CALIBRATION ALGORITHM FOR CURRENT-OUTPUT R-2R LADDERS

Transcription

1 X MEKO World Congress Measurement - upports cence - mproves Tecnology - Protects Envronment... and Provdes Employment - ow and n te Future enna, AUTA, 000, eptember 5-8 CALBATO ALGOTHM FO CUET-PUT - LADDE B. arga and. Zoltán Department of Measurement and nformaton ystems Budapest Unversty of Tecnology and Economcs H-5 Budapest, Hungary Abstract: Te paper presents a new calbraton algortm for current output - ladders. Te - ladders are popular because tey are easy to realse, but te resstance tolerances lmt ter lnearty propertes. However, t s possble to aceve ger lnearty wt self-calbraton tecnques. A formerly publsed algortm by Cutosy s avalable for te so-called Cutosy - ladders. A smlar algortm can be appled to te current-output ladders, wc are wdely used as MDAC or DAC. n te paper te Cutosy dvder s sortly dscussed, and ten a new descrpton s presented as bass of te calbraton algortm. Te calbraton algortm s dscussed n detals, and te error budget s analysed. A smulator was also wrtten to verfy te teory. Keywords: bnary voltage dvders, Cutosy-dvder, DA converter, Gauss metod, - ladder, self-calbraton TODUCTO Te smple and popular metod for convertng a dgtal number nto a quantfed analog sgnal s based on - ladder networs. Te benefts of tese ladders are te relatvely good resoluton and te very smple structure, wc maes tem easy to realze. Tere are at least tree dfferent verson of te basc ladder: voltage-output, current-output (sometmes also called nverse) (Fg..) and Cutosy-dvder (Fg..). 0 0 Fgure. nverse ladder Fgure. Cutosy-ladder

2 X MEKO World Congress Measurement - upports cence - mproves Tecnology - Protects Envronment... and Provdes Employment - ow and n te Future enna, AUTA, 000, eptember 5-8 Te frst two varants are well nown, but not te last one. Te Cutosy-dvder s a modfed - ladder n order to mae t easy to calbrate []. t s often used n natonal standards laboratores and n oter applcatons, were extremely g precson s needed [4, 5, 6]. nce te frst publcaton of te dvder by. D. Cutosy n 978, ts parameters, benefts and drawbacs ave been analyzed n detals by many autors. To llustrate te possbltes of ts specal ladder, tere are realzed ladders up to a resoluton of 5 bts [5]. Te calbraton metod of te dvder nvented by Cutosy [], s an applcaton of te classcal Gauss metod. DECPTO OF THE EE - LADDE Te analyss of te ladder s smple n te deal case. However, te general descrpton of te ladder wt small varatons of te resstances around ter nomnal value s a more complex tas. Even for a 3-bt ladder t s ard to gve te relaton of te nput and te output analytcally. For te calbraton of te ladder, a new descrpton s needed, wc maes te furter analyss easer. Te soluton can be found n a specal - ladder nvented by Cutosy. Altoug from te frst sgt t seems to be completely dfferent from te nverse ladder, te generalzaton of Cutosy s results can solve te problems. Te Cutosy ladder uses te general - ladder structure ( nput resstance s seen from eac dvder stage) wt a modfed swtcng concepton. Cutosy descrbed te ladder n a completely unusual way. He defned new varables, wc caracterzes te goodness of te voltage dvder stages. ( ), ( ) n te case of a -bt Cutosy-ladder wc s one resstance dvder Eq..,. sow te descrpton. Te resstor values, are transformed to varable, and terefore te number of parameters s alved. Te -bt ladder conssts of cascaded -bt dvders, so te algortm can be easly appled to an -bt ladder (for te exact analyss of te Cutosy ladder see []). ow Cutosy s descrpton sould be appled to an nverse ladder. Te man dfference between te Cutosy-dvder and te current-output ladder s tat te Cutosy-dvder s a voltage dvder, and te current-output ladder s a current dvder networ. Te sgnal, wc s carryng te nformaton, s te magntude of current n te nverse ladder. Tese two ladders are dual networs from ts pont of vew. Terefore, te presented descrpton must be modfed to cascaded current dvders. Ts means only cangng some of te ndexes and polartes as t can be seen for a -bt nverse ladder n Eq. 3., 4. : ( ), ( ) After ts sort ntroducton wc sowed te dea of te new descrpton, an -bt nverse ladder wll be dscussed n detals. Te ladder s parttoned to current dvder. For te -t dvder te nput current, te dvded current tat s te nput of te next dvder s, and dvded current wc can be swtced to te output s (Fg. 3.). () () (3) (4) 0 Fgure 3. nverse ladder as cascaded current dvders

3 X MEKO World Congress Measurement - upports cence - mproves Tecnology - Protects Envronment... and Provdes Employment - ow and n te Future enna, AUTA, 000, eptember 5-8 Te relaton between tese varables s usng te new varable rater tan te resstances s determned by te smple current dvdng rule, f defned as Let s calculate currents and ( ),, ( ) From to te output current s te sum of as a functon of terms, and te result s: terms: ( ) Te result s a new descrpton, n wc te statc errors are represented by te terms. Te uncertanty of te bts ncreases gong from te MB to te LB. 3 CALBATO Equaton 0. descrbes te beavour of an nverse ladder wt any resstor values, even for non - relatons. Te resstor values are dden n te terms but t doesn t mae any cange. Tese terms represent te errors of te dvders, and n te deal case ter value s zero. To calbrate te ladder, te terms must be measured someow, and ten a correcton factor can be computed for eac bt and terefore for any code (Eq..). (5) (6) (7) (8) (9) (0) Corr () Te determnaton of te terms s crtcal from te pont of calbraton. t would be possble to measure te output current ( ) of eac dvder stage step by step. However, n ts case currents from to sould be measured, wat would mae t practcally mpossble to realse, because tere s no nstrument avalable wt suc a wde dynamc range. Fortunately, tere s anoter soluton. Te current dvders produce two approxmately equvalent currents, and. Te dfference of and equals to ( ), () f te second order terms of are neglected. As t can be seen from te dfference of te two measured currents, te unnown could be easly determned. Because of te subtracton, t s possble to use te so-called dfference metod. t means tat f te same current offset s used durng te two measurements (M, M n Eq. 3.), te dfference wll not cange, but te absolute value of te measurements wll be n a smaller range:

4 ( ) ( offset ) offset M M Te offset current must be cosen nomnally equal to measured s M M ( ) X MEKO World Congress Measurement - upports cence - mproves Tecnology - Protects Envronment... and Provdes Employment - ow and n te Future enna, AUTA, 000, eptember 5-8 ( ) or (3), and ten te sgnal beng Te frst measurement s made wt all swtces OFF except te -t one. n ts case te output current s. After tat te current sould be measured, wat s not so smple. However, f an auxlary swtc s nserted n te ladder (see n Fg. 3.), te requred current can be measured wt all swtces from to wt poston O. Te output current wll be wt ts bnary code. Te ereby-descrbed results correlate wt Cutosy s calbraton metod. Te prevous mentoned expresson for s te same as for te Cutosy ladder []. Altoug te nverse ladder and te Cutosy ladder seem to be very dfferent for te frst vew, tey are really smlar to eac oter. Te Cutosy ladder contans cascaded voltage dvders wt voltage nput and output sgnals, and te nverse ladder contans cascaded current dvders wt current nput and output sgnals. n most cases, te nverse ladder s used wt voltage nput, wc s converted to current by te nput resstance of te ladder, and te output current s also commonly converted to an output voltage by a smple C/ converter. o t can be sad, tat tese networs sow dualty propertes for some pont of vew. 4 EO BUDGET OF THE CALBATO ALGOTHM Te furter analyss of te ladder needs a carefully consdered error budget. ome of te error sources are tecnology-dependent, and t must be ept n mnd wen dealng wt error sources. Te man error source s te tolerance of te resstors. Before any oter examnatons, ts cardnal error must be studed. However, t s qute smple wt te new descrpton. Te resstances are dden n te terms, as t was mentoned earler (Eq. X.). Durng te analyss, t was never supposed tat tere s a certan relaton between te value of te resstors dfferent varables were used nstead and terefore, te descrpton s vald for any combnaton of te resstances. o te naccuracy of te resstors can be neglected wt respect to te measurement devce (see later). Anoter error source s te non-deal beavour of te swtces. Te analyss s lmted only for DC sgnals ts tme. Before analysng te effects of a real swtc, t must be mentoned tat te analyss s not fnsed yet, because te proper model of an ntegrated swtc depends on te tecnology. Furter examnatons are planned wt co-operaton of C manufacturers to map te error sources. Fgure 4. sows te model of an analog swtc: (4) (5) C D O LKG C D C D C DD O LKG C D Fgure 4. Model of an analog swtc

5 X MEKO World Congress Measurement - upports cence - mproves Tecnology - Protects Envronment... and Provdes Employment - ow and n te Future enna, AUTA, 000, eptember 5-8 Te effect of O s corrected, f te swtces ave te same O for eac cannel. Practcally, t s not true, so separate ts resstance to a typcal part wc s te same for eac cannel and to a devaton one wc represents te varaton of O for te cannels. Ten te typcal part s corrected, because t can be nterpreted as a part of te resstances. Te devaton part can not be corrected, and represents an error source, wc wll reman after te calbraton. Leaage currents are a crtcal problem of te calbraton. Tere are O and OFF leaage currents, wc are dfferent. Ts part of te error budget as not been properly analyzed, because te lac of te correct model of an ntegrated swtc. ome questons, wc terefore could not been answered yet: can te leaage currents be smple added or tere s a correlaton between tem are tey level dependent te effect of feed-troug Te measurement devce as fnte accuracy, addng anoter error source. Te equatons consderng te accuracy of te meter (worst case calulatons): offset M ( ) ( ± M ) offset M ( ) ( ± M ) M M ( ) ( ) offset (6) (7) (8) Expressng te measured and substtutng t to Eq..:, measured Corr M ( ) (9) (0) t means tat te naccuraces of te ladder caused by te resstor tolerances are corrected by a factor of te nstrument accuracy. 5 COCLUO Te paper presented a new descrpton for current-output - ladders. Te new descrpton based on te former wor of Cutosy, mplementng t to te nverse ladder. Te man beneft of te new descrpton s tat te furter analyss of te ladder s smpler. Te calbraton of te ladder based on te new results, and only slgt canges sould be made (an auxlary swtc) to realse t. Te analyss of te calbraton procedure s not fnsed yet. As t was mentoned, te study of te error budget remaned a researc topc. Te Cutosy ladder uses tree precson swtces for eac bt but te current-output ladder needs one swtc per bt and an auxlary one for te calbraton. Ts reducton n te number of te swtces can be an nterestng feature of te nverse ladder. Te calbraton may be used bot n te case of a DAC or an MDAC wc are based on - ladders.

6 X MEKO World Congress Measurement - upports cence - mproves Tecnology - Protects Envronment... and Provdes Employment - ow and n te Future enna, AUTA, 000, eptember 5-8 EFEECE []. van de Plassce, ntegrated analog-to-dgtal and dgtal-to-analog converters, Kluwer Academc Publsers, 994. [].D. Cutosy, A new swtcng tecnque for bnary resstve dvders, EEE Trans. nstrum. Meas.,vol. M-7, pp. 4-4, 978. [3].H. Tsao and. Fletcer, On te Output esstance of elf-cecng oltage Dvders, EEE Trans. nstrum. Meas.,vol. M-3, o. 4, pp , 983. [4].H. Tsao, Mcrocomputer-Based Calbraton ystems for arable oltage Dvders, EEE Trans. nstrum. Meas.,vol. M-3, pp , 983. [5].H. Tsao, A 5-Bt eference esstve oltage Dvder, EEE Trans. nstrum. Meas.,vol. M- 36, o., pp , 987. [6].H. Tsao, An Accurate, Automated 0- Measurng ystem, EEE Trans. nstrum. Meas.,vol. M-38, o., pp. 3-33, 989. [7] B. arga,. Zoltán, Bnary voltage dvders for dc-resstance measurement, Proceedngs of te 999 PD Mnymposum, TUB DM, Budapest, 999. AUTHO: El.-Eng. Balázs AGHA and El.-Eng. dr. stván ZOLTÁ, Department of Measurement and nformaton ystems, Budapest Unversty of Tecnology and Economcs, Mûegyetem rapart 5-7, H-5 Budapest, Hungary, Pone nt , Fax nt Emal: {varga, zoltan}@mt.bme.u