IEC 60444-1 AMD 1-1999 Measurement of quartz crystal unit parameters by zero phase technique in a π-network - Part 1 Basic method for the measurement of resonance frequency and res.pdf

1、NORME INTERNATIONALE CEI IEC INTERNATIONAL STANDARD 604441 1986 AMENDEMENT1 AMENDMENT1 199908 Amendement1 Mesuredesparamtresdesquartz pizolectriquesparlatechniquedephasenulle danslecircuitenpi Partie1: Mthodefondamentalepourlamesuredela frquencedersonanceetdelarsistancede rsonancedesquartzpizolectri

2、quesparla techniquedephasenulledanslecircuitenpi Amendment1 Measurementofquartzcrystalunitparameters byzerophasetechniqueinapinetwork Part1: Basicmethodforthemeasurementofresonance frequencyandresonanceresistanceofquartz crystalunitsbyzerophasetechniquein apinetwork Commission Electrotechnique Inter

3、nationale InternationalElectrotechnicalCommission Pourprix,voircatalogueenvigueur Forprice,seecurrentcatalogue IEC1999Droitsdereproductionrservs Copyrightallrightsreserved InternationalElectrotechnicalCommission 3,ruedeVarembGeneva,Switzerland Telefax:+41229190300 email:inmailiec.ch IECwebsitehttp:/

4、www.iec.ch CODEPRIX PRICECODE H2 604441amend.1CEI:1999 AVANTPROPOS Leprsentamendementattabliparlecomitdtudes49delaCEI:Dispositifs pizolectriquesetdilectriquespourlacommandeetlechoixdelafrquence. Letextedecetamendementestissudesdocumentssuivants: FDIS Rapportdevote 49/442/FDIS 49/445/RVD Lerapportdev

5、oteindiqudansletableaucidessusdonnetouteinformationsurlevoteayant aboutilapprobationdecetamendement. _ Page2 SOMMAIRE AjouterletitredelannexeBcommesuit: AnnexeBMisejourdecertainesformulesdelannexeA Page42 Ajouter,aprslannexeA,lanouvelleannexeBcommesuit: AnnexeB (normative) Misejourdecertainesformule

6、sdelannexeA B.1 Objectifs Danscetteannexe,certainesformulesdelannexeAsontmisesjourenprenanten considrationlaprocduremodifiedtalonnagedunrseauen p aveclarsistancede rfrenceR n =25 W laplacedelalamecourtcircuit. LaformulereliantR r auxtensionsmesuresestdrivepourlesvaleursarbitrairesdela rsistancederfr

7、enceR n .LerreursurR n estpriseenconsidrationdanslanalysedes erreurspour R r . Laformuleestdonnepourlecourantetleniveaudexcitationdunrsonateurquartzinsr danslerseauen p .Lapentedephasedunrsonateurquartzinsrdanslerseauen p estobtenueetlaformulepour Q eff estcorrige.604441Amend.1IEC:1999 3 FOREWORD Th

8、isamendmenthasbeenpreparedbyIECtechnicalcommittee49:Piezoelectricand dielectricdevicesforfrequencycontrolandselection. Thetextofthisamendmentisbasedonthefollowingdocuments: FDIS Reportonvoting 49/442/FDIS 49/445/RVD Fullinformationonthevotingfortheapprovalofthisamendmentcanbefoundinthereporton votin

9、gindicatedabove. _ Page3 CONTENTS AddthetitleofannexBasfollows: AnnexBUpdatingofsomeformulaeofappendixA Page43 Add,afterappendixA,thenewannexBasfollows: AnnexB (normative) UpdatingofsomeformulaeofappendixA B.1 Purposes InthisannexsomeformulaeoftheappendixAareupdated,takingintoaccountthemodified cali

10、brationprocedureofthe p networkwithareferenceresistor R n =25 W insteadofashort. Theformularelating R r tothemeasuredvoltagesisderivedforarbitraryvaluesofthe referenceresistor R n .Theerrorof R n istakenintoaccountintheerroranalysisfor R r . Theformulaforcurrentanddrivelevelofthecrystalinthe p netwo

11、rkisgiven.Thephaseslope ofthecrystalinsertedinthe p networkisderivedandtheformulafor Q eff iscorrected.4 604441amend.1CEI:1999 Circuitendrivation (voirfigure5a) Z Z Z Z Z V B V 0 V A V A V A V A V B R 2 R 4 R 3 R 5 R 6 R 7 Z c B.2 Circuiten p chargpar Z =50 W (aveclecircuitendrivationconforme la fig

12、ure5a) FigureB.1Circuiten p charg B.3 Facteurdetransfertdelatensionduncircuiten p charg Cidessousladrivationlmentairedufacteurdetransfertdelatensionestprsentepour obteniruneformulepluscomplte. Soit 1 6 6 6 1 1 - + = = Z R Z R R Alors 3649 , 0 7 6 6 B B = = + = p k R R R V V (B.1) Dfinir W = = + + =

13、+ = - 5 , 12 1 1 2 T 1 7 6 5 7 6 5 5 R R R R R R R R oR T2 estlarsistancedeterminaisonlasortieducircuiten p commevudelapartdun rsonateur. Alors c 5 5 A B Z R R V V + = (B.2) Dfinir 1 c 5 3 c 5 3 3 1 1 - + + = + = Z R R Z R R R Alors 4 3 3 A A V R R R V + = (B.3) IEC1019/99604441Amend.1IEC:1999 5 B.2

14、 Thep networkterminatedby Z =50 W (withpowersplitteraccordingto figure5a) Powersplitter (seefigure5a) Z Z Z Z Z V B V 0 V A V A V A V A V B R 2 R 4 R 3 R 5 R 6 R 7 Z c FigureB.1Terminated p network B.3 Voltagetransferfactoroftheterminated p network Inthefollowinganelementaryderivationofthevoltagetra

15、nsferfactorispresentedtoprovidea morecomprehensiveformula. Let 1 6 6 6 1 1 - + = = Z R Z R R Then 3649 , 0 7 6 6 B B = = + = p k R R R V V (B.1) Define W = = + + = + = - 5 , 12 1 1 2 T 1 7 6 5 7 6 5 5 R R R R R R R R where R T2 istheterminationresistanceattheoutputofthe p networkasseenbythecrystal.

16、Then c 5 5 A B Z R R V V + = (B.2) Define 1 c 5 3 c 5 3 3 1 1 - + + = + = Z R R Z R R R Then 4 3 3 A A V R R R V + = (B.3) IEC1019/996 604441amend.1CEI:1999 Dfinir 1 4 3 2 4 3 2 2 1 1 - + + = + = R R R R R R R Ilsensuitquepourlecircuitendrivationconformelafigure5aetneprenantpasen considrationlescble

17、s: Z R R V V + = 2 2 A A (B.4) et 2 2 A A = = Z Z V V (B.5) Lefacteurdetransfertdelatension V B /V A estobtenuenmultipliantlesformules(B.1) (B.2) (B.3) (B.4) (B.5): A A A A A A A B B B A B V V V V V V V V V V V V = Aprscertainessubstitutionsetrarrangements,onpeutmontrerque () () ( ) () 2 T 1 T c 7 6

18、 7 6 4 2 4 2 6 2 T 1 T 2 A B 1 2 R R Z R R R R Z R R R R Z R R Z R R V V + + + + + + = (B.6) o 1 1 2 4 3 1 T 1 1 1 1 - - + + + = Z R R R R =12,5 W et 1 1 6 7 5 2 T 1 1 1 1 - - + + + = Z R R R R =12,5 W V B /V A estsymtriqueparrapportlentreetlasortieducircuiten p etsediviseenun facteurquidpendde Zetd

19、esvaleursdelarsistanceducircuiten p seulement,etenun facteurquidpenddelimpdancedursonateur Z c chargeparlesimpdancesde terminaisonducircuiten p .604441Amend.1IEC:1999 7 Define 1 4 3 2 4 3 2 2 1 1 - + + = + = R R R R R R R Then,forapowersplitteraccordingtofigure5aanddisregardingthecables: Z R R V V +

20、 = 2 2 A A (B.4) and 2 2 A A = = Z Z V V (B.5) Thevoltagetransferfactor V B /V A isobtainedbymultiplyingformulae(B.1) (B.2) (B.3) (B.4) (B.5): A A A A A A A B B B A B V V V V V V V V V V V V = Aftersomesubstitutionsandrearrangementsitcanbeshownthat () () ( ) () 2 T 1 T c 7 6 7 6 4 2 4 2 6 2 T 1 T 2

21、A B 1 2 R R Z R R R R Z R R R R Z R R Z R R V V + + + + + + = (B.6) where 1 1 2 4 3 1 T 1 1 1 1 - - + + + = Z R R R R =12,5 W and 1 1 6 7 5 2 T 1 1 1 1 - - + + + = Z R R R R =12,5 W V B /V A issymmetricwithrespecttotheinputandtheoutputofthe p networkandsplitsintoa factorwhichdependsonlyon Zandtheres

22、istancevaluesofthe p networkandafactorwhich dependsonthecrystalimpedance Z c loadedbytheterminationimpedancesofthe p network.8 604441amend.1CEI:1999 () T c 7 2 A B 1 , R Z Z R R K V V + = o R T = R T1 + R T2 =25 W . Acestade,lesapproximationsnesontpasfaites.Lquation(B.6)estvalablemmesion admetqueles

23、rsistancesontuneimpdancecomplexe. Lavaleurde V B /V A pour Z c =0 W est K/R T =0,0333 cequicorrespondlaffaiblissementde29,6dB. B.4 Calibrationaveclarsistancederfrence R n =25 W Comme Knedpendpasde Z c ,lapplicationdelaformule(B.6)donnecequisuit: pourlarsistancederfrence R n insredanslecircuiten p ,

24、T n An Bn R R K V V + = (B.7) etpourlersonateuraveclimpdance Z c insredanslecircuiten p , T c Ac Bc R Z K V V + = (B.8) Endivisant(B.7)par(B.8)etenrsolvantlquationpour Z c ,onobtient () T T n Bc Ac An Bn c R R R V V V V Z - + = (B.9) Alafrquencedersonance f r ,limpdancedursonateurZ c estgalelarsista

25、ncede rsonanceR r ,etonobtient T T n Bc Ac An Bn r 1 1 R R R V V V V R - + = (B.10) Pour R n = R T =25 W ,lquationdonnecidessusapourrsultatlaformuleutiliseen6.2.2.7.604441Amend.1IEC:1999 9 () T c 7 2 A B 1 , R Z Z R R K V V + = where R T = R T1 + R T2 =25 W . Thusfar,noapproximationshavebeenmade.Equ

26、ation(B.6)holdseveniftheresistorsare assumedtohavecompleximpedance. Thevalueof V B /V A forZ c =0 W is K/R T =0,0333 correspondingtoanattenuationof29,6dB. B.4 Calibrationwithreferenceresistor R n =25 W As Kdoesnotdependon Z c ,applicationofformula(B.6)yields: forareferenceresistor R n insertedinthe

27、p network T n An Bn R R K V V + = (B.7) foracrystalwithimpedance Z c insertedinthe p network T c Ac Bc R Z K V V + = (B.8) Bydividing(B.7)by(B.8)andsolvingtheequationfor Z c oneobtains () T T n Bc Ac An Bn c R R R V V V V Z - + = (B.9) Attheresonancefrequency f r thecrystalimpedance Z c isequaltothe

28、resonanceresistance R r ,whichgives T T n Bc Ac An Bn r 1 1 R R R V V V V R - + = (B.10) For R n = R T =25 W theaboveequationresultsintheformulausedin6.2.2.7.10 604441amend.1CEI:1999 B.5 Analysedeserreurssurlarsistancedersonance R r Linfluencedesdviationsdemesuresurlarsistancedersonance R r peuttred

29、duite partirdelquation(B.10). T T r n n r Ac Ac r Bn Bn r r . R R R R R R V V R V V R R D + D + D + + D = D () + + D - D + D - D = T n Bc Ac An Bn Bc Bc Ac Ac An An Bn Bn R R V V V V V V V V V V V V (B.11) T Bc Ac An Bn n Bc Ac An Bn 1 R V V V V R V V V V D - + D + o D V An , D V Bn sontlesdviations

30、demesuredelatensionr.f.danslescanauxAetBavecune rsistancederfrence R n insrdanslecircuiten p ; D V Ac , D V Bc sontlesdviationsdemesuredelatensionr.f.danslecanauxAetBavecle rsonateurquartzinsrdanslecircuiten p ; D R n estladviationdelarsistancederfrencepartirdesavaleurnominale; D R T estladviationde

31、larsistancedeterminaisonduncircuiten p (commevudela partdursonateur)partirdesavaleurnominale. Si R n estgalelarsistancedursonateur,alors V An V Ac et V Bn V Bc ,etledernierterme delaformule(B.11),contenantleserreurssurlecircuiten p ,deviendranulle. Laformule(B.11)correspondcelledelarticleA.4delannex

32、eA. B.6 Courantsurlersonateuretniveaudexcitationdanslecircuiten p ConformmentlafigureB.1,lecourantsurlersonateurlafrquencedersonanceest donnpar r Bc Ac c R V V I - = (B.12) Apartirdelquation(B.1),onobtient Bc Bc 1 V k V p = Lacombinaisondesquations(B.1)and(B.2)donne Bc T2 T2 r Ac 1 V k R R R V p + =

33、 604441Amend.1IEC:1999 11 B.5 Erroranalysisfortheresonanceresistance R r Theinfluenceofmeasuringdeviationsontheresonanceresistance R r canbederivedfrom equation(B.10). T T r n n r Ac Ac r Bn Bn r r . R R R R R R V V R V V R R D + D + D + + D = D () + + D - D + D - D = T n Bc Ac An Bn Bc Bc Ac Ac An

34、An Bn Bn R R V V V V V V V V V V V V (B.11) T Bc Ac An Bn n Bc Ac An Bn 1 R V V V V R V V V V D - + D + where D V An , D V Bn arethemeasuringdeviationsofr.f.voltageinthechannelsAandBwith referenceresistor R n insertedinthe p network; D V Ac , D V Bc arethemeasuringdeviationsofr.f.voltageinthechannel

35、sAandBwitha crystalinsertedinthe p network; D R n isthedeviationofthereferenceresistorfromitsnominalvalue; D R T isthedeviationoftheterminationresistanceofthe p network(asseenbythe crystal)fromitsnominalvalue. IfR n isequaltothecrystalresistance,then V An V Ac andV Bn V Bc andthelasttermof formula(B

36、.11),whichcontainstheerrorsofthe p network,willvanish. Formula(B.11)correspondstotheoneinclauseA.4ofappendixA. B.6 Crystalcurrentanddrivelevelinthe p network AccordingtofigureB.1thecrystalcurrentatresonanceisgivenby r Bc Ac c R V V I - = (B.12) Fromequation(B.1)oneobtains Bc Bc 1 V k V p = Combining

37、equations(B.1)and(B.2)yields Bc T2 T2 r Ac 1 V k R R R V p + = 12 604441amend.1CEI:1999 Lasubstitutiondanslquation(B.12)donne W = = p 56 , 4 1 Bc Bc T2 c V V R k I (B.13) Leniveaudexcitationdursonateurdanslecircuiten p doitalorstrecalculpartirde P c = R r I c 2 (B.14) Pourlappareillagedemesuredelapr

38、sentenorme,lesquations(B.13)et(B.14)sont utilisesavec R n =25 W aulieude R r ,cestdire W = = p 56 , 4 1 Bn Bn T2 n V V R k I et P n = R n I n 2 B.7 Courbedephasedursonateurinsrdanslacircuiren p Silersonateurestapproximparsonbrasdynamique,sonimpdancepeuttrecrite commesuit: Z c R 1 + jX 1 o 1 1 1 1 C

39、L X w - w = Lasubstitutiondecetterelationdanslquation(B.6)donne 1 T 1 T c Ac Bc 1 1 X j R R K R Z K V V + + = + = Puisque Kestrel,laphasede V Bc /V Ac estdonnepar + - = = T 1 1 Ac Bc Ac Bc arctan Re Im arctan R R X V V V V j604441Amend.1IEC:1999 13 Substitutionintoequation(B.12)gives W = = p 56 , 4 1 Bc Bc T2 c V V R k I (B.13) Crystaldrivelevelinthe p networkcanthenbecalculatedfrom P c = R r I c 2 (B.14) Forthemeasurementsetupinthisstandard,equations(B.13)and(B.14)areusedwith R n =25 W insteadof R r ,i.e. W = = p 56 , 4 1 Bn Bn T2 n V V R k I and P n = R n