SQUID Readout Electronics and Magnetometric Systems for Practical Applications

235 Pages·2020·7.763 MB·English

by  Xiaoming Xie, Hui Dong, Guofeng Zhang, Yi Zhang, Hans-Joachim Krause

SQUIDReadoutElectronicsandMagnetometricSystemsforPractical
Applications
SQUID Readout Electronics and
Magnetometric Systems for Practical
Applications
YiZhang
HuiDong
Hans-JoachimKrause
GuofengZhang
XiaomingXie
Authors AllbookspublishedbyWiley-VCH
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v
Contents
Preface ix
Acknowledgments xi
1 Introduction 1
1.1 Motivation 1
1.2 ContentsoftheChapters 3
References 8
2 JosephsonJunctions 9
2.1 JosephsonEquations 9
2.2 RCSJModel 9
References 13
3 dcSQUID’sI–VCharacteristicsandItsBiasModes 15
3.1 SQUID’sI–V Characteristics 15
3.2 AnIdealCurrentSource 19
3.3 APracticalVoltageSource 19
References 21
4 FunctionsoftheSQUID’sReadoutElectronics 23
4.1 SelectionoftheSQUID’sBiasMode 23
4.2 FluxLockedLoop(FLL) 23
4.2.1 PrincipleoftheFLL 24
4.2.2 ElectronicCircuitoftheFLLandtheSelectionofthe
WorkingPoint 25
4.2.3 “Locked”and“Unlocked”CasesintheFLL 28
4.2.4 SlewRateoftheSQUIDSystem 29
4.3 SuppressingtheNoiseContributionfromthePreamplifier 29
4.4 TwoModelsofadcSQUID 29
References 31
5 DirectReadoutScheme(DRS) 33
5.1 Introduction 33
5.2 ReadoutElectronicsNoiseinDRS 33
vi Contents
5.2.1 NoiseCharacteristicsofTwoTypesofPreamplifiers 34
5.2.2 NoiseContributionofaPreamplifierwithDifferentSource
Resistors 37
5.3 ChainRuleandFluxNoiseContributionofaPreamplifier 39
5.3.1 TestCircuitUsingtheSamePreamplifierinBothBiasModes 40
5.3.2 NoiseMeasurementsinBothBiasModes 42
5.4 SummaryoftheDRS 43
References 43
6 SQUIDMagnetometricSystemandSQUIDParameters 45
6.1 Field-to-FluxTransformerCircuit(Converter) 45
6.2 ThreeDimensionlessCharacteristicParameters,𝛽 ,Γ,and𝛽 ,in
c L
SQUIDOperation 48
6.2.1 SQUID’sNominalStewart-McCumberCharacteristic
Parameter𝛽 49
c
6.2.2 SQUID’sNominalThermalNoiseParameterΓ 52
6.2.3 SQUID’sScreeningParameter𝛽 54
L
6.2.4 DiscussionontheThreeCharacteristicParameters 55
References 56
7 FluxModulationScheme(FMS) 61
7.1 MixedBiasModes 61
7.2 ConventionalExplanationfortheFMS 63
7.2.1 SchematicDiagramoftheFMS 63
7.2.2 TimeDomainandFluxDomain 65
7.2.3 FluxModulation 66
7.2.4 FiveAdditionalNotes 71
7.3 FMSRevisited 73
7.3.1 BiasModeinFMS 74
7.3.2 BasicConsiderationofSynchronousMeasurementsofI andV 74
s s
7.3.3 ExperimentalSynchronousMeasurementsofΔiandV s 75
R
7.3.4 TransferCharacteristicsoftheStep-UpTransformer 78
7.3.5 V(Φ)ComparisonObtainedbyDRSandFMS 80
7.4 Conclusion 81
References 82
8 FluxFeedbackConceptsandParallelFeedbackCircuit 85
8.1 FluxFeedbackConceptsandHistory 85
8.2 SQUID’sApparentParameters 87
8.3 ParallelFeedbackCircuit(PFC) 89
8.3.1 WorkingPrincipleofthePFCinCurrentBiasMode 89
8.3.2 WorkingPrincipleofPFCinVoltageBiasMode 94
8.3.3 BriefSummaryofQualitativeAnalysesofPFC 97
8.4 QuantitativeAnalysesandExperimentalVerificationofthePFCin
VoltageBiasMode 99
8.4.1 TheEquivalentCircuitwiththePFCinVoltageBiasMode 99
8.4.2 IntroductionofTwoDimensionlessParametersrandΔ 101
Contents vii
8.4.3 NumericalCalculations 103
8.4.4 ExperimentalResults 108
8.4.5 NoiseComparisonandInterpretation 111
8.4.6 TwoPracticalDesignsforPFC 114
8.5 MainAchievementsofPFCQuantitativeAnalysis 116
8.6 ComparisonwiththeNoiseBehaviorsofTwoPreamplifiers 117
References 119
9 Analysesofthe“SeriesFeedbackCoil(Circuit)”(SFC) 121
9.1 SFCinCurrentBiasMode 121
9.1.1 WorkingPrincipleoftheSFCinCurrentBiasMode 121
9.1.2 NoiseMeasurementsofaWeaklyDampedSQUID(Magnetometer)
SystemwiththeSFC 123
9.2 TheSFCinVoltageBiasMode 125
9.3 SummaryofthePFCandSFC 127
9.4 CombinationofthePFCandSFC(PSFC) 129
9.4.1 PSFCAnalysisUnderIndependenceConditions 129
9.4.2 PSFCExperimentsandResults 132
9.4.3 ConclusionofthePSFC 136
References 137
10 WeaklyDampedSQUID 139
10.1 BasicConsiderationofWeaklyDampedSQUID 139
10.2 SQUIDSystemNoiseMeasurementswithDifferent𝛽 Values 140
c
10.3 StatisticsofSQUIDProperties 143
10.4 SingleChipReadoutElectronics(SCRE) 147
10.4.1 PrincipleofSCREandItsPerformance 148
10.4.2 EquivalentCircuitofSCRE 149
10.4.3 DifferencesBetweentheConventionalVersionofReadoutElectronics
withanIntegratorandSCRE 152
10.4.4 TwoApplicationsofSCRE 153
10.5 SuggestionsfortheDRS 154
References 155
11 Two-StageandDoubleRelaxationOscillationReadout
Schemes 157
11.1 Two-StageScheme 158
11.2 ROSandD-ROS 164
11.3 SomeCommentsonD-ROSandTwo-StageScheme 168
References 169
12 Radio-Frequency(rf)SQUID 171
12.1 FundamentalsofanrfSQUID 171
12.2 ConventionalrfSQUIDSystem 176
12.2.1 BlockDiagramofrfSQUIDReadoutElectronics
(the30MHzVersion) 176
viii Contents
12.2.2 rfSQUIDSystemNoiseinthe30MHzVersion 178
12.3 IntroductiontoModernrfSQUIDSystems 180
12.3.1 MagnetometricThin-FilmrfSQUIDandaConventionalTankCircuit
withaCapacitorTap 181
12.3.2 ImprovedrfSQUIDReadoutElectronics 184
12.3.3 TankCircuitOperatingUpto1GHzwithInductiveCoupling 188
12.3.4 ModernrfSQUIDSystem 190
12.3.4.1 MicrostripResonator 190
12.3.4.2 CoplanarResonator 192
12.3.4.3 InstabilityofrfBiasCurrent 194
12.3.5 SubstrateResonator 196
12.3.6 RegardingtherfSQUID’sThermalNoiseLimit 200
12.4 FurtherDevelopmentsoftherfSQUIDMagnetometerSystem 201
12.4.1 AchievementofaVeryLarge𝜕V /𝜕ΦinaLow-Impedance
rf
System 201
12.4.2 MultiturnInputCoilforaThin-FilmrfSQUIDMagnetometerwith
aPlanarLabyrinthResonator 204
12.4.3 ModernrfSQUIDElectronics 208
12.5 MultichannelHigh-T rfSQUIDGradiometer 211
c
12.6 ComparisonofrfSQUIDReadoutwithdcSQUIDReadout 214
12.7 SummaryandOutlook 215
References 218
Index 225
ix
Preface
Time flies! Thirteen years ago, as a research professor at Shanghai Institute
of Microsystem and Information Technology (SIMIT), Chinese Academy of
Sciences(knownasShanghaiInstituteofMetallurgybythattime),Iwascharged
with a challenging mission, to start a team on superconducting electronics
research.Fromtheinstitute,itwasaquitestraightforwarddecision,asthewhole
institute had been gradually shifting from materials science research toward
electronics and systems. And for myself, it was not so easy to start something
newattheageover40,withastrongbackgroundonsuperconductingmaterials,
somebasicknowledgeonelectronicsbutlittleonsuperconductingelectronics.
JustwhenIwaswonderinghowtodothat,Prof.P.H.Wu,amemberofChinese
Academy of Sciences, a famous professor in the field of superconducting
electronicsinChina,whohadworkedatResearchCenterJulich(FZJ)Germany,
recommended me Dr. Yi Zhang, a reputable German scientist at FZJ, born in
Shanghai,acknowledgedgloballyforhisexcellentresearchonthedevelopment
ofhighT radio-frequencysuperconductingquantuminterferencedevices(high
c
temperaturesuperconducting[HTS]rfSQUIDs),theirreadoutelectronicsand
systems. I contacted FZJ without hesitation, inviting Yi to act as a consultant
to our first project on SQUID-based Magnetocardiography (MCG) system.
ThisrequestletteropenedthedoorofcooperationbetweenSIMITandFZJ.To
date,ourcooperationhasdevelopedfromaprojectcollaborationbetweentwo
professorstotheestablishmentoftwojointresearchlaboratoriesandfurtherto
a virtual joint research institute. The cooperation also has been extended from
superconductivitytotopologicalinsulatorsandquantumcomputing.
After some formal procedures, I got the approval of my request letter from
Prof. Dr. Joachim Treusch, the former chairman of the board of directors of
FZJ, Prof. Dr. Sebastian Schmidt, a current member of the board of directors
of FZJ, and Prof. Dr. Andreas Offenhäusser, director of IBN2 (Institute of Bio
andNanoscience,nowInstituteofBiologicalInformationProcessing),whichYi
belongedto.Besidesthesupportfromthetopmanagement,theinvolvementof
Prof. Dr. Hans-Joachim Krause, team leader of magnetic sensors in IBN2, was
anotherimportantstepforoursuccessfulcooperation.
OurjointresearchondcSQUIDstartedfromthedevelopmentofasymmetri-
calSQUIDcharacteristics,inanattempttosimplySQUIDreadoutandsystem
x Preface
design.Theadventurewasfullofexcitementandfrustration.Earlyinthemorn-
ing,wesattogether,planningtheworkoftheday,lateintheevening,wesum-
marizedourresultsfromthenoteswemadeduringtheday,sometimesexciting
progress,sometimesfrustratingresults,andsometimesconfusingresultswhich
we could not describe easily. I still remember how excited we were when we
firstobservedtheasymmetricalflux-currentcharacteristicsofaSQUIDonthe
oscilloscope,andIrememberedaswellhowmuchwewerefrustratedwhenwe
learnt that the desired asymmetrical characteristics did not lead to the lower
noisewehadsoughtforsolong.Thenotespiledupdayafterday,gettingthicker
andthicker,wecalledthem“Rabe’sDiary.”Afternumerousdiscussionsbackand
forth,wesucceededininterpretingourresults,whichledtoourfirstjointpub-
licationandourjointpatentontheso-called“SQUIDBootstrapCircuit,”andto
manyotherjointpublicationsinthefollowing10moreyears.
TheSQUIDresearchwasmoredifficultthanwefirstthoughtbecausesettingup
SQUIDsystemsforapplicationsrequirestheinvolvementofpeoplefromseveral
differentdisciplines.AcompleteunderstandingforSQUIDsystemsneedscom-
prehensiveknowledgenotonlyinquantumphysicsandlow-temperaturephysics
butalsoinmaterialscienceandelectronicsengineering.Infact,electricalorelec-
tronicsengineersarealwaysneededforsystemdevelopment.Therefore,itisvery
importanttoestablishacommonlanguagethatiseasilyaccessibleforallpeople.
Thatwashowwegottheideatowritethisbook.
Yi Zhang contributed most to writing of this book, with his experience in
SQUIDresearchfor34years,includingmorethan10yearsofjointresearchwith
SIMIT.Wehaveaimedtowritethisbookinawaythatiseasilyunderstandable
forengineersandstudents,inordertoovercometheformidablebarrierof“quan-
tum” physics. In this book, e.g. dc SQUIDs are simply treated as resistor-like
elements,whicharemodulatedbythemagneticflux.Wehopethatthisbookwill
beappreciatedbyallpeopleinterestedindevelopingandworkingwithSQUIDs
and SQUID systems. By inviting engineers into the SQUID “family,” we will
haveabetterchancetotransformSQUIDfromalaboratorytoytoanenabling
technologythatwilleventuallyshapeourlife.
Thisbookislargelyadocumentationofthejointachievementsaccomplished
inthecooperationbetweenSIMITandFZJinthefieldofsuperconductingelec-
tronics.Webelievethattheongoingcollaborationbetweenthetwopartieswill
continuetogrow,andthecooperationwillbringmoreachievementsnotonlyin
thefieldofsuperconductingelectronicsbutalsoinotherfieldsinthefuture.
November2019. XiaomingXie
Shanghai,China