Unconventional double-current circuit accuracy measures and application in twoparameter
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1 th IMEKO TC Wokshop on Techncal Dagnostcs dvanced measuement tools n techncal dagnostcs fo systems elablty and safety June 6-7 Wasaw Poland nconventonal double-cuent ccut accuacy measues and applcaton n twopaamete measuement Zygmunt Wasza dam Idzkowsk Wojcech Walendzuk eseach Insttute of utomaton and Measuements PIP (l. Jeozolmske -86 Waszawa Poland e-mal: zlw@op.pl alystok nvesty of Technology Depatment of Electcal Engneeng (Wejska 5D st. 5-5 alystok Poland e-mal: a.dzkowsk@pb.edu.pl w.walendzuk@pb.edu.pl bstact- In ths pape some nteestng and novel featues of a fou-temnal (T netwok ae pesented. sngle DC cuent souce s swtched ove and connected n tuns to opposte ams of the fou-element bdge ccut. Ths two-voltage-output ccut s called a double cuent bdge. The output voltages ae dependent on the am esstance ncements and the values ae gven n absolute and elatve unts. The accuacy measues (lmted eos and standad uncetantes of two tansfe functons ae pesented. smple applcaton wth two sensos actng as stan gauges and TD s s pesented. The smplfed sgnal condtonng fomulas of twopaamete measuement of stan and tempeatue of a cantleve beam ae dscussed. Some esults acheved wth the use of the ccut ae pesented. I. Intoducton Wheatstones bdge s one of basc and well known measuement tool. Ths ccut equpped wth addtonal elements of moden technology such as analog-to-dgtal convete (DC o mcopocesso systems povdes geat accuacy and speed of conducted measuement [] [5]. Most of those systems ae based on measung one quantty. Howeve a goup of measuement methods whch ae used to measue seveal quanttes at the same tme s also woth notcng [] [] [8] [9]. system measung mmttance vaaton based on smultaneous measuement of two paametes of esstance ncements n a fou-temnal (T netwok can be an example [] [7] [8]. Two types of such condtonng and analog sgnal measuement ae pesented n lteatue [9]. One of them s a double ccut of two fou-am classc bdges connected n cascade. s fa as the authos know the poposed bdge ccut and ts applcaton (measuement of two quanttes s novel. The authos of the atcle have not come acoss a wok descbng an accuacy analyss fo two smultaneously measued paametes. The two-component appoach [] of descbng the bdge ccut accuacy (lmted eos and standad uncetantes s used. II. nconventonal double-cuent ccut and the paametes The smple elatons n a double cuent bdge ae descbed. Fgue. Double cuent bdge (J - theoetcal ccut [6]. s shown n Fg. a double cuent bdge s suppled by two equal cuent souces JJ J. The output voltages of the bdge ae: - J J ( ( 7
2 th IMEKO TC Wokshop on Techncal Dagnostcs dvanced measuement tools n techncal dagnostcs fo systems elablty and safety June 6-7 Wasaw Poland DC - J J DC ( ( whee: DC - open-ccut voltage to cuent paametes of D-C and - outputs. In futhe analyss t s assumed that esstances n the bdge ae vaables and ae epesented by equaton: ( whee - ntal (nomnal esstances - elatve ncements of esstances (. dge tansfe functons ( ( can be smplfed to poducts of the ntal senstvtes t t n the balance and nomalzed unbalance functons f ( f (. The fomulas can be expessed by ntal values and ncements of all esstances.e. ( and efeencng to one of the fst am.e.: m n and (m/n o (n/m as s shown n Table. It esults fom two balance states of ths bdge-ccut. Table. Open-ccut voltage to cuent paametes n functon of elatve ncements of esstance Ccut wth Open-ccut voltage to cuent paametes of - and D-C outputs ( abtay In balance: - ( - (5 ( t f ( J t " f " J whee: whee: m n m n (m/n L ( m( m ( n m m n L"( m( n ( n n t f ( o ( m n( m t " f "( (m n ( m ( m n( n " (m n ( n L( L" ( m n (n/m If the sensos ae stuated n all ams of the bdge ccut and the nomnal esstances ae equal and the esstance changes ae small (thus j << and j Σ << Σ the smplfed veson of the equatons can be povded as follows: DC t"( - - ( (6 t ( - -. (7 III. ccuacy measues ssume that open-ccut voltage to cuent paametes constst of two components. The paametes DC ae ntal values and ae the ncements of. (8 Then one can modfy equatons ( and ( as follows: J ( J t f ( (9 ( J ( J t f (. ctual (absolute eos of paametes and DC ae elated to ntal senstvtes t t. The elatve eos ae the functons of algebac sum of the ntal (zeo eos of all the esstances [] - - t ( ( 75
3 th IMEKO TC Wokshop on Techncal Dagnostcs dvanced measuement tools n techncal dagnostcs fo systems elablty and safety June 6-7 Wasaw Poland - -. t " ctual elatve eos of esstances can be expessed by ntal eos and eos of the ncements ( ( ( (. (5 ctual (absolute eos of paametes and DC ae also elated to ntal senstvtes t t : t. " t (6 (7 The equatons ae moe complcated. ctual values of measuement eos of bdge tansfe functons and esult fom the total dffeental of analytcal equatons ( and (5 fom Table. fte odeng all components of actual eos of esstances one can estmate absolute eos (a and (b. Then wth (- 7 the followng accuacy measues can be expessed: elatve actual eos (a and (b elatve lmted eos (a and (b andom (mean squae measues (a and (b. ll the accuacy measues ae odeed n Table. ddtonally actual eos of ncements - and - ae defned. They wee elated to and paametes as follows: - t - t ( - - t f - - ( - ( ( - ( f - -. "( f - (8 (9 Paametea of ccut Geneal case ( ( ( ( - Table. ccuacy measues of the voltage to cuent paametes of J bdge n geneal case. Measue ccuacy measues of ccuacy measues of ctual eos: absolute and elatve Lmted eos (a w w ( t (a whee: w ( w ( w ( w ( w w (a t w (b (b w ( whee: w ( w w w ( w w (b ( ( 76
4 th IMEKO TC Wokshop on Techncal Dagnostcs dvanced measuement tools n techncal dagnostcs fo systems elablty and safety June 6-7 Wasaw Poland Measues fo Measues fo andom measues ctual eos w w ( (a coelaton coeffcent k j Lmted eos m (a w w ( (b coelaton coeffcent k j m (b Mean squae measues k j (5a (5b ctual (6a 6b 8a 8b and lmted (7a 7b 9a 9b elatve eos fo the ccut wth two sensos (wth two esstances and vaable s shown n Table. ll of eos depend on the two ncements and (what epesent two measued quanttes and. They ae also the functons of (zeo eos and (gan eos of esstos and sensos. Ths s novelty n defnng of the accuacy measues n two paamete (D measuement. Table. ccuacy measues of the voltage to cuent paametes of J bdge f all am ntal esstances ae equal and two ncements of esstance vaable. Paametes of May elated accuacy measues of bdge of ccut elated to ntal senstvtes t o t of ncements - and - and vaable ( ( abtay ( ( ( ( (6a (6b -. ( f abtay f ( 6 (7a ( ( (8a ( 6 (9a ( 6 (7b ( ( ( (8b ( (9b IV. Two-paamete measuement of stan and tempeatue change In ode to llustate the concept of opeaton of a system measung two paametes at the same tme a pototype veson was woked out. The system pesented n Fg. can be used to examne stan n one axs (e.g. x-axs by stan gauge and tempeatue (stan gauge o esstance themomete. Smultaneous measuement of stan n two axes (e.g. x-axs stan gauge y-axs stan gauge s anothe possblty. Ths type of measuement system can be also appled to measue othe quanttes whch can be measued wth the use of esstance paametc sensos. Possblty of compensaton of tempeatue nfluence on a measuement stan gauge esstance (wthout usng addtonal tempeatue sensos s also geat advantage of such soluton. It can be acheved though smultaneous measuement of tempeatue and esstance of a stan gauge by ndect method examnng appopate voltage on the dagonals of a double-cuent bdge. 77
5 th IMEKO TC Wokshop on Techncal Dagnostcs dvanced measuement tools n techncal dagnostcs fo systems elablty and safety June 6-7 Wasaw Poland Fgue. Double cuent bdge (xj. as an nput analog pat of measuement system (J-cuent souce sensos esstos K K electonc swtches The expemental test on the xj ccut was made. The goal was to measue the eal change n tempeatue of stan gauges n the pont of senso placement and the mechancal stess (deflecton of cantleve beam. The ccut was tested wth two metal (fol stan gauges TF-/ (Tenmex. oth output voltages ae the means of voltages measued n two cycles [] DCs.5t"( ( s.5t ( -. The changes n esstance of stan gauges consst of two components: - espectvely. One of them s the ncement of tempeatue change T the othe one s the ncement (o decement of mechancal stess caused by bendng foce F. sng two dentcal stan gauges n a bdge ndcates the same sgn and value of the elatve ncements n tempeatue. If one gauge s compessed (Fg. and the othe one s stetched at the same tme the ncements of the mechancal stess have the opposte sgns. (T (T ( ( ( e - (. e ( Fgue. Localzaton of heate TD senso and stan gauge. The measuements wee taken fo seveal (constant tempeatues of a cantleve beam ( C C C 6 C whle the beam was bent wth the use of mcomete scew n the ange fom untl mm. s shown n Fg. thee s a sgnfcant nfluence of sng tempeatue T on the ntecept. The slope s nealy the same. The efeence tempeatue s C. 78
6 th IMEKO TC Wokshop on Techncal Dagnostcs dvanced measuement tools n techncal dagnostcs fo systems elablty and safety June 6-7 Wasaw Poland Fgue. The elatve esstance ncements n the functon of the beam X deflecton whle tempeatue T s changng V. Conclusons The two-component appoach of descbng the unconventonal double-cuent ccut accuacy s poposed. It has a fom of sum of the ntal stage and the bdge mbalance accuacy measues (Table. Tansfe coeffcents the lmted eos and standad uncetantes as the functons of elatve ncements of esstance ae shown fo the bdge ccut wth two sensos. The applcaton of ths ccut n smultaneous measuement of stan and the tempeatue change s pesented. The measuements confmed that thee s lnea elatonshp between and deflecton and elatve esstance ncements of stan gauges (Fg.. efeences [] P. Cappa F. Manozz S.. Scuto novel method fo the smultaneous measuement of tempeatue and stan usng a thee-we connecton Measuement Scence and Technology vol. no. pp []. Idzkowsk J. Makal Z. L. Wasza Smultaneous measuement of two paametes by double cuent suppled bdge Jounal of utomaton Moble obotcs and Intellgent Systems vol. 6 no. pp. 6-. [] E. Sfuentes O. Casas F. evete. Pallas-eny Dect nteface ccut to lnease esstve senso bdges Sensos and ctuatos -physcal vol. 7 pp [].. Pake Smultaneous Measuement of Tempeatue and Stan sng Fou Connectng Wes NS Techncal Memoandum [5] P. H. Sydenham. Thon Handbook of Measung System Desgn John Wley & Sons Chapte 6: Electcal dge Ccuts asc Infomaton by Z. L. Wasza New Yok pp [6] Z. L. Wasza dges Suppled by Two Cuent Souces New Tool fo Impedance Measuements and Sgnal Condtonng Poc. of IMEKO-TC-7 Symposum pp. -6. [7] Z. L. Wasza Fou-Temnal (-T Immtance Ccuts (T n Multvaable Measuements Monogaph of Industal Insttute of Contol and Measuement PIP Wasaw (n Polsh. [8] Z. L. Wasza Two Paamete (D Measuements n Double cuent Supply Fou-temnal esstance Ccuts Metology and Measuement Systems Polsh cademy of Scences vol. XIII no. pp [9] Z. L. Wasza ackgounds of two vaable (D measuements of esstance ncements by bdge cascade ccut Poc. of SPIE vol. 67 pat [] Z. L. Wasza New appoach to the accuacy descpton of unbalanced bdge ccuts wth the example of Pt senso esstance bdges Jounal of utomaton Moble obotcs and Intellgent Systems vol. no. pp
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