PC-BASED MEASUREMENT INSTRUMENTS: CHARACTERISATION

Transcription

1 Measrement - Spports Scence - Improves Technology - Protects Envronment... and Provdes Employment - ow and n the Ftre Venna, AUSTRIA, 000, September 5-8 PC-BASED MEASUREMET ISTRUMETS: CHARACTERISATIO S. Caldara, S. cco and C. Spataro Dpartmento d Ingegnera Elettrca -Unverstà degl Std d Palermo, Vale delle Scenze, Palermo, ITALY Abstract: In ths paper the problem of charactersaton, n terms of ncertanty, of the measrement dgtal nstrments performances, based on the typcal archtectre of PC bs plgged data acqston boards s consdered. Accordng to the GUM the measrng model and the varos sorces of ncertanty have been taken nto accont and the law of ncertanty propagaton has been appled. Then theoretcal and nmercal analyses of combned ncertantes are carred ot obtanng formlas for the estmaton of the standard ncertanty of the measrement reslt of varos hardware and software blocks of the measrement chan. The reslts of nmercal smlatons and expermental tests are presented to valdate the proposed method. In partclar a vrtal nstrment, wth a complex measrement chan, for flcker evalaton has been consdered. The so obtaned reslts are n a very good agreement wth the theoretcal and nmercal ones. Keywords: PC-based nstrment, Vrtal Instrments, Uncertanty estmaton. ITRODUCTIO The measrement nstrments based on a data acqston board, nsde a PC, wth transdcers, sgnal condtonng accessores and the necessary software, (PC-based nstrments), are becomng more and more wdespread. In order to characterse these measrement nstrments based on the AD converson and dgtal sgnal processng from a metrologcal pont of vew, many papers have dealt wth the varos sorces of ncertantes whch can be ntrodced n the varos hardware and software components of the measrement chan, bt payng attenton only n a partclar ncertanty sorce and wthot dealng wth how these ncertantes propagate trogh the measrement system. Bt after the pblcaton of the ISO gde (GUM) [], whch establshes general rles for the evalaton and the expresson of measrement ncertanty of the whole measrement process, some applcatons of the GUM method have been proposed n lteratre. In [] and [3] the problem of evalatng the ncertanty that characterses some algorthms (mean vale, rms vale and DFT) s dscssed by consderng dfferent sorces of ncertanty (qantzaton, tme jtter, fnte wordlength). In [4] a classfcaton of measrement models, that s more general than that consdered by ISO GUM, s presented and the se of samplng technqes for the evalaton of ncertanty s compared wth the applcaton of the GUM. In ths paper we consder the typcal archtectre of a PC-based measrement nstrment takng nto accont the man ncertanty sorces, n partclar the ones generated n the acqston board (secton ). In secton 3, by applyng the GUM method, we stdy how ncertantes propagate throgh some dgtal sgnal processng blocks, obtanng formlas for the evalaton of combned standard ncertantes. In secton 4, by means of nmercal smlatons, dfferent types of ncertanty are ntrodced on the npt data n order to test the behavor of varos processng blocks and verfy the reslts of the theoretcal consderatons. In secton 5 we apply the proposed ncertanty evalaton procedre to a vrtal nstrment flcker measrement realsed by athors [5] and we verfy expermentally the proposed method. PC-BASED ISTRUMETS AD SOURCES OF UCERTAITY A typcal PC based nstrment s consttted of the followng blocks: transdcers and sgnal condtonng accessores (crrent and voltage transformers, attenators and amplfers, anttalsng flter, mltplexer, track and hold crcts); data acqston board wth sampler, A/D converters and clock generator; general-prpose compter (e.g. PC);

2 Measrement - Spports Scence - Improves Technology - Protects Envronment... and Provdes Employment - ow and n the Ftre Venna, AUSTRIA, 000, September 5-8 software (control, data processng, analyss, presentaton, nterfacng). Each block of the measrement chan can generate ncertantes, whch propagate throgh the sccessve blocks, gvng a contrbton to the combned standard ncertanty of the measrement reslt. In ths context we focs only on ncertantes de to A/D converson board and processng algorthms. Errors de to transdcers and condtonng accessores are already well modelled and known; errors de to software can be not taken nto accont f tested and valdated control and processng software packages are sed. In the A/D converson process we have to take nto accont, as qanttes that can sgnfcantly contrbte towards ncertanty to the measrement reslt: offset, gan, qantzaton, nose, lnearty, tme jtter, settlng tme, cross-talk, temperatre drft and stablty. The charactersaton of these ncertanty sorces can be carred ot by means of statstcal methods (Type A evalaton accordng to the GUM) based on tradtonal approaches (beat freqency testng, hstogram analyss, sne wave crve fttng, dscrete fnte Forer transform) or novel approaches (jont tme freqency analyss, wavelet analyss). It s also possble to trn to manfactrers specfcatons (Type B evalaton accordng to the GUM). Usally, from techncal specfcatons t s possble to drectly get standard ncertanty related to offset, gan, qantzaton, nose, lnearty, settlng tme, cross talk, temperatre drft, stablty. Accordng to the GUM, provded that there s no contradctory nformaton, each npt qantty devaton s to be consdered eqally probable to le anywhere wthn the nterval gven by specfcaton, that s modelled by a rectanglar probablty dstrbton. The best estmate of the ncertanty s then: a 3 where a s the half-ampltde of the dstrbton nterval. To evalate the tme jtter ncertanty, whch s a fncton of samplng rate, t s possble to se the followng expresson [6]: log f 3π sampτ α jtter V range where τ α s the apertre jtter and f samp s the samplng rate. Uncertanty related to the mcroprocessor fnte wordlength can be modelled as follows [], [7], [8]: fxed Bx for each mltplcaton carred ot by a fxed-pont processor; B m floatng, mltpl 0.8 floatng p B m, add 0.8 for each mltplcaton and addton, respectvely, carred ot by a floatng-pont processor; where B x s the fxed wordlength; B m s the nmber of bt sed to represent the mantssa; p s a factor dependng on the probablty of rondng occrrence n an addton. Becase the nmber of bts sed by common processng software packages rnnng on PCs to represent the mantssa s hgh (for nstance LabVew ses 5 bts n doble precson), the ncertantes ntrodced by mcroprocessor fnte wordlength are sally neglgble compared wth the other ones. 3 THEORETICAL ESTIMATIO OF COMBIED UCERTAITIES When a measrand estmate y s determned from other qanttes x, x,, x, throgh a fnctonal relaton y f(x, x,, x ), the combned standard ncertanty estmate c (y) of the measrement reslt s the postve sqare root of the estmated varance c(y), obtaned from: () () (3) (4) (5) c f ( x ) x + j, j x f x j r( x, x j ) ( x ) ( x j ) (6)

3 Measrement - Spports Scence - Improves Technology - Protects Envronment... and Provdes Employment - ow and n the Ftre Venna, AUSTRIA, 000, September 5-8 where (x ) s the estmated standard ncertanty assocated wth the npt estmate x and r(x,x j ) s the estmated correlaton coeffcent assocated wth x and x j. Ths eqaton s based on a frst-order Taylor seres approxmaton of y. Usally, n dgtal sgnal processng algorthms, each otpt sample y s a fncton of more than one npt samples whch can be correlated or not; as a conseqence, t can be stable to dstngsh ncertantes of completely correlated npt qanttes (gan and offset) and ncertantes of absoltely not correlated npt qanttes (the other ones). Moreover, n case of errors de to gan, the relatve standard ncertanty r (x)(x)/ x s to be consdered constant on each npt sample. In all other cases t s the absolte standard ncertanty, to be consdered constant on each npt sample. Accordng to these consderaton we can dvde the aforementoned sorces of ncertanty n three classes: I. offset and ts temperatre drft: completely correlated npt qanttes and I const; II. gan, ts temperatre drft and stablty: completely correlated npt qanttes and const;. qantzaton, nose, lnearty, tme jtter, settlng tme, cross talk: not correlated npt qanttes and const. For I class sorces (x ) const I and r(x,x j ), so the (6) becomes: ci I x For II class sorces r (x ) const and r(x,x j ), so the (6) becomes: cii x x For class sorces (x,x j ) 0 j and (x ) const, so the (6) becomes: x In the followngs, we take nto accont the applcatons to some processng algorthms, whch are typcal of a measrement chan. Let s consder a fnte mplse response flter. In ths case y a x and f x a so the (7),(8) and (9) become respectvely: ci cii a I r cii (7) (8) (9) (0, ) a x ( x) (3) a In the case of an nfnte mplse response flter t s mpossble to drectly apply the (6), becase each otpt sample s a fncton not only of the npt samples, bt also of some prevos otpt samples. Bt we can calclate the mplse response h of the flter, and se ths seqence to estmate the ncertantes. Therefore the (7), (8) and (9) become respectvely: ci y) r cii I 0 h ( (6) 0 h In practcal applcaton yo wll consder a stable fnte nmber of terms sch as the resdals of the two seres are neglgble wth respect to other errors. () (4) (5) (7)

4 Measrement - Spports Scence - Improves Technology - Protects Envronment... and Provdes Employment - ow and n the Ftre Venna, AUSTRIA, 000, September 5-8 For a cascade of flters (FIR and/or IIR), obvosly we mst consder the whole system mplse response. Let s consder an ponts DFT and pay or attenton on the modles. It s easy to recognse that: for the I class sorces ncertantes ci (y) 0, except the DC component for whch ci (y) I ; for the II class sorces ncertantes rcii (y) ; for the class sorces ncertantes applyng the (9), t s possble to obtan []: except the DC component for whch In order to perform a correct ncertanty estmaton, the model of all the sorces of ncertanty have to be known and charactersed. Moreover the problem of correlaton determnaton, between npt qanttes, s often dffclt to manage, and n the evalaton of the ncertanty, the errors de to possble dgtal processng algorthms bas, f present, mst be taken nto accont. 4 UMERICAL SIMULATIO Wth the am of testng the behavor of each processng block and verfyng the approxmatons of the GUM approach, we ntrodce the three classes of ncertanty sorce on the npt data, sng the LabVew 5. envronment. The smlated npt sgnal s a varosly modlated and dstorted 50 Hz snsodal voltage waveform, typcal of electrcal power systems, sampled at 048 Hz. Rnnng 0000 tmes the varos algorthms we can calclate the standard devaton of each otpt sample for several vales of ncertanty. For nstance, ntrodcng a class ncertanty sorce and consderng the followng DSP blocks, workng at a 048 S/s: A) A 048 samples DFT; B) A frst order IIR hgh pass flter wth 0.05 Hz ct off freqency; C) A sxth order IIR Btterworth low pass flter wth 35 Hz ct off freqency; D) A 5 coeffcents FIR flter sed as weghtng flter n the flckermeter (see secton 5); E) A frst order IIR low pass flter wth 0.57 Hz ct off freqency; F) The cascade of the B,C and D flter, we obtan (for vale of r (x) 5%) [9]: Table Theoretcal obtaned ncertanty mercal obtaned ncertanty A (x) (x) B (x) (x) C (x) (x) D (x) 0.03 (x) E (x) (x) F (x) (x) Accordng to the central lmt theorem, t s also verfed that the observed dstrbton of the otpt samples s a normal one. The obtaned reslts are perfectly concdent wth the theoretcal ones. The (6) can also be appled by means of nmercal calclatons. Therefore, when t s dffclt to fnd analytcal expressons of ncertantes propagaton, a nmercal smlaton based method can be carred ot to obtan the evalaton of combned ncertanty. In each case, t s very mportant to correctly model and qantfy the ncertantes sorces on the A/D board. 5 A VI FLICKERMETER: TESTS FOR UCERTAITY ESTIMATIO In ths secton we apply the proposed ncertanty estmaton procedre to a vrtal nstrment for flcker evalaton on power systems [5]. The measrement chan can be separated nto an hardware block and a software block. The frst one s consttted by an analog flter to prevent the alasng phenomenon and a dgtal acqston board (DAQ) nserted on a PC whch rns the data processng algorthms. The board s the atonal Instrments PCI-MIO-6XE0 whose featres are lsted below: (8) (9)

5 Measrement - Spports Scence - Improves Technology - Protects Envronment... and Provdes Employment - ow and n the Ftre Venna, AUSTRIA, 000, September sngle-ended or 8 dfferental channels; sccessve approxmaton 6 bt ADC; 00 ks/s max samplng rate; ±0V maxmm npt sgnal range. A Type B evalaton of standard ncertantes, based on manfactrer s specfcatons, s consdered and rectanglar dstrbtons are assmed. By smmng the contrbton of each sorce of ncertanty the vales of Tab. are obtaned [9]: Table Sorce class Uncertanty sorce Standard devaton I Off set 8 µv II Gan % Qantzaton, nose, IL 406 µv The PC s based on a 33 MHz Pentm II Intel processor. The software block s the mplementaton, based on LabVew 5. programmng langage, of sted dgtal sgnal processng algorthms. The DAQ samples the npt voltage at 048 S/s and sends samples vectors to the flckermeter block, whch frnshes the nstantaneos flcker level S(t), consttted (accordng to [0]) by:. sqarng mltpler;. frst order hgh pass flter wth 0.05 Hz ct off freqency; 3. sxth order Btterworth low pass flter wth 35 Hz ct off freqency; 4. eye-bran system smlaton flter (weghtng flter) whose transfer fncton s establshed n [0]; 5. sqarng mltpler; 6. frst order low pass flter wth 0.57 Hz ct off freqency. Becase the nmber of bts sed to represent the mantssa s eqal to 5, the ncertantes ntrodced by mcroprocessor fnte wordlength are neglgble compared wth the other ones. Also the ncertantes de to the tme jtter and the settlng tme are neglgble for a so low samplng rate and beng the apertre jtter eqal to 5 ps. We don t consder the cross-talk ncertanty, assmng a sngle channel acqston. In or analyss we consder a coherent samplng, wthot generatng the leakage phenomenon. The offset errors, modlatng wth the carrer, generate, after the sqarng, a carrer freqency component and a DC component, whch are elmnated by the hgh pass flter, the Btterworth flter and the weghtng flter. A notch flter, centred at the carrer freqency, cold be ntrodced to redce the flckermeter senstvty to the offset ncertanty. The gan ncertanty, for the presence of two sqarng mltplers, s mltpled by for. Regardng the class ncertanty sorces, the sqarng mltplers case that the otpt ncertanty depends on the npt dstrbance vale and so, on the S(t) vale. By means of nmercal calclaton [9], we have obtaned the followng exp resson for the otpt ncertanty: ( S) k S (0) where k s a coeffcent dependng on the npt dstrbance freqency and form. Consderng the worst case, t reslts k 0/V when s expressed n volts. The otpt ncertanty de to all aforementoned ncertanty sorces s then: ( S) 4 S k S () c + Expermental tests have been carred ot, consderng the testng procedre prescrbed by [0]. In Tab. 3, for a 0 Hz snsodal dstrbance, the standard ncertantes obtaned sng the (0) ( worst case ), by means of nmercal smlaton ( nm. ) and expermentally ( exper. ) are reported. Table 3 V/V% S(t) worst case. nm. exper

6 Measrement - Spports Scence - Improves Technology - Protects Envronment... and Provdes Employment - ow and n the Ftre Venna, AUSTRIA, 000, September 5-8 The expermental reslts are n good agreement wth the worst case theoretcal ones and wth the nmercal smlaton obtaned ones and valdate the consdered model and the vales of the varos ncertanty sorces of the tlsed data acqston board. For each measrement reslt, the nstrment can frnsh the assocated standard ncertanty. 6 COCLUSIOS Analytcal, nmercal, by smlaton and expermental approaches are presented and compared to evalate the ncertanty that characterses the measrement reslts of PC-based dgtal nstrments. Accordng to the GUM the measrng model and the varos sorces of ncertanty have been taken nto accont and the law of ncertanty propagaton has been appled. Then a theoretcal and/or nmercal analyss of combned ncertantes s carred ot obtanng formlas for the estmaton of the standard ncertanty of the measrement reslt of varos blocks (hardware and software) of the measrement chan. The reslts of nmercal smlatons, wth also expermental tests, have valdated the proposed method, the consdered model and the vales of the varos ncertanty sorces of the tlsed data acqston board. The proposed approach for evalaton of ncertanty appled to a PC-based nstrment can be helpfl both n the phase of nstrments desgn (hardware and dgtal sgnal processng algorthms set p), n the phase of metrologcal charactersaton and to mplement, n the VI nstrments, algorthms whch frnsh the standard ncertanty of the measrement reslt. REFERECES [] ISO - GUIDE TO THE EXPRESSIO OF UCERTAITY I MEASUREMET (995) [] G. Betta, C.Lgor, A. Petrosanto: Uncertanty analyss n Fast Forer Transform algorthms, IMEKO TC-4 Internatonal Symposm, aples, Italy, September 998, pp [3] G. Betta, C.Lgor, A. Petrosanto: Strctred approach to estmate the measrement ncertanty n dgtal sgnal elaboraton algorthms, IEE Proc. Sc. Meas. Technol., Vol. 46, o., Janary 999, pp. -6. [4] M. Cox, M. Danton, P. Harrs,. Rdler: The evalaton of ncertantes n the analyss of calbraton data, IMTC, Vence, Italy, May 999. [5] S. Caldara, S. cco, C. Spataro: A vrtal nstrment for measrement of flcker, IEEE Trans. on Instrmentaton and Measrement, Vol. 47,.4, Agst 998. [6] R. H. Walden: Analog-to-Dgtal Converter Srvey and Analyss, IEEE Jornal on selected areas n commncaton, Vol.7,. 4, Aprl 999. [7] K. Kallojarv, J. Astola: Rondoff errors n block-floatng-pont system, IEEE Trans. on Sgnal Processng, Vol.44,. 4, 996, pp [8] I. Ptas, M. Strntzs: Floatng-pont error analyss of two dmensonal Fast Forer Transform algorthms, IEEE Trans. on Crcts and Systems, Vol. 35, n.,988, pp. -5. [9] S. Caldara, S. cco, C. Spataro: Measrement ncertanty estmaton of a Vrtal Instrment, IMTC, Baltmore, Maryland, USA, May 000. [0] IEC (997-) Electromagnetc compatblty (EMC) - Part 4: Testng and measrement technqes - Secton 5: Flckermeter - Fnctonal and desgn specfcatons. AUTHORS: Dr. Salvatore CALDARA, Unv. Prof. Dr. Salvatore UCCIO, Dr. Cro SPATARO, Dpartmento d Ingegnera Elettrca - Unverstà degl Std d Palermo, Vale delle Scenze, Palermo, Italy, Phone Int. (+39) , Fax Int. (+39) ,E-Mal: ncco@npa.t.