ELECTROMAGNETIC MEASUREMENTS

Calibration of IVDs at frequencies up to 1 MHz by permuting capacitors

S.A.Awan, B.P.l<ibble and I.A.Robinson

Abstract: A dcvicc liiis been constriiclcd wliicli permutes clcvcii nominally equiil 50pF capacitors i n a bridge lo calibrate tl ic 101 inid 1 : l O ralios of induclive voltage dividers (IVDs) al frequencies up to I MHz. A coinpael design, wliicli is iiiiportanl for high frcqiiciicy nicastirenicnls, was implcniented using printed circiiil boiirds and ceramic N P O dielectric capacitors. The capacilors are individually shielded to reduce errors l'rom stray cqxicilances. Comparisons inadc with rcsnlts l'roin an cxisting NPL inelhod of calilmiling lVDs at frcqucncics tip to 10OkHz and with irestilts li-om a rccciitly cleveloped high-frequency Toui- tcriniixil-paii- bridge show tluit bcttcr thaii I O parls-per-million unccrlainly h a s bccn allaincd a l I MHz.

1 Introduction

A1 prcsciit, tlicrc is ii lack of trace;ihility for many coinnicr- cia1 inslrumcnls that claim lo be ahle lo nicasurc imped- ance iip LO a few MHz with an nccuracy of hctlci- tlim 0.5'%>. '1'0 bridge this traceability gip hctwccn the IOW li-cqneiicy region (typically l - lOkH~) and i l i c h i g h rrctpclicy region or up io I MHz, a numbcr ofconiponcnls have bccn fabricalecl from wliicli 11 high-l'reqiiency Ibur terniinal-pair Ixiclgc c i i i i he ;isscmhlcd, wliicli is iiii :ilterna- live method 10 tliiit iised in 11, 21. These coiiipoiients include deciidc vliliic re. nice ;ind cqxicitancc standiirds, high li.cqiiciicy inductivc voltage dividers (IVDs), isolation transforiners, and 21 'periniiling capacitors' dcvicc (PCU). The PCD is iiccdcd to iinplcmcnl ii well known lechiiiquc of pcrmutiiig ((11. transfcrriiig) nominally cqtiiil value capac- ilors hetwecn Llic two arms of a bridge, thcrchy deterniiii- ing the error of llic I V D at a given setting and cxcitiition frequency 13, 41. For acciiraic dctcl-mination of tlic li.cquency dcpcndcnce 01' l l ic impcdiincc s landmls , id1 sources of c r r ~ r s in ii bridge system must bc invcsligaled so l1i;it tlicsc ciin citlicr he cliiiiinatcd or, if1Ii;it is not possible, included iii tl ic i i i i linty hidget. Tlircc 01' the main sourccs d c r r o r iii iiii impcdaiicc hridgc arc associaled with llic st;indards themsclvcs, llic high lioqucncy IVDs aiid the conncclion cables. '1.0 charactcrisc lhc st;indards ;scur;itely, tlic crrors introduccd h y tlic lVDs and thc cahlcs tnusl he rcduccd to a surficicnt lcvcl to inccl the desired ovc1..11I accul-acy. The crroi- coiiirihution koin cahlcs is iiiinimiscd by using short lengths iiiid by applying ealculalcd corrcc- lions using tlicir nie~isurcd pinimclcrs [4]. The crroi- of tlic high f'rcqucncy IVDs ciiii be iiie;isurcd by the permtiling capacitors method, adapted Iicrc for higher l'rcqiicncics. A

cross-scctiiiiiiil view or tlic basic concept is illustralcd in Fig. I

l ' l i c eleven capacitors of 5opF iioiiiinal value were inade by connccling, in scrics, two 100pF capiciiors. Their values WCI-c closely nxitclicd by selecting tlicni koni a large hatch. There ai-c several bcncfiis from tising capacitors having ccrmiic NPO a s llie diclcctric. These include a sma l l tcm- pcralurc coefficient of approximately (0 i 30) x I O '/K, a dissipalioii fiictor of only about 7 x I O and negligible capacilance Iiystcrcsis from lcmperatiirc cycling. Their min- iiiiiil residual self-inductance duc to their small physical size (3.2mm x I.6mm x 0.5nim) inakes l l icin suitable Tor use at l'rcquencics tip to at lciist 1 MHz [5]. An error which can occur in this incthod ;irises from the voltage dependence oC l l ic capacitors as iliey arc pcriiiuted between tlic high and low vollagc arms of [lie hridgc. However, iiieiistirements at various rrcqiieiicics showed negligible voliage dependence ol' thc ceramic NPO dielcclric capacitors.

2 Permuting capacitors device

Thc eleven capacitors arc connected lo a central point (the detector IJO~I, D) in a circulu configuration, similar to spokes on a wheel. There is considewhlc benefit to he gaincd from this c i rcdw gcotneirical consiruction in that it

I 'J l

ensures the near equivalcncc of each capacitor by making their parasitic impedances nearly idcntical. Each piiil- oli IOOpF capacilancc clcments tire conncctcd in scsies hy a small loop of thin llexihlc copper roil (having low sell'- inductiancc) between them 10 ininiiiiise mechanical stress. Each 01' the clcveii segments on [ l ie printed circuit hoiard (PCB) has two SMB sockets mounted on one side which Corm an inner and tan outer circle olconnectors. Any oli tlic cap:icitoss can he connccted iii parallel b y inserting i ts cos- responding shorting plug ( t i s shown iii Fig. I) in Ihc outer circle of conncctoi-s. This eliminates tlic nsc 01' cables, which at high frequencies would limit the atl;iinahlc ~ICCII-

racy. To complclc the pasallcl connection of ten capacitors (for I I IO: I or ii I ;IO ratio). thcrc ih a thin copper platc (drawn a s hold line in Fig. I) on the other side o f the bozard which is connected to the shields of' all the clcveii outer cir- cle of connectors. Thcrcl'ore. b y shorting appropriate SM B sockets, the capacitors can he pcrmutctl betwccn the high and IOW volkige ariiis OS the tnelisiirciiient hridgc. The inner circle of connectors have their shields connected to the ovcrall device shield, to wliicli tlic detector shicld is also connected. There is a photograph or tlic devicc iii [6]. The circuit board i s thermally coupled LO, yet electrically iso- lated lirom, a copper platc, whose temperature i s controlled by hcating clenients attached to the platc. T h e hcating i s rcgulatcd by an electronic temperature-colitrolling circuit.

The valuc of the ciipacitoss to be used in a permuting device depends 011 two inaiii Factors. l h t , the impedance of the permuting capacitors i l l high frequencies should he much larger than the output iinpcdancc o l the IVD, so that loading errors are minimised. hiid secondly, by closcly matching capacitances, tlie value ol' the injection capacitor tiscd to halancc the bridge is kcpi small. This prevents load- ing errors and gives sufficicnt resolution rrom the injcction I V D (discussed in the next Sirtion).

3 Calibration bridge

The bridge which calibriitcs the test IVI) by p " m n g capacitors i s shown i n Fig. 2. I t is hdanccd by injecting a small current via a capacitor oi' admillance A Y connccled to thc output of an IVI), which is connccted to the same potential tcrininals tis the I V D undcs test. Since the dissipa- tion hctors of tlic capacitors iirc sniall, ii quadraturc biil- ancing circuit wias unnecessary. 'l'his siinplilicd hrklge design resulted in bcttcr iiccur;icy at higlicr l'rcquencics. I f the IVI) being calibrated is of two-stage consiraiction, i l s magnetising winding must be energised as shown iii Fig. 2.

njection IVD

The bridge iilso requires a Wagncr halancing capacitor, C,, and current equalisers [4]. Por a ratio .U, the balance cquiitions obtained. by permuting (r + s) capacitors in turn l'rom one arm of the hridgc to tlic other, arc [3. 41:

I94

where 1: i s the it11 v;ilue ofthe adiiiitlance being permuted. I n OIIL' work r = I iintl s 7 10. The I I mid k m~lucs arc Llic settings of tlic tcst and in.jection IVDs, rcspectivcly. Eqii. I siniplilies lo:

where K is the average viiluc tlic injection IVD settings. and t is t l ie nitio of t l ie injection admillance A Y to tlic average admiltaiicc of tlic elcvcn capacitors at I k l Iz. Sincc tlic calibration is carsicd out at only oiic l'requcncy at ii time, the variation in valuc of the individual c;ipacitors with lircquency is ininiaterial. In addition, the lrcqiicncy depentl- ciice of k and consequently i. which change slightly a s the permuting capacitors change value with rrcquency, has only ii sccond-order c k c t in cqn. 2, and does not contrih- utc signi lican t uncerlii in ty.

4 Results and discussion

The fi.equcncy dcpendcnce 01' IV1>/02 set to 1O:l (or 17 = 0.90909) ratio niCiisiired hy l l i c pel-milling capacitors inclhod i s sliowii in Fig. 3. Thc solid line in tlie graph is a l m squares lit, ol the form w) = (I i h i + c/?, to the data. I t is clear I'roni tlic fitted pal'aincters that the ratio crroi. g/) ol' the 1VD mostly sliows ii qiiadratic lircquency dcpcnd- cnce, although sonic lincar frequency depeiidcncc is also present. In iiddition, the results from tlic PCU wei-e coni- pared with iiieasurcnients using ii iicw liigli-frcqticncy hridgc, which has rcccntly hccn developed and its details will he snhiiiitlcd for publication clsewhcrc, are also sliowii.

0 200 400 600 800 io00 frequency, kHr

iI = U.111I7Y - ii.on2'1 I , L~ mi136 ii.nnz , ~ ~ (2.4 * 2.2) x IO 6

0 = Iligl~-rrci~oc.cy hll, IQC

In placc of tlic permuting capacitors, twn gas-dielectric capacitors oli iioiiiiiial values 1 nF md l00pF were used in the high-fi-cquency four tcsminalpeir bsidge. Tlii: main bciiclits o f using gas-diclcctric capacitors is tliiat their frc- quency depcndcnce can be calculalcd from ii knowledge or their resonance frcqiiency (71, and that their voltage cocl'fi- cieiit is qnite sniall, hoth oli which makes thein vcsy iiscliul l'or high fscqiicncy work. It is iiitcresting to iiote Csoin

< - ( x . 2 * 3 1 ) ~ 1 n " 9 ~ 1t:"I SI) ~ 0.52 W = pcmuling cqwcilom

A-NI 'L

I' ~~ O.'J477'> SI1 =~ 11,4841

Fig. 3 that two very dillbrcnl methods give similar I'rc- quency dependence. Mowcvcr, the cxiict Ibrm of llic frc- qucncy dependence is difficult to asccrpctin due lo the combincd sktndai-il iinccrlainlics in the two mcasurctncnls. At I MHz thcsc arc cstiinatcd lo hc alniost t I O parts-per- niillioii (ppm) ior 21 level 01' conlidcncc o f approximalcly OS%, with it covemgc factor o f 2. This is ii fiiclor o f three improvemenl on l l i e slep-up inelhod described iii 181. Also shown in Fig. 3 arc the results from i in existing NPIL standard IVD calihralion appitrattts [9] tit 50kHz and IOOkl~lz. Although the agreernent between the three meth- ods is rcasonably good al thcsc li.cqiicncics, the uiiccr(ain(y o i l hc NPI, standiird calibration result a l IOOkl I / is givco as *9.2pptn, wliicli is approximately iiii order 01' magnitude higher than lhc two foriner nictliods.

20

It sccins likely tlial Ilierc arc snxill Type R unccrlainty con- tributions in one or both 01' (lie measurement ciiniils, iind thiit fitrlhcr work ;rimed at rcducing llicsc coii ld laid lo iiii even lower uncerliiinty iit I Mtlz. 01' perhiips ii I'ew ppin.

5 Conclusions

A conipacl dcvicc hiiscd 011 ii plinied circuit board 1'or per- muting ciipacilors l i i i s been miidc lo calihrak lVDs scl 10 IO: I o r I: IO ratios k i t ~rcqi~ci~cics lip l o I Mliz . Comparison oi l l ic tneiisureinents between the permuting c;ip;icitors iiietliod ;ind ii new higli-li.cqticncy, Ihur kriiiinal-pair hridgc rcsitllcd in hcltcr lliiin + I O pptn uncerlaitity iit I M l l z . I1 may bc possihlc lo liirlhcr iiiipi-ovc LIicsc Incas- urcinciils to a Ibw ppm nnccl-kiinly by rcducing Ihc c1'1'ccl 01' any remaining Type I3 contributions. I n addition good agrceinciit was also [ibscrvctl will1 an existing NPI, sl;nid- iird IVII calibration sct--iip a t 5I)kHz ;ind IllOktlz.

6 Acknowledgments

The ittithors wortld like to thank I<ohin Ilullct- ;ind I'ravin Patel Ibr discussions on pi-intcd circuit hoard design, and Slcphcu Bryant and .lanet I k l l i s s lor IVD calibrations using l l i c slandard NPL. mclhod. This work was supporlcd witliiii l l ic Technical I'rograiiimc 01' Ihe N;ition;tl Mcasurc- iiient System Policy IJnil of the I)cparlnicnl 111' Tfiidc tind Induslry, UI<.

7 References

I SIJZIJUI, K.: ',\ iicw i i i i ivc i ihriilioii Inuhod h r Ibur-laniinii l- imir i,,.yirl,,,,, ,b/clir., IWI, 40, (2 ) . piiir ixliiiiitiiiiw s l : ~ ~ l m l s ' , I