OFFSET CORRECTION IN A DIGITAL INTEGRATOR FOR ROTATING COIL MEASUREMENTS

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1 XX IMEKO World Cogress Metrology for Gree Growth September 9 4, 0, Busa, Republic of Korea OFFSET CORRECTION IN A DIGITAL INTEGRATOR FOR ROTATING COIL MEASUREMENTS P. Arpaia,, P. Cimmio,, L. De Vito, ad L. Fiscarelli, Europea Orgaizatio for Nuclear Research (CERN), Geeva, Switzerlad, {pasquale.cimmio, lucio.fiscarelli}@cer.ch Uiversity of Saio, Departmet of Egieerig, {arpaia, devito}@uisaio.it Abstract: The rotatig coil techique is extesively used i high-precisio measuremets for accelerator maget testig. Oe of most relevat error sources is the drift arisig from the itegrator offset. I this paper, a correctio algorithm for the offset drift i digital itegrators is preseted. Prelimiary experimetal results for the measuremet correctio of the mai field of a supercoductig dipole maget of the Large Hadro Collider at CERN show the effectiveess for fast rotatig coil measuremets. Keywords: Magetic field measuremets, accelerator magets, sigal processig.. INTRODUCTION I particle accelerators, a accurate cotrol of the beam is achieved by imposig costraiig toleraces o the magetic field of the magets. Clearly, high-quality magetic measuremets are crucial also durig all the phases of desig, costructio, testig, ad operatio of the accelerator magets []. I maget testig, ihomogeeous magetic fields are measured by meas of the rotatig-coil method. Accordig to Faraday s law, by rotatig i a magetic field, a coil geerates a voltage. The voltage sigal is itegrated by agular steps i order to measure the magetic flux. The harmoic cotet of the flux, podered with sesitivity factors, is related to the distributio of the field i the volume spaed by the coil []. Typically, the coil sigal is acquired ad treated by usig a digital itegrator with o-lie data process capability. Recetly, at CERN, a fast digital itegrator (FDI) has bee developed, i order to satisfy the demadig requiremets of testig the supercoductig magets of the Large Hadro Collider (LHC) []. By meas of a accurate time base ad specific itegratio algorithms provide high performace []. The itegrator, as well as the other compoets of the measuremet system, has to provide low ucertaity. I particular, dc voltages comig from the trasducer (e.g. thermocouple effect) ad offset voltage of the aalogue frot-ed of the istrumet determie a drift i the itegratio. If ot corrected, this affects the spectrum of the flux ad corrupts the field measuremet [4]. Some correctios ca be applied to mitigate the offset drift. I geeral, the dc-offset voltage ca be estimated immediately before startig the measuremet ad successively subtracted from the data. This straightforward correctio provides good results for short measuremets compared to the stability of the offset. I the case of log measuremets, the correctio becomes useless. I the particular case of rotatig coils, the periodicity of the sigal ca be also exploited to correct the drift. At a costat speed, the flux poits correspodig to the same coil positio must be at the same level. This method is ieffective i the very-commo case of a maget powered by a cyclig curret. The field variatio produces a modulatio of the coil sigal makig the periodicity assumptio uacceptable. I this paper, a correctio method for the offset drift i digital itegrators for log measuremets is preseted. The proposed procedure, based o a automatic feedback loop, is also effective i the case of data take o cycled magets. Due to its low computatioal complexity, it ca be easily performed o-lie directly o the istrumet processor. The paper is orgaized as follows: i Sectio, the procedure for measurig the magetic flux spectrum is recalled; the, i Sectio, the proposed correctio is preseted. Fially, i Sectio 4, prelimiary experimetal results are reported, showig the method effectiveess i actual flux measuremets.. FLUX HARMONICS MEASUREMENT The flux spectrum is measured as the sequece dφ() of digital defiite itegrals, computed o a fractio of the period of the rotatig coil, correspodig to the agle betwee two successive ecoder measuremets, by applyig, i each period of the coil, the followig procedure []:. The samples dφ() of a coil period are collected i a array;. The magetic flux is obtaied by itegratig the samples dφ(): N N ( ) = dφ( ) φ, () = where N is the umber of samples per period.

2 . A liear correctio for the evelope of the sequece is carried out o the samples by ormalizig the samples of the period by the value of the curret measured from the coil: φ() ec ( ) = φ( ) bm a + b φ () a + b is the expressio of a liear fit of the where measured curret i the coil, correspodig to the cosidered period ad b m is the average value of the fit. 4. The Fast Fourier Trasform (FFT) of the corrected flux is evaluated, ad the ratio of the real parts ad imagiary parts of each harmoic, versus the fudametal harmoic is take. I() k- k- k- k m m. DC OFFSET CORRECTION ALGORITHM The proposed correctio is desiged as a automatic feedback loop workig o the sequece dφ() of digital itegrals (Fig. ). I a iitial step, the cotrol sequece c() is set to 0. Therefore, the dφ() sequece is itegrated, thus obtaiig the flux sequece φ(). A specific block measures the dc offset affectig the flux sequece. The measured dc offset b() is fially filtered i order to obtai a cotrol sequece c() to be subtracted to the dφ() sequece. The feedback filter is a 4-order FIR (Fiite Impulse Respose) low-pass filter, with a cut-off frequecy equal to π/. A. dc offset measuremet block The dc offset measuremet method operates o the flux sequece φ(). Assumig the evelope of φ() approximated by a straight lie over two periods, two lies ca be idetified, represetig the upper ad the lower evelope, respectively. Therefore, the average I() of the flux samples over each semi-period is evaluated. The, the lies represetig the upper ad the lower evelopes of the I() sequece are obtaied for each semi-period. The offset at the semi-period dφ() + c() - Feedback Filter b() dc offset measuremet dφ corr () Digital itegratio φ corr () Fig.. Block scheme of the dc offset correctio loop. Fig.. The dc offset measuremet procedure. The average I() of the flux samples over each semi-period is evaluated. The, the lies represetig the upper ad the lower evelopes of the I() sequece are obtaied for each semi-period. The offset at the semi-period k is give by the value of the average lie at the semi-period k. k is give by the value of the average lie at k, as show i Fig.. Give I(k), I(k-), I(k-) ad I(k-), the values of the average sequece I() obtaied i the last four semi-periods, the parameters of the upper ad lower evelope lies are give by: I = ( k ) I( k ) m () I = ( k) I( k ) m () ( ) ( k ) () = I k I m =. (4) The parameters of the average lie betwee the upper ad the lower evelope are give by: m m + m = (5) + =. (6) Therefore, the dc offset measuremet is give by: b 4m + =. (7)

3 Fig.. Coil shaft cross sectio [5]. 4. EXPERIMENTAL RESULTS Fig. 4. Rotatig coil measuremet system for LHC mai dipoles [6]. The proposed correctio method has bee implemeted i MATLAB ad experimetal tests have bee carried out o the absolute ad compesated sigals typical of the rotatig coils techique [4]. I particular, the mai field of a LHC mai dipole supercoductig maget is measured by a Fast Digital Itegrator (FDI) acquirig the absolute sigal of the cetral coil sketched i the shaft cross-sectio of Fig.. Aother FDI measures the compesated sigal obtaied by coectig a tagetial ad the cetral coils i oppositio i order to cacel the mai compoet ad ehace the sigalto-oise ratio [5]. The measurig shafts are rotated at tur per secod by a motor uit, icludig a agular ecoder ad slip rigs for the coil sigals (Fig. 4). The magetic flux is measured betwee 5 agular positios per tur. A PC cotrols the measuremet bech ad stores the itegrated coil data. I Figs. 5a ad 5b, the measured sequece of the magetic flux is reported before ad after the correctio for both the compesated ad ucompesated coil cofiguratios, respectively. a) b) c) d) Fig. 5. Magetic flux before ad after correctio for absolute (a) ad compesated (b) cofiguratio; measured dc compoet for absolute (c) ad compesated (d) cofiguratio.

4 a) b) c) d) e) f) g) h) Fig. 6. Measuremets of the harmoics for a acquired ucompesated sigal, without (blue lie) ad with (red lie) offset correctio: real parts of d (a), rd (b), 4 th (c) ad 5 th (d) harmoic; imagiary parts of d (e), rd (f), 4 th (g) ad 5 th (h) harmoic

5 The curret cycle i the maget is composed by a plateau at 850 A, a descedig ramp to 500 A, a ascedig ramp up to 760 A, ad a plateau at 760 A. The method is able to cacel out completely the dc offset, eve whe it has ot a liear tred ad a cyclig curret modulates the flux (Figs. 5c ad 5d). I Figs. 6, the measuremets of the d, rd, 4 th, ad 5 th harmoics are reported, i the case of a ucompesated sigal, without (blue lie) ad with (red lie) the dc offset correctio. A small differece ca be appreciated i the real part, while a cosiderable correctio is made i the imagiary part. I ay case, the harmoics are brought to a more regular behavior by meas of the offset correctio method. 5. CONCLUSIONS I this paper, a dc offset correctio method to improve log-duratio magetic flux harmoic measuremets i a rotatig coil sceario, has bee preseted. Prelimiary experimetal tests show the capability of the method of correctig the dc offset itroduced by the measuremet system ad givig a oticeable cotributio to the harmoic measuremets of the magetic flux. 6. REFERENCES [] A. Chao, M. Tiger, Hadbook of Accelerator Physics ad Egieerig, World Scietific Publishig, Lodo, d ed., 999. [] M. Buzio, Fabricatio ad calibratio of search coils, Proc. of CERN Accelerator School CAS 009: Specialised Course o Magets, Bruges, Jue 009, pp. 87-4, [] P. Arpaia, V. Iglese, G. Spiezia, Performace Improvemet of a DSP-Based Digital Itegrator for Magetic Measuremets at CERN, IEEE Trasactios o Istrumetatio ad Measuremet, vol. 58, o. 7, July 009, p.. [4] L. Walckiers, Magetic measuremet with coils ad wires, Proc. of CERN Accelerator School CAS 009: Specialised Course o Magets, Bruges, Jue 009, pp [5] J. Billa, L. Bottura, M. Buzio, G. D'Agelo, G. Defere, O. Dukel, P. Legrad, A. Rijllart, A. Siemko, P. Sievers, S. Schloss, L. Walckiers, "Twi rotatig coils for cold magetic measuremets of 5 m log LHC dipoles," IEEE Trasactios o Applied Supercoductivity, vol.0, N., March 000, pp [6] P. Arpaia, L. Bottura, L. Fiscarelli, L. Walckiers, Performace of a fast digital itegrator i o-field magetic measuremets for particle accelerators, AIP Review of Scietific Istrumets, N. 8, February 0.