A TWO-STAGE INDUCTIVE VOLTAGE DIVIDER FOR COAXIAL BRIDGES

Transcription

1 A TWO-STAGE IDUTIVE VOLTAGE DIVIDER FOR OAIAL BRIDGES G. A. Kyriazis, J. A. Moreno, J. Melcher 3 Inmetro, Dqe de axias, Brazil, gakyriazis@inmetro.gov.br EAM, Qerétaro, Mexico, jmoreno@cenam.mx 3 PTB, Braschweig, Germany, jergen.melcher@ptb.de Abstract: The traceability chain to derive the capacitance nit from the qantm Hall resistance comprises some coaxial bridges. These bridges employ a main two-stage indctive voltage divider to provide the voltage ratio needed. One sch divider has recently been constrcted and calibrated at Inmetro. The design techniqes responsible for the small ratio errors of the device are detailed. Keywords: indctive voltage dividers, coaxial bridges, traceability, garding, two-stage techniqes.. ITRODUTIO The main indctive voltage divider (IVD to be sed in coaxial ratio bridges [] shold be constrcted to provide an overall bridge ncertainty at : and 0: ratios of a few parts in 0 8. This reqires the se of special garding and two-stage techniqes typically adoptedd in the 0-00 khz range []. A similar IVD had been constrcted previosly dring the development of Inmetro s two terminal-pair coaxial capacitance bridge [3][]. This bridge has been in operation since 005. The IVD design details and calibration reslts had been reported in [5]. The new IVD discssed here was completely constrcted at Inmetro and presents mch smaller ratio errors than the previos one. We detail in section the design changes thatt we believe were responsible for the reslts obtained. This work benefitted from the technical expertise of entro acional de Metrología (EAM and Physikalish-Technische Bndesanstalt (PTB. The IVD calibration is discssed in section 3. The old IVD was replaced by the new one in the coaxial capacitance bridge and the overall bridge ncertainty was reevalated and reported in section. The conclsions are drawn in section 5.. DESIG AD OSTRUTIO A schematic diagram showing the arrangement of cores, windings and garding is shown in Fig.. The IVD operates with p to 00 V (at khz across the 0 and M0 taps. Therefore the first stage core comprises two plastic-encased spermalloy toroidal cores with 76. mm inner dia. x 0.6 mm oter dia. x 5. mm height and 0.05 mm tape thickness (Magnetics 0500F placed one on top of the other. (ote: the previos design described in [5] sed alminm-encased cores. A niform one-layer 0-trn (with 0.57 mm dia. magnet wire magnetizing winding covers the entire first stage core. This winding has three main taps for external connection whose leads are colored for easy identification, namely, 0 (red, M0 (ble and M (black, which are eqivalent to ratios 0,.0 and., respectively. The gard sorce for the divider winding is obtained by tapping the magnetizing winding at appropriate points (yellow. The gard sorce taps are eqally spaced arond the core (arranged in a star configration see Fig.. The gard voltages are 0.05 V, 0.5 V, 0.5 V.05 V (assming V inpt. Fig.. Schematic diagram showing the arrangement of cores, windings, and garding (the gronding condctors are not shown for clarity. The magnetizing winding is covered with kapton tape (an inslating tape with good electrical, mechanical and thermal properties and enclosed in a soldered toroidal shield made of 0. mm copper foil (Fig.. The shield is set at mid-tap potential, i.e. connected to the magnetizing winding tap corresponding to 0.55 ratio (see Fig.. The cross-sectional areaa of the second stage core was chosen so that it has a magnetic permeance of abot /3 that of the first stage core. Therefore two plastic-encased spermalloy toroidal cores with dimensions 76. mm inner dia. x 95.3 mm oter dia. x 9.5 mm height and 0.05 mm

2 tape thickness (Magnetics F were chosen. One core is placed on top of the shielded magnetizing winding and the other below it (Fig. 3. This symmetric arrangement was chosen to minimize leakage fields. (ote: both the first and the second stage cores had been enclosed together within the toroidal shield in the design described in [5]. tap. In this type of constrction each section has the same resistance and is eqally well copled to all other sections, ths balancing the mtal and leakage impedances. Fig.. Shielded magnetizing winding with gard sorce taps. Fig. 3. Shielded magnetizing winding with second stage cores (a second stage core is located below the assembly and cannot be seen. Fig. 5. A wire soldered to the middle of the oter condctor. Before arranging the cables in a rope, a colored wire is soldered as accrately as possible to the middle of the oter condctor of each coaxial cable (Fig. 5. The whole assembly is then inslated with glass-fiber tape and the separate wires are connected to the corresponding magnetizing winding taps (Fig. 6. olored wires are sed to ensre that the wire is being connected to the correct gard tap. We confirmed that mistakes here are common and always reslt in large IVD ratio errors. This garding method is an attempt to eqalize the admittances between each half of each gard and nearby condctors. The coaxial cable is GORE GS 659 (condctor size: 9 x 0.7 mm AWG (9/36, 0. mm ; condctor material: Ag, 78.5 mω/m; dielectric diameter: 0.8 mm; dielectric material: PTFE; screen details: braided screen from Ag AWG 38 (; jacket material: 0.5-mm PTFE; nominal diameter:.6 mm.. Fig.. Ratio winding (rope arrangement. The IVD ratio winding consists of a 0-trn rope of coaxial cables wond arond the core assembly whose ends are connected in series to create a 0-trn winding (Fig.. (ote: here lies another difference from the previos design: a rope arrangement of the cables had not been employed in [5]. The tapped terminals... 0 are broght ot from these interconnections (see Fig.. The centre condctor is tapped at ten points, which are eqivalent to ratios 0., 0., The oter shield of the cable is ct (and inslated at each Fig. 6. Separate wires connected to the magnetizing winding taps. The whole assembly is then inslated with kapton tape, isolated from mechanical vibrations (with 5 mm extrded polystyrene slabs fixed by two opposing inslating boards kept firm with for alminm rods and enclosed in a metal box with holes on its top panel for later penetration of the coaxial otpt sockets (Fig. 7. The method of bringing ot the taps to the coaxial connectors reqires consideration if the highest possible accracy is to be attained. The coaxial otpt sockets (BPO

3 connectors are fixed to a rigid inslating board placed above the IVD assembly (Fig. 8. They are inslated from the metal box. Stot condctors (.3 mm dia. magnet wire are taken from the socket oters for the IVD ratio winding, roting them close to the short tap connections to a point well within the volme of the box where they are joined together (see Fig. 7. This point is gronded to the metal box throgh an otpt socket. The electrical resistance between each socket oter and the metal box was measred to be less than 0.05 Ω. plgs of the two independent grond connections are not shown in the figre. Fig. 9. Main IVD final assembly. Fig. 7. The whole assembly is inslated from mechanical vibrations. The same arrangement for bringing ot the taps to the coaxial connectors is adopted for the IVD magnetizing winding leads. The joint point of the stot condctors is also gronded to the metal box throgh another otpt socket. The resistance between each socket oter and the metal box was measred to be less than Ω. The BPO connectors for the magnetizing winding are the three ones located in the right side of Fig. 8. See [] for more details on this gronding arrangement. Fig. 8. oaxial otpt sockets (BPO connectors. The metal box is made of.5 mm chromim-coated carbon steel and the box inner srface is covered with 0.79 mm mmetal sheets. The box panel has the following otpts: (a divider taps: 0 (twofold,,, 3,, 5, 6, 7, 8, 9, 0 (twofold, and (twofold, (b magnetizing winding taps: 0, M0 and M, and (c two independent grond connections (both the magnetizing winding and the ratio winding stot condctor joint points were always gronded to the metal box in the IVD calibration and capacitance bridge measrements see ref. [3]. The final assembly of the main IVD is shown in figre 9. The short-circiting 3. ALIBRATIO The IVD 0: ratio error was calibrated at Inmetro. The old IVD was replaced by the new one in the coaxial capacitance bridge (see [3][] for constrctional details of this bridge and the bridge was sed to compare 0 pf and 00 pf fsed-silica standard capacitors which had been previosly calibrated by BIPM with a relative ncertainty of parts in 0 8. With this method one can only measre the in-phase component of the complex ratio error. The calibration was performed at 0 V (across the 0 and M taps and at both khz and.59 khz. 3.. Measrement model The simplified scheme of the capacitance bridge is shown in Fig. 0. The main IVD operates with a voltage U across the 0 and taps for the : ratio or across the 0 and. taps for the 0: ratio. The voltage vale depends on the bridge ratio and the standard capacitor vale (Table I. The vale of ratio / depends on the bridge ratio and the voltage predivider ratios (Table II. The reslting dividing factors of the bridge main balance are (a 0.5/0.5 and β (b 0.5/0.5, where a and b are the settings of each six-decade main balance IVD. See [3] for predivider and balance IVD details. The nominal ratio of the main IVD is D / for the : ratio and D / for the 0: ratio. Here we want to determine the in-phase component of the complex ratio error ε from the known vales of capacitors (with nknown condctance G and (with nknown condctance G. is a pf fsed-silica standard capacitor. G and are the condctance and parasitic capacitance, respectively, of a T- network box (with connecting cables, measred with a commercial capacitance bridge. The ratio error is here expressed as a fraction of nit. In this case, the IVD ratio is expressed as a sm of the nominal ratio D and of the complex ratio error k jk (k and k are respectively the in-phase and qadratre components, U 0.-0 / U.-0 D ε D k jk ( The main balance is obtained when I I I I 0 ( B M

4 Fig. 0. Simplified scheme of the capacitance bridge. The balance eqation for the : ratio is ( ( β β (3 The dividing factors and β are obtained by balancing the bridge with the capacitors positioned as shown in Fig. 0, and and β are obtained by rearranging the cables so that the capacitors are in the reversed position. The complex ratio error of the main IVD is cancelled ot by this techniqe. It is interesting however to compte the complex ratio error of the main IVD for the : ratio, that is k G k ω ( ( β β ( β β This is typically done for qality control prposes. Table I. Total applied voltage U. (pf Bridge ratio U (V 0 : : 0 00 : : 000 : Table II. Vale of. Predivider ratio Bridge ratio 0: : 00 0: 0: 0 : : 0 : 0: Fig.. Bridge simplified scheme with cable modeling. ( The balance eqation for the 0: ratio is where t t ( g (5a t D k g k t k ( t β ( t k tan δ βg ( t ω (5b where ω is the anglar freqency and tan δ is the loss tangent of. Here it is neither possible nor necessary to se the aforementioned cabling reversal techniqe. The dividing factors and β can be expressed as R β β R β σ σ β where and β are the vales, R and R β are the resoltions and σ and σ β are the random deviations of the and β readings, respectively. eglecting the contribtion from k, and rearranging terms, the IVD ratio can be expressed as t where A (6 (7 ( β A (8 The vales of and in (5 inclde their drifts with time and the cable parasitic contribtions. We mst first correct the capacitance vales for the cable errors. A simplified scheme of the capacitance bridge with the connecting cables modeled as delta networks is shown in Fig.. As high qality cables are sed cable losses can be neglected here. L and are, respectively, the indctance and half the capacitance of the cable that connects to the main IVD (see Fig. 0. L 3 and 6 are, respectively, the indctance and half the capacitance of the cable that connects to the main IVD. The contribtion of (and 5 is not taken into accont since these capacitances are in parallel with the sorce. The contribtion of (and 8 is negligible when the bridge is balanced. L and 3 are, respectively, the indctance and one-forth the capacitance of the cable that connects to the bridge nll. L and 7 are, respectively, the indctance and one-forth the capacitance of the cable that connects to the bridge nll. HG and LG are the parasitic capacitances to grond of the high and low inpts

5 of, respectively. HG and LG are the capacitances to grond of the high and low inpts of, respectively. The cable relative error for is approximately ε R T ω [ L ( L ( ] where T is the total capacitance of (capacitor pls cables, HG HG and 3LG 3 LG. The cable relative error for is approximately ε R T ω HG 3LG [ L ( L ( ] 3 6HG 7LG (9 (0 where T is the total capacitance of (capacitor pls cables, 6HG 6 HG and 7LG 7 LG. Hence, ( ε R d ( ε R d ( where and are the capacitance vales reported in the calibration certificate, ε R and ε R are the relative corrections of the cables connected to each capacitor, and d and d are the capacitor drifts in the period between the date the capacitor calibration certificates were issed by BIPM and the date of the IVD calibration. We regard both the standard capacitor and its associated cable as a whole standard. The vale of is therefore inserted in the spreadsheet as ( ε R and the vale of is inserted in the spreadsheet as ( ε R. Since the main ncertainty contribtions to the cable error are associated with the parasitic indctances and capacitances of the capacitor and cable, we may neglect the ncertainty contribtion associated with the capacitor vales and write δ δ d d ( where δ and δ are the absolte corrections of the cable errors (in F, that is [ L ( HG L ( 3LG ] [ L ( L ( ] δ (3a ω δ (3b ω 3 6HG 7LG Here 0 pf and 00 pf, and it is assmed that their contribtions to the ncertainty associated with δ and δ are negligible. 3.. Measrement ncertainty It is important to observe that the variables and are strongly correlated as the capacitors were calibrated at BIPM with the same system. Therefore, ( 0 (, 0 (, The sqared standard ncertainty associated with the IVD ratio is then [6] ( t where, ( A ( ( ( ( A ( ( ( δ ( d ( ( ( δ ( d ( δ ω ( L ω ( HG ω ( 3LG ( δ ω ( L3 ω ( 6HG ω ( ( A ( ( ( A( A (, ( (5 [ ] ( A ( ( ( β β ( ( β ( ( ( ( R ( σ ( β ( β ( Rβ ( σβ (, (, ( ( 7LG, since a correlation ( 3.3. IVD calibration reslts ω ω ρ is assmed here. ( L ( L The in-phase 0: ratio errors k and their expanded ncertainties U(k evalated respectively from (7 and (5 are listed in Table III. Table IV lists the in-phase and qadratre : ratio errors evalated from (. Table III. In-phase 0: ratio errors (new IVD. Freqency (Hz k U(k Table IV. In-phase and qad : ratio errors (new IVD. Freqency (Hz k k The old IVD whose constrction was reported in [5] was calibrated again sing the same method described here. The reader shold compare the reslts listed in Table V and VI with those for the new IVD. Table V. In-phase 0: ratio errors (old IVD. Freqency (Hz k U(k Table VI. In-phase and qad : ratio errors (old IVD. Freqency (Hz k k The ratio errors of the new IVD are indeed mch smaller.

6 . OAIAL APAITAE BRIDGE The new IVD was installed in the two terminal-pair coaxial capacitance bridge and the ncertainty obtained in capacitance calibration was assessed again here. This bridge has been sed at Inmetro for calibrating stable standard capacitors since its constrction in 005. An experiment was made recently to evalate the consistency of the measrement reslts obtained with this bridge. onsider three 0 pf fsed-silica standard capacitors labeled here for convenience as A, B, and. apacitor A is traceable to BIPM. Firstly, capacitor B was calibrated by comparing it with known capacitor A. Secondly, capacitor was similarly calibrated and the (compted difference between B and vales was recorded. apacitor B (assming it to be nknown was then calibrated by comparing it with the (now known capacitor and the (measred difference between B and vales was also recorded. All measrement reslts were corrected for cable errors. The compted and measred differences between B and vales differed by at.59 khz when the new IVD was installed in the bridge. ontrast this with the figre obtained when the old IVD was installed in the bridge (or even with the figre reported earlier in [3]. This is a bridge systematic error which is detected when comparing several standards of same nominal vale for consistency in the reslts. This error contribtes to the overall ncertainty of the bridge at : ratio. So, this ncertainty contribtion was redced by one order of magnitde as a reslt of the redced ratio errors presented by the new IVD. Table VII. Uncertainty bdget (0 pf.59 khz. Qantity Standard ncertainty Sensitivity coefficient Eval. Type ( pf B pf A β pf A 0 8 pf B pf B pf B ( ε R 0 8 pf B ( pf omb. Error ( pf B ( pf omb. (6 R K pf B Biannal pf A Drift (7 ( pf omb. ( Relative combined standard ncertainty reported in the BIPM calibration certificate for (a 0 pf capacitor. ( Uncertainty contribtion associated with the correction for the cable errors. (3 ombined standard ncertainty associated with the difference between the capacitances of the standards being compared (see text. ( Systematic error that is detected when comparing several standards for consistency in the reslts. (5 ombined standard ncertainty associated with withot taking into accont the ncertainty contribtions associated with R K-90 and the reference standard biannal drift. is a 0 pf capacitor. (6 Standard ncertainty associated with the recommended vale of R K-90. (7 Drift evalated by fitting a straight line to data reported in BIPM calibration certificates in the last six years. (8 ombined standard ncertainty associated with by taking into accont all known ncertainty contribtions. Table VII shows the ncertainty bdget for the calibration at : ratio and at.59 khz of a stable 0 pf fsed-silica standard capacitor ( from a similar capacitor ( traceable to BIPM. The combined relative standard ncertainty associated with the difference between the capacitance vales of the standards being compared ( is less than one part in 0 8. The ncertainty contribtion de to the capacitance bridge is therefore negligible compared to other contribtions sch as the relative ncertainty reported in the BIPM certificate, the reference standard drift, and the ncertainty associated with the recommended vale of R K-90 (von Klitzing constant. The major ncertainty contribtions are now the / ratio and the stability of the ( readings. Table VIII. Uncertainty bdget (00 pf.59 khz. Qantity Standard ncertainty Sensitivity coefficient Eval. Type ( pf 0 B pf A k B ( ε R 0 8 pf B ( pf omb. ( R K pf B Biannal pf A Drift (5 ( pf omb. ( Relative combined standard ncertainty reported in the BIPM calibration certificate for (a 0 pf capacitor. ( Uncertainty contribtion associated with the correction for the cable errors. (3 ombined standard ncertainty associated with withot taking into accont the ncertainty contribtions associated with R K-90 and the reference standard biannal drift. is a 00 pf capacitor. ( Standard ncertainty associated with the recommended vale of R K-90. (5 Drift evalated by fitting a straight line to data reported in BIPM calibration certificates in the last six years. (6 ombined standard ncertainty associated with by taking into accont all known ncertainty contribtions. Table VIII shows the ncertainty bdget for the calibration at 0: ratio and at.59 khz of a stable 00 pf fsed-silica standard capacitor ( from a similar 0 pf capacitor ( traceable to BIPM. The combined relative standard ncertainty associated with the calibration reslt (withot the ncertainty contribtions associated with R K-90 and with the reference standard drift is The major contribtion to the overall bridge ncertainty at the 0: ratio is that associated with the in-phase component of the IVD ratio error. As mentioned in the introdction, the main IVD to be sed in coaxial ratio bridges shold be constrcted to provide an overall bridge ncertainty at : and 0: ratios of a few parts in 0 8. In order to achieve this for the 0: ratio it is necessary to redce the ncertainty associated with the IVD in-phase ratio error by one order of magnitde. This demands the constrction of a special system for calibrating the IVD 0: ratio with an ncertainty of a few parts in 0 9. ote: Qantities not listed in Tables VII and VIII were fond to have negligible ncertainty contribtions.

7 5. OLUSIO The constrctional details of the new IVD recently bilt at Inmetro were presented along with the design changes implemented. The design changes are: (a plastic-encased cores are sed as first stage cores, (b only the magnetizing winding and the first stage cores are copper shielded and (c a rope arrangement is employed for the coaxial cables in the ratio winding. The method sed to calibrate the IVD ratio error was also described in detail. The in-phase 0: ratio error was determined from known vales of two stable decadic standard capacitors. It was confirmed that the ratio errors of the new IVD are mch smaller than those reported previosly for another IVD. Upon installing the new IVD in the coaxial capacitance bridge, the major contribtions to the overall ncertainty of the : ratio bridge are those associated with the predivider ratio and with the stability of the readings. The major contribtion at 0: ratio is that associated with the in-phase component of the IVD ratio error. A special system for calibrating the IVD 0: ratio with an ncertainty of a few parts in 0 9 is reqired if one needs to achieve an overall ncertainty of parts in 0 8 with the 0: ratio bridge. REFEREES [] B. P. Kibble and G. H. Rayner, oaxial A Bridges, Adam Hilger Ltd., 98. [] D. Homan and T. Zapf, Two stage, garded indctive voltage divider for se at 00 khz, ISA Trans., Vol. 9, no. 3, pp. 0-09, 970. [3] G.A. Kyriazis, R.T.B. Vasconcellos, L.M. Ogino, J. Melcher and J. A. Moreno, Design and constrction of a two terminal-pair coaxial capacitance bridge, in Proc. of the VI SEMETRO, pp. 57-6, Rio de Janeiro, 005. [] G. A. Kyriazis, R. T. B. Vasconcellos, L. M. Ogino, J. Melcher and J. A. Moreno, A two terminal-pair coaxial capacitance bridge constrcted at Inmetro, in PEM Digest, pp. 5-53, Trin, 006. [5] G.A. Kyriazis, J. Melcher and J.A. Moreno, A two-stage, garded indctive voltage divider for se in coaxial bridges employed in the derivation of the capacitance nit from qantized Hall resistance, in PEM Digest, pp. 3-3, London, 00. [6] BIPM, IE, IF, ISO, IUPA, IUPAP and OIML, Gide to the Expression of Uncertainty in Measrement, Geneva, Switzerland: Int. Org. Standardization, 995.