topmeasurementresultsareshown. 40

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Figure3-1. BiphasicIFencodermodel 3.1.1Integrate-and-FireEncodingOverview TheIntegrate-and-Fire(IF)circuitisshowninFigure 3-1 .Inputcurrent,x(t),getsintegratedonthecapacitorCresultinginavoltagesignalz(t).Thisvoltageiscomparedtoapositiveandanegativethresholdvoltagedenotedas+and)]TJ /F4 11.955 Tf 9.3 0 Td[(,respectively.Whenz(t)becomeshigherthan+orlowerthan)]TJ /F4 11.955 Tf 9.3 0 Td[(,anoutputpulseisgenerated.Theoutputpulseresetsthecapacitor.Thecapacitorisresetafterapredenedtimedelay,knownastherefractoryperiod,afterwhichtheprocessrepeats.Thepulsesgeneratedareconstrainedbythefollowingequation: 1 CZtiti)]TJ /F11 5.978 Tf 5.76 0 Td[(1+x(t)dt=i(3) wherei2f)]TJ /F4 11.955 Tf 26.57 0 Td[(,+g,andtiisthetimeoftheithpulseevent. TheencodingprocessisthesimplestmodeloftheIFconverter,whichdoesnotconsiderotherfeatures,suchasleakyeffectandadaptiverate.Assumingthatthepulsetimeintervalsaremuchlargerthanthepulsewidthandtherefractoryperiod,thentheoutputp(t)containingNpulsescanbewrittenas: p(t)=Xi=1...Nsign(i)(t)]TJ /F3 11.955 Tf 11.95 0 Td[(ti)(3) 41

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wheresign()isthesignumfunction.TheIFconverterencodesthesignalsintothepulsetrainswitheachpulserepresentingoneoutputevent.Wehavepreviouslyshownthatthesignalcanbeperfectlyrecoveredfromthepulseeventsundersomeconstraints[ 23 24 ]. Thus,theinputsignalinformationisconvertedintothetimingsoftheasynchronouspulseeventsgeneratedbytheIF.Thisfeatureissimilartotheneuroscienceresearchresultsthatsuggesttheneuralsignalitselfrepresentsinformationusingtimingsofall-or-nothingspikes[ 25 ].So,theIFconverterisalsocalledtheIFneuroninthisdissertationandinsomeotherpublications.TheIFneuronplacesmorepulseswherethesignalmagnitudeislargerandfewerpulseswherethesignalmagnitudeissmaller.Therefore,theIFneuronreducesthedatarateespeciallywhenencodingneuralsignals,forexample,theneuralsignalwith50spikespersecondand1msdurationofeachspike.IftheIFneuronencodeseachspikewith20pulses,thedataratefortheentiresignalisonly1Kpulses/s(50spikes/s20pulses/spike).IfthesameneuralsignalisencodedbyasynchronousADCwith8bitresolutionand20Ksample/sclocksignal,theoutputdatarateofonechannelis160kb/s.ComparedtothesynchronousADC,theIFreduces160timesdatarate.Thesignalinthespikeregionscanberecoveredfromthepulsetrainwith20Kpulses/sandtherecoveredsignalisabletoachieve42dBsignal-to-errorratio[ 21 ].BesidestheadvantageofreducingthedataratecomparedtothesynchronousADCs,sincetheIFneurongeneratesasynchronouspulses,thesystemislesssensitivetothenoiseassociatedwiththedigitalsignaltransitionsandisfreefromthenoiseintroducedbytheclockataxedrate. Deningz(t)astheintegralofx(t)andignoringtherefractoryperiod,witharst-orderTaylorseriesexpansion,wecanrewriteequation 3 as: Ci=z(ti))]TJ /F3 11.955 Tf 11.95 0 Td[(z(ti)]TJ /F6 7.97 Tf 6.58 0 Td[(1)z(ti)]TJ /F6 7.97 Tf 6.59 0 Td[(1)+ti)]TJ /F6 7.97 Tf 6.59 0 Td[(1dz(t) dtjt=ti)]TJ /F11 5.978 Tf 5.75 0 Td[(1)]TJ /F3 11.955 Tf 11.96 0 Td[(z(ti)]TJ /F6 7.97 Tf 6.59 0 Td[(1)=ti)]TJ /F6 7.97 Tf 6.59 0 Td[(1dz(t) dtjt=ti)]TJ /F11 5.978 Tf 5.76 0 Td[(1(3) 42

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wheretisdenedasthetimeintervalbetweentwoconsecutivepulses,andthesubscriptirepresentstheorder,i.e.,ti)]TJ /F6 7.97 Tf 6.58 0 Td[(1=ti)]TJ /F3 11.955 Tf 11.95 0 Td[(ti)]TJ /F6 7.97 Tf 6.59 0 Td[(1. Wecanthenrelatetheresultingpulsedensityas: Pulsedensity/1 tjx(t)j jCj(3) Wecanseethatthepulsedensityisproportionaltothemagnitudeofx(t)andisinverselyproportionaltoC.IftheinputsignalissuperposedonalargeDCoffset,theIFneuronrequirestoomuchbandwidth[ 26 ]. 3.1.2Voltage-ModeImplementationoftheIFEncoder Figure3-2. Integrated-circuitvoltage-modeimplementationoftheIFconverter TheIFneuronhasbeenimplementedinhardwareincludingintegratedcircuits(IC)andoff-the-shelfboards.Incircuitry,thefunctionofintegrationisimplementedbyacapacitortochargetheinputcurrent.Iftheinputsignalisintheformofvoltage,avoltage-to-currentconverterisrequiredtoprovidethecurrent.Figure 3-2 showsthediagramofanICimplementationoftheIFneuronincludingavoltage-to-currentconverter.Theoperationaltransconductanceamplier(OTA),twodiode-connectedtransistorsM1,M2,andtheinputAC-couplingcapacitorC1worktogetherasthevoltage-to-currentconverterwhichtransducestheinputvoltageintocurrent.ThecapacitorC2isusedtointegratethecurrentintovoltageVmem,whichisdenedasz(t) 43

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inFigure 3-1 .TwocomparatorsrepulseswheneverVmemcrossesthethreshold+and)]TJ /F4 11.955 Tf 9.3 0 Td[(.M3istheswitchcontrolledbythepulseoutputtoresetVmem. Figure3-3. ThedriftissueoftheIFencoderobservedinthebench-topmeasurements:1)Thesymmetricinputsignal;2)TheintegralvoltageVmemwithresetwhenitreachesthethresholds;3)Outputpulsetrainofpositivechannelp+;4)Outputpulsetrainofnegativechannelp)]TJ /F1 11.955 Tf 7.09 1.79 Td[(.p+andp)]TJ /F1 11.955 Tf 10.41 1.79 Td[(areexpectedtogenerateequalpulseswheninputsignalissymmetric.However,p+producesmoreandmorepulsesandp)]TJ /F1 11.955 Tf 10.41 1.79 Td[(producesfewerandfewerpulses. ThecircuitshowninFigure 3-2 exhibitsaninstabilityissueobservedinthebench-topmeasurements.Iftheinputsignalissymmetric,thebiphasicpulsetrainattheoutputisexpectedtobesymmetricaswell.However,theoutputisnotsymmetricinthebench-topmeasurements;andwhatisworse,pulsesgraduallyshifttoonesideasshowninFigure 3-3 .Thelasttwowaveformsaretheoutputpulsetrainsofpositiveandnegativesides.Onesideoutputhasmoreandmorepulseswhiletheotherside 44

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outputhasfewerandfewerpulsesandeventuallythepulsescompletelydisappear.Thishappensduetotheleakagecurrentandoffsetvoltageofthediode-connectedtransistorsM1,M2inthefeedbackpathoftheOTA,whichresultsinalargeoffsetvoltageofthevoltage-to-currentconverterandcausesthequiescentvalueofVmemtodriftfromtheexpectedvalue,i.e.,themiddlevoltagebetween+and)]TJ /F4 11.955 Tf 9.29 0 Td[(.Theseleakageandoffsetaresignalandtemperaturedependentandtheequivalentoffsetvoltageofthediode-connectedtransistorscouldbeashighasfewhundredmillivolts[ 27 ].Toreducetheleakageandtheoffset,asinglediode-connectedtransistorisusedinsteadoftwo,whichhelpsthesystemgeneratesymmetricstableoutputsduringthebench-topmeasurementswhentestingwiththesymmetricinputsignals.However,usingasingletransistorshrinkstherangeofthresholdvoltages+and)]TJ /F4 11.955 Tf 9.3 0 Td[(.cannotbelargerthanthetransistorthresholdvoltage;otherwisethetransistorisconducting.Alsocannotbesmallerthantheoffsetvoltageofdiode-connectedtransistor;otherwisetheeffectivethresholdvoltagesaredominatedbythesignal-dependentandtemperature-dependentoffsets,whichresultindriftingpulsetrains. 3.2Electrolyte-ElectrodeInterfaceElectricalModel Figure3-4. Equivalentcircuitoftheelectrolyteandtheinterfacebetweentheelectrolyteandtheelectrodeconnectingarecordingcircuit Figure 3-4 showstheelectricalmodeloftheelectrolyte(i.e.,biologicaltissue)andtheinterfacebetweentheelectrolyteandtheelectrodeconnectingtoarecordingcircuit[ 28 ][ 29 ].Thebio-potentialisrepresentedbyavoltagesource,Vin.Thevoltagesource 45

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Vinisdeterminedbythechangingconcentrationofionicspeciesneartherecordingelectrode.Themathematicalrelationshipbetweenionicconcentrationandelectrostaticpotentialhasbeendiscussedin[ 30 ].Re,inserieswithVin,representstheelectrolytespreadingresistance.Rmistheseriesresistanceoftheinterconnectmetals.TheinputresistanceandcapacitanceoftherecordingamplieraredenotedasRaandCa,respectively.Thespacechargeregioninelectrodeandelectrolyteinterfaceshasbeenknowngenericallyasthedoublelayer[ 31 ][ 32 ].Thedoublelayercanbemodeledbyaparallelconnectionofadouble-layercapacitorCdlandachargetransferresistorRct.ChargetransferbetweentheelectrolyteandmetalduringelectrochemicalreactionsresultsintheleakageeffectbetweenthedoublelayerandthiseffectisrepresentbyRct.Ifnoelectrochemicalreactionsoccurattheinterface,whichiscallednonfaradaicinterface[ 33 ],Rctisapproachinginnity[ 34 ]. ReisaboutseveraltensofKfortypicalrecordingsitesize(areaof100m2)[ 28 ].Rmisdependentonthesheetresistance,thecrosssectionareaandlengthoftheinterconnectline.Generally,Rmisverysmall.ThedoublelayercapacitorCdlistypically10v20F/cm2[ 35 ].TheimpedancesoftheUtaharrayelectrodeat1KHzisintherangeof10v20K[ 36 ].TheimpedancesofthetungstenexibleelectrodesdevelopedbyUniversityofFloridais50K10Kat1KHz[ 34 ].TheexperimentaldataoftungstenelectrodeshowsthatRe=5K,Rct=3M.Theresultalsosuggeststhatthecapacityofthedoublelayerisnotthesameasaphysicalcapacitor,butisequalto1 (j!Cdl),whereCdl=11nFand=0.87duetoinhomogeneoussurface[ 34 ]. 3.3Current-ModeImplementationoftheIFEncoder Allknownimplantableneuralrecordingcircuitsamplifyavoltagesignalfromelectrodesinsertedintothebrain[ 37 40 ].UsingvoltageastherecordingvariableprovidesseveraladvantagessuchascapacitivecouplingwhicheliminatestheDCcomponentofthesignalandtheabilitytorelyonalonghistoryofdesignsofvoltage-basedampliers,typicallythosederivedfromHarrison'soriginaldesign[ 15 ]. 46

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TheHarrison'sampliercanbesimplytreatedasanamplierwithcapacitoratinputandresistoronthefeedbackpath,asshowninFigure 3-5A .IntheIFencodingapproachinneuralrecordingusingavoltage-modefront-end,anawkwardvoltage-to-currentconvertermustbeaddedafterthefront-endvoltageamplier,complicatingthecircuit. AVoltage-modeIFdiagramwithelectrode BCurrent-modeIFdiagramwithelectrode Figure3-5. Electrode-IFcircuitdiagram:A)Voltage-modeIFcircuitdiagram;B)Current-modeIFcircuitdiagram Insteadofholdingthecurrentconstantwhilemeasuringthevoltageontheelectrode,weproposetoholdthevoltageconstantandmeasuretheresultingcurrentfromtheelectrode.AsanalysisinSection 3.2 ,theelectrodecanbemodeledasaparalleledcombinationofresistorandcapacitor.Figure 3-5B showstheIFencodingdiagramincurrent-modewithelectrode.TheproblemischangedfromamplifyingVrangesignaltoamplifyingwhatweestimatetobepAofcurrent.Amplifyingsmallcurrentlevelscanbeaccomplishedsimplybyintegratingthecurrentontoalargecapacitor.Thismethodisstraightforward,efcient,andimprovestheSNRbasedontheintegrationtime. 47

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InFigure 3-5B ,theinputtothecircuitisintheformofacurrent.Inneuralrecording,thecurrentisdeterminedbytheionicconcentration.VoltageinputanditsequivalentcurrentinputarerelatedbyThevenin'stheorem.Foramoregeneralcase,theinputismodeledasavoltagesourcewithaseriesimpedance[ 28 ].Figure 3-6 showsacurrentconveyorcircuitconnectingtoavoltagesourceVsatinputthroughanelectrode.ThedetailofthecurrentconveyorwillbecoveredinSection 3.3.1 .ThetransconductanceoftransistorT0isgm.TheimpedanceoftherecordingelectrodeisZ.TheOPAcchasnitegainofA.ThecurrentowingthroughnodeXcanbecalculatedasbelow. Ix=Vx)]TJ /F3 11.955 Tf 11.96 0 Td[(Vs Z(3) )]TJ /F3 11.955 Tf 11.95 0 Td[(VxA=Vx+Ix gm(3) ReplaceIxinEq. 3 withEq. 3 ,andrearrangetheresult,wecanget Vx=Vs 1+(1+A)gmZ(3) Ideally,inthecurrentconveyorcircuitry,VxisxedtoVyandisnotdisturbedbyVs.However,iftheloopgainAgmZisnotlargeenough,VxvarieswithVs.ThecurrentowingthroughthecurrentconveyorinputnodeXisequalto Ix=)]TJ /F3 11.955 Tf 9.3 0 Td[(Vs(1+A)gm 1+(1+A)gmZ)]TJ /F3 11.955 Tf 23.12 8.09 Td[(Vs Z(3) Figure3-6. Currentconveyorcircuitwithvoltagesourceinput 48

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wherethesign-meansthecurrentowingintheoppositedirectiontothecurrentdirectiondrawinginFigure 3-6 Inthissection,Wereviewthecurrentconveyorwhichisthekeyelementusedinthecurrent-modeapproach.Thenbasedonthebidirectionalcurrentconveyorwithclass-Boutputstage,thebidirectionalcurrentconveyorwithclass-ABoutputstageisproposedtoavoidthecrossoverdistortionproblem.Next,abidirectionalcurrentamplierisproposedtogetherwithafeedbackpathtolterouttheoffsetcurrent.Finallyinthissection,thecompleteintegrate-and-recircuitryincurrent-modeispresented. 3.3.1CurrentConveyorOverview TherstcurrentconveyorknownasCCI,whichhascurrentowinginbothinputterminalswasproposedbySmith,K.CandSedra,A.S.in1968[ 41 ].Twoyearslater,theimprovedsecond-generationcurrentconveyornotatedasCCIIwasproposedbythesameauthors[ 42 ].Recently,theCCIIhasbeenwidelyusedinactivelterdesignandsignalprocessing[ 43 ],[ 44 ],[ 45 ],[ 46 ].TheCCintheacronymCCIIstandsforcurrentconveyor.TheIIsigniesthatitisasecondgenerationcurrentconveyor AsshowninFigure 3-7 ,theCCIIisathree-portnetworkanditsterminalsaredenedasX,YandZ.ThecharacterizationofCCIIcanbedescribedbythematrixofEq. 3 24iYvXiZ35=240001000103524vYiXvZ35 (3) Figure3-7. Blackboxrepresentationofthecurrentconveyor:athree-portnetwork,twoinputterminalsX,YandoneoutputterminalZ.V~isthevoltageatterminal~andi~isthecurrentowingintoterminal~. IntheCCII,theinputterminalYhasnocurrentowingandthevoltageatterminalXfollowsthevoltageatY.Ideally,theinputimpedanceofterminalYisinniteandtheinputimpedanceofterminalXiszero.ThecurrentowingthroughterminalXisconveyedto 49

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thehighimpedanceoutputterminalZwithgainof1.Thepositivecurrentconveyor(CCII+)hasgainequalto+1andthenegativecurrentconveyor(CCII-)hasthegainequalto-1. ACCII-usingNMOS BCCII-usingPMOS Figure3-8. Negativesecond-generationcurrentconveyors(CCII-):A)ANMOSintheOPAfeedbackloop,currentowingoutofterminalX;B)APMOSintheOPAfeedbackloop,currentowingintoterminalX ACCII-canberealizedbyatransistorandanoperationalamplier(OPA)asshowninFigure 3-8 .InFigure 3-8A ,thecurrentowingoutofterminalXmustowintoterminalZ(drainofNMOS).InFigure 3-8B ,thecurrentowingintoterminalXmustowoutofterminalZ(drainofPMOS). AbidirectionalcurrentconveyorcontainingacomplementarypairofMOStransistorsinthefeedbackpathisshowninFigure 3-9 [ 47 ].ThevoltageVxfollowsthevoltageVybecauseofthenegativefeedback.TheinputcurrentsuppliedtonodeXisconveyedtothesourceoftransistorsN0andP0.Dependingonthepolarityoftheinputcurrent,eitherthePMOScascodecurrentmirrorsourcesthecurrenttonodeZortheNMOScascodecurrentmirrorsinksthecurrentfromnodeZ.ThisimplementationisabidirectionalCCII+.AbidirectionalCCII-circuitcanalsobeimplementedwithanadditionalcurrentmirrorpair. Figure 3-10 isatransientsimulationofthebidirectionalcurrentconveyorcircuit.Thebluedashedlineistheinputcurrentandtheredsolidlineistheoutputcurrent.Theoutputcurrentisalmostidenticaltotheinputcurrentexceptwhentheinputcurrentchangespolarity.ThereasontothisdeadbandisthatoneofthetransistorsN0and 50

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Figure3-9. BidirectionalpositivecurrentconveyorCCII+ Figure3-10. SimulationofinputandoutputcurrentofbidirectionalCCII+ 51

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P0connectingtotheoutputoftheOPAcannotturnonimmediatelywhentheotheronetransistorturnsoffduetothecertaintimerequiredfortheOPAoutputtransition.WhentheinputcurrentowingintonodeX,thecurrentgoesthroughtransistorP0andtheNMOScurrentmirror.TheoutputvoltageoftheOPA,Vo,OPA,islowerthanVxbyjVGS,P0j.Sincethefeedbackpathisworking,Vx=Vy.Whentheinputcurrentchangespolarity,owingoutofnodeX,transistorP0doesnotsinkcurrentanymoreandN0triestosourcethecurrent.However,atthemomentofcurrentpolaritychanging,thegate-sourcevoltageofN0isnegative,sobothP0andN0areoff.ThefeedbackpathisinvalidandVxdoesnotfollowVy.AsN0triestosourcecurrent,Vxdecreases,Vo,OPAincreasesandtheoutputcurrentiszerountilVo,OPAishigherthanVxbyVGS,N0.WhenVo,OPAreachesthevaluehigherthanVxbyVGS,N0,N0isturnedonandthefeedbackpathisbacktowork.ThenVx=Vy,N0sourcesthecurrentandthePMOScurrentmirrorsthecurrenttotheoutput.ThedeadbandintroducescrossoverdistortionofthesignalandmakesthisbidirectionalcurrentconveyorunsuitableforbiphasicIFencodercircuitry. 3.3.2BidirectionalCurrentConveyorIFCircuit 3.3.2.1Class-ABbidirectionalcurrentconveyor ThecomplementarytransistorpairN0andP0inthebidirectionalcurrentconveyorshowninFigure 3-9 worksasaClass-Boutputstageandhasthedeadbandissue.ThecrossoverdistortiondescribedabovecanbeeasilyreducedbyadoptingaClass-ABoperationofthecircuit.Figure 3-11 showstheClass-ABbidirectionalcurrentconveyorcircuit.Thediode-connectedtransistorsNs0andPs0shiftN0gatevoltagejVGS,Ps0j+VGS,Ns0higherthanP0gatevoltage.N0andP0alwaysconductabiascurrentproportionaltothebiascurrentofNs0andPs0.Figure 3-12 showsatypicaltransfercharacteristicoftheClass-ABcurrentconveyor.Thedeadbandhasbeeneffectivelyeliminated.TheoutputcurrentsaturateswhentheinputcurrentincreasesbecausetheNMOSorthePMOScurrentmirrorgoesintotrioderegion. 52

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Figure3-11. Class-ABbidirectionalcurrentconveyor Figure3-12. ThansfercharacteristicoftheClassABbi-directionalcurrentconveyor 53

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TheOPAofthecurrentconveyorisatwostageamplier,whichcontainsatleasttwopolesandonezerolocatedat !P1=1 gmN3R1R2Ccomp!P2=gmN3 C1+C2!Z=1 Ccomp(Rlead)]TJ /F6 7.97 Tf 20.35 4.7 Td[(1 gmN3)Rlead=1 CoxW LVe(3) whereR1=ro,P2jjro,N2,R2=ro,N3jj(ro,B3+1 gmNs0+1 gmPs0),C1=Cdb,P2+Cdb,P3+Cgs,N3,andC2=Cdb,N3+Cdb,Ps0+Cgs,Ps0+Cgs,P0. Theopenlooplowfrequencygainisequalto A0=gmP2R1gmN3R2(3) Astableloopgenerallyrequiresaphasemarginlargerthan45.Toachievethis,thegain-bandwidth-productGBW=gmP2 Ccompneedstobenotlargerthantheequivalentsecondpole!eqandusuallyRlead1 gmN3. 3.3.2.2Class-ABcurrentconveyorIFcircuit Figure3-13. SchematicoftheClass-ABcurrentconveyorIFcircuit 54

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Figure 3-13 showsasimpleimplementationoftheIFconverterwiththeClass-ABbidirectionalcurrentconveyor.TheoutputoftheClass-ABcurrentconveyoristheinputtotheIFencoder.NodeYconnectstoareferencetoprovidethereferencevoltageofnodeX.TheinputcurrentowingthroughnodeXisconveyedandmirroredtotheintegrationcapacitorC2.TheintegratedvoltageVmematC2iscomparedtothresholds.IfVmemcrossesthethresholds,itisresettoacground. Figure3-14. CadencesimulationoftheClass-ABcurrentconveyorIFcircuit ThecircuitshavebeendesignedandsimulatedinAMI0.5mprocess.Figure 3-14 showsatransientresponseofthecircuitshowninFigure 3-13 .Theinputcurrentisshownattherstrow.ThecurrentsowingthroughtransistorN0andP0areshowninthesecondandthethirdwaveforms.ThebiasingcurrentofN0andP0is428nA.ThedifferencebetweenthecurrentsowingthroughN0andP0isequaltotheinputcurrent,asshowninthefourthwaveform.Thedifferencebetweenthetwocurrentsisthetotal 55

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Figure3-15. ReconstructionresultoftheClass-ABcurrentconveyorIFcircuit currentmirroredandconveyedtotheintegrationcapacitor.TheintegrationvoltageVmemisshownatthefthrow.Vmemisresetwhenitreachesthethresholdvoltages.Thelasttwowaveformsarethebiphasicoutputpulsestrains.Withthesettingofthethresholdvoltage200mVandthecapacitor800fF,theIFcircuitconvertsa4nA1KHzsinewaveinputtoa10Kpulses/soutput.Thecircuitsimulationoutputhasbeenreconstructed.Figure 3-15 showstherecoveredsignal,theinputsignalandtheerrorbetweenthem.Thereconstructionobtains44dBSER.ThedropoftheSERisduetothecurrentmirrormismatch,signaldependentthresholdoffsetsofthecomparators,thechargeinjectionnoiseoftheswitchesandtheothernonidealeffects. 3.3.3CurrentAmplierandFeedbackLoop Therearetwodifcultiesindesigningthecurrent-basedIFcircuitry.First,formeasuringextremelysensitiveandweakcurrentsignal,alow-noiseandhighgaincurrentamplierisnecessary.Second,inordertofurtherreducethedatarate,itisbettertohigh-passtheinputsignalandeliminatetheoffsetcurrentandtheoffsetoftheOPA.Next,twocircuittopologiesareproposedtosolvethesedifculties. 56

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3.3.3.1Currentamplier Alow-noisehigh-gaincurrentamplierisrequiredforconveyingandamplifyingthesensitiveandweaksignals,suchasneuralsignals.Currentamplicationusingcurrentmirrorsisapopularapproach,howevertheirsensitivityislimitedtotensofpAlevel[ 48 ].Themirroringaccuracyandsensitivitygetworseinpracticalimplementationbecauseoffabricationmismatchesandsecondordereffectssuchaschannellengthmodulation.Thetransimpedanceamplier(TIA)whichconvertsthecurrentintoavoltage,isanotherpopularapproachforcurrentamplication[ 49 ].TheTIAusingcapacitordividerscanachievehighgainwithlownoise. Figure3-16. Currentconveyoramplier Figure 3-16 showsthecurrentampliferschematicusingTIAandcapacitordividers.TransistorT0inFigure 3-16 representsthecomplementarypairtransistorsN0andP0inFigure 3-11 .Becauseofthenegativefeedbackandtherequirementofthecurrentconveyor,thevoltageatnodeXfollowsthevoltageatnodeY.CapacitorC1sensestheinputsignalixandchargescapacitorC2resultinginvoltageva.vainducesthecurrentthroughC2proportionaltoix.Theoutputcurrentizcanbeexpressedas: va=)]TJ /F3 11.955 Tf 15.45 8.09 Td[(ix sC1(3) 57

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iC2=vasC2=)]TJ /F3 11.955 Tf 9.3 0 Td[(ixC2 C1(3) iz=iC2)]TJ /F3 11.955 Tf 11.96 0 Td[(iC1=)]TJ /F3 11.955 Tf 9.3 0 Td[(ix(1+C2 C1)(3) Thus,theoutputcurrentisampliedbyafactorof(1+C2=C1). Tobeclear,theanalysisinthischapterfollowstheconventioninanalogcircuitsdesign:uppercaseletterswithlowercasesubscriptsrepresenttotalcomponents;uppercaseletterswithuppercasesubscriptsrepresenttheDCcomponents;andlowercaseletterswithlowercasesubscriptsrepresenttheACcomponent.Forexample,In=IN+in,inwhichInisthetotalcurrent,INistheDCcurrentandinisthesmallsignalcomponent. 3.3.3.2Low-passlterfeedbackloop TheDCcomponentoftheinputcurrentortheoffsetoftheOPAwillresultinincreasingdatarateanddegradingaccuracy.Sotheoutputofthecurrentconveyormustbeahigh-passlteredversionoftheinputsignalandtheoffsetshouldbeminimized.Apossiblesolutionistouseaninductorattheinputnode.However,anextremelylargevalueinductorwouldberequiredforalowcutofffrequencyvalue.Alow-passlterfeedbackloop,proposedin[ 50 ],canbeusedtopreventtheoffsetcurrentfromowingtotheoutput.Thelow-passlterfeedbackloopalsoprovidesanegativefeedbackpathforthecurrentconveyor,sothatthevoltageatnodeXfollowsthevoltageatnodeY. Figure3-17. Continuous-timeresetbiasnetwork Figure 3-17 showsthelow-passlterfeedbackloopcircuit.NodesAandXinFigure 3-17 correspondtonodesAandXshowninFigure 3-16 .Thecircuitconsistsof 58

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alow-passlter,andalineartransconductor.Thecutofffrequencyofthelow-passlterismuchlowerthanthefrequencyofinterest.Thelow-passlterwithaDCgainofjH(0)jpassestheaveragevalueofVatonodeB.ThenVbcontrolsthetransconductortoeithersourceorsinkcurrentix.ThefeedbackpathensuresthatthetransconductoroutputcurrentisthesameastheoffsetcurrentowingthroughnodeXinFigure 3-16 Workingourwaybackwards,ifthetransconductoroutputisequaltotheoffsetcurrent,thevoltageatnodeBcanthenbewrittenasvb=IDC=Gm,whereIDCistheinputoffsetcurrentandGmistheeffectivetransconductance.ThisimpliesthatthevoltageatnodeAcanbewrittenasva=vb=jH(0)j.IfjH(0)jislarge,thenvaisapproximatelyequalto0,makingitindependentofIDC.Whentheinputsignalfrequencyishigherthanthecutofffrequencyofthelow-passlter,thefeedbackbiaspathnolongeroperates,andthesignalpassesthroughC1andgetsamplication.Thetransferfunctionforthelow-passltercanbewrittenas: H(s)=)]TJ /F5 11.955 Tf 29.32 8.09 Td[(1 sRLPCLP(3) whereRLPistheeffectiveresistanceofthediode-connectedtransistorTLP. ThelterhasahighDCgainandtheunity-gainfrequencyof1=(2RLPCLP).Inordertoachievealowcutofffrequency,largevaluesofthecapacitorandtheresistancearerequired.Forexample,foradesiredcutofffrequencyof100Hz,withacapacitorvalueof10pF,theresistanceneedstobeaslargeas160M.Thephysicalresistorinintegratedcircuitsofsuchabigvalueconsumeslargediearea,forexample,estimated0.8mm2inAMI0.5mprocess.Itisnotfeasibletoimplementsuchalargeresistanceonachip.Thesolutionistouseareversebiaseddiodeasaresistor.Typically,thediode-connectedtransistorhasahighresistanceintherangeofafewGwhenthevoltageacrossitismuchlowerthanthethreshold[ 16 ],[ 51 ].TheparasiticcapacitorsCgbandCgsofthediode-connectedtransistorintroduceazerotothetransferfunctionofthelow-passlter. 59

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Thenoiseofthetransconductorcontributestotheinputnoisedirectly.SincethetransconductorcurrentnoiseisdirectlyproportionaltoGm,anextremelysmallGmvalueisnecessarytoreducethenoise.FormakingtheGmsmallweusethepseudoresistordividertopology[ 52 ].ThepseudoresistordividerisimplementedusingtransistorsTattandTspillasshowninFigure 3-17 .ThedrainsoftransistorsTattandTspillconnecttotheirgatesrespectively,andtheirsourceandbulksareconnectedtogetherwiththeoutputoftheOPAGM.Whenthegate-sourcevoltageVGSofthetransistorsisnegative,thetransistorsworkinsaturationregionorinsubthresholdregion.WhenVGSispositive,thetransistorsworkaspnpbipolartransistorsandforwardbiasedp-njunctions.Thecurrentofatransistorineachconditionis[ 53 ],[ 54 ]: Saturation:ID=eCoxW L(VGS)]TJ /F3 11.955 Tf 11.95 0 Td[(VTH)2 (3a) Subthreshold:ID=eCoxW L()]TJ /F5 11.955 Tf 11.96 0 Td[(1)UT2eVGS)]TJ /F12 5.978 Tf 5.75 0 Td[(VTH UT(1)]TJ /F3 11.955 Tf 11.95 0 Td[(e)]TJ /F12 5.978 Tf 7.78 4.62 Td[(VDS UT) (3b) pnjunction:ID=qni2(Dn LnNa+Dp LpNd)(2TE+W(2T+E))(eVGS UT)]TJ /F5 11.955 Tf 11.95 0 Td[(1) (3c) whereeistheeffectivemobility;Coxistheoxidecapacitanceperunitarea;VTHisthethresholdvoltageoftransistor;UT=kT qisthethermalvoltage;isthebodyeffectcoefcientwhichistypically1.11.4.qistheelectroncharge.niistheintrinsiccarrierdensity.NaandNdaretheacceptorimpuritydensityandthedonorimpuritydensity;Dn,Dparethediffusioncoefcientsofelectronandhole;LnandLparethediffusionlengthsofelectronandholeminoritycarrier,respectively;WandLarethewidthandthelengthofthetransistors;TandEarethethicknessandthewidthofp+drainjunction. WhenWTandWE,thecurrentisproportionaltowidthW.Theequivalentresistanceofeachtransistorisvariesdependingontheworkingconditions.However,nomatterwhatevertheworkingcondition,theratioofthecurrentthroughthetransistorsTattandTspillisproportionaltotheratiooftheirrespectivewidths,sincethetransistors 60

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arebiasedatthesamevoltage. IDatt IDspill=WTatt WTspill(3) SizingtransistorTattMtimeslargerthantransistorTspill,impliesthecurrentowingthroughRattisMtimeslargerthantheinputoffsetcurrentIDC.MtimeslargercurrentthroughRattalsoresultsinthethermalnoisedecreasingbyafactorofM2.ThusthetransconductorvalueGmisequalto: Gm=Iout Vin=IDC VDC=1 RattM(3) Forexample,choosingRatt=400KandM=100resultsintheequivalentresistorof40M,whosenoiseisequivalenttotheresistorof4G.Thediode-connectedtransistorcurrentdividercansplitcurrenteveninthefArange[ 52 ]. 3.3.3.3Frequencyresponse Figure3-18. Currentconveyoramplierswithbiasnetwork Therearetwofeedbackloopssuperimposedtogethertostabilizethecircuitandamplifythesignal.Simply,itcanbetreatedasonefeedbackpathforDCcomponentandanotherfeedbackpathforACsignal.However,moredetailsofthefrequencyresponsearenecessarytoguidethedesign.Tocarefullyanalyzethefrequencyresponse,the 61

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currentconveyorampliercircuitisredrawninFigure 3-18 ,alsoincludingparasiticcapacitorsCpX,CpLPattheinputnodeandinthelow-passlter. AssumingOPALPandOPAGMhaveinnitegainandthecurrentmirrorshaveinniteoutputimpedance.OPACChasaDCgainA0andadominantpole!pa.ThetransconductanceofT0isgmT0.EquivalentresistanceofTattisRo,andtheequivalentresistanceofTspillisMRo. A(s)=A0 1+s !pa (3) H(s)=)]TJ /F5 11.955 Tf 10.49 8.09 Td[(1+sRLPCpLP sRLPCLP (3) Ix=(Vx)]TJ /F3 11.955 Tf 11.95 0 Td[(Va)sC1+VxsCpX+VaH(s)Ro+VxRatt MRattRo (3) Iz=gmT0()]TJ /F3 11.955 Tf 9.3 0 Td[(VxA(s))]TJ /F3 11.955 Tf 11.95 0 Td[(Va) (3) Iz=VasC2+(Va)]TJ /F3 11.955 Tf 11.96 0 Td[(Vx)sC1+Va(1+sRLPCpLP) RLP (3) Fromtheaboveequations,thetransferfunctionIz Ixcanbeobtained. Iz Ix(s)=)]TJ /F3 11.955 Tf 10.49 10.78 Td[(s(1+s(C2+C1+CpX)RLP+s2C1RLP A0!pa)CLPMRatt D(3) where D=1+s(CpLPRLP+CLPRatt(gmT0RLP+1) gmT0RoA0)]TJ /F3 11.955 Tf 24.4 8.09 Td[(C1 gmT0A0)+s2(CLPC1MRattRLP+CLPRatt(gmT0RLP+1) gmT0RoA0!pa+CLP(C1+CpX)MRatt(gmT0RLP+1) gmT0A0+CLP(C2+C1+CpLP)RattRLP gmT0RoA0)]TJ /F3 11.955 Tf 13.15 8.09 Td[(C1CpLPRLP gmT0A0)]TJ /F3 11.955 Tf 32.62 8.09 Td[(C1 gmT0A0!pa)+s3(CLP(C1+CpX)MRatt(gmT0RLP+1) gmT0A0!pa+CLP(C2+C1+CpLP)RattRLP gmT0RoA0!pa+CLP(C2+C1+CpLP)(C1+CpX)MRattRLP gmT0A0)]TJ /F3 11.955 Tf 13.15 8.09 Td[(C1CpLPRLP gmT0A0!pa)+s4(CLP(C2+C1+CpLP)(C1+CpX)MRattRLP gmT0A0!pa)(3) 62

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FromEq. 3 ,wecanseethatthesystemisaband-passlterwithfourpolesandthreezeros.Onezeroisatorigin.However,suchacomplicatedequationdoesnotexplainspecicinformationonhowtocontrolthelocationsofzerosandpoles.Eq. 3 canbesimpliedwiththereasonableassumptionsofA01,C2C1,CLPCpLP,C2CpLPandgmT0RLP1.WhenRLPC1Ro CLPgmT0Ratt,gmT0 C2!pa,C1MRo1 A0!paandgmT0MRattCpLP CLP, Iz Ix(s)=)]TJ /F3 11.955 Tf 10.5 10.78 Td[(s(1+sC2RLP+s2C1RLP A0!pa)CLPMRatt D0(3) where D0=1+s(CpLPRLP+CLPRattRLP RoA0)+s2(CLPC1MRattRLP)+s3(CLP((C1+CpX)gmT0MRo+C2)RattRLP gmT0RoA0!pa)+s4(CLPC2(C1+CpX)MRattRLP gmT0A0!pa)=(1+s !LQL+s2 !L2)(1+s !HQH+s2 !H2)(3) Eq. 3 tellsthatthersttwopolesarelocatedatlowfrequencyandtheothertwopolesareathighfrequency.Figure 3-19 showsageneralfrequencyresponsedenedbyEq. 3 ,andspecicallylabelsthepoles.Threezerosarelocatedattheorigin,lowfrequencyandhighfrequency,respectively. !z0=0;!z1=1 C2RLP;!z2=C2 C1A0!pa.(3) Thegainatmidfrequencyis Ai=js(1+sC2RLPA0!pa)CLPMRatt 1+s(CpLPRLP+CLPRattRLP RoA0)+s2(CLPC1MRattRLP)jC2 C11 q 1+(CpLP CLPMRatt+1 MRoA0)2C2 C1(3) 63

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Thepoleswillbediscussedundertwosituations:1)CpLPisnegligible;2)CpLPissignicant. IfCpLPCLPRatt RoA0, !L=1 p CLPC1MRattRLP (3) !H=s C1gmT0A0!pa C2(C1+CpX) (3) QL=s C1MRo2A02 CLPRattRLP (3) QH=q C1C2(C1+CpX)gmT0M2Ro2A0!pa (C1+CpX)gmT0MRo+C2 (3) IfCLP RoA0CLPC1Mand((C1+CpX)gmT0MRo+C2)C2(C1+CpX)MRo,fourpolescanbeeasilysolved. !p1,2=!L=1 p CLPC1MRattRLP (3) !p3=(C1+CpX)gmT0MRo+C2 C2(C1+CpX)MRo (3) !p4=C1gmT0MRoA0!pa (C1+CpX)gmT0MRo+C2 (3) IfCpLPisnotnegligible,CpLPCLPRatt RoA0,itaffectsthelocationsandthequalityfactorofthetwopolesatlowfrequency.!L,!H,!p3,!p4andQHareasEq. 3 3 3 3 and 3 QL=s CLPC1MRatt CpLP2RLP(3) IfCpLPCLPC1MRatt,thetwolow-frequencypolesarelocatedat !p1=1 CpLPRLP;!p2=CpLP CLPC1MRatt(3) Theloopgainofthebiasfeedbackloopis T0(s)=)]TJ /F3 11.955 Tf 22.01 8.08 Td[(H(s) sC1MRatt=1+sCpLPRLP s2C1CLPMRattRLP(3) 64

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Figure3-19. Frequencyresponsedenedbyeq 3 SincecapacitorsC1introduces90phaseshift,stabilityofthisloopisguaranteedifthelow-passlterH(s)addslessthan90phaseshiftatthefrequencieslessthantheunity-frequencyf0oftheloopwhichisdenedasjT0(f0)j=1. f0=CpLP 2C1CLPMRatt(3) Thelow-passlterhasapoleattheoriginandazerofzat1 2CpLPRLP.Aslongasfz
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3.3.4Current-ModeImplementationoftheIFwithAmplication 3.3.4.1Current-modeIFcircuit Figure3-20. Currentconveyorintegrate-and-recircuitimplementation ThecompletecurrentmodeIFcircuitincludingtheamplier,thedcremovingfeedbackloopandtheintegrate-and-recircuitisshowninFigure 3-20 .AllOPAsareimplementedusingclassicaltwo-stageoperationalamplierstructuresasshowninFigure 3-21 .ThedesignofeachOPAisfocusedonitsownprimaryconcernssuchasnoise,power,gain,phasemarginandsize.Adcbiascurrent,Ib1isaddedtotheinputsignaltokeeptransistorN0alwaysintheactiveregion.Thesameamountofdcbiascurrentislatersubtractedfromtheoutputsignal,denotedasIb2inFigure 3-20 .Thus 66

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Figure3-21. Two-stageoperationalamplier onlytheampliedsignalcurrentisowingintooroutoftheintegrationcapacitorC3,andthecurrentconveyorisabletodeliverbidirectionalcurrent.TheClass-ABbidirectionalcurrentconveyorIFasshowninFigure 3-13 canalsoworkwiththecapacitordivideramplierandthelow-passlterfeedbacklooptoamplifythesignalandremovingthedcoffsetcurrent(notshownhere). Inputcurrentixisamplied(1+C2=C1)times,dependingonthepolarityiteitherdischargesorchargesthecapacitorC3,resultinginthevoltage,Vmem.Vmemissimultaneouslycomparedtothethresholdvoltages+and)]TJ /F4 11.955 Tf 9.3 0 Td[(.IfVmembecomeslargerthan+anoutputpulse,Pout+,isgeneratedwhichresetsC3toVmid.Similarlyforthenegativecomparator,ifthevoltagegoesbelow)]TJ /F4 11.955 Tf 9.3 0 Td[(,thenegativecomparatorgeneratesapulseresultinginthecapacitorgettingreset.Thecapacitorvoltageiskeptresetforaxedtimet,afterwhichtheprocessrepeats. Animportantpointofconcernistheaccuracyofthecurrentmirrorsthataddandsubtractthebiascurrents,Ib1andIb2.IfthebiascurrentsthroughthetransistorsN3andN5arenotequal,orcurrentIzowingthroughtransistorN0isnotcopiedexactly,anerrorisintroducedandresultsindistortions.Cascodecurrentmirrorsareadopted 67

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todecreasethecurrentmismatchduetothechannellengthmodulationandthebodyeffect[ 55 ],buttheperfectmatchingcanneverbeobtained. Iz=IC2)]TJ /F3 11.955 Tf 11.95 0 Td[(IC1+Ib1=)]TJ /F3 11.955 Tf 9.3 0 Td[(ix(C2 C1+1)+Ib+Ib1=)]TJ /F3 11.955 Tf 11.96 0 Td[(ix(C2 C1+1)+Ib+VA+va)]TJ /F3 11.955 Tf 11.96 0 Td[(VgsN1 RoN(3) I0z=Iz+Iz=Iz+VMEM+vmem)]TJ /F5 11.955 Tf 11.95 0 Td[((Vdd)]TJ /F3 11.955 Tf 11.95 0 Td[(VgsP1) RoP(3) whereRoPandRoNaretheoutputimpedancelookingbackintoPMOScurrentmirrorandNMOScurrentmirrors,respectively. RoP=[1+(gmP4+gmbP4)roP3]roP4+roP3gmP4roP3roP4(3) RoN=[1+(gmN4+gmbN4)roN3]roN4+roN3gmN4roN3roN4(3) Therefore,thenaloutputcurrentIouttointegrationcapacitorC3is Iout=I0z)]TJ /F3 11.955 Tf 11.96 0 Td[(Ib2=(Iz+Iz))]TJ /F5 11.955 Tf 11.96 0 Td[((Ib+Ib2)=)]TJ /F3 11.955 Tf 9.3 0 Td[(ix(C2 C1+1)+Ib1)]TJ /F5 11.955 Tf 11.96 0 Td[(Ib2+Iz=)]TJ /F3 11.955 Tf 11.95 0 Td[(ix(C2 C1+1)+(VA)]TJ /F3 11.955 Tf 11.96 0 Td[(VMEM)+(va)]TJ /F3 11.955 Tf 11.95 0 Td[(vmem) RoN+(VMEM)]TJ /F3 11.955 Tf 11.96 0 Td[(Vdd)]TJ /F3 11.955 Tf 11.96 0 Td[(VGSP1)+(vmem)]TJ /F3 11.955 Tf 11.96 0 Td[(vgsP1) RoP(3) Generally,VA=VYbecauseofthebiasnetwork,andcapacitorC3canberesettothesamepotentialasVY.ThusVMEM=VA.AssumeC2 C1C3 C1,theIoutcanbefurthercalculatedas Iout)]TJ /F3 11.955 Tf 23.91 0 Td[(ix(C2 C1+1)+ixC2 sC1C3RoN+)]TJ /F3 11.955 Tf 9.3 0 Td[(VDSN0)]TJ /F3 11.955 Tf 11.95 0 Td[(ix(C2 C1+1)(1 sC3)]TJ /F6 7.97 Tf 20.18 4.7 Td[(1 gmP1) RoP(3) Iout=Iout)]TJ /F3 11.955 Tf 11.95 0 Td[(Kampix=ixC2 sC1C3RoN+)]TJ /F3 11.955 Tf 9.3 0 Td[(VDSN0)]TJ /F3 11.955 Tf 11.95 0 Td[(ix(C2 C1+1)(1 sC3)]TJ /F6 7.97 Tf 20.18 4.71 Td[(1 gmP1) RoP(3) Thus,analysisandsimulationresultsbothindicatethatincreasingtheoutputimpedanceandreducingtheratiosofC2 C3helpsreducingcurrentmismatch. 68

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3.3.4.2Noiseperformance Oneofthedesignchallengesofneuralsignalrecordingdevicesisthenoiseperformance.ThenoiseshouldbelowerthantheminimalsignallevelwhichisabouttensofpAfortheextracellularneuralsignals.Thecurrentampliernoiseanalysisisfocusedonthethermalnoise,theickernoiseandtheshotnoise.Thenoisesofaresistor,atransistorandadiode,respectively,are i2R=4kT Rf (3) i2P,N=(8kTgmP,N 3+KP,Ng2mP,N WP,NLP,NCoxf)f (3) i2D=2qID (3) wherekistheBoltzmannconstant;Tistheabsolutetemperature;gmPandgmNarethegatetransconductanceofthePMOSandNMOS;IDisthecurrentowingthroughadiode;andKPandKNarethetechnology-dependentconstants(independentofbiascondition).UsuallyKPismuchlessthanKN. EverycomponentinthecurrentampliershowninFigure 3-20 contributesnoise.Themajornoisesourceswillbediscussedindividuallybelow. ThenoiseofalltheOPAsusingthetwo-stageOPAstructureshowninFigure 3-21 aremainlyfromtherststage.Sincetheinputimpedanceislarge,theinput-referrednoiseofeachOPAcanbemodeledasavoltagesourcev2n,OPA, v2n,OPA=2(v2P1+v2N1g2mN1 g2mP1)=[16kT 3gmP1(1+gmN1 gmP1)+2KP WP1LP1Coxf(1+KN KP WN1LN1 WP1LP1g2mN1 g2mP1)]f(3) TominimizethenoiseoftheOPA,gmP1mustbemaximizedandgmN1mustbeminimizedasmuchaspossible.UsingPMOStransistorsatinputstageandincreasingtheirsizehelpreducingtheickernoise. 69

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BeforecomputingthenoisecontributionofeachOPA,wederivethetransconductancesfromtheinputnodeofeachOPAtonodeZwhennodeXisopen.TheinputandoutputvoltagesofOPALParelabeledasvi,OPALPandvb.TheinputandoutputvoltagesofOPAGMarelabeledasvi,OPAGMandvo,OPAGM.Ignoringtheparasiticcapacitors,wehave: vb=vi,OPALP)]TJ /F3 11.955 Tf 13.15 8.09 Td[(va)]TJ /F3 11.955 Tf 11.96 0 Td[(vi,OPALP sCLPRLP (3) vo,OPAGM=vi,OPAGM)]TJ /F3 11.955 Tf 13.15 8.09 Td[(vb)]TJ /F3 11.955 Tf 11.95 0 Td[(vi,OPAGM RattRo (3) ThecurrentowingthroughC1mustbeequaltothecurrentowingthroughTspillbecausenodeXisopen. (va)]TJ /F3 11.955 Tf 11.96 0 Td[(vx)sC1=vx)]TJ /F3 11.955 Tf 11.95 0 Td[(vo,OPAGM MRo=[vx+vi,OPALP(1+1 sCLPRLP)Ro Ratt)]TJ /F3 11.955 Tf 11.95 0 Td[(vi,OPAGM(1+Ro Ratt))]TJ /F3 11.955 Tf 11.95 0 Td[(va1 sCLPRLPRo Ratt]1 MRo(3) Rearrangingtheaboveequation,weget va=vx(1+sC1MRo)+vi,OPALP(1+1 sCLPRLP)Ro Ratt)]TJ /F3 11.955 Tf 11.96 0 Td[(vi,OPAGM(1+Ro Ratt) 1 sCLPRLPRo Ratt+sC1MRo(3) ThecurrentowingthroughterminalZis iz=vasC2+(va)]TJ /F3 11.955 Tf 11.95 0 Td[(vx)sC1+va)]TJ /F3 11.955 Tf 11.96 0 Td[(vi,OPALP RLP=va(sC1+sC2+1 RLP))]TJ /F3 11.955 Tf 11.96 0 Td[(vxsC1)]TJ /F3 11.955 Tf 11.96 0 Td[(vi,OPALP1 RLP=vx((1+sC1MRo)(sC1+sC2+1 RLP) 1 sCLPRLPRo Ratt+sC1MRo)]TJ /F3 11.955 Tf 11.96 0 Td[(sC1)+vi,OPALP((1+1 sCLPRLP)(Ro Ratt)(sC1+sC2+1 RLP) 1 sCLPRLPRo Ratt+sC1MRo)]TJ /F5 11.955 Tf 19.79 8.08 Td[(1 RLP))]TJ /F3 11.955 Tf 11.96 0 Td[(vi,OPALP((1+Ro Ratt)(sC1+sC2+1 RLP) 1 sCLPRLPRo Ratt+sC1MRo)(3) 70

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SinceC2C1andtheassumptionsof!C2RLP1,!2C1CLPMRattRLP1arevalidinthesignalbandwidth,theaboveequationcanbesimpliedas iz=vxsC2+vi,OPALPC2 C1MRatt)]TJ /F3 11.955 Tf 11.96 0 Td[(vi,OPALPC2(Ratt+Ro) C1MRattRo(3) Theinput-referrednoisecontributedbyeachOPAare: i2ni,OPACC=v2n,OPACC!2(C1+CpX)2 (3) i2ni,OPALP=v2n,OPALP1 M2R2att (3) i2ni,OPAGM=v2n,OPAGM(Ro+Ratt)2 M2R2attR2o (3) ThenoiseofOPACCissignicantathighfrequencyandisproportionaltothecapacitorsatinputnodeincludingC1andparasiticcapacitorCpX.Therefore,decreasingtheinputparasiticcapacitorhelpsdecreasethenoise.WhenRoismuchlargerthanRatt,OPALPandOPAGMcontributesimilaramountsofnoise,otherwise,OPAGMcontributesmorenoisethanOPALPdoes.IncreasingMRattdecreasesnoise. ThetransistorsofthecurrentmirrorsP1,P3,N3andN5addnoisedirectlytotheoutput,thustheircontributionstotheinput-referrednoisecanbecalculatedbydividingthecurrentgain. i2ni,P1,P3=2i2n,P3C21 C22 (3) i2ni,N3,N5=2i2n,N3C21 C22 (3) wherei2n,P3andi2n,N3followEq. 3 .Increasingthecurrentamplicationcoefcientreducestheinput-referrednoise. Inthelow-passlter,alargeresistorvalueisnecessarytoachieveaverylowcutofffrequencyforbiasingthecircuitwithoutaffectingthesignalbandwidth.This 71

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largeresistorisimplementedbythediode-connectedtransistorTLP,whichcontributenegligiblenoisebecausethereislittlecurrentowingthroughit. Thediode-connectedtransistorpairTattandTspillwithratioMisusedtoprovidelinearattenuationinthevoltage-to-currentconverterforleakingtheinputoffsetcurrent.NomatterwhenVGSispositiveornegative,theratioMisconstant,however,thenoisesoftransistorTspillandTattdependontheworkingconditions.WhenVGSisnegative,thenoiseofthediode-connectedtransistoristheshotnoiseofthedraincurrentsincethetransistoractsasadiode.WhenVGSispositive,thenoiseofthediode-connectedtransistoristheshotnoiseofthebasecurrentsincethetransistoractsasabipolarpnptransistor.Generally,thebasecurrentoftheparasiticbipolartransistorismuchsmallerthantheoffsetcurrent,thusthenoisecontributionoftransistorsTspillandTattaresmallerwhenVGSispositivethanthecontributionwhenVGSisnegative.SincethenoisegeneratedbyTattisattenuatedMtimestobecountedintotheinput-referrednoisecurrent,itsnoisecontributionisnegligiblecomparedwithTspill.ThenoiseofTspillisdirectlyaddedtotheinputnode,thus,itisasignicantpartoftheinputreferrednoise. NegativeVGS:i2ni,Tspill=2qIX (3) PositiveVGS:i2ni,Tspill=2qIBpnp (3) TransistorN0connectingtotheOPACCoutputactslikeacommongatetransistorinthecascodestage,whichcontributesnegligiblenoise[ 55 ].Fromanotherperspective,thenoiseofN0representedbyavoltagesourceatthegatecanbeconvertedtotheOPACCinputandregardedaspartoftheOPACCnoise.SincetheOPACChasaverylargegainA0,thenoisecontributionofN0isnegligible. ThecurrentamplierconveyorcontainsaphysicalresistorRattforthepurposeofthelineartransconductor.Thenoiseofthephysicalresistorcanberepresentedbyaparallelcurrentsource.ThiscurrentsourceisattenuatedMtimeswhenowingthrough 72

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inputnodeX,sothenoisecontributionofRattis i2ni,Ratt=4kT M2R(3) Thetotalinput-referrednoiseiscalculatedbyaddingalluncorrelatednoisesourcecontributions: i2ni,total=i2ni,OPACC+i2ni,OPAGM+i2ni,P1,P3+i2ni,N3,N5+i2ni,Tspill+i2ni,Ratt(3) 3.3.4.3Circuitsimulation OPACCusedinthecurrentconveyorisdesignedtoachieve0.5MHzGain-bandwidthproductand90degreephasemarginwithacompensationcapof12pF.Itsinput-referrednoiseis28.8nV/p Hzanditspowerconsumptionis33W.OPALPandOPAGMusedinthebiasnetworkhave2MHzGain-bandwidth-productand80degreephasemarginwithacompensationcapof3pF.Theinput-referrednoiseis28.1nV/p Hzandeachconsumes33W.ThebiascurrentoftransistorN0is2A.Thedesignsofthecomparatorsandthedigitalbuffersisthesameasthevoltage-modecircuitoftheIFencoder.Thetotalpowerconsumptionofthecurrentamplieris132W. Figure3-22. Simulatedfrequencyresponseofcurrentamplier 73

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ThefrequencyresponseofthecurrentamplierfrominputnodeXtonodeZ(referredtoFigure 3-20 )isshowninFigure 3-22 .TheresultisconsistentwithEq. 3 .TheratioofC2toC1ischosenas200whilethesimulatedgainis175(44.85dB).ThelostgainisduetothenonidealeffectsofthecurrentmirrorsandthesmallequivalentresistorvalueofTspillwhenthevoltageacrossitislarge.Thesimulatedlowercutofffrequencyis40Hzandthesimulatedhighercutofffrequencyis127KHz.Theintegratedinput-referrednoisecurrentinthesignalbandwidthis2.7pA.ThetransientsimulationissimilartoFigure 3-14 3.3.4.4Chipmeasurement ThecircuitshowninFigure 3-20 hasbeenfabricatedinAMI0.5mCMOStechnology.Thecurrentamplieroccupies573413m2and50%areaisconsumedbythecapacitors.Theentirecircuitincludingthecurrentamplierandtheintegrate-and-reneuronconsumes0.3mm2.Thechipoperatesatthepowersupplyof3.3V,thecurrentamplierplusthefeedbackpathconsumes66A,theintegrate-and-recircuitconsumes6Aofstaticcurrent.Thedifferentpowerconsumptioninbench-topmeasurementthantheconsumptioninsimulationisduetotheinaccuratemodelinsimulationandfabricationvariations. Thecircuithasbeentestedwithasinusoidalcurrentinput.TheinputsignalisgeneratedbyconnectingoneendoftheresistortonodeXandconnectingtheotherendoftheresistortoasinusoidalvoltagesource.ThenegativefeedbackensuresthatvoltageVxisxedatVy.Thus,theinputcurrentisequaltothevoltageamplitudedividedbytheresistance.Theinputvoltagesignalisthe50mVamplitudeat2KHzfrequencysinewavewithaDCoffsetof400mV,anda100Mresistorisused.Theinputcurrentisapproximatelya500pApeak-peaksinusoidwithafrequencyof2KHz.RecordedpulsesfromthechipareshowninFigure 3-23 .TheoutputpulsetrainsarerecordedusinganAgilentLogicAnalyzerwitha200MHzsamplingclock.Figure 3-24 showsthereconstructedsignal(inreddashedline)andtheoriginalsignal(inblacksolidline).The 74

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Figure3-23. Measurementresultsfromthecurrentmode-IFchip.Theinputtothecircuitshowninthetopsubplotis0.05sin(22000t).TheinputsignalwasconvertedtoasinusoidalcurrentinputwithIpk)]TJ /F8 7.97 Tf 6.58 0 Td[(pk500pA.Theoutputpulsesfromthepositiveandthenegativesidesareshowninthebottomtwosubplots. Figure3-24. Thereconstructedsignalandtheoriginalsignalsareshownonthetopgraph.Theerrorbetweenthetwosignalsisshownonthebottomgraph.Thesignalwasreconstructedusingthepulsesgeneratedfromthechip.Thereconstructedsignalresultsinasignal-to-noiseratioofabout36dB 75

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waveformatbottomshowserrorsignale(t)whichisthedifferencebetweentheinputsignalandtherecoveredsignal. e(t)=x(t))]TJ /F5 11.955 Tf 12.14 0 Td[(^x(t)(3) Oneparameterofevaluatingtheaccuracyperformanceisthesignal-to-errorratio(SER),whichisdenedastheratiobetweenthesignalpowerandtheerrorpower: SER=Rx(t)2dt Re(t)2dt=10log10Rx(t)2dt Re(t)2dtintheunitofdB(3) Resultshowsthatthecurrent-modeIFachieves36dBSER.Theaccuracyoftherecoveredsignalisnotashighasitwasexpectedorwasachievedinthesimulations.Thereareseveralreasonsforthis.Therstreasonisthemethodologyforgeneratingthecurrentthrougharesistoraddsnoiseanddistortionstotheinputcurrent.Also,sincewearedealingwithextremelylowamplitudecurrentsignals,thetestingenvironmentcansignicantlydistorttheinputsignal. 3.4ComparisonofCurrent-ModeandVoltage-ModeIFImplementation TheinputoftheIFencoderisintheformofacurrent.Thevoltage-modeIFimplementationusesavoltage-to-currentconvertertotransformthevoltageinputtothecurrentinput.Thecurrent-modeIFimplementationusesacurrentconveyortodeliverthecurrentinputtotheIFencoder.Thevoltage-modeandcurrent-modeIFcircuitswereshowninFigure 3-2 andFigure 3-13 ,respectively.Table 3-1 presentsthesimulatedperformancesofboththeIFimplementations.Thecurrent-modeIFconsumesxedamountofthepower.Thevoltage-modeIFpowerconsumptionisdependentonthetransconductancegmvalueofthevoltage-to-currentconvertersincethevoltage-to-currentconvertercontainsatunablelineartransconductor.Ahighergmrequiresahigherpowerconsumption.BoththeIFimplementationscanachievesimilaraccuracyperformance.However,thecurrent-modeIFusesamuchsmaller 76

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capacitorwhichsavessiliconarea.Thecurrent-modeIFsolvesthedriftingproblemofthevoltage-modeIF,however,thecurrent-modeIFcircuitcannotremovetheinputoffsetwhichcanincreasethedatarate. Table3-1. ThesimulatedperformancesoftheIFcircuitsinvoltageandcurrentmodes V-IFI-IF ComponentforcurrentinputVoltage-to-currentconverterCurrentconveyorPowersupply3.3V3.3VCurrentconsumption2.3A(gm=1A=V)+6A9.3A+6ATestedinput20mV,1KHz4nA,1KHzSER45dB(Pulserate:10Kp/s)44dB(Pulserate:10Kp/s)Capacitorusage9.6pF0.8pFCircuitproblemThedriftingissueInputoffsetcurrent AnAC-coupledamplierhasbeendesignedanddescribedinSection 3.3.3 toremovetheinputoffsetofthecurrentinputtotheIFencoderincurrent-mode.TheperformancecomparisonofthesimulatedcurrentamplierchipandthefabricatedvoltageamplierdescribedinChapter 2 arelistedinTable 3-2 .Thebandwidthandpowerconsumptionofthecurrentamplieraretunedtobesimilartotheperformancesofthevoltage-moderst-stageamplier.Withsimilargain-bandwidthandpowerconsumption,thevoltage-modeamplierinput-referrednoiseis3.75Vandthecurrent-modeamplierinputreferrednoiseis4.07pA.Iftheelectrodeimpedanceisexact3.75V=4.07pAwhichisequalto920K,thenthetwosystemwouldhaveexactsameperformance.Iftheelectrodeimpedanceislowerthan920K,thecurrent-modeamplierhaslessnoisethanthevoltage-modeamplier,andviceversa.However,thevoltage-modelow-noiselow-poweramplierhasbeenstudiedwell,whilethecurrent-modedesignoftheprojectmaystillhavelargespaceforimprovement. 3.5Summary Anovelimplementationoftheintegrate-and-re(IF)encoderincurrent-modeapproachispresented.ThebidirectionalcurrentconveyorwithClass-ABoutputstagedeliversabidirectionalcurrentdirectlytotheintegrationcapacitorintheIFencoderwithoutintroducingcross-overdistortion.Thecurrent-modecircuitreducesthedesign 77

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Table3-2. Theperformancesoftheamplierinvoltageandcurrentmodes V-amplierI-amplier Powersupply3.3V3.3VCurrentconsumption14.7A14.9AGain40dB40dBBandwidth20mHzv5.7KHz25Hzv5.7KHzNoise3.75V4.07pA complexityandpowerconsumption.Anothercurrent-modeimplementationoftheIFincludingthecurrentamplierandthebiasfeedbackloopcanamplifytheinputcurrent,conveythecurrenttointegrationcapacitorandremovetheoffsetcurrent.Thecurrent-modeintegrate-and-reneuronhasbeendesigned,simulatedandfabricatedintheAMI0.5m3-metal2-polyCMOStechnology.Theentirecircuitconsumes254Wpowerand0.3mm2diearea.Thebench-topmeasurementresultsshowsthatthecurrentamplierconveyorIFencodercanachieve36dB. 78

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CHAPTER4THETIME-DERIVATIVEENCODINGANDITSCIRCUITIMPLEMENTATION 4.1Introduction Theintegrate-and-re(IF)encodingschemeintroducedinChapter 3 ,generatespulseswithadensityproportionaltotheinputsignalmagnitude.Whenencodingsignalswhicharequietformostofthetimeandonlygeneratesporadicallylargepotentials,suchasneuralsignals,theIFconverterreducesthedataratecomparedtothesynchronousanalog-to-digitalconverters(ADCs)bytakingadvantageofthelowamplituderegionswhichcontainlittleinformation.However,ifthesignalhasalargeDCoffset,morepulseswillbegeneratedbecauseoftheDCoffseteventhoughthereisnoinformation.Thus,aconverterisinsensitivetotheDCoffsetthatonlyrespondstotheACsignalcanfurtherreducethedatarate.AdecouplingcapacitorcanbeusedforblockingtheDCcontentoftheinputsignal.However,thecircuitwithonlythedecouplingcapacitorandwithoutbiasnetworkorfeedbackmaynotbehavecorrectlyduetooffsets. Thebandwidthoftheextracellularneuralsignalsisfrom300Hztoabout5KHz[ 56 ].Inordertobuildaband-passlterforsuchlowfrequency,weneedalargetimeconstant.Withalimitedsiliconsizeandparasiticissues,buildingalargeresistororcapacitoronchipisnotpractical.Thevoltage-modeimplementationoftheIFusesadiode-connectedtransistortoprovidealargevaluedresistorwithcompactsize[ 22 ].Unfortunately,theleakageandoffsetissuesofthepseudo-resistorcancausethedriftingproblemdescribedinSection 3.1.2 .Thecurrent-modeimplementationoftheIFhasalow-passlterfeedbacknetworktoleaktheoffsetcurrent.However,thefeedbacknetworkincreasescircuitnoiseanddesigncomplexity. Weproposeanothertypeofevent-basedcompressionconverter,thetime-derivative(TD)neuron,whichisinsensitivetotheDCoffset.Itusesswitchestosetthebiaspoints,solvesthedriftingproblemanddoesnotincreasethenoiseorcomplexityinthesystem.Inthischapter,theTDencodingschemeandthereconstructionalgorithm 79

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willbedeveloped,andaCMOSimplementationoftheTDconverterwillbepresented.Finally,theperformanceoftheTDencoderincomparisontotheIFencoderandthesynchronousADCswillbedemonstrated. 4.2TheTime-DerivativeEncodingModel Figure4-1. TheTime-Derivativeencodingmodel Figure 4-1 depictsthemodelofTime-Derivative(TD)encoding.TheTDresetsthesignalattheintegratoroutput,andalsoresetsthesignalattheintegratorinput.AndtheinputsignalisACcoupledthroughacapacitortotheintegrator.Theencodingprocesscanbewrittenas 1 Ztiti)]TJ /F11 5.978 Tf 5.76 0 Td[(1+(x(t))]TJ /F3 11.955 Tf 11.95 0 Td[(x(ti)]TJ /F6 7.97 Tf 6.59 0 Td[(1+))dt=i(4) wherei=+forthepositivepulseori=)]TJ /F4 11.955 Tf 9.3 0 Td[(forthenegativepulse.ti)]TJ /F6 7.97 Tf 6.58 0 Td[(1isthepreviouspulsetiming.istherefractoryperiodtime.ti)]TJ /F6 7.97 Tf 6.58 0 Td[(1+isthetimeofstartingtheithintegrationphase.tiiswhentheithintegrationendsandtheithpulseres.x(ti)]TJ /F6 7.97 Tf 6.59 0 Td[(1+)istheinputsignalvalueattheintegrationbeginningtime,andarethethresholdvalues. Deney0(t)astheACcomponentofx(t)andz(t)astheintegralofy0(t).Ignoringtherefractoryperiod,weexpandEq. 4 usingasecond-orderTaylorseries 80

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expansionas: i=z(ti))]TJ /F3 11.955 Tf 11.96 0 Td[(z(ti)]TJ /F6 7.97 Tf 6.59 0 Td[(1))]TJ /F5 11.955 Tf 11.95 0 Td[(ti)]TJ /F6 7.97 Tf 6.59 0 Td[(1x(ti)]TJ /F6 7.97 Tf 6.59 0 Td[(1)z(ti)]TJ /F6 7.97 Tf 6.58 0 Td[(1)+ti)]TJ /F6 7.97 Tf 6.58 0 Td[(1dz(t) dtjt=ti)]TJ /F11 5.978 Tf 5.76 0 Td[(1+1 2(ti)]TJ /F6 7.97 Tf 6.59 0 Td[(1)2d2z(t) dt2jt=ti)]TJ /F11 5.978 Tf 5.75 0 Td[(1)]TJ /F3 11.955 Tf 11.96 0 Td[(z(ti)]TJ /F6 7.97 Tf 6.59 0 Td[(1))]TJ /F5 11.955 Tf 11.95 0 Td[(ti)]TJ /F6 7.97 Tf 6.59 0 Td[(1x(ti)]TJ /F6 7.97 Tf 6.58 0 Td[(1)=1 2(ti)]TJ /F6 7.97 Tf 6.59 0 Td[(1)2d2z(t) dt2jt=ti)]TJ /F11 5.978 Tf 5.76 0 Td[(1(4) wheretiisthetimingoftheithpulseandti)]TJ /F6 7.97 Tf 6.58 0 Td[(1isthetimeintervalbetweenthe(i)]TJ /F5 11.955 Tf 11.95 0 Td[(1)thandtheithpulses.ti)]TJ /F6 7.97 Tf 6.59 0 Td[(1=ti)]TJ /F3 11.955 Tf 11.96 0 Td[(ti)]TJ /F6 7.97 Tf 6.59 0 Td[(1. ThereforethepulsedensityoftheTDneuronisproportionaltothederivativeoftheinputsignal. Pulsedensity/1 ts jdx(t)=dtj 2jj(4) A B Figure4-2. IllustrativeexampleofthespiketimesofIFandTDneurons.Thethresholdofeachmodelwasmodiedtoachieveexactly6spikesduringthelengthofthesignal.Notethatthespikelocationsin(A)occurmostlyatthehighregionsandin(B)tendtooccurwherethesignalisrapidlychanging. ComparingtheTDmodelwiththeIFmodel,weknowthattheTDencoderconcentratesitsspikesintheregionsofrapidchange,whiletheIFneurongeneratesspikesintheregionsofhighamplitude.Figure 4-2 demonstratestheirrespectivecharacteristics.ThisimpliesthatalargeDCvalueaddedtoaregionofthesignalwillleadtoanexcessivetransmissionbandwidthfortheIFencoder.Similarly,ifaDCvalue 81

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issubtractedfromaregionoftheinputsignal,theIFoutputdataratecoulddropbelowtheminimumrequirementforproperreconstruction.TheTDencoderwouldnotgeneratepulsesduetotheadditionofaDCoffsetversustheIFwhichwould.SettingasinglevalueoffortheentirerangeoftheinputsignalbecomesproblematicfortheIFwhendealingwiththesignalshavinglargeDCvariation.Nevertheless,thisisnotachallengetotheTDencoder. 4.3ReconstructionAlgorithm ThesignalreconstructionoftheTDconverterisderivedbasedonnon-uniformsamplingtheory.Non-uniformsamplingtheorysuggeststhatanybandlimitedsignalcanbeexpressedasalow-passlteredversionofanappropriatelyweightedsumofdelayedimpulsefunctions[ 57 ].ThissectionwillshowthatthebandlimitedanalogsignalcanbereconstructedfromthebiphasicpulseeventoutputoftheTDencoder. Ifinputsignalx(t)isbandlimitedto[)]TJ /F5 11.955 Tf 9.3 0 Td[(,],asufcientconditionforperfectreconstructionisthatthelargestintervalbetweenanytwoadjacentpulsesislessthantheNyquistperiodT= .x(t)canthenbeexpressedas x(t)=Xj=1,2,...,Nwjh(t)]TJ /F3 11.955 Tf 11.95 0 Td[(sj)(4) wherewjarescalarweights;sjarethetimingofthekernelfunctionh(t);andjstandsfortheorderoftheoutputevents.Thekernelfunctionh(t)istheimpulseresponseofthelow-passlterwhichisdescribedbythesincfunction: h(t)=sint t(4) Thesignalreconstructionproblemissimpliedtocomputingtheweightswj,wherej=1,2,...,N.Asinuniformsampling,sj=jTandwj=x(sj).Calculationofwjisusuallymorecomplicatedinnon-uniformsampling. TheconsecutivepulsesproducedbytheTDconvertermustsatisfyEq. 4 .Thetimingofthekernelfunctioneithercanbeuniformlyspacedsj=jTorcanbedenedas 82

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thecenterbetweenthetwoconsecutivepulses, sj=ti+ti)]TJ /F6 7.97 Tf 6.59 0 Td[(1+ 2(4) Assumingtheinputsignalisbandlimitedto[)]TJ /F5 11.955 Tf 9.3 0 Td[(,],ifallthetimeintervalsbetweenadjacentimpulsessatisfytheconstraintofsj)]TJ /F3 11.955 Tf 11.95 0 Td[(sj)]TJ /F6 7.97 Tf 6.59 0 Td[(1 ,thenEq. 4 canbewrittenas i=Ztit0i)]TJ /F11 5.978 Tf 5.76 0 Td[(1(x())]TJ /F3 11.955 Tf 11.96 0 Td[(x(t0i)]TJ /F6 7.97 Tf 6.58 0 Td[(1))d=Ztit0i)]TJ /F11 5.978 Tf 5.76 0 Td[(1(Xjwjh()]TJ /F3 11.955 Tf 11.95 0 Td[(sj))]TJ /F14 11.955 Tf 11.95 11.36 Td[(Xjwjh(t0i)]TJ /F6 7.97 Tf 6.58 0 Td[(1)]TJ /F3 11.955 Tf 11.96 0 Td[(sj))d=XjwjZtit0i)]TJ /F11 5.978 Tf 5.75 0 Td[(1h()]TJ /F3 11.955 Tf 11.96 0 Td[(sj)d)]TJ /F14 11.955 Tf 11.95 11.35 Td[(Xjwjh(t0i)]TJ /F6 7.97 Tf 6.58 0 Td[(1)]TJ /F3 11.955 Tf 11.96 0 Td[(sj)(ti)]TJ /F3 11.955 Tf 11.95 0 Td[(t0i)]TJ /F6 7.97 Tf 6.58 0 Td[(1)=Xjwjgij)]TJ /F14 11.955 Tf 11.95 11.36 Td[(Xjwjmij(4) wheret0i)]TJ /F6 7.97 Tf 6.58 0 Td[(1=ti)]TJ /F6 7.97 Tf 6.58 0 Td[(1+.ti)]TJ /F6 7.97 Tf 6.58 0 Td[(1isthepreviouspulsetiming;istherefractoryperiodtimeandt0i)]TJ /F6 7.97 Tf 6.59 0 Td[(1isthebeginningtimeoftheithintegrationphase.gijandmijcanbenumericallycomputedwith: gij=Ztit0i)]TJ /F11 5.978 Tf 5.75 0 Td[(1h()]TJ /F3 11.955 Tf 11.96 0 Td[(sj)d (4a) mij=h(t0i)]TJ /F6 7.97 Tf 6.59 0 Td[(1)]TJ /F3 11.955 Tf 11.95 0 Td[(sj)(ti)]TJ /F3 11.955 Tf 11.95 0 Td[(t0i)]TJ /F6 7.97 Tf 6.59 0 Td[(1) (4b) Eq. 4 canbeexpressedinthematrixformas =GW)]TJ /F3 11.955 Tf 11.96 0 Td[(MW=[G)]TJ /F3 11.955 Tf 11.96 0 Td[(M]W(4) whereWandarethecolumnvectorscomposedofwjandi,respectively;GandMarethesquarematricescomposedofgijandmij,respectively. 83

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Thus,wecansolvetheweightvectorWandplaceWbackintoEq. 4 torecovertheinputsignal: W=[G)]TJ /F3 11.955 Tf 11.96 0 Td[(M])]TJ /F6 7.97 Tf 6.59 0 Td[(1 (4) ^x(t)=WTH (4) =XiXjh(t)]TJ /F3 11.955 Tf 11.95 0 Td[(sj)gm)]TJ /F6 7.97 Tf 6.59 0 Td[(1jii (4) whereHisthematrixinwhichtheithrowisthedelayedsincfunction,h(t)]TJ /F3 11.955 Tf 12.1 0 Td[(sj)andgmjiisthejthrowithcolumelementintheinversematrixof[G)]TJ /F3 11.955 Tf 9.97 0 Td[(M].Eq. 4 showsthatx(t)canbeperfectlyrecoveredfromthebiphasicpulsetraingeneratedbytheTDencoder.Theperformanceofthereconstructionalgorithmislimitedbypracticalimplementationissuessuchasnon-idealsincfunctionimplementationandthenumericalprecisionoftheprocessor. 4.4CircuitImplementationoftheTime-DerivativeConverter 4.4.1Time-DerivativeConverterCircuit Figure4-3. Circuitimplementationoftime-derivativeconverter Figure 4-3 showstheTDconvertercircuit.Thecircuitcontainstwoparts:theAC-coupledintegratorandthepulsegenerator.Theintegratedsignalisconvertedtothebiphasicpulsetrainthatissuitableforwirelesstransmissionandwillbereconstructedoutsidethebody. 84

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Duringtheresetphase,boththeinputandtheoutputofGmareresettotheiroperatingpoints.Aftertheresetphase,onlytheinputACcontentoftheinputsignalscanbepassedthroughthecapacitorsC1andC2andtheDCcontentoftheinputsignalsareblocked.GmisalineartunabletransconductorwhichgeneratesthecurrentwhichislinearlyproportionaltotheinputvoltageandC3integratesthecurrentintothevoltageVmem.TheintegrationphasewillbestoppedifVmemislargerthan+orsmallerthan)]TJ /F4 11.955 Tf 9.3 0 Td[(. Thresholdvoltages+and)]TJ /F4 11.955 Tf 9.3 0 Td[(controlthedeltastepamplitudeandtransistorsM1,M2andM3operateasswitchestoresettheconverter,whentheasynchronousresetsignalishigh.TheresetsignalistheORgateoutputwithpositiveandnegativepulsesasinputs. WhenVmemreachesthepositivethreshold+ofthecomparator,theoutputofthecomparatorPout+risestohigh,andsodoestheresetsignal.ThehighresetsignalsetstheGminputstothecommonmodevoltageoftheinputsVincmandsetstheGmoutputtotheACsignalgroundVmid.Toobtainthesymmetricoutputiftheinputsignalissymmetricandcomparatoroffsetsareignored,Vmidshouldbeatthemidwaybetween+and)]TJ /F4 11.955 Tf 9.3 0 Td[(.AssoonasthevoltageVmemisresettoVmid,theoutputofthecomparatorgoestolow.Afterthedelay,denedastherefractoryperiod,alltheswitchesareopenandanewphaseofintegrationbegins.Similarly,whenVmemdropsbelow)]TJ /F4 11.955 Tf 9.3 0 Td[(,apulseofthenegativesideisgenerated.Thisprocessresultsinapulse-basedanalog-to-digitalconversionbygeneratingapulsetrainattheoutputsofthecomparatorsaccordingtotheinputsignal.Theself-resetschememakesthecircuittobeaclock-freeADC. BecausethepulserateoftheconverteroutputisproportionaltotheamplitudeoftheinputsignalofGm,whichisequaltothechangeoftheinputsignalVinaftertheresetmoments.Inotherwords,theinputsignalofGmisthenitedifferenceofVinduringeachintegrationphase,whichapproximatestothetimederivativeofVin. 85

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Therefore,theoutputpulsetrainoftheconverterencodestheinformationbasedonthederivativeoftheinputsignal. 4.4.2LinearTransconductor ThelineartransconductorGmisanimportantblockoftheTDconverter.NonlinearityanddistortionofGmdegradestheTDconverterperformancedirectly.AsingleMOStransistororadifferentialpairhasanarrowlinearrangeduetothesquare-lawmodel(Eq. 4 )inthesaturationregion,noteventomentionthesecond-ordereffectssuchasthebodyeffectandthechannellengthmodulation. ID=(VGS)]TJ /F3 11.955 Tf 11.96 0 Td[(Vth)2(4) whereVGSisthegate-sourcevoltage,Vthisthethresholdvoltageofthetransistor,isthetransistorparameterwhichisequalto1 2CoxW L.,Cox,W,Larethemobilityofchargecarrier,thegateoxidecapacitanceperunitarea,thechannelwidthandthechannellength,respectively. Figure4-4. LinearGmschematic Figure 4-4 showstheschematicofthelineartransconductorGmblock.Thetransconductoradoptsthemethodologyofusingasymmetricandsymmetricdifferentialpairstoaddandtosubtractthecurrentswithpropersizing,asshowninFigure 4-5 ,to 86

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Figure4-5. TheideaofthelinearGmdesign improvethelinearity[ 58 ].Thecircuitcontainsacross-coupledquadcell(M1-M4)withalinearizingdifferentialpair(M5,M6)attheinputstagetoincreasethelinearity,andtheregulatedcascodecurrentmirrorsattheoutputstagetoincreasetheoutputimpedance. 1)Cross-coupledquadcell TransistorsM1,M2formanasymmetricaldifferentialpairwiththesizeratioof1:nandsodotransistorsM4andM3.ThesourceofM1connectstothesourceofM3andthesourceofM2connectstothesourceofM4.FollowingthenotationsinFigure 4-4 ,currentsineachtransistorare M1:pI)]TJ /F3 11.955 Tf 11.96 0 Td[(i1=(Vx)]TJ /F3 11.955 Tf 11.95 0 Td[(V+)-222(jVth1j)2(4) M2:npI+i1=n(Vx)]TJ /F3 11.955 Tf 11.95 0 Td[(V)]TJ /F2 11.955 Tf 9.75 1.8 Td[()-221(jVth2j)2(4) M3:npI)]TJ /F3 11.955 Tf 11.95 0 Td[(i2=n(Vy)]TJ /F3 11.955 Tf 11.96 0 Td[(V+)-222(jVth3j)2(4) M4:pI+i2=(Vy)]TJ /F3 11.955 Tf 11.96 0 Td[(V)]TJ /F2 11.955 Tf 9.74 1.79 Td[()-222(jVth4j)2(4) SinceallthecurrentowingoutfromthedrainofaPMOStransistorcannotbesmallerthanzero,fromtheaboveequations,wecanget =r npI+i1 n)]TJ /F14 11.955 Tf 11.96 19.09 Td[(r pI)]TJ /F3 11.955 Tf 11.95 0 Td[(i1 ,for)]TJ /F3 11.955 Tf 9.3 0 Td[(npIi1pI(4) =r pI+i2 )]TJ /F14 11.955 Tf 11.96 19.09 Td[(r npI)]TJ /F3 11.955 Tf 11.95 0 Td[(i2 n,for)]TJ /F3 11.955 Tf 9.3 0 Td[(pIi2npI(4) whereisthedifferentialinputsignal,whichisequaltoV+)]TJ /F3 11.955 Tf 12.72 0 Td[(V)]TJ /F1 11.955 Tf 7.08 1.79 Td[(.IgnoringthebodyeffectandassumingthethresholdvoltageVtharethesameforthecross-coupledquadcellM1)]TJ /F3 11.955 Tf 12.15 0 Td[(M4.Bysolvingtheaboveequations,theI)]TJ /F3 11.955 Tf 12.15 0 Td[(Vrelationshipsofeachtransistor 87

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pairare i1=8>>>>>>>><>>>>>>>>:)]TJ /F3 11.955 Tf 11.95 0 Td[(npI,for<)]TJ /F14 11.955 Tf 9.3 19.41 Td[(r (n+1)pI )]TJ /F5 11.955 Tf 13.15 8.09 Td[((n)]TJ /F5 11.955 Tf 11.95 0 Td[(1)n (n+1)22+2nq (n+1)2 pI)]TJ /F3 11.955 Tf 11.95 0 Td[(n2 (n+1)2,for)]TJ /F14 11.955 Tf 11.95 19.42 Td[(r (n+1)pI r (n+1)pI npI,for>r (n+1)pI n(4) i2=8>>>>>>>><>>>>>>>>:)]TJ /F3 11.955 Tf 11.95 0 Td[(pI,for<)]TJ /F14 11.955 Tf 9.29 19.42 Td[(r (n+1)pI n(n)]TJ /F5 11.955 Tf 11.95 0 Td[(1)n (n+1)22+2nq (n+1)2 pI)]TJ /F3 11.955 Tf 11.96 0 Td[(n2 (n+1)2,for)]TJ /F14 11.955 Tf 11.95 19.41 Td[(r (n+1)pI nr (n+1)pI npI,for>r (n+1)pI (4) Byaddingequations 4 and 4 ,wecanobtainthetotalsmallsignalcurrentofM1)]TJ /F3 11.955 Tf 11.95 0 Td[(M4. i12=8>>>>>>>>>>>>>><>>>>>>>>>>>>>>:4nq (n+1)2 pI)]TJ /F3 11.955 Tf 11.95 0 Td[(n2 (n+1)2,forjj<)]TJ /F14 11.955 Tf 9.3 19.42 Td[(r (n+1)pI nsign()(pI+(n)]TJ /F5 11.955 Tf 11.95 0 Td[(1)n (n+1)22+2nq (n+1)2 pI)]TJ /F3 11.955 Tf 11.95 0 Td[(n2 (n+1)2jj),for)]TJ /F14 11.955 Tf 11.95 19.42 Td[(r (n+1)pI njjr (n+1)pI sign()(n+1)pI,forjj>r (n+1)pI (4) 88

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ThederivativeofEq. 4 isthetransconductanceofthecross-coupledquadcell,whichisequalto gm12=@i12 @=8>>>>>>>>><>>>>>>>>>:4n((n+1)2 pI)]TJ /F5 11.955 Tf 11.95 0 Td[(2n2) (n+1)2q (n+1)2 pI)]TJ /F3 11.955 Tf 11.95 0 Td[(n2,gm,forjj<)]TJ /F14 11.955 Tf 9.3 19.41 Td[(r (n+1)pI n2(n)]TJ /F5 11.955 Tf 11.96 0 Td[(1)n (n+1)2jj+1 2gm,for)]TJ /F14 11.955 Tf 11.96 19.42 Td[(r (n+1)pI njjr (n+1)pI 0,forjj>r (n+1)pI (4) 2)Source-coupleddifferentialpair TransistorsM5andM6formanormalsymmetricaldifferentialpairwhoselargesignalscanbewrittenas M5:qI+i3=m(Vz)]TJ /F3 11.955 Tf 11.96 0 Td[(V+)-222(jVth5j)2(4) M6:qI+i3=m(Vz)]TJ /F3 11.955 Tf 11.96 0 Td[(V)]TJ /F2 11.955 Tf 9.74 1.79 Td[()-222(jVth6j)2(4) Followingthestepsillustratedinthecross-coupledquadcellsection,thesmallsignalcurrenti3andthetransconductancegm3are i3=8>>><>>>:r mqI)]TJ /F5 11.955 Tf 13.15 8.09 Td[((m)2 4,forjjr 2qI msign()qI,forjj>r 2qI m(4) gm3=@i3 @=8>>><>>>:2mqI)]TJ /F5 11.955 Tf 11.96 0 Td[((m)2 p 4mqI)]TJ /F5 11.955 Tf 11.95 0 Td[((m)2,forjjr 2qI m0,forjj>r 2qI m(4) Thetotaltransconductanceoftheinputstageisequaltogm12)]TJ /F3 11.955 Tf 12.34 0 Td[(gm3.Theoretically,thelinearityismaximizedwithn=4.236,m=1.288andq=0.796inthecaseofp=1[ 59 ]. 3)Regulatedcascodeoutputstage 89

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Theregulatedcascodetechniqueisusedattheoutputinordertoincreasetheoutputimpedance[ 60 ],whichhelpsincreasetheRCtimeconstantandalleviatetheleakageeffect.Thoughtheleakagefeatureissometimesgoodfortheencodingrepresentationintermsofbandwidthandnoise[ 61 ],itispreferabletohaveacontrollabelresistivecomponenttomanagetheleakagefeatureoutsidetheGmblock. TheNMOSN5,N6andPMOSP5,P6transistorsformtwoloopsandtheloopgainsare TN0=gmN6(r0N6jjr0N8) 1+N5 (4a) TP0=gmP6(r0P6jjr0P8) 1+P5 (4b) respectively,wherejjstandsfortwoimpedancesinparallel.Theoutputimpedancecanbewrittenas Rout=RNoutjjRPout=[r0N3gmN5r0N5(1+N5)TN0]jj[r0P3gmP5r0P5(1+P5)TP0]=[r0N3gmN5r0N5gmN6(r0N6jjr0N8)]jj[r0P3gmP5r0P5gmP6(r0P6jjr0P8)](4) Theoutputsignalrangeis VGSN6+VDsatN5VoutVdd)-222(jVGSP6j+jVDsatP5j(4) ThedesignsofthecomparatorandthedelaycomponentcircuitarethesameasintheIFconverter[ 23 ]. 4.5NonidealEffects 4.5.1FiniteTimeConstantRCLeakyEffect Inpracticalcircuitimplementation,theniteinputandoutputimpedancesofthelineartransconductorandotherparasiticresistancesinparallelwiththecapacitorsresultinleakyintegration.BecauseoftheniteRCtimeconstant,thesignalcannotchangeabruptly. 90

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Figure4-6. First-orderRCsystem 4.5.1.1First-orderRCleakyequation Figure 4-6 showstherst-ordersystemswithcapacitorCandresistorR.ViandIistandfortheinputvoltageandtheinputcurrent,respectively,andVoistheoutputvoltage.WewillderivethetransientequationsoftheRCeffectrst. TheRCcircuitscanbewrittenintherst-ordernonhomogeneouslineardifferentialequationsas dVo(t) dt+Vo(t) RC=dVi(t) dt (4a) dVo(t) dt+Vo(t) RC=Ii(t) C (4b) Thehomogeneousformofthedifferentialequations 4 andthehomogeneoussolutionare dVo(t) dt+Vo(t) RC=0(4) Vo(t)=K(t)e)]TJ /F12 5.978 Tf 5.76 0 Td[(t RC(4) TakingthederivativeofEq. 4 resultsin dVo(t) dt=)]TJ /F5 11.955 Tf 9.3 0 Td[(1 RCK(t)e)]TJ /F12 5.978 Tf 5.76 0 Td[(t RC+dK(t) dte)]TJ /F12 5.978 Tf 5.76 0 Td[(t RC(4) PlacingtheresultsofVo(t)anddVo(t) dtbackintoEq. 4 gives dKa(t) dte)]TJ /F12 5.978 Tf 5.76 0 Td[(t RC=Vi(t) RC (4a) dKb(t) dte)]TJ /F12 5.978 Tf 5.76 0 Td[(t RC=Ii(t) C (4b) 91

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Ka(t)=ZdVi(t) dtet RCdt+Ka0 (4a) Kb(t)=1 CZIi(t)et RCdt+Kb0 (4b) whereKa0andKb0aretheinitialconditions.Therefore,thetransientresponsesoftherst-orderRCcircuitsstartingfromt=0canbedescribedas Vo(t)=Zt0dVi() de)]TJ /F12 5.978 Tf 5.76 0 Td[(t RCd+Ka0e)]TJ /F12 5.978 Tf 5.76 0 Td[(t RC (4a) Vo(t)=1 CZt0Ii()e)]TJ /F12 5.978 Tf 5.76 0 Td[(t RCd+Kb0e)]TJ /F12 5.978 Tf 5.76 0 Td[(t RC (4b) ThetransientresponsescanalsobederivedusingtheLaplacetransformwhichwillgivethesameresultsasinEq. 4 4.5.1.2Leakytime-derivativeencoding Practically,theRCtime-constanteffectisnon-trivialfortheTDconverterandmustbeconsideredunlesstheintervalsbetweenadjacentpulsesaremuchsmallerthanthetime-constant.IntheTDconvertercircuit,theswitchcanbereplacedbytheresistorRoduringtheintegrationphaseorRonduringtheresetphase,respectively.Generally,Ronvalueisaslowasinthe100to5KrangedependingonthetransistorsizingandRovalueisaslargeasinthetensofGrange[ 18 ].TheoutputimpedanceofthelineartransconductorRoutexpressedinEq. 4 isboostedtoGortensofGrangebyregulatedoutputstage.Theinputimpedanceofthelineartransconductoristhegateresistanceoftheinputtransistor,whicharegenerallyconsideredverylarge.Thesmall-signalequivalentcircuitoftheTDduringtheintegrationphaseisdrawninFigure 4-7 AssumingC1=C2andRo1=Ro2,andignoringtheoffsetvoltageofGmblockandthevoltagedropacrosstheswitches,foreveryintegrationphase,thefollowingconstraintsmustbesatised: Vx)]TJ /F3 11.955 Tf 11.95 0 Td[(Vy=Ztt0i)]TJ /F11 5.978 Tf 5.75 0 Td[(1d(V+())]TJ /F3 11.955 Tf 11.95 0 Td[(V)]TJ /F5 11.955 Tf 7.09 1.8 Td[(()) de)]TJ /F12 5.978 Tf 5.76 0 Td[(t Ro1C1d(4) 92

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Figure4-7. Small-signalequivalentcircuitoftheTDconverterduringtheintegrationphase Vmem(t)=1 C3Ztt0i)]TJ /F11 5.978 Tf 5.75 0 Td[(1)]TJ /F3 11.955 Tf 9.29 0 Td[(gm(Vx)]TJ /F3 11.955 Tf 11.96 0 Td[(Vy)e)]TJ /F12 5.978 Tf 5.75 0 Td[(t (Ro3jjRout)C3d(4) Vmem(t0i)]TJ /F6 7.97 Tf 6.59 0 Td[(1)=0(4) UsuallyRo3ismuchlargerthanthetransconductanceoutputimpedanceRout.AssumingtheinputsignalisVin=V+)]TJ /F3 11.955 Tf 12.63 0 Td[(V)]TJ /F1 11.955 Tf 7.09 1.79 Td[(,theoutputsignalVmemacrossC3canbeobtainedbythecombinationofequations 4 and 4 Vmem(t)=)]TJ /F3 11.955 Tf 9.3 0 Td[(gm C3Ztt0i)]TJ /F11 5.978 Tf 5.76 0 Td[(1"Zt0i)]TJ /F11 5.978 Tf 5.75 0 Td[(1dVin() de)]TJ /F22 5.978 Tf 5.75 0 Td[( Ro1C1d#e)]TJ /F12 5.978 Tf 5.75 0 Td[(t RoutC3d(4) Therefore,thenextpulsewillreattimetiif i=)]TJ /F3 11.955 Tf 9.3 0 Td[(gm C3Ztit0i)]TJ /F11 5.978 Tf 5.76 0 Td[(1"Zt0i)]TJ /F11 5.978 Tf 5.75 0 Td[(1dVin() de)]TJ /F22 5.978 Tf 5.75 0 Td[( Ro1C1d#e)]TJ /F12 5.978 Tf 5.76 0 Td[(ti RoutC3d(4) wherei2f)]TJ /F4 11.955 Tf 26.57 0 Td[(,+g. Ifthetime-constantRo1C1islargeenoughtobeignored,Vmemcanbesimpliedas Vmem(t)=)]TJ /F3 11.955 Tf 9.3 0 Td[(gm C3Ztt0i)]TJ /F11 5.978 Tf 5.75 0 Td[(1Vin())]TJ /F3 11.955 Tf 11.95 0 Td[(Vin(t0i)]TJ /F6 7.97 Tf 6.58 0 Td[(1)e)]TJ /F12 5.978 Tf 5.76 0 Td[(t RoutC3d(4) IfRoutC3islarge,theTDencodermodelasinEq. 4 canbefurthersimpliedto Vmem(t)=)]TJ /F3 11.955 Tf 9.3 0 Td[(gm C3Ztt0i)]TJ /F11 5.978 Tf 5.76 0 Td[(1Vin())]TJ /F3 11.955 Tf 11.95 0 Td[(Vin(t0i)]TJ /F6 7.97 Tf 6.58 0 Td[(1)d(4) Eq. 4 isconsistentwithEq. 4 whentheleakyresistancesscaletoinnity. 93

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4.5.1.3SERdegradationduetoleakyeffect Inpracticalimplementation,theleakyeffectisunavoidableandtheaccurateestimationoftheRCconstantisdifcult.HerewewilltreattheTDconverterideallywithouttheleakyeffectduringreconstructionandinvestigatetheperformanceduetotheleakyintegration.WiththeTaylorseriestheorem,x()x(ti)+dx() dj=ti()]TJ /F3 11.955 Tf 12.27 0 Td[(ti)+1 2dx2() d2j=ti()]TJ /F3 11.955 Tf 10.79 0 Td[(ti)2=x(ti)+_x(ti)()]TJ /F3 11.955 Tf 10.79 0 Td[(ti)+1 2x(ti)()]TJ /F3 11.955 Tf 10.78 0 Td[(ti)2.TheleakyTDencodingprocessdescribedinEq. 4 isrewrittenhereandexpandedto i=Ztit0i)]TJ /F11 5.978 Tf 5.76 0 Td[(1x())]TJ /F3 11.955 Tf 11.95 0 Td[(x(t0i)]TJ /F6 7.97 Tf 6.59 0 Td[(1)e)]TJ /F12 5.978 Tf 5.75 0 Td[(ti RCdZtit0i)]TJ /F11 5.978 Tf 5.76 0 Td[(1_x(t0i)]TJ /F6 7.97 Tf 6.59 0 Td[(1)()]TJ /F3 11.955 Tf 11.95 0 Td[(t0i)]TJ /F6 7.97 Tf 6.59 0 Td[(1)+1 2x(t0i)]TJ /F6 7.97 Tf 6.58 0 Td[(1)()]TJ /F3 11.955 Tf 11.95 0 Td[(t0i)]TJ /F6 7.97 Tf 6.59 0 Td[(1)2e)]TJ /F12 5.978 Tf 5.75 0 Td[(ti RCd=_x(t0i)]TJ /F6 7.97 Tf 6.59 0 Td[(1)RC[ti)]TJ /F6 7.97 Tf 6.59 0 Td[(1)]TJ /F3 11.955 Tf 11.95 0 Td[(RC(1)]TJ /F3 11.955 Tf 11.96 0 Td[(e)]TJ /F11 5.978 Tf 7.79 5.46 Td[(ti)]TJ /F11 5.978 Tf 5.76 0 Td[(1 RC)]+x(t0i)]TJ /F6 7.97 Tf 6.59 0 Td[(1)RC[t2i)]TJ /F6 7.97 Tf 6.59 0 Td[(1 2)]TJ /F3 11.955 Tf 11.96 0 Td[(RCti)]TJ /F6 7.97 Tf 6.59 0 Td[(1+(RC)2(1)]TJ /F3 11.955 Tf 11.95 0 Td[(e)]TJ /F11 5.978 Tf 7.78 4.4 Td[(ti1 RC)]_x(t0i)]TJ /F6 7.97 Tf 6.59 0 Td[(1)(t2i)]TJ /F6 7.97 Tf 6.59 0 Td[(1 2)]TJ /F5 11.955 Tf 13.16 8.6 Td[(t3i)]TJ /F6 7.97 Tf 6.59 0 Td[(1 6RC)+x(t0i)]TJ /F6 7.97 Tf 6.58 0 Td[(1)(t3i)]TJ /F6 7.97 Tf 6.59 0 Td[(1 6)(4) wheretheTaylorseriesapproximationofexisusedinthederivationwiththeassumptionofti)]TJ /F6 7.97 Tf 6.59 0 Td[(1RC.Sincetheleakyeffectisignoredduringthereconstruction,theestimatedthresholdovertheithintegrationperiodisequalto: bi=Ztit0i)]TJ /F11 5.978 Tf 5.76 0 Td[(1x())]TJ /F3 11.955 Tf 11.95 0 Td[(x(t0i)]TJ /F6 7.97 Tf 6.58 0 Td[(1)dZtit0i)]TJ /F11 5.978 Tf 5.76 0 Td[(1[_x(t0i)]TJ /F6 7.97 Tf 6.58 0 Td[(1)()]TJ /F3 11.955 Tf 11.96 0 Td[(t0i)]TJ /F6 7.97 Tf 6.58 0 Td[(1)+1 2x(t0i)]TJ /F6 7.97 Tf 6.59 0 Td[(1)()]TJ /F3 11.955 Tf 11.96 0 Td[(t0i)]TJ /F6 7.97 Tf 6.58 0 Td[(1)2]d=_x(t0i)]TJ /F6 7.97 Tf 6.58 0 Td[(1)t2i)]TJ /F6 7.97 Tf 6.59 0 Td[(1 2+x(t0i)]TJ /F6 7.97 Tf 6.59 0 Td[(1)t3i)]TJ /F6 7.97 Tf 6.58 0 Td[(1 6(4) Thesignalpowercanbecalculatedas Psignal=Zx2()d=Z"XiXjh()]TJ /F3 11.955 Tf 11.95 0 Td[(sj)gm)]TJ /F6 7.97 Tf 6.59 0 Td[(1jii#2d=2Z"Xihi()i#2d(4) 94

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wherePjh()]TJ /F3 11.955 Tf 11.95 0 Td[(sj)gm)]TJ /F6 7.97 Tf 6.59 0 Td[(1jiisequaltohi()forthesimpleexpression. WiththepreviousresultsinEq. 4 4 and 4 ,theerrorpowerduetotheleakyeffectisequalto: Perror,leaky=Z[x())]TJ /F14 11.955 Tf 14.74 3.82 Td[(dx()]2d=Z"Xihi()(i)]TJ /F14 11.955 Tf 12.95 3.15 Td[(bi)#2d=Z"Xihi()_x(t0i)]TJ /F6 7.97 Tf 6.59 0 Td[(1)t3i)]TJ /F6 7.97 Tf 6.59 0 Td[(1 6RC#2d=23 9(RC)2Z"Xihi()jij3 2 p j_x(t0i)]TJ /F6 7.97 Tf 6.59 0 Td[(1)j#2d(4) Thesignal-to-noiseratio(SER)duetotheleakyintegrationis: SERleaky=Psignal Perror,leaky=9(RC)2 2R[Pihi()i]2d R[Pihi()iq jij j_x(t0i)]TJ /F11 5.978 Tf 5.75 0 Td[(1)j]2d9R2CGm 2E[j_x j](4) whereEstandsfortheexpectedvalueand=C Gm. Thus,withoutconsideringtheoutputresistanceeffect,Eq. 4 suggeststhattheSERdegradesmorewhentheconvertercircuithasasmallerRCtimeconstant.Figure 4-8 showsthesimulationresultofthedependenceofSERontheoutputresistorR.Thesimulatedinputsignalisa1KHzsinewave.Theintegrationcapacitoris7.2pF.Thesimulationtimeresolutionis10ns.Thepulserateoftheoutputis15Kpulse/sbychoosingthecorrespondingvalue.ThesimulationresultisconsistentwithEq. 4 result,showingaslopeof20dB/decadebutwithsomevariations. 4.5.1.4Leakytime-derivativereconstruction IftheRCtimeconstantcanbeestimatedaccurately,theleakyeffectcanbecorrectedinthereconstructionalgorithm.ByrewritingEq. 4 whichdescribesthe 95

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Figure4-8. SERdependencyonresistanceR TDencoderincludingleakyeffectsattheinputandtheoutputoftheGmblock,andmakingthesameassumptionsthattheinputsignalx(t)isbandlimitedto[)]TJ /F5 11.955 Tf 9.3 0 Td[(,],andthemaximalintervalbetweentwoadjacentpulsesislessthantheNyquistperiodT= ,weget i=Ztit0i)]TJ /F11 5.978 Tf 5.75 0 Td[(1"Zt0i)]TJ /F11 5.978 Tf 5.75 0 Td[(1dx() de)]TJ /F22 5.978 Tf 5.76 0 Td[( )]TJ 3.62 -1.86 Td[(1d#e)]TJ /F12 5.978 Tf 5.76 0 Td[(ti )]TJ 3.61 -1.86 Td[(3d=XjwjZtit0i)]TJ /F11 5.978 Tf 5.76 0 Td[(1"Zt0i)]TJ /F11 5.978 Tf 5.76 0 Td[(1dh()]TJ /F3 11.955 Tf 11.96 0 Td[(sj) de)]TJ /F22 5.978 Tf 5.75 0 Td[( )]TJ 3.62 -1.87 Td[(1d#e)]TJ /F12 5.978 Tf 5.76 0 Td[(ti )]TJ 3.62 -1.87 Td[(3d=Xjwjpij(4) where=)]TJ /F8 7.97 Tf 6.59 0 Td[(C3 gm,)]TJ /F6 7.97 Tf 6.77 -1.79 Td[(1=Ro1C1and)]TJ /F6 7.97 Tf 6.78 -1.79 Td[(3=RoutC3.pijcanbenumericallycalculatedas: pij=Ztit0i)]TJ /F11 5.978 Tf 5.75 0 Td[(1"Zt0i)]TJ /F11 5.978 Tf 5.75 0 Td[(1dh()]TJ /F3 11.955 Tf 11.95 0 Td[(sj) de)]TJ /F22 5.978 Tf 5.76 0 Td[( )]TJ 3.61 -1.86 Td[(1d#e)]TJ /F12 5.978 Tf 5.75 0 Td[(ti )]TJ 3.61 -1.86 Td[(3d(4) Andinmatrixform, =PW(4) 96

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wherePisasquarematrixcomposedofpijandWandarethecolumnvectorscomposedofwjandi. W=P)]TJ /F6 7.97 Tf 6.59 0 Td[(1 (4) ^x(t)=WTH (4) 4.5.2OffsetVoltages Uncertaintiesineachstepoffabricationprocessbringmismatchestonominally-identicaldevices,suchastheasymmetriesindimensions,dopingconcentrationvariationandthresholdvoltagevariation[ 62 ].Themismatchesresultinanoffsetvoltageinnominally-identicaldevices.Theinput-referredoffsetvoltageofaMOSdifferentialpairisequalto[ 55 ]: Vos=VGS)]TJ /F3 11.955 Tf 11.96 0 Td[(VTH 2(W L W L+RD RD))]TJ /F5 11.955 Tf 11.95 0 Td[(VTH(4) wherestandsforthemismatch,W Listhetransistorsize,VTHisthethresholdvoltage,VGSisthegate-sourcevoltageandRDistheloadimpedance.Themismatchofthethresholdvoltagecontributestotheinput-offsetvoltagedirectlyandthedimensionmismatchcontributestotheoffsetvoltagebymultiplyingtheoverdrivevoltage. IntheTDcircuitry,theoffsetsresultingfromthelineartransconductorandthecomparatorscontributetotheinput-referredoffsetvoltagetogether.Practically,Vosalsovarieswithtemperature.Forimplantation,thesurroundingtemperatureoftherecordingunitisconstant,thus,wecantreatVosasaconstant. 4.5.2.1SERdegradationduetooffset Theoffsetvoltageofthelineartransconductorcontinuouslychargesthecapacitorduringtheintegrationperiodandtheoffsetvoltageofthecomparatorsmodiestheeffectivethresholdvoltage.TheTDencodingprocessconsideringthebothoffsetvoltagesVos,gmandVos,compismodiedas: (i+Vos,comp)=Ztit0i)]TJ /F11 5.978 Tf 5.76 0 Td[(1[x(t))]TJ /F3 11.955 Tf 11.95 0 Td[(x(t0i)]TJ /F6 7.97 Tf 6.58 0 Td[(1)+Vos,gm]dt(4) 97

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Iftheoffseteffectisnotcorrectedinthereconstruction,theerrorpoweris Perror,Vos=Z"Xihi()(i)]TJ /F14 11.955 Tf 12.95 3.16 Td[(bi)#2d=Z"Xihi()(ti)]TJ /F6 7.97 Tf 6.59 0 Td[(1Vos,gm)]TJ /F4 11.955 Tf 11.95 0 Td[(Vos,comp)#2d(4) SERVos=Psignal Perror,Vos=R[Pihi()i]2d RPihi()(ti)]TJ /F6 7.97 Tf 6.58 0 Td[(1Vos,gm)]TJ /F4 11.955 Tf 11.96 0 Td[(Vos,comp)2d(4) Withthesecond-orderTaylorseriesexpansion,Eq. 4 isapproximatelyequalto: (i+Vos,comp)1 2t2i)]TJ /F6 7.97 Tf 6.59 0 Td[(1_x(t0i)]TJ /F6 7.97 Tf 6.59 0 Td[(1)+Vos,gmti)]TJ /F6 7.97 Tf 6.59 0 Td[(1(4) IfVos,gmisverysmall,i.e.,Vos,gm1 2ti)]TJ /F6 7.97 Tf 6.58 0 Td[(1_x, Perror,Vos2Z"Xihi()(s i+Vos,comp _x(t0i)]TJ /F6 7.97 Tf 6.59 0 Td[(1)Vos,gm)]TJ /F14 11.955 Tf 11.96 17.51 Td[(r 2Vos,comp)#2d(4) IfVos,gmislargerthan1 2ti)]TJ /F6 7.97 Tf 6.59 0 Td[(1_x,ti)]TJ /F6 7.97 Tf 6.58 0 Td[(1(+Vos,comp) Vos,gm,and Perror,Vos2Z"Xihi()i#2d=Psignal(4) TheSERduetothetransconductoroffsetVos,gmisequalto SERVos,gm8>><>>:C 2GmV2os,gmE[j_xj],Vos,gm<1 2ti)]TJ /F6 7.97 Tf 6.59 0 Td[(1_x0,Vos,gm>1 2ti)]TJ /F6 7.97 Tf 6.59 0 Td[(1_x(4) ConsideringonlytheoffsetofthelineartransconductorVos,gm,ifVos,gmissmall,theSERisalsoinverselyproportionaltoVos,gmwithaslopeof20dB/decade,whileifVos,gmislarge,theSERisdegradedto0dB. IfVos,gmis0,theSERduetothecomparatoroffsetVos,compisequalto SERVos,comp=2 V2os,comp(4) 98

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Figure4-9. SERdependencyontheinputoffsetvoltageoftheGM Figure4-10. SERdependencyontheoffsetvoltageofthecomparators TheoffsetofthecomparatorsVos,compresultsintheSERdegradationwithaslopeof20dB/decade. Figure 4-9 showsasimulationresultoftheSERdependencyontheinput-referredoffsetvoltageofthelineartransconductor.Figure 4-10 showsasimulationresultoftheSERdependencyontheoffsetvoltageofthecomparators.ThesimulationresultsmatchwellwiththeSEREq. 4 andEq. 4 99

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4.5.2.2Offsetcorrectioninreconstruction Iftheoffsetvoltagesareconstantandtheycanbedeterminedaccurately,theerrorduetotheoffsetcanbeeasilycompensatedinthereconstructionbymodifyingEq. 4 to W=[G)]TJ /F3 11.955 Tf 11.96 0 Td[(M])]TJ /F6 7.97 Tf 6.59 0 Td[(1[(+Vos,comp))]TJ /F3 11.955 Tf 11.96 0 Td[(Vos,gmT](4) whereTisavectorinwhichtheithelementisequaltothetimeintervalbetweenithand(i+1)thpulses,i.e.,ti=ti+1)]TJ /F3 11.955 Tf 11.96 0 Td[(ti. 4.5.3SignalDependentThresholdVariationoftheComparator Besidestheeffectoftheconstantoffsetvoltage,thecomparatorsalsointroduceerrorbecauseofitssignaldependentdelayandthusthevariationofthethresholdvoltage.Ideally,thecomparatorcaninstantaneouslyraiseitsoutputtoahighlogicstatewhentheinputvoltagereachesthethresholdvoltage.However,inreality,thenitegainandthenitebandwidthofthecomparatorresultinadelaybetweenthetimingoftheinputcrossingthethresholdandthetimingoftheoutputswitching.Unfortunately,thedelayissignaldependent.TheeffectofthesignaldependentdelayontheSERhasbeenanalyzedin[ 20 ].Theintroducederrorisverydifculttobecorrectedinthereconstructedalgorithm.Increasingthepowerofthecomparatorhelpstoreducetheerrorduetothesignaldependentdelay. 4.5.4MOSFETSwitches TheswitchesintheTDconvertercircuitryareimplementedbyMOStransistors.Thetransistorswitchcannotbetreatedasanidealswitch.Thenon-idealitiesofthetransistorswitchcanimpactthecircuitintermsofnon-zeroon-resistance,niteoff-resistance,channelchargeinjectionnoise,clockfeedthroughnoiseandsampledthermalnoise.Theeffectsduetothenonidealresistancehasbeentreatedastheleakyeffects.Thechargeinjectionnoiseandclockfeedthroughnoiseinduceanoffsetvoltagethatcanbeeffectivelycombinedwiththelineartransconductoroffsetvoltageandthecomparator 100

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offsetvoltage.Theswitchoffsetvoltageiscalculatedas[ 55 ]: V=qinj 2Ci+Csw Csw+CiVdd(4) whereqinjisthechargeofthechannelwhenthechannelisabouttobeoff,Ciisthecapacitorconnectingtotheswitches,Cswistheparasiticgate-sourceandgate-draincapacitorsoftheswitchandVddistheswingofthecontrolsignalonthetransistorgate.Thersttermstandsfortheeffectofthechargeinjectionandthesecondtermisfromtheclockfeedthrougheffect.Thechannelchargeqinjcanbereducebyusingacomplementaryswitchesoradummyswitches.IncreasingCicanreducetheswitchingerror. Thethermalnoisevoltageofaswitch-capacitorisequaltoq KT Ci.Thisnoiselimitstheperformanceofthesystem.IncreasingCihelpstodecreasethenoiseandimprovetheperformance. 4.5.5TimingJitteroftheTimeQuantizer TheTDencoderisaclock-freeconverterandworksincontinuous-time.Thetimingofthepulseeventoutputisstillinanalogform.Theeventtimesmustbequantizedinordertobeprocessedbyadigitalcomputer.Thequantizationprocessisusuallydonebysynchronizingthepulsetraintoaquantizationclockandrecordingthequantizedtimestamp.Unfortunately,timingjitterisintroducedduringthequantizationandresultsinerror.Thefasterquantizationclockis,thesmallertheerrorwillbe,andthus,thebetterSERwillbeachieved. Figure 4-11 showstherelationshipbetweenthereconstructionSERandthequantizationclock.Generally,theSERisimprovedwithaslopeof20dB/decadewhenthetimingresolutionismoreaccurate,untilthequantizationperiodislessthan10ns,wheretheSERsaturatesduetothecalculationround-offerrors.Thesimulationresultisconsistentwiththeanalysisresultin[ 20 ]. 101

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Figure4-11. SERvsClockperiod 4.6MatlabSimulationResults IntheMatlabsimulation,theconverterparametersaresetasthesamevalueasthecircuitrycharacteristicsandarexedduringthesimulation,unlesstheyarepointedoutspecically.Gmis22.6A/V;C1,C2are7.3pF;C3is8pF;+is0.4Vand)]TJ /F4 11.955 Tf 9.29 0 Td[(is-0.4V;Rinis500G;Routis286M;andtherefractoryperiodis10s. 4.6.1SimulationwithSyntheticSignalasInputSignal Thesyntheticsignalisacombinationofseveralsinusoidalwaveswithdifferentamplitudes,frequenciesandphases,i.e.,x(t)=PiAisin(!it+i).Figure 4-12 showsanexampleofthesyntheticsignalwhichcoversthefrequenciesof500,1000,1500andsoonupto5000Hz. TheIFencoderresetsonlytheoutputoftheGmblock,whiletheTDencoderresetsboththeinputandtheoutputoftheGmblock.Figure 4-13 depictsatransientsimulationoftheTDconverter.TherstwaveformistheinputsyntheticsignaltotheTDencoder.ThesecondwaveformisthesignalattheinputofGm,whichfollowstheinputsyntheticsignaluntilreset.ThethirdwaveformshowsthesignalVmemattheoutputofGm,also 102

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Figure4-12. OneexampleoftestedsyntheticsignalanditsmagnitudeofFFT Figure4-13. TransientsimulationoftheTDencoder:1)InputsignaltotheTDencoder;2)Signalattransconductorinputnode;3)Signalattransconductoroutputnode;4)OutputpulsestrainoftheTDencoder 103

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atthenodeoftheintegrationcapacitor.Vmemischargedordischargeduntilreachesthethresholds,andatthesametime,apulseisgenerated,asshowninthelastwaveform.Meanwhile,thesignalsofthesecondandthethirdwaveformsarereset.Therefore,theoutputpulsetrainshowninthelastwaveformisproportionaltotheslopeoftheinputsignal.Themaximumpulseintervalis96.84sandtheminimumpulseintervalis20.7sinthesimulation. ATDwithoutleaky BTDwithleaky Figure4-14. SimulationoftheTDencodingsyntheticsignalandreconstructionresults Figure 4-14A showstheperformanceofthereconstructionalgorithminEq. 4 fortheTDencoderwithouttheleakyeffect,andFigure 4-14B showstheperformanceofthereconstructionalgorithmconsideringleakyeffectsinEq. 4 fortheleakyTDencodermodel.Asthetime-constantislarge,forthesameinputsignal,bothmodelshavesimilaroutputpulsestrainsandtheinputsignalcanberecoveredwell.Thewaveformsatthethirdrowshowerrorsignale(t),whichisthedifferencebetweentheinputsignalandtherecoveredsignal. TheTDalgorithmachievesSERof80.2dBandtheleakyTDalgorithmgetsSERof85.4dB,whichcanberegardedasthesameduetothecomputationalresolution.However,iftheencodermodelandtheleakyparametersarenotestimatedcorrectly,theperformancewilldegrade,asexplainedinSection 4.5.1.3 .Forexample,ifthepulsetrain 104

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generatedfromtheleakyTDencoderisreconstructedwiththereconstructionalgorithmwithoutconsideringleaky,theperformanceisonly50dB. Figure4-15. SERvsPulserate,varyingpulseratebyvaryingtheamplitudeofthesignal TheperformanceofanyADCisdirectlyrelatedtothedatarate.Thefastersamplingclockandthehigherbitresolutionleadtobetteraccuracy.ThisbasicruleisalsovalidintheTDconverter.Figure 4-15 istheplotbetweentheSERandthepulserate.ThetestedinputsignalisthesamesyntheticsignalasshowninFigure 4-12 .Thegraduallyincreasingpulserateisachievedbyamplifyingtheinputsignallargerandlarger.Itcanalsobeachievedbydecreasingthethresholdvoltages.ThisFigureshowsthattheSERispoorwhenthepulserateisundertheNyquistrate,whichis10KHzfortheinputsignalwiththebandwidthof5KHz.TherecoveredsignalisstillnotverygoodwhentheaveragepulserateisjustabovetheNyquistrate,becausetheminimumlocalpulserateismuchlessthantheNyquistrate.FromtheFigurewecantellthat60dBSERisachievedatthepulseratelargerthan16Kpulses/s,whichis1.6timesoftheNyquistrate.Asthepulserateincreases,theSERincreasesbutthistrendisnotvalidforever. 105

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TheSERstartstodropoffaftercertainpulserate,becausethetimejitterdisturbsthepulsetimingsmoreseriouslyrelativetothesmallerpulseintervals. Figure4-16. Refractoryperiodeffect:1)SERvsRefractoryperiod;2)PulseRatevsRefractoryperiod Onecharacteristicofbiologicalneuronsistherefractoryperiod,whichmeansthattheneuronscannotinitiateanotheractionpotentialafterapreviousactionpotentialuntilacertaintimehaspassed.Therefractoryperiodfeaturelimitsthemaximumringrate.Similarly,thehardwareconverteralsohasthefeatureoftherefractoryperiod.Duringtherefractoryperiod,theinputnodeandtheintegrationcapacitornodearetiedtozero.Itmaybeofconcernthattheinformationduringtherefractoryperiodislost,however,theperfectreconstructionisachievedaslongasthemaxinterpulseperiodsatisesNyquistrule.Figure 4-16 showstheeffectoftherefractoryperiodontheSERandthepulseratewithdifferentamplitudeofthesyntheticsignal.Astherefractoryperiodincreases,thepulseratedecreasesasexpected.Aslongastherearesufcientpulses,theSERstaysthesame.TheSERrollsoffatthelargerrefractoryperiodforthesignalwiththelargeramplitudeaswellasthelargerslope,becausethelargersignalproducesmorepulses.Toobtainthesamepulserateforthelargersignalbyvaryingtherefractory 106

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period,alargerrefractoryperiodisnecessary.Therefore,theinformationduringtherefractoryperiodcanberecoveredaslongasthepulseeventsaresufcientandthepulseintervalsdonotbreaktheNyquistrule. 4.6.2ComparisonBetweentheTDandtheIFConverters AAverage BStandarddeviation Figure4-17. SimulationresultsoftheTDandtheIFencoding100randomsyntheticsignals ThecomparisonbetweentheTDandtheIFisfocusedontherelationshipbetweentheSERandthepulserate,sincetheacquisitionaccuracyandthedataratearetwoofthemostimportantconcerns.Figure 4-15 istheresultoftheTDencoderwhentestedwithonesyntheticsignal.Withthesameapproachofvaryingthepulseratebyvaryingtheamplitudesoftheinputsignals,100randomsyntheticsignalshavebeentestedonboththeTDandtheIFencoders.Arandomsyntheticsignalisasummationofmanysinusoidalsignalswithrandomamplitudeandrandomphaseatfrequency500,1000,1500,2000andsoonupto5000Hz.Theaverageandthestandarddeviationof100trialresultsintermsofSERversuspulserateareshowninFigure 4-17 .Wecantellthatatlowpulserate(buthigherthanNyquistrate),theTDencoderachieveshigherSERthantheIF;athighpulserate,bothencodershavethesameSER,buttheIFsuffersfromlargervariationthantheTD. 107

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Figure4-18. InputsignalwithDCvariation Figure4-19. ResultsoftheTDandtheIFencodingthesignalwithDCvariation 108

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TheIFintegratesfrom0aftereachpulse,whiletheTDintegratesfromthedatavalueatthelastpulsewhicheliminatestheDCoffset.SotheTDisexpectedtoencodethesignalwithlargeDCvariationwhichisbetterthantheIFdoes.Figure 4-18 showsaninputsignalthatisdesignedtoaccentuatethedifferencesbetweenthetwoencoders.TheinputsignaliscomposedofthesyntheticsignalasshowninFigure 4-12 andasigmoidsignal.Insomeregions,thesignalamplitudeislow,whileintheotherregions,theamplitudeishigh.Figure 4-19 showsthereconstructionresultsinSERversuspulserate.TheperformanceoftheTDencoderisunaffectedbytheDCshift,whilethepulserateoftheIFencoderinordertoachieveagoodSER,hasbeenpostponedtoamuchhighervalue.Soforalowpulserate,theTDencodergivesamuchbetterreconstructionresultthantheIFencoder.Thisisbecauseforthelowpulserate,thenumberofthepulsesgeneratedbytheIFencodertorepresentthesignalinthesmallamplituderegionsisnotadequate.Therefore,amuchhigherpulseratefortheIFencodertoreconstructthelowamplitudesignalisrequired,butthesignalinthehighamplituderegionsistremendouslyover-sampled.TheTDencoder,ontheotherhand,respulsesinresponsetothechangesofthesignal,andignoresthelargeDCshifts.Overall,theTDencoderperformsverywellatthemuchlowerpulseratesthantheIFencoder. 4.6.3SimulationwithNeuralActionPotentialSignalasInputSignal TheIFconverterhasbeenproventosavedatarateonencodingtheneuralactionpotentials[ 21 ],becauseneuralsignalsburstinfrequentlyandatmostofthetimethereisjustnoise.TheTDconvertercanalsosavedatarate.TheTDconverterproducesmorepulseswhenthesignalhassharperchangingwhilenopulsesareproducedwhenthesignalstaysstill.Sincetheinterestedinformationoftheextracellularneuralsignalsisinactionpotentialsbutnotinnoise,insteadofsamplingtheentiresignal,theTDencoderautomaticallygeneratesmorepulsesfortheinterestedsignal,whichusuallyhaslargetransitions,andgenerateslesspulsesfortheuninterestedsignal.Therefore,thelarge 109

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portionofthedatarateisdistributedtorepresenttheusefulinformationandtheaveragedataratecanbereduced. ASurgerydataanditsrecoveryresults BZoom-inoftheactionpotentials Figure4-20. ReconstructionresultoftherecordedextracellularneuralsignalduringthesurgeryencodedbytheTDconverter:1)Originalsignal(inblacksolidline)andrecoveredsignal(inreddashedline);2)Pulserateoftheoutputpulsetrain;3)SERoftherecoveredsignal APost-surgerydataanditsrecoveryresults BZoom-inofthepossibleactionpotentials Figure4-21. ReconstructionresultoftherecordedextracellularneuralsignalafterthesurgeryencodedbytheTDconverter:1)Originalsignal(inblacksolidline)andrecoveredsignal(inreddashedline);2)Pulserateoftheoutputpulsetrain;3)SERoftherecoveredsignal TworecordedextracellularneuralsignalsofarathavebeenencodedbytheTDconverterandrecoveredbackfromtheoutputbiphasicpulsetrains.Figure 4-20 shows 110

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thesimulationresultsoftheTDencodingthesurgerysignal,whichwasrecordedduringthesurgeryofimplantinganelectrodearrayintotherat'sbrain,andFigure 4-21 showsthesimulationresultsoftheTDencodingthepost-surgerydatawhichwasrecordedseveraldaysafterthesurgery.TherecordedsurgerydataasshownintherstwaveforminFigure 4-20A hasahighsignal-to-noise(SNR)ratio,whilethepost-surgerydataasshownintherstwaveforminFigure 4-21A hasabadSNR,inwhichtheactionpotentialsareburiedintonoise.TheregionsinsidethegreendotlinescontainspikesorpossiblycontainspikesandarezoomedinasshowninFigure 4-20B and 4-21B ,respectively.Theentiresignalsarerecoveredbackusingtheoff-lineTDreconstructionalgorithm.Thesurgerydatasimulationgets42dBSERwiththeaveragepulserateof22Kpulses/s,andthepost-surgerydatasimulationgets39dBSERwiththeaveragepulserateof18.4Kpulses/s.ThesecondandthethirdwaveformsinFigure 4-20A and 4-21A showthewindowedpulserateandthewindowedSER,respectively.Eachwindowlengthis5ms. 4.6.4ComparisonoftheTDandIFConvertersonEncodingNeuralSignals Thesamerat'sneuralsignalsshowninFigure 4-20 andFigure 4-21 wereencodedbytheIFmethodinordertocomparetheperformancesoftheTDandIFencodersonneuralsignals.Figure 4-22A andFigure 4-23A showthesimulationresultoftheIFencodingonneuralsignals.Thesurgerydatasimulationgets26dBSERwiththeaveragepulserateof21Kpulses/s,andthepost-surgerydatasimulationgets18dBSERwiththeaveragepulserateof19Kpulses/s. Inneuralsignalrecordingapplications,theaccuracyinthespikeregionsismuchmoreimportantthantheaccuracyinthenoiseregions.Inordertoreducebandwidth,thepulserateofthebiphasicoutputpulsetrainsgeneratedbytheTDandIFconverterscanbereducefurtherwithoutdegradingtheperformanceofrecoveringthesignalinthespikeregions.TheaccuracyperformanceoftheTDandIFconverterson50spikesiscomparedinFigure 4-24 .X-axisistheaveragepulserateof50spikesandY-axis 111

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ASurgerydataanditsrecoveryresults BZoom-inoftheactionpotentials Figure4-22. ReconstructionresultoftherecordedextracellularneuralsignalduringthesurgeryencodedbytheIFconverter:1)Originalsignal(inblacksolidline)andrecoveredsignal(inreddashedline);2)Pulserateoftheoutputpulsetrain;3)SERoftherecoveredsignal APost-surgerydataanditsrecoveryresults BZoom-inofthepossibleactionpotentials Figure4-23. ReconstructionresultoftherecordedextracellularneuralsignalafterthesurgeryencodedbytheIFconverter:1)Originalsignal(inblacksolidline)andrecoveredsignal(inreddashedline);2)Pulserateoftheoutputpulsetrain;3)SERoftherecoveredsignal 112

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istheaveragereconstructionaccuracyinSERof50spikes.TheresultsshowthattheTDconverterachievesbetteraccuracythantheIFconverterforthesamepulserate.Therefore,forthiscase,theTDconverteroutperformstheIFconverterforcompressionneuralsignals. Figure4-24. ComparisonoftheTDandIFconverteraccuracyperformanceonneuralspikes 4.6.5ComparisonoftheTDConverterwithSynchronousADCs Table4-1. PerformancecomparisonoftheTDconverterandthesynchronousADCs SamplingADCRes.DataRateSERonSERonClkNeuralSignalSinewave Michigan[ 11 ]62.5KHz8bit500Kb/s37dB49dBUtah[ 12 ]15.7KHz10bit157Kb/s49dB61dBDuke[ 13 ]31.25KHz12bit375Kb/s61dB75dBBrown[ 14 ]34-40KHz12bit408-480Kb/s61dB75dBTD-10MHz14.1Kpulse/s45dB64dB(Quant.Clk) Table 4-1 comparestheperformancesoftheTDconverterwiththeconventionalsynchronousADCsusedintheotherneuralrecodingsystemresearchgroups[ 11 ],[ 12 ],[ 13 ],[ 14 ].Afull-scalesinewaveisthestandardsignalwhichmeasurestheaccuracyofaconverter.Butthesinewaveisverydifferentfromtheneuralsignals.Soboththe 113

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sinewaveandtheneuralsignalshavebeenencodedbytheconverters,andrecoveredbacktochecktheaccuracyinMATLABsimulation.Thereisabout13dBSERlossfromencodingthefull-scalesinewavetoencodingtheneuralsignals.TheaccuracyofthesynchronousADCisdeterminedbytheamplitudequantizationresolution,buttheaccuracyoftheTDconverterisdependentonthetimingquantizationresolution.Fromtheresult,wecanseethattheTDwith100nsquantizationtiminghassimilaraccuracyofthe10-bitconventionalADC,butthedatarateisatleast10timeslessthanthesynchronousADCs. 4.7CircuitSimulationResults Theproposedtime-derivativeconvertercircuitwassimulatedintheAMI0.5mCMOStechnologyandthesimulatedresultsarereportedinthissection. 4.7.1SimulationoftheLinearTransconductor ThesimulatedcharacteristicsofthetransconductorGmarelistedinTable 4-2 .ThemostimportantspecicationisthelinearityofGm.Figure 4-25 showsthetransconductancevalueversustheinputsignalamplitude.Thenominaltransconductanceis22.62A/V.Thetransconductancevariationandthetotalharmonicdistortion(THD)arelistedinTable 4-3 .Thevariationiscalculatedasthemaximumtominimumdifferencewithintheinputamplituderangedividedbythenominaltransconductancevalue.Thefrequencyresponseoftheoutputcurrentrelativetotheinputvoltagewith8pFcapacitiveloadisshowninFigure 4-26 .The3dBcornerfrequenciesare66Hzand15MHz. Table4-2. SimulatedcharacteristicsofGm Supplyvoltage3.3VInputcommonmodevoltage1.5VTransconductance22.62A/VOutputcommonmodevoltage1.5VOutputvoltagerange0.8v2.2VCurrentconsumption28A 114

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Figure4-25. TransconductanceofGmincadencesimulation Table4-3. GmtransconductancevariationandTHD VinamplitudeVariationTHD 1mV-3.72E-042mV-7.44E-045mV-1.86E-0310mV-3.72E-03100mV0.00250.0354200mV0.0130.0786300mV0.0320.2797 Figure4-26. ACresponseofGm:1)Magnitude;2)Phase. 115

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Figure4-27. CadencesimulationsoftheTDconvertercircuit 4.7.2SimulationoftheTDConverterCircuit TheTDconvertercircuithasbeendesignedintheAMI0.5mprocesswithapowersupplyvoltageof3.3V.ItisexaminedwiththesamesyntheticinputsignalasinFigure 4-12 andoutputsareshowninFigure 4-27 .Therstwaveformistheinputsignal;thesecondandthethirdwaveformsshowthesignalattheinputandtheoutputnodesofGm.ThelasttwowaveformsformtheabiphasicpulsetrainwhichisthenaloutputoftheTDconverter.Thenominalrefractoryperiodis800ns.Thesignalisreconstructedoff-lineusingtheleakyTDalgorithminMATLAB.ThereconstructedresultisshowninFigure 4-28 .TheTDconvertercircuitachieves39dBSERwiththepulserateof41.5Kpulses/s.ThelimitationofachievinghigherSERisthenon-idealeffectsofthecircuit,suchasthesignaldependentoffsetandthesignaldependentthresholdvariationofthecomparators,theoffsetandthenon-linearityofthetransconductance,theswitchoffsetandthechargeinjectionnoise.Inaddition,theparasiticcapacitorsandresistances 116

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Figure4-28. ReconstructionresultfromtheTDconverterpulseoutputincadencesimulation:1)Recoveredsignal(inreddashedline)andinputsignal(inblacksolidline);2)Errorbetweentheinputandtherecoveredsignals Table4-4. PowerconsumptionoftheTDconverter PowersupplyAnalog3.3VDigital3.3V Currentconsumption(Static)Tansconductor28AComparators(analogpart)6ARefractorycomponent0v5AOtherdigitalcircuits2pA maketheestimationoftheparametersinaccurate.Besidesthenonidealeffectsofthecircuit,thetruncationofsincfunction,thecomputationalprecision,andthetimingjitterinreadoutofpulseeventsarelimitationsaswell. ThestaticpowerconsumptionofeachofthecomponentoftheTDconvertercircuitislistedinTable 4-4 .ThedynamicpowerconsumptionisfCV2dd,wherefisthepulserate,andCistheeffectivecapacitorincludingtheintegrationcapacitor,theloadcapacitorandtheparasiticcapacitorsatalldigitalnodes. 117

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4.8Bench-TopMeasurementResults ThechiphasbeenfabricatedintheAMI0.5m3-metal2-polybulkCMOSprocessandpackagedintheDIP40package.Thelayoutofthetime-derivativeneuroncircuitoccupies400m530marea.50percentoftheareaisconsumedbythecapacitors. 4.8.1MeasurementwithNon-NeuralSignalsasInputSignals Figure4-29. Bench-toptestoftheTDconverterchip.Firstrow:inputsignal,fromlefttorightaresinewave,sawtoothwaveandsquarewave;secondrow:intermediatevoltageontheintegrationcapacitor;lasttworows:outputpulsetrains Figure 4-29 plotsthetestresultsoftheTDconverterchipwithsinewave,sawtoothwaveandsquarewavesignalsprovidedbyafunctiongenerator.Therstrowshowstheinputsignals.ThesecondrowshowsthecorrespondingvoltageVmemontheintegrationcapacitor.Thepositivepulses(inpink)andnegativepulses(inred)areshownatthe 118

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bottomofthegure.TheresultsshowthattheTDconverterrespulsesaccordingtothechangeoftheinputsignal:A)Thepulseeventsaregeneratedmostlyatthezerocrossingregionsandaregeneratedleastatpeakofthesinewavesignal;B)positivepulsesareequallyspacedplacedintheregionsoflinearrisingandthenegativepulsesareproducedatwherethesignaljumpstozero;C)theTDgeneratesapositivepulsewherethesquarewavejumpsfromlowtohighoranegativepulseatwherethesquarewavejumpsfromhightolow.Therearecouplingnoisesassociatedwiththepulsesandtheotherdigitalsignals.Thisismainlyduetotheelectrostaticdischarge(ESD)padsofthesensitiveanalogsignalsandthenoisydigitalsignalssharingonepowerline.Theheavilydopedpsubstratealsocontributestothenoisecoupling.Thecorrelationsamongtheoscilloscopeprobesresultinthecouplingnoisedisplayedontheoscilloscopeaswell. Figure4-30. Calibrationofchipcomparatoroffsetvoltage Theoutputpulsesaretime-stampedto5nsprecisionbyalogicstateanalyzer.TheoutputwiththesinewaveasinputwasprocessedusingtheleakyTDreconstructionalgorithmtorecovertheinputsignalinMATLABandisusedtocalibratetheTDconvertersystemandcompensatethenonidealeffectsincludingtheniteresistance 119

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Figure4-31. Calibrationofchipresistance Figure4-32. ReconstructionresultfromtheTDconverterchipoutputinbench-toptest:1)OutputpulsetraingeneratedbytheTDconverterchip;2)Recoveredsignal(inreddashedline)andestimatedinputsignal(inblacksolidline);3)Errorbetweeninputandrecoveredsignal 120

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andtheoffsets.The4-parametersinewavettingmethodbyIEEE1241standardisusedtoestimatetheinputsinewavesignalfromtherecoveredsignalbyndingthebestttingone.Figure 4-30 andFigure 4-31 showthecalibrationofthecomparatorthresholdoffsetvoltageandtheleakyresistance,respectively.Theoffsetandtheresistanceareestimatedbasedonthesiliconparametersandmeasurementsetup.ThenthereconstructionprocesssweepstheoffsetandtheresistancevaluesintheestimationrangetondoutthemaximumSERsotodeterminethecalibratedoffsetandresistancevalues.Asanalyzedinsection 4.5.2 ,theoffsetismainlyduetothedevicemismatchandisdependentonthetemperature.Fortunately,foranimplantedchip,thetemperaturearoundthechipisconstant,thustheoffsetisconstant.Oncetheoffsetiscalibrated,theoffseteffectcanbeminimized.Accordingtotheresult,theequivalentoffsetofthetransconductorfollowedbythecomparatoris30mVandtheresistanceis100M.Figure 4-32 showsthereconstructionresultfromthebiphasicpulsetraingeneratedbytheTDconverterwiththe100mVpeak-to-peakamplitude1KHzfrequencysinewaveasinputsignal.TherstwaveformisthebiphasicpulsetrainattheTDoutputandthesecondFigureshowstherecoveredsignalandthettedsinewaveinputsignal.Thelastwaveformistheerrorbetweentherecoveredsignalandthettedinputsignal.TheTDconverterchipachieves46dBwiththepulserateof10Kpulses/s.Theaveragerefractoryperiodis4sandthethresholdsare0.4V. 4.8.2MeasurementwithNeuralSimulatorSignalasInputSignal TheneuralsignalfromtheneuralsimulatorhasbeenencodedbytheTDconvertertoverifyitsdataratecompressionability.TheneuralsimulatorsignalhasbeendescribedinSection 2.3.1 .TheampliedneuralsimulatorsignalfromtheUFcustomamplierasshowninFigure 4-33A ispassedtotheinputoftheTDconverter. ThebiphasicoutputpulsetrainoftheTDconverterwiththeneuralsimulatorsignalasinputisrecordedbythelogicstateanalyzerwithasynchronoussamplingfrequencyof200MHz.Asegmentofthepulsesisprocessedbythereconstructionalgorithmwith 121

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AInputsignalfromtheneuralsimulator BOutputpulseeventsandtherecoveredsignal Figure4-33. TheTDconverterbench-topmeasurementwiththeneuralsimulatorsignalasinput.A):AmpliedneuralsimulatorsignalastheinputtotheTDconverter;B):Biphasicoutputpulsetrainandrecoveredsignalwiththeneuralsimulatorsignalasinput 122

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thecalibratednonidealparameterstorecovertheampliedneuralsimulatorsignal.Figure 4-33B plotsthebiphasicpulseeventsandtherecoveredsignal.Asexpected,thepulsesaregeneratedmostlyintheactionpotentialregionswheretheslopesarelargest.However,intheregionsbetweentheactionpotentials,somepulsesarestillgeneratedduetothenoiseoftheinputsignalandthecircuit.Theneuralsimulatorsignalcontainsarepeatedpattern.TheinputsignalshowninFigure 4-33A andtherecoveredsignalinFigure 4-33B areshiftedintimetoshowthesamepattern,buttheyarenotsimultaneous.Thepulserateduringtheburstingperiodisonly5.8Kpulse/s.Therecoveredsignalisquitesimilartotheinputsignal,butwithsomedistortion.Thereasonstothedistortionarethenoisesinthesystem,thetruncationofthedata,thetimingjitterandtheviolationoftheNyquistrule. 4.9Summary Inthischapter,anasynchronousdataconvertercalledtheTime-Derivative(TD)encoderhasbeenproposedtoreducethedatarate.ThemathematicmodeloftheTDhasbeenanalyzedandthereconstructionalgorithmhasbeendeveloped.Theoretically,thesignalcanbeperfectlyrecoveredbackfromtheoutputbiphasicpulsetraingeneratedbytheTDconverter.TheTDconverterconcentratesitspulsesintheregionsofsharpchange,whiletheIntegrate-and-Fire(IF)converterproducesmostpulsesintheregionsofhighmagnitude.100randomsyntheticsignalstestedonboththeconvertersshowsthattheTDconvertercanachievethesameSERastheIFconverter,butrequiresalowerpulseratethantheIFconverter.TheTDconverteralsohasbeensimulatedwiththerecordedneuralsignalfromtherat,andtheresultsshowthattheTDconvertercanreducedataratewithoutdegradingtheacquisitionaccuracy. TheICimplementationoftheTDconverterhasbeendesigned,simulated,fabricatedandtestedintheAMI0.5mCMOSprocess.Thechipachieves46dBSERwith110Wstaticpowerconsumptionandithasgooddataratereductionperformanceonneuralsignals. 123

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CHAPTER5NEURALSIGNALENCODINGMETHODS 5.1Introduction Animplantablemulti-channelneuralrecordingdevicemustmeetstringentconstraintsoflowpower,lownoise,lowtransmissionbandwidthandcompactsize.Theseverestchallengeincurrenttechnologyisthelimitedbandwidthofthewirelesstransmissionlink.Duetothepowerconsumptionconstraint,thewirelesstransmissionbandwidthisusuallyaroundfewMb/s[ 11 ],[ 12 ].Itisimpossibletotransmitmultiplechannelsofentireneuralsignals.Someresearchgroupsdospikedetectionbeforedigitization,andtransmitoutonlythetimingofspikeeventsoronlysegmentsofspikes.However,theentiresignalsarehighlypreferredthanonlythespikedetectionresultssincetheentiresignalsprovidesmoreinformation.Therefore,thestudyoftheneuralsignalencodingisfocusedonhowtoefcientlyencodetheinformationwithlimitedbandwidth. Thischapterdiscussesvariousencodingmethods,inordertogureoutthemostefcientencodingmethodintermsofdatarateinneuralrecordingapplications.First,theconventionalsynchronousanalog-to-digital(ADC)willbeconsidered.Then,wewillseethedataratereductionabilitiesofsomeasynchronousADCsincludingasynchronouslevel-crossing,asynchronousdeltasigma,asynchronousdelta,theintegrate-and-reandthetime-derivativeconverters.Followedbytheneuralsignalencodingwithanon-lineartransformationmethodanditsperformance.Finally,theconclusionispresented. 5.2NeuralSignalEncodingwithSynchronousADC ConventionalsynchronousADCshavebeenusedpopularlyinneuralrecordingsystemsformanyyears[ 11 14 ].However,transmittingtheentireneuralsignalsampledbysynchronousADCsfromhundredsofchannelsisnotfeasibleduetothewirelesscommunicationbandwidthlimitations.ThesynchronousADCsamplesasignalataxed 124

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datarateindependentofthesignalproperties.FollowingShannon'ssamplingtheory,thesynchronousADCrequiresthesamplingfrequencytobeatleasttwiceoftheinputsignalfrequencybandwidth.Intheprocess,alargenumberofsamplesaregeneratedtorepresentthesignal,includingtheinterestingregions(i.e.,spikes),andtheuninterestingregions(i.e.,noise).Forneuralsignalsforbrainmachineinterfaces(BMIs),dataissparse.Thus,asynchronousADCisnotoptimalforencodingtheneuralsignalsfromthedatarateperspective.Forexample,aneuralsignalwiththespikerateof50spikespersecond,thespikedurationof1ms.Ifthesignalissampledbyan8-bit20Ksample/ssynchronousADC,thedataratefortheentiresignalis160kb/s.Ifthisneuralrecodingsystemcontains100channels,thedatarategoesupto16Mb/s.Foreachchannel,only8Kb(1ms/spike50spikes/s20Ksamples/s8bits/sample)areusedtorepresentthespikesinonesecond,and95%oftheoutputdatarepresentsnoise.Thishighdatarateexhibitsachallengetothewirelesstransmissionofmulti-channelsignals. 5.3NeuralSignalEncodingwithAsynchronousADC Neuroscientistsdonotwanttodecreasethenumberofrecordingchannels,ifthedatarateofeachchannelcanbereducedwhilestillpreservingthepertinentinformation.Asneuralsignalshavearathersparsenumberofspikesmixedwithnoise,itwillbebesttoconsumethebandwidthonthespikeregionsofthesignalandnobandwidthatallonthenoiseregions. Figure5-1. Generalarchitectureofasynchronousanalog-to-digitalconverter Unlikesynchronouscircuits,asynchronouscircuits,asshowninFigure 5-1 ,donothaveglobalclocks,anddenethestatesintermsofinputsignalsandinternalactions.Ingeneral,asynchronouscircuitsconsumelesspower,generateless 125

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electromagneticinterferenceandgetridofthemetastablebehaviorcomparedtosynchronouscircuits[ 63 ],[ 64 ].Atthefront-end,theinputanalogsignalx(t)isconvertedintoanasynchronousdigitalpulsetrainwhosetimingencodesthesignalinformation.Aftertransmission,thepulsetrainisprocessedwithareconstructionalgorithmtorecovertheinputsignal.Generally,anasynchronousADCcanleadtofront-endswithadvantagesoflowerpower,lesssiliconareaandlowerbandwidthcomparedtosynchronousADCbasedapproaches.TheasynchronousADCbasedsystemisparticularlywellsuitedforapplicationssuchasbiomedicalimplantedsensors,whichmustbelowpower,compactandlowbandwidth.Thetradeoffisthatacomputationalsignalprocessingalgorithmisrequiredontheback-endtorecoverthesignal.Fortunately,thisisnotproblematicsincethereconstructionisdoneataplacewherepowerandsizeconstraintsarenotthatsevere,e.g.outsidethebodyforbiomedicalimplants. Next,wedescribevariousasynchronousevent-basedA/Dconversionschemes.DependingontheprocessesH1,H2,referencesignals(t),thelevelquantizerandthedigital-to-analogconverter(DAC),theasynchronousconversionschemeshavedifferentcharacteristicsandsomeofthemaresuitableforcompressionofneuralsignals. 5.3.1AsynchronousLevel-CrossingEncoding Allieretal.havedesignedanasynchronouslevel-crossing(LC)ADC[ 65 ].Figure 5-2 showsanexampleofthenonuniformsamplingofanalogsamplingoftheanaloginputx(t)byaM-bitresolutionasynchronousLCADC.Intheexample,Misequalto2,andtherearethreequantizationlevels.Aneventisgeneratedonlywhentheinputsignalx(t)crossesanyofthequantizationlevels.TheA-LCADCcanbemodeledasshowninFigure 5-3 .H1=H2=1.Thesample-and-hold(S/H)blocksamplestheDACoutputsignalc(t)whenacksignalishighandholdstherecentsampledvaluewhenackislow.Thedifferencesignalz(t)betweentheanaloginputx(t)andthereferencevaluec(ti)]TJ /F6 7.97 Tf 6.59 0 Td[(1)sampledatthelatestsamplingtimeiscomparedtothequantizationlevels.Ifone 126

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Figure5-2. WaveformsoftheasynchronousM-bitlevel-crossingconverter:1)Theblackwaveformistheinputsignalx(t);thebluewaveformsarethequantizationlevels.HereM=2,andthereare3quantizationlevels.2)TheredwaveformsaretheasynchronousLCoutputsp<0:M)]TJ /F5 11.955 Tf 11.96 0 Td[(1>. Figure5-3. ArchitectureoftheasynchronousM-bitlevel-crossingconverter 127

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ofthesethreeconditions,i.e.z(t)=+,z(t)=0orz(t)=)]TJ /F4 11.955 Tf 9.3 0 Td[(,issatised,whereonlyonecanbesatisedatonetime,thecorrespondingcomparisonoutputs,i.e.inc,eq,ordec,respectivelygoestohighandsodoesack.Whenackishigh,thetimerstampsthecurrenttimetiandthelevelcounterrecordsthecurrentcrossedquantizationlevelbycountinguponestep,countingdownonestep,orstayingatthesamelevelfromthepreviouscrossedquantizationlevel.Inthemeantime,theS/Houtputchangestoanewvaluec(ti),andthecomparatorsareresetsinceackishigh.Thus,afterashortdelay,ackgoesbacktolowandtheprocessrepeats. ThetotalnumberofquantizationlevelsisdeterminedbytheresolutionoftheDACandthecounterinanasynchronousLCADC.AnM-bitasynchronousLCADChas2M-1quantizationlevels.Iftheinputsignalishigherthanthemaximumquantizationlevelorlowerthantheminimumquantizationlevel,theasynchronousLCADCissaturatedandisnotabletoencodethesignalcorrectly.TheasynchronousLCADCgeneratesoutputeventswhentheinputsignalscrossthequantizationlevels.Therearethreepossiblequantizationlevelsforeachsample:onelevelhigherthan,onelevellowerthan,orthesameasthecrossedquantizationleveloftheprevioussample.Ifthesignalstaysconstant,nosampleswillbegenerated.However,ifthesignaluctuatesaroundthequantizationlevel,manysampleswillbegenerated.Thus,theasynchronousLCencodingissensitivetonoise. 5.3.2AsynchronousDeltaSigmaEncoding Synchronousdeltasigmaconvertershavebeengreatlyexploredandpopularlyusedforhigh-resolutionmedium-to-low-speedapplications.Asynchronousdeltasigma()conversionsviapulsedensitymodulationalsohavebeenstudied,andthereconstructionmethodshavebeendevelopedrecently[ 66 ],[ 67 ].[ 67 ].UnlikesynchronousADC,asynchronousconvertersdonotinvolveanyclocktosampleanaloginputsignals,anddonotrequiretimequantizationoperationduringtheconversion.Figure 5-4A depictsthearchitectureofthe1storder1-bitasynchronousencodingscheme, 128

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AASchmitttriggerwithhysteresisasquantizer BAnequivalentrepresentationoftheabovearchitectureusingtwocomparatorswith-outhysteresis,sample-and-hold,andedge-triggeredDip-op Figure5-4. Architectureofthe1storder1-bitasynchronousdelta-sigmaconverter whichcontainsanintegrator,aSchmitttriggeras1-bitquantizer,anda1-bitDAC.Theconvertercanbeimplementedusingsimpleandlow-powercircuitry[ 68 ].Referencesignals(t)isequaltothepositivevalue+bwhentheSchmitttriggeroutputp(t)ishigh,whiles(t)isequaltothenegativevalue)]TJ /F3 11.955 Tf 9.3 0 Td[(bwhenp(t)islow.Theamplitudeofx(t)mustbewithinthequantizationrange,i.e.,jx(t)j
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hysteresisandanedge-triggeredtoggleip-op.Theasynchronoustoggleip-opisbuiltbyanedge-triggeredDip-opwithitsDinputfedfromitsowninvertedoutput.Sincethequantizationrangeislargerthanthesignal,i.e.,jx(t)j
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Figure5-6. Waveformsofthe1storder1-bitasynchronousdelta-sigmaconverter:1)Theblackwaveformistheinputsignalx(t);theredwaveformisthereferencesignals(t);theblue-purplearearepresenttheintegrationofcorrespondstothepositivethreshold+andpurplecorrespondstothenegativethreshold)]TJ /F4 11.955 Tf 9.3 0 Td[(.2)Theblue-purplewaveformistheintegratoroutputintegratoroutputz(t),correspondingtotheareainthesamecolorin1);theredwaveformistheasynchronousoutputp(t) ThedisadvantageoftheasynchronousLCADCencodingthesignalwithnoisearoundthequantizationlevels,originatesfromtheconditionthatz(t)=0.The1-bitasynchronousasynchronousconverterandthethreeothertypesofasynchronousevent-basedconvertersdescribednext,usebi-phasiccomparisonasaquantizerinsteadofthetri-phasiccomparisontoovercomethisproblem.ThenumberofquantizationlevelsoftheasynchronousLCandtheasynchronousaredeterminedbytheresolutionoftheDACs.Differently,thefollowingthreeothertypesoftheasynchronousconvertersdonotuseDACs.Theirreferencesignalsaregeneratedfromthefeed-forwardsignalsinsteadoftheoutputofDAC,thus,thenumberofquantizationleveldependsontheinputsignalandthequantizationstepsize. 5.3.3AsynchronousDeltaEncoding Thebasicstructureofbi-phasiccomparisonwithsamplingandholdingtheinputsignalasthereferencesignalisshowninFigure 5-7 ,whichisnamedtheasynchronous 131

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Figure5-7. Architectureoftheasynchronousdeltaconverter delta()converter.Ifthedifferencesignalz(t)betweentheinputsignalx(t)andtheheldinputvaluesampledattherecentsamplingtimex(ti)]TJ /F6 7.97 Tf 6.59 0 Td[(1)meetsoneofthesetwoconditionsi.e.z(t)+orz(t))]TJ /F4 11.955 Tf 23.98 0 Td[(,thenthecorrespondingcomparisonoutputi.e.p+(t)orp)]TJ /F5 11.955 Tf 7.09 1.79 Td[((t)goestohighandsodoestheacksignal.Inthemeantime,thetimerstampsthecurrenttimeti,andalsotheS/Houtputchangestoanewvaluex(ti).Thisresetsz(t)tozeroandmakesthecomparatoroutputsandackgotologiclowvalue. Figure5-8. Waveformsoftheasynchronousdeltaconverter:1)Theblackwaveformistheinputsignalx(t);thebluewaveformsarethequantizationlevels.2)Theredwaveformistheasynchronousoutputbiphasicpulsetrainp+(t),p)]TJ /F5 11.955 Tf 7.09 1.8 Td[((t) 132

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TheasynchronousADCgeneratesthesameeventsastheasynchronousLCADC,iftheyhavesamequantizationstepsize,excepttheeventswhichareonthesamequantizationlevelasthepreviousevents.Anexampleoftheasynchronousencodingsignalx(t)isillustratedinFigure 5-8 .Aoutputeventisonlygeneratedwhentheinputsignalcrossesaquantizationlevel,andthecurrentcrossedquantizationlevelisdifferentfromthepreviouscrossedquantizationlevel.Thus,moresamplesaregeneratedwhenthesignalchangessharperandnosamplewhenthesignalstaysconstant. Theamplitudeofreferencesignals(t)isanintegermultipleofthequantizationstepsize,i.e.,s(t)=Pki)]TJ /F6 7.97 Tf 6.59 0 Td[(1[u(ti)]TJ /F6 7.97 Tf 6.59 0 Td[(1))]TJ /F3 11.955 Tf 11.98 0 Td[(u(ti)],wheretiisthetimingoftheithpulseevent,u(t)isthestepfunctionandkiisaninteger.kicanbeanyintegerwhichisnotlimitedto2M-1asintheM-bitasynchronousLCconverter.Thequantizationlevelisrepresentedbythebiphasicoutputpulsetrainp+(t)andp)]TJ /F5 11.955 Tf 7.08 1.79 Td[((t).Whenz(t)+,aneventisgeneratedinthepositivepulsetrain,indicatingthatthequantizationlevelincreasesonestep,andwhenz(t))]TJ /F4 11.955 Tf 24.38 0 Td[(,asampleisgeneratedinthenegativepulsetrain,indicatingthatindicatingthatthequantizationleveldecreasesonestep.Thus,unliketheasynchronousLCconverter,thequantization-leveloftheasynchronousconverterisexibleandisdependentonsignalandquantizationstep. AnimplementationoftheasynchronousADChasbeenreportedbutthereconstructionalgorithmtoconvertthenonuniformsampletotheinputsignalhasnotbeendiscussed[ 70 ]. 5.3.4TheIntegrate-and-FireEncoding TheIntegrate-and-Fire(IF)encodingmethodwasrstproposedandimplementedbyWei,andextendedtothebiphasicIFbyChenandfurtherdevelopedbyLiduringtheirPh.DstudiesattheUniversityofFlorida[ 20 ],[ 21 ]and[ 22 ].Abriefoverviewhasbeencoveredinsection 3.1.1 TheIFencodingschemeisshownhereagaininFigure 5-9 ,whichiscomposedbyanintegratoratrstandtheasynchronousconverterafter.Thecodingprocessofthe 133

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Figure5-9. Architectureoftheintegrate-and-reconverter Figure5-10. Waveformsoftheintegrate-and-reconverter:1)Theblackwaveformistheinputsignalx(t).Theblue-purplearearepresenttheintegrationofx(t),bluecorrespondstothepositivethreshold+andpurplecorrespondstothenegativethreshold)]TJ /F4 11.955 Tf 9.3 0 Td[(.Apulseinredisgeneratedwhentheintegralvaluereachesthethresholds.2)Theblue-purplewaveformistheintegratoroutputz(t),correspondingtotheareainthesamecolorin1);theredwaveformistheIFoutputbiphasicpulsetrainp+(t),p)]TJ /F5 11.955 Tf 7.08 1.79 Td[((t) 134

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IFisequivalenttoencodingtheintegralresultoftheinputsignalbytheasynchronousconverter.AccordingtothegeneralstructureofasynchronousconvertershowninFigure 5-1 ,H1(s)=1 sandH2(s)=1.Figure 5-10 givesanexampleofencodingasignalx(t)withtheIFconverter.Whentheinputsignalamplitudeincreases,morepulseswillbeproduced;whentheamplitudedecreases,fewerpulseswillbeproduced.TheIFhasbeenproventobeanefcientmethodtocompressneuralsignalsandhasbeenusedinFloridaWirelessImplantableRecodingElectrode(FWIRE)project. 5.3.5TheTime-DerivativeEncoding Figure5-11. Architectureofthetime-derivativeconverter Thetime-derivative(TD)encodingmethodwasdiscussedindetailinChapter 4 .Inshort,themotivationisasfollows.SinceneuralsignalspossiblyaremixedwithlargevaryingDCoffsetandnoise,theIFencoderplacesmoresamplesontheregionswithlargerDCoffseteventherearenotmuchvaluableinformation.Thus,generatingpulseeventsproportionaltotheslopemaybepreferredtoproportionaltotheamplitudeformanyapplicationssuchasneuralsignalrecording.Theintegrationhelpslterthehighfrequencynoiseandimprovesthenoiseimmunity.Anasynchronousconverterhavingintegrationfeaturesandproducingoutputeventsaccordingtothetransitionfeatureispreferable. 135

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Figure5-12. Waveformsofthetime-derivativeconverter:1)Theblackwaveformistheinputsignalx(t);theredwaveformisthereferencesignalbeforetheintegrators1(t);theblue-purplearearepresenttheintegrationofx(t))]TJ /F3 11.955 Tf 11.96 0 Td[(s1(t),bluecorrespondstothepositivethreshold+andpurplecorrespondstothenegativethreshold)]TJ /F4 11.955 Tf 9.29 0 Td[(.2)Theblue-purplewaveformisthedifferencesignalz(t)betweentheintegratoroutputy(t)andthereferencesignalaftertheintegrators2(t),correspondingtotheareainthesamecolorin1);theredwaveformistheTDoutputbiphasicpulsetrainp+(t),p)]TJ /F5 11.955 Tf 7.08 1.8 Td[((t) Figure 5-11 demonstratesthetime-derivative(TD)encodingmodelwhichsatisesthefeatures.ThetwoS/Hblockssampletheinputsignalx(t)andtheintegrationoutputy(t)whenacksignalishighandholdtherecentsampledvalueswhenacksignalislow.Thedifferencesignaly0(t)betweenx(t)ands1(t)whichisequaltotheheldinputvaluesampledattherecentsamplingtimex(ti)]TJ /F6 7.97 Tf 6.59 0 Td[(1)iscontinuouslyintegrated.Iftheotherdifferencesignalz(t)risesabovethehighreferencevoltage+,thecomparatoroutputofpositivechannelp+(t)goesfromlowtohigh.Ifz(t)dropsbelowthelowreferencevoltage)]TJ /F4 11.955 Tf 9.3 0 Td[(,thecomparatoroutputofnegativechannelp)]TJ /F5 11.955 Tf 7.08 1.8 Td[((t)goesfromlowtohigh.Whenp)]TJ /F5 11.955 Tf 7.08 1.79 Td[((t)orp+(t)ishigh,ackgoesfromlowtohighandtriggersthetimertostampthecurrenttimeti,andalsosamplesthecurrentsignalvaluex(ti)andy(ti).Thisresetsy0(t)andz(t)tozeroandresetsboththecomparatoroutputsandacktozero.Figure 5-12 showsthewaveformsoftheTDconverterwhenencodingsignalx(t). 136

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5.4NeuralSignalEncodingwithNon-LinearTransformation ItisdifculttosetasinglethresholdvoltageoftheIntegrate-and-Fire(IF)encoderwhendealingwiththesignalshavinglargedynamicranges.Thethresholdissethightoreducethedatarateinregionsofhighmagnitude,resultingininsufcientdatarateinregionsoflowmagnitude.Ifthethresholdissetlowenoughtoguaranteeasufcientdatarateinregionsoflowmagnitude,thedatarateinregionsofhighmagnitudewillbeextremelyhighorsaturated.Nonlinearcompressingtransformsarewidelyusedinsystemsthatprocessverylargedynamicrangesignals.HerewewillinvestigatewhethernonlineartransformsareagoodmethodintheIFortheTDconverter. Figure5-13. Nonlineartransferfunctions TheIFconversionitselfisanonlinearoperation.Thenonlinearoperationinthissectionspecicallymeansthenonlineartransformationoftheinputsignal.Theinputsignalx(t)withbandwidth!istransformedbyanonlineartransferfunctionf(x)suchaslogarithm,squarerootorsquare,asshowninFigure 5-13 .Thenthetransformedsignalf[x(t)]issenttotheIFconverter.TheIFoutputpulsescanbereconstructedtoachievethetransformedsignal\f[x(t)].Theinversenonlinearoperationf)]TJ /F6 7.97 Tf 6.59 0 Td[(1(x)willrecovertheinputsignalback.Suchnonlineartransferfunctionscanreducethesignal 137

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dynamicrange.Itseemsthatthenonlineartransformationcansolvethedatarateproblemcausedbythelargedynamicrange. Supposetheinputsignalx(t)iscomposedofalocalmeanvalueKDC)]TJ /F8 7.97 Tf 6.58 0 Td[(localandasmallsignalcomponentxAC(t),i.e.,x(t)=KDC)]TJ /F8 7.97 Tf 6.59 0 Td[(local+xAC(t).TheKDC)]TJ /F8 7.97 Tf 6.59 0 Td[(localcomponentinlargedynamicrangesignalvariesinawiderrangethanthemaximumamplitudeofxAC(t).Forsimplicity,thefollowinganalysisassumesthesignalx(t)=K+cos!t,x(t)>0allthetimeandadoptthelogarithmfunctionasthenonlineartransferfunction,i.e.,f(x)=ln(x+1).SotheconditionfortheIFconvertertogenerateapulsebecomes i=Ztit0i)]TJ /F11 5.978 Tf 5.76 0 Td[(1f[x(t)]dt=Ztit0i)]TJ /F11 5.978 Tf 5.75 0 Td[(1ln(1+K+cos!t)dt.(5) SinceisusuallysmallerthanK,thenonlineartransformedsignalf[x(t)]canbeexpandedas ln(1+K+cos!t)=ln[(1+K)(1+ 1+Kcos!t)]=ln(1+K)+/Xn=1()]TJ /F5 11.955 Tf 9.3 0 Td[(1)n+1 n( 1+K)ncosn!tln(1+K)+ 1+Kcos!t)]TJ /F4 11.955 Tf 33.12 8.09 Td[(2 2(1+K)2cos2!t+3 3(1+K)3cos3!t+...=ln(1+K))]TJ /F4 11.955 Tf 33.12 8.08 Td[(2 4(1+K)2+4(1+K)2+3 4(1+K)3cos!t)]TJ /F4 11.955 Tf 33.12 8.08 Td[(2 4(1+K)2cos2!t+3 12(1+K)3cos3!t+...ln(1+K)+ 1+Kcos!t)]TJ /F4 11.955 Tf 33.12 8.08 Td[(2 4(1+K)2cos2!t+3 12(1+K)3cos3!t(5) Thus,thenonlineartransformationintroducesharmonics,resultinginsignalbandwidthexpansion.Forreconstructingthesignal,thebandwidthparameterisimportanttoachievegoodaccuracy.IfthebandwidthoftheIFissetasthebandwidthoftheoriginalinputsignalbeforethenonlineartransformation,thetransformedsignalcannotbereconstructedwellbecausetheharmonicsarenotincluded.Tocovertheharmonicfrequencycomponents,thebandwidthparameteroftheIFreconstructionneedstobesettoahighvalue,whichrequiresahigherdataratebasedonthe 138

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Nyquist-Shannonsamplingtheorem.Thepurposeofthenonlineartransformationistoreducethedatarate,whichiscontrasttothehigherNyquistraterequirement.Thus,settingahighbandwidthparameterwillalsodegradethereconstructionaccuracy. Figure5-14. Signalcompressioncoefcientoflogarithmoperation Furthermore,Eq. 5 indicatesthatthemeanvalueofthesignaliscompressedbyln(1+K) Ktimesandthesmallsignalcomponentisattenuatedby1+K.Figure 5-14 showsthecompressioncoefcientsonthemeanvalueandthesignalcomponent.Asthesignalmagnitudeincreases,thesignaliscompressedbyalargeramount,whichhelpsreducethedatarateandhelpsplacethepulsemoreevenly.However,wecanalsondoutthatforthelogarithmtransferfunction,thesmallsignalcomponentiscompressedmorethanthedccomponent,whichdegradesthereconstructionaccuracy. Whendealingwiththeinterestedsignalwhichliesinthesmallsignalcomponentbutnotthelocalmeanvalue,tokeeptheaccuracyanddecreasethedatarate,weexpecttocompressthedccomponentmorethancompressthesmallsignalcomponent.Unfortunatelysomenonlineartransferfunctionsincludingthelogarithmoperationfailtomeettheexpectation.Someothernonlineartransferfunctionscancompressthedccomponentmorethancompressthesmallsignalcomponent,forexample,thesquare 139

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operationintheregionof0.51,thesignaldynamicrangewillbeenlargedandthepulseratewillbeincreased,againstthepurposeofreducingthedatarate.Whenthesignalissmall,x<0.5,thesignaliscompressedmoreandthisaggravatestheproblembetweenthedynamicrangeandthexedthreshold. Figure5-15. TheIFconversiononthelogarithmictransformedlargedynamicrangesignal.Topgure:inputsignalandthelogarithmiccompressedsignal.Bottomgure:thebiphasicoutputpulsesgeneratedbytheIFwiththelogcompressedsignalasinput. TheIFconversionwithlogarithmicnonlinearcompressionhasbeensimulatedonanarticialsignalshowninFigure 5-15 .Thearticialsignalisa5KHzbandwidthsignalsuperposedonasigmoidsignaltoenlargethedynamicrange.Inthersthalfregion,thesignalmagnitudeislowwhileintheotherhalfregion,thesignalmagnitudeishigh.Figure 5-15 showstheinputsignalhavinglargedynamicrangeanditslogarithmictransformationastheinputsignaltotheIFconverter.ThebottomFigureshowsthebiphasicoutputpulsesgeneratedbytheIFwithandwithoutthelogarithmiccompressedsignalsasinputs.Thelogarithmoperationreducesthesignaldynamicrange,reducesthepulseratefrom58.5Kpulses/sto49.5Kpulses/s,andalleviatestheunevenpulsedistributionproblem. 140

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Figure5-16. ReconstructionresultsoftheIFconversionwithnonlinearoperation.TopFigurearetheoriginalsignalwithlogtransformationandtherecoveredlogcompressedsignal.BottomFigurearetheoriginalandtherecoveredinputsignal. Thereconstructionresultsoftherecoveredlogarithmiccompressedsignalandtheinverse-logarithmicrecoveredsignalareshowninFigure 5-16 .Theaccuracyis30dBfortherecoveredlogarithmiccompressedsignaland32dBfortheinverse-logarithmicrecoveredsignalwiththepulserateof49.5Kpulses/s.InMATLABsimulation,wecanassumethatthenonlinearoperationandtheinversenonlinearoperationdonotintroduceextraerror.TheaccuracyhasbeendegradedmuchcomparedtotheIFencodingwithoutlogarithmictransformation.TheIFencoderachieves76.4dBSERonencodingtheinputsignalwithoutnon-lineartransformation. Therelationshipbetweenacquisitionaccuracyanddatarateisanimportantevaluationmetricforaconversionsystem.Byvaryingthesignalamplitudeorthethresholdvoltage,wecanchangethedatarate.Afterreconstructionoftheoutputpulseswithdifferentdatarates,therelationshipbetweenthedatarateandtheaccuracyisobtained.Figure 5-17 demonstratestheacquisitionaccuracyinSERversusdatarateperformancesoftheTDconverter,theIFconverterandtheIFconverterwithlogarithmicnonlineartransformation.Theresultsshowthatthenonlineartransformationdegrades 141

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Figure5-17. AccuracyversuspulserateperformancecomparisonamongtheTDconverter,theIFconverterandtheIFconverterwithlogarithmicnonlineartransformation. theperformanceseriously.Evenwithouttheconstraintofminimizingthedatarate,theaccuracyoftheconversionwiththenonlineartransformationislessthanthehalfaccuracyoftheIFandtheTDconversion.Thesimulationresultisconsistentwiththemathematicanalysis.Amongalltheseconverters,theTDoutperformstheotherswhenencodingthesignalwithlargedynamicrangesincetheTDconverterplacespulseaccordingtothechangeofthesignalandignoresthelocalmeanvalue. 5.5Summary Inthischapter,theconventionalsynchronousADC,vedifferentasynchronousevent-basedconvertersandthenon-linearcompressionmethodhavebeenanalyzed.ThedatarateofsynchronousADCisxedtoquantizationbitsmultipliedbysamplingclockfrequency,nomatterwhatinputsignalis.Anasynchronouslevelcrossingschemeencodesthesignalbasedonthederivativeoftheinputsignal.Ifthesignaluctuatesaroundquantizationlevels,manypulseswillbegenerated.Anasynchronousdelta-sigmaencodergeneratesoutputeventsinverselyproportionaltotheamplitudeofthesignal.Whenthesignalissmaller,theeventdensityishigher.Thismakesthe 142

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asynchronousdelta-sigmaencodingunsuitableforneuralsignalcompression.Theasynchronousdeltaconvertergenerateseventsproportionaltothederivativeofthesignal.Becausetheasynchronousdeltaconverterlacksalow-passlteringoperation,iftheinputsignalhashighfrequencynoise,suchasthecouplingnoiseinthemixedcircuit,unnecessarypulseswillbegenerated.EventdensityoftheIFencoderisproportionaltothemagnitudeofthesignal.TheIFencoderwillwastethebandwidthifthesignalhasaDCoffset.TheIFencoderalsohasdifcultytoselectasinglethresholdifthesignalhaslarge-energylow-frequencycomponent.SotheIFrequiresafront-endcircuittorejectDCandthelowfrequencyencodergeneratespulsesdependentonthechangeofthesignal.ItisnotsensitivetotheDCoffsetanditcontainsintegrationtolterthehighfrequencynoise.Thenon-lineartransformationbeforeencodingintroducesaliasingfrequencyintotheinputsignalandresultsinthedegradationofSERaccuracyperformance.Overall,theTDencoderisthemostefcientonetocompresstheneuralsignals. 143

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CHAPTER6CONCLUSION Thechallengesofdesigningwirelessneuralrecordingsystemsarelowpowerconsumption,lownoise,lowbandwidthandsmallsize.Thedissertationmainlyfocusesonthelowbandwidthconstraint.Bystudyingthecharacteristicsofneuralsignals,weknowthatasynchronousevent-basedconverterscanreducethedataratecomparedtosynchronousconverters,iftheasynchronousevent-basedconverterstakeadvantageofthesparsityofthesignal. Beforedigitizingthesignalforwirelesstransmission,theneuralsignalmustbeampliedandlteredtoextracttheinterestedcontent.Atwo-stagelow-noiselow-poweramplierwithprogrammable-gainandtunable-cutoff-frequencyhasbeendesignedandfabricated.Thechipconsumes86Wandtheinput-referrednoiseis3Vrms.Thegaincanbeconguredfrom47dBto64dBandthelow-cornerfrequencyistunablefrom20mHzto700Hzandthehigh-cornerfrequencyis5.7KHz.Theamplierhasbeentestedwiththeneuralsimulatorsignalsasinputandalsohasbeentestedinvivowiththeexiblepolyimideelectrodetodemonstratethattheampliersatisestheconstraintsandisabletorecordtheneuralactivitiessuccessfully. Next,aneffectivesignalcompressionscheme,theintegrate-and-re(IF),hasbeendescribed.TheIFgeneratespulseeventsaccordingtothemagnitudeofthesignal.SincetheinputoftheIFisintheformofacurrent,insteadofholdingacurrentconstantwhilemeasuringthevoltageontheelectrodeandthenconvertingthevoltagetocurrentusingatransconductor,thecurrent-modecircuitimplementationoftheIFconverterispresentedtoholdthevoltageconstant,andmeasuretheresultingcurrentfromtheelectrodetosimplifythedesigncomplexity.ThebidirectionalcurrentconveyorwithaClass-ABoutputstagethatcandeliverbidirectionalcurrentinputtotheintegrationcapacitorispresented.Wealsopresentanothercurrent-modeimplementationoftheIF,includingacurrentamplierandabiasfeedbacknetworkthatcanamplifytheinput 144

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current,andlterouttheDCcomponent.Thesimulatedcurrent-modeIFconverterconsumes132Wstaticpowerandisabletoachieve40dBresolution.ThefabricatedIFconverterinAMI0.5m3-metal2-polyCMOStechnologyhasbeentestedwithasinewaveinput,andthebench-topmeasurementresultsshowsthatthechipcanachieve36dB. SincetheDCoffsetandmotionartifactsareunavoidableintheneuralrecording,anoffset-insensitiveevent-basedconverterispreferred.UnliketheIFconverterthatproducesmorepulseeventsintheregionsofhighermagnitude,theTime-Derivative(TD)converterconcentratesitsoutputpulseeventsintheregionsofsharpchange.ThecircuitimplementationoftheTDusestheswitch-capacitorapproachtosetthebiaspointsandsolvesthedriftingproblemofthevoltage-modeimplementationoftheIF.TheTDencodingmodelhasbeendescribedandthereconstructionalgorithmhasbeendeveloped.Theoretically,thesignalcanbeperfectlyrecoveredbackfromtheoutputbiphasicpulsetraingeneratedbytheTDconverter.ThesimulationoftheTDandtheIFconverterswith100randomsyntheticinputsignalsdemonstratesthattheTDcanachievethesameSERastheIFwithlowerpulseratethantheIF.Thus,theTDencoderisbetterthantheIFencoderwhendealingwiththesignalcontainingalargeDCvariation.TheTDconverteralsohasbeensimulatedwiththerecordedneuralsignalsfromtheratandtheresultsindicatethattheTDconvertercanreducethedataratewithoutdegradingtheresolution.TheresultsalsoprovethattheTDconvertercanachievethesameaccuracyasthesynchronousanalog-to-digitalconverter(ADC),buttremendouslyreducesthedatarate.TheTDconverterhasbeendesigned,simulated,fabricatedandtestedintheAMI0.5mCMOStechnology.Thebench-topmeasurementresultsshowthattheTDconverterchipisabletoachieve44dBresolutionwith110Wstaticpowerconsumption.ThefabricatedTDconverterchiphasalsobeentestedwiththeamplierchipalongwiththeneuralsimulatorsignal,and 145

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themeasurementresultssuggesttheTDconverterhaspromissingdataratereductionperformanceontheneuralsignals. Finally,theanalysisandcomparisonofsynchronousADC,asynchronouslevel-crossingencoding,asynchronousdelta-sigmaencoding,asynchronousdeltaencoding,theIFencoding,theTDencodingandtheencodingwithnon-lineartransformationweredescribed.TheconclusionsuggeststhemostefcientdatacompressionmethodforneuralrecordingapplicationsistheTDencoding. 146

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BIOGRAPHICALSKETCH JieXuwasborninGuilin,China.ShereceivedherB.S.degreeinelectronicandinformationengineeringfromZhejiangUniversity,China,in2005.ShealsoreceivedherM.S.degreeinelectricalandcomputerengineeringfromtheUniversityofFloridain2007.ShehasbeenaresearchassistantintheComputationalNeuro-EngineeringLab(CNEL)attheUniversityofFloridasince2006,workingunderDr.JohnHarrisontheFloridaWirelessImplantableRecordingElectrodes(FWIRE)Project.Herresearchinterestsincludebiologicallyinspiredanalogsignalprocessingandmixed-signalintegratedcircuitdesign. 153