A High-Resolution, Linear Resistance-to

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A High-Resolution, Linear Resistance-to-Frequency Converter
Watanabe, Kenzo; Mochizuki, Kouji
IEEE Transactions on Instrumentation and Measurement.
45(3), p. 761-764
1996-06
http://hdl.handle.net/10297/3518
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761
巨IEEETRANSACTIONSONINSTRUMENTATIONANDMEASUREMENT，VOL．45，NO．3，JUNE1996
REFERENCES
ll］C・J・Alonzo，R・H・Blackwell，andH・V．Marantz，“Directreadingfu11y
automatic
vectorimpedance
meters，MHewlettPackaTdJ”pP・12−20，
Jan．1967．
［2］R・J・Reis，“Measurementofanunknownimpedanceinanautomatic
tester，”躇M乃ch・DisclosureBuLletin，VOl・24，nO・7A，Pp・3147−3148，
Dec．1981．
［3］K・M・IbrahimandM・A・H・Abdul−Karim，“Digitalimpedancemea−
SurementbygeneratlngtWOWaVeS：’LEEEThms．血stTum．Meas．，VOl．
IM−34，nO．1，pp．2−5，Mar．1985．
［4】S・M・R・恥ha，“Digitalmeasurementofthepolarandrectangularfbrms
Fig・1・Alinearresistance−tO−frequencyconverter‥Basiccon負guration・
Ofimpedances，”IEEEThnsactionsonInstTumentationandMeasule−
me〝持，VOl．38，nO．1，pp．59−63，Feb．1989．
［5】B・M・01iverandJ．M．Cage，ELectronicMeasunmentandInstrumen−
tation．New York：McGraw−Hill，1971．
PrOPOSedbyJohnson andRichehl5］．TheircircuitisaresistanCe−
to−duty−ratio converter，and the ftedback circuit，COnSistlng Ofan
［6］K・Karandeyev，BridgeandPotentiometerMeEhodiQfElectricalMea−
SuTemenEs．Moscow：Peace．
、・．▲．．．．．∴・L ■lLIr、・▲∴：L↑サ■．．−∴、、．ト．．．h、．・．
［7］K・LSmith，“Theubiquitousphasesensitivedetector−apPlicationsand
pnncipleofoperation，Mmnless肋rLd，pP・367−370，Aug・1972・
integrator and acomparator，maintains the balanCe Ofthe bridge
by controlling the switched resistorsincorporatedinthe訂mS Of
thebridge・ThispaperdescribesatrueR−tO−Fconverterdesigned
［8】D・P・BlairandP．H．Sydenham，“Phasesensitivedetectionasameans
basedontheabove−mentionedapproach・Difftrentfromtheearlier
torecoverslgnalsburiedinnoise，MhzstrumentSci・−J・Physics：Sect・E：
∫cfg〃榔C血一触肌，UK，VO1．8，pp．621−627，1975．
Circuit【5］，the Wheatstone bridgeis used merely to detect the
［9］EmbeddedContTDllerHandbook，VOl．land2，Intel，Illinois，1988．
resistanCedeviationfromtheoffsetvalue・SincenobalanCeOPeration
isinvoIved，thecircuitcon負gurationismuchsimpler・ThesensltlVlty
ishighenough，becauseofthedifftrentialintegrationinvoIved，tO
be compared to that ofthe resistance−tO−duty−ratio converter【5］．
Therefbre，theR−tO−Fconverterdescribedindetailinthefollowlng
SeCtions wi11負nd wide applicability as the signalconditioner of
A High・Resolution，Linear
Platinum
Resistance−tO−FrequencyConverter
RTD’s
fbr
temperature
measurements，Strain
gauges
fbr
、． 1 ＝．こも l ・が ■ ′ 、﹁ ■ ′ ㌧＼．． ■ 一 −
electronic balances，PleZOreSistors fbr pressure detection，and the
Otherresistivesensors fbrinstrumentationandmeasurements．
KoltiiMochizukiand KenzoWatanabe
II．CIRCUIT DESCRIPT10N
AbsLTaCE−Aresistance−tO・frequencyconverterconsistingofaWheat・
StOnebridgefbllowedbyanintegratorandacomparatOrisdescribed．
hconceptthecircuitrepresentsarelaxationoscillatorwhose什equency
Changeslinearlywitharesistancechangedetecledbythebridge・Analyses
Show thata resolution betterthan O・05％is possiblewith thesimpIe
COn航gurationIandanexcelIentlinearityismaintainedoverthewidere・
SistancechangebyuslngaSimpIecompenSationmethod．Theconverteris
therefbresuitedasasLgnaIconditionerofaresistivesensor・ExperimentaI
rcsultsareincludedtodemonstrateitsperfbrmance．
Fig・l shows the circuit diagram of thelinearreSistance−tO−
frequency（R−tO−F）converter．Itisessentiallyarelaxationoscillator
COnSistlngOfaWheatstonebridge，anintegrator，andazero−CrOSSlng
detector・TheresistorRX Whoseresistancechangeistobedetected
fbrmS Onearm Ofthe bridge・The unbalanCe VOltage due tothe
resistanCeChangeisintegrated，anditspolarityisftdbacktothe
bridgeasthebiasvoltage，tOSuStaintheosci11ation．
Whenop−ampSinvoIvedareideal，nOdevoltagesareglVenby
γα ＝αγout
Detectionofasmallresistancechangeisoftenneededinindustrial
andprocesscontroIsystemsandmedicalinstrumentationl1］，【2］．In
Vc＝むら三／（γα−即も）df
SuChsystems，microprocessorsareuSedexclusivelyfbrdigitalsignal
PrOCeSSlng，andthuslnPutdatainadigitalfbrmatishighlydesired．
Aconventionalwayofdetectlngtheresistanceinthedigitalfbrm
istousearelaxationoscillatorwhosefrequencyisdeteminedby
where
月3
月2＋月3
月1
theresistanceundermeasurementandaknowncapacitorl3］，［4］．
Thoughsimple，thismethodsufftrsfromnonlineanty・Inaddition，
月1＋月エ
highsensitivltyCannOtbeexpectedsincetheoscillationn・equenCylS
inverselyproportionaltothetotalresistanCe．
︶︶︶
1 2 つ J
︵︵︵
I．INTRODUCTION
（5）
and
ThemostsensitivemeansofdetectlngtheresistanCeChangeisa
Wheatstonebridge・CombiningaWheatstonebridgewitharelaxation
丁＝CrRT．
OSCillatorappearstobeapromlSlngapPrOaChtothehigh−SenSitivlty
resistance−tO−frequency（R−tO−F）converter．Suchaschemehasbeen
Output voltage wavefbrms ofthe zero−CrOSSlng detector and the
（6）
integratorareShowninFig．2（a）．Here，
ManuscrlptreCeivedMarCh7，1994；reVisedAugust30，1995・
K・M∝hizukiiswiththeDepartmentofElectricalEngineenng，Numazu
γout ＝
Collegeoflもchnology，Numazu410，Japan・
K・Watanabeis with the ResearchInstitute of Electronics，Shizuoka
Universlty，Hamamatsu432，Japan・
PublisherItemIdentifierSOO18−9456（96）03092−6．
1年，ifγ。
〈 −1㌔，if即。
≡汀（7）
isassumed，and了もandT．aretheperiodsduringwhichv。。taSSumeS
V；and−1左，reSPeCtively．Refbrring tothesewavefbmS，OneCan
′ ■
0018−9456／96＄05．00◎1996IEEE
IEEETRANSACTIONSONINSTRUMENTAT10NANDMEASUREMENT・VOL・45・NO・3，JUNE1996
762
（a）
Fig．2・Ⅶ1tagewavefbrmsinFig・1，（a）whenop−ampSareidealand（b）whenthezero−CrOSSingdetectorhastheresponsedelay7b・
isthevoltagechangeintheintegratoroutputduringthedelaytime
derivethefbllowlngeXPreSSionsfbr了もand7L
7L．ReftrringtoFig．2（b），Iiand焉arederivedas
ち＝詩（1＋7）T
（8）
焉＝ち＋（1＋7）れ（17）
n＝言㌔（1弓）T
（9）
焉＝い（1弓）九・（18）
ちand7Lgivenby（8）and（9），reSpeCtively，Changeinverselywith
where
△R，andthusthenonlinearityduetoTbincreaseswith△R・
T＝lK／ql・
（10）r。諾認諾悪霊霊還崇霊霊i慧慧
quencycouldbeeliminatedbyreplacingthezero−CrOSSlngdetectorby
thec。mparat。rWhichcompareStheintegratoroutputwith△tjp／n）
TheoscillationfrequencyisthusglVenby
α−β 7
＝九＋△J （11）
β（1＋7）2丁
substitutingthecomparatOrthresholdvoltage△Vjp／n）givenby（16）
into（3）explicitly，OneCangetthedesignequationwhichdescribes
where
RoR3−月1月2
Jo＝
（12）
Rl（月2＋R3）
istheoffsetfrequencycorrespondingtothebridgeoffset，
△J＝
月3△月
γC一卵out一字（α㈱ut＝一三／（α−㌍tdf・（19）
Theright−handsideindicatesthedifftrentialintegratlOnWhilethe
left−handsidethecomparison・Thethresholdinthecomparisonis
（13）
Rl（月2＋月3）
Pv。。t，Shiftedby△Vjp／n）fbrthedelaycompensation・
Thedelay−COmpenSatedR−tO−Fconverterthusdesignedisshown
inFig．3（a）．Itshouldbenotedthatthevoltageattheinvertinginput
isthefrequencyshiftduetotheresistancechange△RinRr，and
7 1
才，＝
（14）
（1＋7）2γ
月エ＝凡）＋△月．
（15）
teminal⑳ofop−amPAlisPv。。t；andR3issplitintotwoparts・
∂R3and（1−∂）R3，tOShiftthethresholdvoltage・Fig・3（b）shows
waveformsoftheintegratoroutputvcandthethresholdvoltagevTH・
Whichis glVenby
‘lITH ＝
Equation（13）indicatesthattheresistanCeChangeislinearlyconverted
into the ffequency・
One ofthe error sources which degrades thelinearltyis the
responsedelayofthezer0−CrOSSlngdetector・Wavefbrmswhenthe
（β（1−∂）1−
∂（α−β）
γ。ut．（20）
Reftrringtothesewavefbrms・OneObtains
了も＝
delaytimeis了もareShowninFig・2（b）・Here，
△げ′n）一字（α−β）加＝掌（α一明p′n）（16）
〈
r−＝
β（1−∂）い＋7）（1−α）
α一β
丁＋（1＋7）（n−∂可（21）
β（1−∂）（1十で1）（1−α）
α−β
丁・（1弓）（n一項（22）
IEEETRANSACTIONSONINSTRUMENT〟rIONANDMEASUREMENT，VOL．45，NO．3，JUNE1996
763
靂
‡
】
i
t
l
I
】
l
．
。
．
．
．
＿
…⊥
l
t
l
l
1
t
t
l
l
l
l
l
t
I
l
⊥
l
】
】
‡
4 −2 0 2 4
AR（Q）
！
l
鵬
（b）
l
l
Fig・3・（a）The circuit diagram of the delay−COmpenSated resistance−
to−frequency converter，（b）Vbltage wavefbrms at theinput teminals of
事
COmParatOrA3．
暮
l
・
一
．
一
一
・
・
＿
＿
．
＿
．
■
．
l
l
‡
i
！
Therefbre，if∂is chosen suchthat
∂丁＝了も
霊
」
（23）
t
thentheoscillationfrequencychangeslinearlywith△R
1
l
−4 −2 0 2 4
J＝ふ＋△J
l
（1−∂）月1月2
AR（Q）
（（月3月0−風月2）＋月3△月）才，．（24）
Fig・4・Theoscillationfrequencychange△foftheprototypeconverterfor
theresistancechange△R．
III．RESOLUTION
Anothererrorsourcethatinfluencestheconverteroperationshown
inFig・3（a）istheoffsetvoltageofanop−amP．LetlもslandlもS2be
l
︶
1
一
7
1−∂
（1・芸）（た−朝一か・（31）
FortheresistanCeChange△Rtobedetectedunambiguously，△fR
Shouldbelargerthan△fE・Theresolutionlimitedbythiscondition
1−△
r−
is glVen by
1＋△／7
△月min
Where
月0
△＝三景（竜一弓
︵
二
byitsoutputvoltagev。。t WhichassumestheconstantValuelちor
tL・Therefore，theoffsetvoltageisequlValenttothechangeinv。。t
andscales了もand7L as
△
九
′お
VOltagesproducetheconstanterrorvoltage・Theconverterisdriven
tothefirstorder，by
△
theoffsetvoltagesofop−amPSAlandA2，reSpeCtively・Theseoffset
△R，andtheotheris△feduetotheoffsetvoltage．△fEisgiven，
（27）
and
＝（1＋芸）…（ト‡）｛い（1−α）ど2｝（32）
Where△RmindenotestheminimumdetectableresistanCeChange・
Theoffsetvoltage ofcomparatOrA3alsoafftctstheconverter
OPeration・Its efftct on the oscillationfrequencylS SeCOnd−Order，
becauseitinfluencesonlythedelaycompensationthroughshifting
El＝鴨sl／鴨
（28）
thethresholdvoltage．Anotherfactorthatlimitstheresolutionisthe
ど2＝叱S2／鴨．
（29）
temperaturedrift△fTOftheo蝕etfrequency．△fTCanbeevaluated
nLeOSCillationfrequencyf′isthengivenby
了＝毒＝相−△）（1＋姉）（30）
Wherefistheoscillationfrequencyofthedelay−COmPenSatedR−tO−F
COnVertergivenby（24）．
Itisclearfrom（27）thatiftheampli負edoff岳etvoltageofop−amP
AICanCelstheoffsetvoltageofA2，thennooffseterrorappearS・This
COnditiondoesnotalwaysholdtruebecauseofthetemperaturedrifts
intheoffsetvoltages・Thedeviation△ffromtheoffsetfrequencyfb
thenconsistsoftwoparts；Oneis△fRduetotheresistancechange
等＝（箸′∂r）△r （33）
Where△TrepresentstheoperatlngtemPeraturerangeOfthecon−
Verter・Thefrequencystability（∂ふ／fb）／∂TofacPnVentionalre−
laxation oscillator built uslng reSistors and capacltOrS Withlow
temperature coefficientsis typicallylO￣5／Oc．Assuming△T＝
400C，theresolutionlimitedbythetemperaturedriftis
仝賢＝4×10￣4（ト諾）・（34）
IEEETRANSACTIONSONINSTRUMENTATIONANDMEASUREMENT，VOL・45，NO・3・JUNE1996
764
is defined here by
1．
0
lT ＝
0．
5
△fmeasured−△fgivenby（24）
△fgivenby（24）
（35）
TheresultsshowninFig．5indicatethataresolutionhigherthan
0．
0
O．1％is achievable overthe wide resistance range withthe delay
・
0．
5
−
1．
0
・
1．
5
compensation，thuscon鮎mingtheperfbrmanceevaluationinthe
／
／
previous sections・
V．CoNCLUSION
●
M．
025
▲
M
／
Anovelcircuithasbeenpresentedwhichprovidesthefrequency
−
2．
0
−1∝氾 −500 0 500 100O
AR（Q）
equlValentofaresistancechange・Thecomponentrequlrementis
minimum．Besidesthesimpleconfiguration，itftaturesahighresolu−
tionandanexcellentlineantyOVerthewideresistancerange・These
advantagesmaketheR−tO−Fconverterproposedhereinespecially
usefulfbrslgnalprocesslngOfsuchtransducersas straingauges，
1 ．
0
RTD，S，andpiezoresistivedevices・
0 ．
5
AcKNOWLEDGMENT
0 ．
0
Theauthors wouldliketothankS．Katoh，AssistantProftssor，
・
0 ．
5
−1 ．
0
・
1 ．
5
NumazuCollegeofrIbchnology，fbrusefu1discussionsandencour−
／
／
agement・
REFERENCES
●M ．
025
▲M
／
ll］G．Payer，…Laconversiondirecteenfrequenceetsonapplicationau
−
2 ．
0
一1000 −500 0 ∝氾 100O
pesagenumenque，MELectTVnlqueetMicIVElectlVniquehduslrielles，nO・
146，pp・29−31，1971・
［2］J．A．Vinas，“Digitalpercentageresistancebridge，”Elec・Eng・，nO・5，
pp・15−17，1973・
Fig・5・Thenonlinearerrorqoftheprot？typeCOnVerterWith（6＝0・025）
andwithout（6＝0）thedelaycompensatlOn・
［3］A．P．Shivaprasad，HAwide−rangeVariable−frequencyphase−Shiftosci1−
1ator：，IEEE77tzns．Instrum．Meas．，VOl．IM−21，Pp・180−182，1972・
［4】LJ．Weiss，HMeasuringresistancedeviationsquicklyandaccurately，’’
gJec．g〝gりnO・8，pp・41−13，1972・
［5］C．D．JohnsonandH・AIRicheh，HHighlyaccurateresistancedeviation
Assuming一七sl＝−tts2＝2mV，V；＝5V，7＝0・95，α．＝1／2，
tofrequencyconverterwithprogrammablesensitivityandresolution：’
Ro宍ゴRl，OneCaneStimatetheoffset−1imitedresolutionglVenby
ほgg7ね〝∫．血∫Jmm．〟で“．，VOl．IM−35，pp・178−181，1986・
（32）to be
仝塾生＝10−4．
Ro
Summanzlngtheaboveestimation，itisconcludedthattheresolu−
tionlimitedbytheoffsetvoltagesiscomparabletothatlimitedbythe
ASimpleMeasurementMethodtoDetermine
theBurstAcquisitionTimeofDigitalSystems
temperaturedriftoftheoffsetfrequency，andtheoverallresolution
is ofthe order ofO．05％．
CurtisHatamoto，HuqiingFu，andKamiloFeher
IV．ExpERIMENTAL RESUIJS
synchronization・CauSedbiterrorsisdisclosed・ThisinventionenableSthe
AbsLTYZCt−A cost・efRcient solution fbr measunng hst and ultrafhst
Tbcon負rmthepnncipleofoperation，theR−tO−Fconvertershown
inFig・3（a）wasbreadboardedusingoff−the−Shelfcomponents・The
op−amPSuSedareLF411・Itsoffsetvoltageislessthan2mV，andthe
delaytimeisabout2．7FLS・Noaqjustmentwasmadefbrtheoffset
compensation・Thepowersuppliesare土12V・Theotherrelevant
usertomodifyconYentionaltestinstrumentsandtoeliminatetheneed
toobtainveryexpensivetestequlpment・Ournewinstrumentationimple・
mentationconceptcompnsesagatedswitchaddedtoapseudorandombit
sequencegeneratorandanalyzer・Thesynchroni祖tiontimeofacouple
or circuibis testd．
I．INTRODUCT10N
parameterSareRl＝R3＝1・6kn，R2＝2・4kO・Theconversion
sensltlVltyWaSa4justedtobelHz／0・Theintegrationtimeconstant
Incertainapplications，SuChasinthewirelessfield，SynChronization
T＝CTRT WaSthenaboutllOps．Theoscillationfrequencywas
timeiscruCialtothetranSmissionofdata．Forinstance，infrequency−
measuredbythefrequencycounterwithO・1Hzresolution・
Fig・4showsthemeasuredfrequency changeswhen Rr was
hoppingspreadspectrum（FH−SS），thecamierfrequencyisconstantly
changedinO・50stepsfromitsoffsetvalueofRo＝3・4kn・The
resultsindicatethattheresolutionishigherthanO・015％・Fig・5shows
thenonlinearerrOrqOftheprototypec竺VerterWith（∂＝0・025）
andwithout（∂＝0）thedelaycompensatlOn・ThenonlinearerrOrq
ManuscriptreceivedMayl，1995・
nle authorsare Withthe Digitaland Wireless Communications Lab・・
DepartmentofElectricalandComputerEngineenng，UniversityofCalifbrnia，
Davis，CA95616USA．
PublisherItemIdentiGerSOO18−9456（96）03094−X．
0018−9456／96＄05．00⑥1996IEEE

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