construction, measurement, shimming, and performance of

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 63, NO. 12, DECEMBER 2014 3027

Construction, Measurement, Shimming, andPerformance of the NIST-4 Magnet System

Frank Seifert, Alireza Panna, Shisong Li, Student Member, IEEE, Bing Han, Leon Chao, Austin Cao,Darine Haddad, Member, IEEE, Heeju Choi, Member, IEEE, Lori Haley, and Stephan Schlamminger, Member, IEEE

Abstract— The magnet system is one of the key elements ofa watt balance. For the new watt balance currently under con-struction at the National Institute of Standards and Technology, apermanent magnet system was chosen. We describe the detailedconstruction of the magnet system, first measurements of thefield profile, and shimming techniques that were used to achievea flat field profile. The relative change of the radial magnetic fluxdensity is <10−4 over a range of 5 cm. We further characterizethe most important aspects of the magnet and give order ofmagnitude estimates for several systematic effects that originatefrom the magnet system.

Index Terms— Electromagnetic measurements, magneticcircuits, measurement standards, measurement units, permanentmagnets.

I. INTRODUCTION

AREDEFINITION of the International System of Units,the SI, is impending and might occur as early as 2018.

A system of seven reference constants will replace the sevenbase units that form the present foundation of our unitsystem [1]. Specifically in the context of mass metrology,the base unit kilogram will be replaced by a fixed valueof the Planck constant. With this transition, the InternationalPrototype of the Kilogram, will lose its status as being the onlyweight on Earth, whose mass is known with zero uncertainty.In the future, mass will be realized from a fixed value of thePlanck constant by various means. A promising apparatus torealize mass at the kilogram level is the watt balance [2], [3].Watt balances have a long history at the National Institute ofStandards and Technology (NIST). In 1980, NIST’s first wattbalance was designed to realize the absolute ampere and thenlater to measure the Planck constant [4]. In the past three anda half decades, several measurements of the Planck constanthave been published, the most recent in 2014 [5]. Currently,a new watt balance, NIST-4, is being designed and built. Thiswatt balance will be used to realize the unit of mass in theUnited States.

A watt balance is a force transducer that can be calibratedin absolute terms using voltage, resistance, frequency, and

Manuscript received January 27, 2014; revised April 28, 2014; acceptedMay 1, 2014. Date of publication May 9, 2014; date of current versionNovember 6, 2014. The Associate Editor coordinating the review processwas Thomas Lipe.

F. Seifert, A. Panna, S. Li, L. Chao, A. Cao, D. Haddad, andS. Schlamminger are with the National Institute of Standards and Technology,Gaithersburg, MD 20899 USA (e-mail: [email protected]).

B. Han is with the National Institute of Metrology, Beijing 100013, China.H. Choi and L. Haley are with Electron Energy Corporation, Landisville,

PA 17538 USA.Color versions of one or more of the figures in this paper are available

online at http://ieeexplore.ieee.org.Digital Object Identifier 10.1109/TIM.2014.2323138

length reference standards, i.e., without dead weights. Theinstrument is used in two modes, typically referred to as forcemode and velocity mode. In force mode, the gravitationalforce of a mass, mg, is compensated by an electromagneticforce. The electromagnetic force is produced by a currentin a coil that is immersed in a radial magnetic field. Theequation governing the force mode is mg = IBl, where Iis the current in the coil, l the wire length of the coil, and Bthe magnetic flux density of the field at the coil position. Thelocal acceleration g and the current I can be measured usingdedicated instruments. The flux integral Bl can be calibratedto very high precision in velocity mode. The coil is movedthrough the magnetic field with constant velocity v yieldingan induced voltage, U = v Bl. The flux integral is inferredby dividing the voltage by the velocity. Using this calibratedvalue of Bl in the equation of the force mode, the value forthe mass can be obtained by

m = U I

gv. (1)

Equation (1) connects mass to electrical quantities: 1) cur-rent and 2) voltage. The electrical quantities can be linked tothe Planck constant and two frequencies using the Josephsoneffect and the quantum Hall effect. This connection is beyondthe scope of this paper. A review can be found in [2].

The considerations that led to the design of the permanentmagnet system described here are given in [6]. While thefindings in [6] were based on simulations and theoretical cal-culations, this paper presents measurements that were made onthe real magnet system. We describe in detail the constructionof the magnet system and focus on the implications for theperformance of NIST-4.

II. BASIC DESIGN

The design of the NIST-4 magnet system was inspiredby a magnet design put forward by the BIPM watt balancegroup [7]. In our design, shown in Fig. 1, two Sm2Co17 ringsare opposing each other and their magnetic flux is guided bylow-carbon steel, also referred to as mild or soft steel, througha cylindrical air gap. The gap has a width of 3 cm and is15 cm long. The inner 10 cm of the gap is called the precisionair gap and it is desired to have a very uniform field in thecentral 8 cm of this precision air gap. Short of 12 access holesin each top and bottom, the gap is entirely enclosed by iron.

To insert the coil into the air gap, the magnet can be splitopen such that the top two thirds of the magnet separate fromthe bottom third. CAD drawings of the magnet and the splitter

0018-9456 © 2014 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

3028 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 63, NO. 12, DECEMBER 2014

Fig. 1. Left: cross-sectional view of the magnet system. Assembly exhibitsazimuthal and up–down symmetry. Gray parts are made from AISI 1021 steeland the hatched parts from Sm2Co17. Arrows: direction of magnetization.A total of eight large components are required to build the magnet system.Components are indicated by the encircled numbers. 1 = upper yoke cap.2 = outer yoke. 3 = lower yoke cap. 4 = upper Sm2Co17 ring. 5 = upperinner yoke. 6 = middle inner yoke. 7 = lower inner yoke. 8 = lower Sm2Co17ring. Circles in the precision air gap indicate the current in the coil. Right:Segmentation of the Sm2Co17 rings.

Fig. 2. Left: rendering of the magnet in the magnet-splitter with the magnetin the open state. Right: technical drawing of the magnet in the magnet-splitterin the closed state. To install the magnet in the splitter, the magnet is cranedonto the base plate. Then, the splitter can be slipped over the magnet usinga crane. Finally, the middle ring is fastened to the magnet using four anglebrackets in the middle and 16 bolts through the lower ring.

are shown in Fig. 2. A cross-sectional view of the basic designof the magnet system is shown in Fig. 1. The eight basiccomponents of the magnet are indicated by encircled numbers.We refer to components 2 and 6 as the outer yoke and inneryoke, respectively.

While NIST was responsible for the schematic designof the magnet, the detailed design and manufacturing wascontracted to Electron Energy Corporation (EEC).1 During themanufacturing process, few changes were made to improvethe performance of the magnet. One such change pertains tothe grade of the low-carbon steel used to produce the yokeparts. While in [6] the parts were identified to be made fromA36, instead AISI 1021 steel was used to make the parts. Thischange was made because a large ingot of AISI 1021 could bepurchased that allowed building all yoke parts from a singlecasting. Using raw material from one cast, a better homo-geneity of the magnetic properties can be ensured in the final

1Certain commercial equipment, instruments, or materials are identified inthis paper to specify the experimental procedure adequately. Such identifica-tion is not intended to imply recommendation or endorsement by the NationalInstitute of Standards and Technology, nor is it intended to imply that thematerials or equipment identified are necessarily the best available for thepurpose.

Fig. 3. Exploded view of the magnet. The eight major components shown inthe cross-sectional view in Fig. 1 are labeled on the right and additionalhardware is labeled on the left. Circled numbers: numbers in the cross-sectional drawing. The purpose of the centering sleeves is to center the inneryokes and the magnet rings on the yoke caps. Dowel pins ensure that themagnet only opens in the vertical direction. The stainless steel bands constrainthe magnets in the radial direction.

product. Both alloys are low-carbon steels, i.e., < 0.3% carbonby weight. The weight fraction of the carbon content of A36steel is on average 0.05% higher than that of AISI 1021. Otherthan the improved homogeneity of the material, this change isinsignificant for the performance of the magnetic circuit.

In the final design, shown in Fig. 3, two stainless steelsleeves were added to center the Sm2Co17 and the inneryokes. Also, two stainless steel bands around the Sm2Co17magnet rings were added to aid the assembly process.In addition, dowel pins made from low-carbon steel allow usto reproducibly open and close the magnet.

III. MATERIAL PROPERTIES

Three different materials were used in constructing thepermanent magnet system: 1) Sm2Co17; 2) low-carbon

SEIFERT et al.: CONSTRUCTION, MEASUREMENT, SHIMMING, AND PERFORMANCE OF THE NIST-4 MAGNET SYSTEM 3029

Fig. 4. Measured demagnetization curve on a Sm2Co17 sample. The samplewas measured at 26 °C.

steel 1021; and 3) stainless steel. The stainless steel partswere annealed to reduce the relative magnetic permeability tonear unity and are therefore irrelevant for the magnetic circuit.Hence, the stainless parts are not considered any further.

A. Permanent Magnet—Sm2Co17

Two Sm2Co17 rings, with a combined mass of 91 kg,form the active magnetic material. Because it requires a lotof power and a large fixture to magnetize one ring, eachring was segmented to 40 pieces (Fig. 1). Each piece wasindividually magnetized. The segmentation was carried out inthree concentric rings comprised of 9, 13, and 18 segmentseach. Each of the largest segments in the outer ring has avolume of 138.6 cm3. The Sm2Co17 rings had to be assembledwith the segments fully magnetized. To facilitate this assemblyprocess and to keep the repulsive forces between individualsegments under control, the rings were assembled on the inneryoke pieces using vacuum compatible epoxy. In addition, astainless steel band around the ring, as shown in Fig. 3,contains the Sm2Co17 segments in the radial direction.

To verify the magnetic properties of the Sm2Co17, fivecylindrical test specimens (10 mm diameter and 10 mm height)were fabricated in addition to the 80 segments. The magneti-zation curve of these samples were measured at EEC. Fig. 4shows the measurement of one such sample. This sample hada remanent flux density of 1.08 T and a maximum energyproduct of (BH )max = 224.7 kJ/m3. Of the five samples tested,the remanence values were within 0.2% and the maximumenergy density within 0.6% of each other.

For each of the 80 segments, the total flux was measured.After all measurements were obtained and recorded, a positionfor each segment was chosen to ensure uniform magnetizationin the azimuthal direction and between the two rings. Afterassembly, the total flux values of the two ring magnet assem-blies were measured and found to be within 0.2% of eachother.

B. Yoke—1021 Steel

The yoke of the magnet is made from AISI 1021 carbonsteel. To verify the composition, five samples were taken fromthe material and a chemical analysis was performed usingatom emission spectroscopy. All samples conformed to the

steel grade 1021. In the five samples, the carbon fractionvaried from 0.20% to 0.23% and the manganese fraction from0.87% to 0.88%. Phosphorus and sulfur had a relative weightof 0.013% and 0.012%, respectively. The yoke parts wereannealed after machining by heating to 850 °C for at least 4 hfollowed by a slow cool down. The outside parts of the yokewere nickel coated to prevent corrosion. The inside parts andthe surfaces that are relevant for the magnetic circuit were notnickel coated. Instead, the surfaces were coated with a smallamount of vacuum compatible oil (Krytox 1506) to preventoxidation.

The magnetic properties of the low-carbon steel wereinvestigated using two toroidal samples made from the sameingot as the magnet yoke. After machining, one sample wasannealed using the same recipe as the yoke parts, the othersample was not annealed after machining. The results fromthe annealed samples are relevant for the NIST-4 magnetsystem. However, the results of the non-annealed sampleserve as a reference and worst case scenario. On each toroid,two sets of windings were placed: 1) an excitation windingand 2) a pick-up winding. Each winding had N1 = N2 =200 turns. The toroidal cores had a rectangular cross sectionwith inner and outer radii of ri and ro, respectively. Eachtoroid had slightly different dimensions. The mean radius,rm = (1/2)(ri +ro), of the annealed sample was 38.0 mm andthat of the not annealed sample was 30.2 mm. In the first case,the cross-sectional area was A = 5.73 × 10−5 m2 and in thesecond case, 6.09 × 10−5 m2, respectively. Sinusoidal currentwith a frequency of 0.4 Hz was sent through the excitationwinding and the induced voltage, V (t), was measured acrossthe pick-up winding. The current in the excitation coil wasmeasured as a voltage drop across a series 1 � resistor. Themagnetic field Hb(t) generated by the current in the excitationwinding is calculated using Ampere’s law

Hb(t) = N1i(t)

2πrm. (2)

The derivative of the total flux, which we assume to beuniformly distributed and normal to the cross section of thetoroid is

dB

dt= − V (t)

N2 A. (3)

The magnetic flux density is found by integrating (3), wherethe constant of integration is chosen such that

∫B(t)dt = 0

over one cycle. The relative permeability μr and differentialpermeability μd of the yoke can be found as a function of themagnetizing field, from the hysteresis curves using

μr = 1

μ0

B

Hand μd = 1

μ0

dB

dH. (4)

Five sets of measurements were taken for each sample. Aftereach set, the magnetized core was degaussed by subjectingit to a damped AC field, with an amplitude higher than Hsatand gradually reducing the amplitude to zero. Because of thelow-excitation frequency, the magnetic measurements can beconsidered as pseudostatic, allowing us to neglect eddy-currenteffects on these measurements.


Fig. 5. One set of B–H measurements for the annealed sample. A totalof 10 sets, five for the annealed sample and five for the nonannealed samplewere taken. Thick line: normal hysteresis curve.

Fig. 6. Differential (dashed lines) and relative (solid lines) permeability ofthe annealed (circles) and nonannealed sample (squares). The data points areobtained from five sets shown in Fig. 5. Vertical dotted lines: magnetic field atwhich the iron parts adjacent to the coil operated. Vertical error bars: standarddeviation of the five sets of measurements that were taken for each sample.

Fig. 5 shows a set of hysteresis curves with the normalhysteresis curve [8] for the annealed sample, obtained byprogressively varying the amplitude of the AC excitationcurrent. The saturation field is derived from the magnetizationcurve (M–H ) and is found to be Hsat = 1.64 kA/m.

Fig. 6 shows the relative (μr) and differential (μd) per-meability curves for the annealed and non-annealed samplesderived from the normal hysteresis curve. The point wherethe μd and μr curves intersect is the maximum relativepermeability μm of the yoke. Results indicate that annealingthe yoke increases μm by a factor ≈1.2.

The point at which the yoke operates in the μr − H plotshown in Fig. 6 can be found by combining a measurementwith the hysteresis data. In the center of the gap, rc = 215 mmand the magnetic flux density is Bc = 0.55 T. Inside thegap, the magnetic field follows a 1/r relationship, B(r) =Bcrc/r , hence the magnetic flux density at the surface of theinner/outer yoke can be calculated to be Biy = 0.59 T/Boy =0.51 T, respectively. On the normal hysteresis curve (Fig. 5),

these values correspond to Hiy = 420 A/m and Hoy =380 A/m, which are close to the maximum of μr(H ), yieldinga value of μr ≈ 1100.

Operating the yoke near the maximum value of μr, makesthe reluctance of the yoke, to first order, independent of thefield H . This is the preferred operating point for a watt balancebecause the reluctance of the magnetic circuit is independentof the weighing current. In our magnet, we are not quite at themaximum value of μr, but close. The effect of the weighingcurrent on the yoke reluctance needs to be analyzed in detail.With the measurements shown in Figs. 5 and 6, we providea basis to further model these effects.

C. Temperature Dependence of the Magnetic FluxDensity in the Gap

The temperature dependence of the radial magnetic fluxdensity in the gap is governed primarily by the temperaturecoefficient of the Sm2Co17. In addition, the flux densitydepends, to a smaller extent, on changes in reluctance of themagnetic circuit caused by temperature dependence of the per-meability of the iron and changes in geometry due to thermalexpansion. The temperature coefficient of the magnetic fluxdensity in the gap was measured and found to be

�Br/Br

�T= (−330 ± 20) × 10−6 K−1 (5)

at a temperature of 21.5 °C.

IV. MEASUREMENT OF THE VERTICAL

GRADIENT OF THE RADIAL FIELD

One of the key objectives in designing this magnet was toobtain a flat field profile, i.e., a small change of the radialfield as a function of the vertical position. In other words,the vertical gradient of the radial field should be as smallas possible. There are two reasons for this objective. First,the force mode consists of two different measurements calledmass-on and mass-off. Between the two measurements, thecoil position changes slightly in vertical position. If the fieldprofile is flat, the flux integral remains the same for bothmeasurements and no correction is required. Second, duringthe velocity mode the coil is moved through the magneticfield such that the induced voltage stays constant. In a flatfield profile, the velocity required to achieve constant inducedvoltage remains constant and is thus easier to measure. A flatfield profile reduces uncertainties in watt balance experiments.The goal was that the magnetic flux density should vary by<±0.01% over the inner 8 cm of the gap.

Two methods were employed to measure the verticalgradient of the radial field: 1) a guided Hall probe (HP) and2) a gradiometer (GM) coil. Two setups were used for the HPmethod, one built by EEC and the other by NIST. In bothsystems, a brass tube is centered on the gap of the magnetin which a second brass tube containing a HP (LakeshoreMMZ-2518-UH and HMMT-6704-VR for the EEC and NISTsystem, respectively) is guided. The guide tube was centeredin the air gap by two tapered teflon plugs, one at the topand other at the bottom. The probe was centered to be


concentric with one access hole each at the upper and loweryoke cap. The guide tube was mounted in a coaxial holein both teflon cones. The magnetic field was recorded atdifferent positions. The EEC setup required manual verticalpositioning of the HP, while the NIST setup used a motorizedtranslation stage. The resolution of each HP is 1 × 10−4 T,which corresponds to a relative change in the magnetic fluxdensity of 2 × 10−4. To measure smaller changes in the field,multiple measurements have to be averaged. We averaged thefield profile measured in all 12 holes to one profile. Thisprocedure discards the azimuthal information and obtains anaverage vertical profile.

The GM coil consists of two identical coils wound on asingle former displaced in the vertical direction. Each coil hasN = 464 turns and a mean radius of r = 217.5 mm. Theheight of each coil is 10 mm and the centers of the coils aredisplaced by �z = 11.5 mm. The two coils are electricallyconnected in series opposition. Two voltmeters are used tomeasure the induced voltages as the coil assembly is movedwith constant velocity, v ≈ 2 mm/s through the magnet. Onevoltmeter measures the voltage induced in one coil, the otherthe difference. The ratio of the two measurements is given by

V1(z) − V2(z)

V1(z)= Br(z) − Br(z − �z)

Br(z)≈

�z dBr(z)dz

Br(z). (6)

The absolute magnitude of the radial magnetic flux densitycan be estimated from the mean velocity, v ≈ 2 mm/s ofthe coil and the coil’s dimensions using Br = V1/(v N2πr).Vibrations induced by the coil motion cause excess noise onV1 with several millivolt amplitude. To get a good estimate ofthe magnetic flux density, the voltage was averaged over thecentral 80 mm. Note that the mean value is not the importantquantity in this measurement.

The vertical variation of the field is calculated by numeri-cally integrating (6) yielding

Br(z) = Br

V1�z

∫ z

b

(V1(z

′) − V2(z′))

dz′ + O, (7)

where O is chosen such that Br(0) = Br. Since both coilsare mounted on the same coil former and are immersed inapproximately the same flux density, the voltage noise onthe difference is reduced by a large factor (about 1000).Fig. 7 shows a typical measurement. In the central region, thedifference of V1 and V2 is −0.19 mV, indicated by the dashedline in the middle plot of the figure. This voltage differencecorresponds to a slope in the field of −13 µT/mm. To excludesystematic errors, i.e., caused for example by a coil windingerror, we performed one measurement with the coil mountedupside down. After correcting for the electrical connections,we obtained the same field profile.

The GM coil was preferred over the guided HP to measurethe field profile with high accuracy because of several reasons.The measurement with the GM coil is first order independentof the concentricity of coil and magnet. The result is also infirst order insensitive to the parallelism of the motion axisto the magnet axis. Furthermore, the coil integrates the fieldalong the azimuthal direction. The GM coil measurement

Fig. 7. Measurements with the GM coil. Top two graphs: raw data, V1 andV2 −V1. Bottom graph: radial flux density as a function of position calculatedfrom the raw data. Horizontal axis is such that zero is the center of the magnetand positive numbers are above the center.

Fig. 8. Four measurements of the radial flux density as a function ofvertical position after the magnet has been assembled for the first time. Themeasurements performed with the HP and the GM coil.

has enough resolution to measure even small field gradients.During the construction of the magnet, measurements withthe GM coil were performed twice. The manufacturer usedthe guided HP to measure the field profile. As it is detailedbelow, the attempts to shim the field by grinding the outeryoke did not converge. This was not due to limitations of thefield measurements. It was, as we learned later, due to thechange of the field profile caused by opening and closingthe magnet.

V. INITIAL ASSEMBLY AND ATTEMPTS

TO SHIM THE FIELD

After all pieces of the magnet were manufactured, the mag-net was assembled for the first time and the radial magneticflux density of the magnet was measured. This measurementwas performed at the manufacturer’s facility with three differ-ent methods. Besides the GM coil, two HPs were used. Themeasurement with the EEC HP was performed on two differentdays about 1.5 weeks apart. The results of the measurementsare shown in Fig. 8. To overlay the measurements, the value


Fig. 9. Points: data measured with the EEC HP after initial assembly, first,and second grinding process. Lines: measurements performed with the GMafter initial assembly and after the second grinding. The GM coil readings are4.2 mT higher. For this plot, 4.2 mT were subtracted from the measurementsperformed with the GM coil.

of Br(0) has been subtracted from each measurement. All fourmeasurements show a similar slope of the radial magnetic fluxdensity, about −13 µT/mm, which is about a factor of 10 largerthan intended.

The measured variation of the radial flux density in theprecision gap of at least 1 mT failed the requirement of�Br/Br < 2×10−4 by a factor of 10. Based on this measure-ment, it was decided to regrind the inner diameter of the outeryoke (part 2 in Fig. 1). The specification for this regrindingwas to add a taper such that the gap is nominally 3.000 cm atthe top to 3.008 cm at the bottom. Varying the gap is a knowntechnique to engineer a desired field profile [9], [10].

Fig. 9 shows the measurement of the radial magnetic fluxdensity after grinding the outer yoke. This measurement wasperformed only at EEC with their HP. The slope of the radialmagnetic flux density at the center has changed from −13 to7 µT/mm. From this measurement, it was concluded that thegrinding overshot by ∼50%. The outer yoke was sent backto the grinding house with the instruction to grind the gapsuch that it is nominally 3.003 cm at the top to 3.008 cm atthe bottom, reversing 1/3 of the first grinding process. Afterthe second grinding process, the magnetic flux density wasmeasured again at EEC. This result was almost identical tothe previous measurement. From this, it was concluded thatthe measurements with the HP are not reliable at this level.It is possible that the trajectory of the HP was not centeredwell enough on the gap. For example, to measure a slope in theradial magnetic flux density of 7 µT/mm in a perfectly uniformfield, the probe only needs to travel sideways by 0.24 mm overthe 8 cm region. While the probe was certainly positionedbetter than 1 mm in the center of the gap, an accuracy of0.2 mm could not be ensured. After the second grinding, theGM coil was brought to EEC to remeasure the profile of theradial magnetic flux density. A slope of −3.5 µT/mm wasobserved (Fig. 9).

Since the grinding process did not seem to converge to aflat field profile, other shimming techniques were explored.

Fig. 10. Radial magnetic flux density as a function of vertical position. Inset:central region magnified such that the total size of the vertical axis extends±4 × 10−4 around the value at z = 0. Two shimming methods lead to asimilar profile. Dashed line: introducing a small air gap. Solid lines: reducingthe relative permeability of the iron.

The first approach was to insert low-carbon steel rods in theinner diameter of the lower Sm2Co17 ring. As can be observedfrom Fig. 9, the flux density was larger at the lower partof the magnet (negative z values). Inserting iron in the ringchanged the slope of the radial magnetic flux in the center ofthe magnet by ∼1 µT/mm, which was a factor of three smallerthan needed. Hence, this strategy was abandoned.

A better way to shim the field is to introduce a small airgap between the lower third of the magnet and the upper twothirds, i.e., a gap between the pieces 2 and 6 on the top andthe pieces 3 and 7 on the bottom in Fig. 1. A flat profile isobtained when this additional air gap is about 0.5 mm high.A stable and uniform air gap can be achieved by insertingaluminum shim stock pieces at several azimuthal locations.This small air gap increases the reluctance of the lower partof the yoke. Hence, the lower Sm2Co17 ring contributes lessflux to the magnetic flux density of the gap. The profile thatis obtained with this method is shown as the dashed line inFig. 10. While this shimming method obtains a flat profile,it has one disadvantage, a small air gap connects the precisionair gap inside the magnet to the outside world and flux leaksout of the magnet. Hence, the shielding of the magnet iscompromised.

We noted that the slope in the center of the gap changedby a few µT/mm every time the magnet was opened andclosed. An examination of this effect yielded another shim-ming strategy. The variability in the vertical linear gradient ofthe magnetic flux density is caused by nonparallel opening andclosing of the magnet. In this case, a situation occurs where thelower part of the yoke touches the upper part of the yoke onone spot along the outer circumference. A large amount of fluxis driven through this contact point (Fig. 11). This effectivelyshifts the working point of the iron at the contact zone on theB–H curve to the right, i.e., to a point with smaller relativepermeability. Even after the magnet is closed, the iron remainsin a state of smaller relative permeability due to the hystereticbehavior of the B–H curve. Hence, in the closed state this


Fig. 11. Change in the outer part of the yoke before, during, and after openingwith an angle. We consider the locations S and W at the small and wide sideof the gap on the outer yoke. At the beginning, the magnetic state is givenby the point I on the B–H curve. During opening, the point W moves alonga minor hysteresis loop to smaller values of B and H . The point S movesalong the major curve to a higher value of B and H . After closing, the pointW moves almost back to the original point (the solid W ). The point on thesmall side of the wedge moves along a minor loop to a new point (solid S)that has substantial more B . The mean value can be found at the point denotedby F for final point. Overall, the μr of the yoke has decreased, reducing theflux in the air gap.

part of the yoke conducts the magnetic field less well and theflux in the gap is lower.

The shimming process works as follows: 1) the magnet isopened by a little more than 1 mm; 2) a 0.5 mm thick shimpiece with a size of ∼5 cm by 5 cm is inserted in the 1 mmgap at an azimuthal position α; and 3) the magnet is closed.Due to the shim, the magnet closes in a tilted fashion andthe iron at the azimuthal position α + 180° is driven to thestate with less relative permeability. Steps 1) through 3) areperformed a total of six times, where the azimuthal positionis advanced by 60° every time. After this, the iron is at a lesspermeable state for the entire circumference.

This shimming process is repeatable. We were able toreproduce the shimming procedure several times, yielding analmost identical field profile.

We have two concerns using this shimming proce-dure. How stable is the field in the gap obtained withthis method? Does this process change the azimuthalsymmetry of the field? We measured the field profileover 3 days every 30 min and we found that theslope of the radial magnetic flux density changed lin-early with time from −0.594 µT/mm to −0.609 µT/mmover 60 h. Hence, the slope changes with a rate of2.5 × 10−10 T/(mm h). This is enough stability for a wattbalance experiment, where the flux integral is measured everyhour. The azimuthal variation of the magnetic flux density ishard to measure with high precision. It can only be measuredwith the HP, since coils integrate over the azimuthal depen-dence. Using the HP, however, requires precise positioningalong the radial direction inside the gap. To compare themagnetic flux density at two azimuthal angles, the HP mustbe positioned at the center of the gap through differentaccess holes in the top of the magnet. A difference in probeplacement of 1 mm causes a different measurement of 2.3 mT.The measurements before and after the shimming performedthrough all 12 access holes (30° increments) showed a similarmaximum difference of 1.51 mT. This difference could be due

to a real field inhomogeneity or due to a positioning error.Within the measurement uncertainty, the shimming proceduredid not make the azimuthal asymmetry worse.

In summary, a flat profile of the magnetic flux densityas a function of vertical position can be achieved with twodifferent shimming methods. One can introduce a small air gapbetween the lower and upper part of the magnet or lower thepermeability of the iron yoke in the lower half of the magnetby exposing it to a large magnetic field. Both methods increasethe reluctance of the flux path around the lower Sm2Co17 ring.Fig. 10 shows the field profile achieved with both methods.With these two methods, a slope of < 0.1 µT/mm or in relativeterms 2×10−7/mm, can be achieved. The relative flux densitystays between ±1 × 10−4 over at least 5 cm. This is a bit lessthan the initial goal of 8 cm. We plan on using the shimmingmethod that decreases the permeability of the yoke for the firstwatt balance measurements with this magnet.

VI. RADIAL DEPENDENCE OF THE

MAGNETIC FLUX DENSITY

The insight that a 1/r dependence of the radial flux densityallows the construction of a better watt balance is attributedto Olsen. His argument goes as follows. Assume that

Br(r) = Boro

r(8)

the coil is centered on the magnetic field, has a radius r andN turns. The flux integral is given as a line integral along thewire

f (r) ≡ Bl = z∫

∂S

�B × d�l. (9)

Assuming no azimuthal dependence of the field, this integralequates to f (r) = 2π N Br(r)r . For the field given in (8), theflux integral evaluates to f = 2π N Boro, which is independentof r . In other words, for a 1/r -field, d f/dr = 0.

One important assumption in the watt balance experimentis that the flux integral in the force mode is identical to theone in the velocity mode. In the force mode, current is passedthrough the coil that leads to heating and subsequently thermalexpansion of the coil. If the flux integral is independent of thecoil radius r , the above assumption holds. If this is not thecase, a bias is introduced into the experiment.

To investigate the deviation from a perfect 1/r -field, it isuseful to expand the flux integral for small changes in radiusand assume d f/dr �= 0. In this case

f (r + rγ ) ≈ f (r) + rγd f

dr, (10)

where γ � 1. The last term can be rewritten as

rγd f

dr= γβ f with β = r

f

d f

dr. (11)

Here, β is a unitless number describing the deviation of theflux density from a 1/r dependence.

To measure the radial dependence of the radial flux density,a radial GM coil was built. This GM coil consists of threecoils on a single former. Each coil has 295 turns, a verticalsize of 17 mm and a radial width of 4.9 mm. The mean radii


Fig. 12. Measurement of the deviation of the radial field from 1/r , see textfor a definition of the unitless constant β. The measurement was performedat rm = 0.216 m.

of the three coils are ri = 211.45 mm, rm = 216.35 mm, andro = 221.25 mm. For the measurement, the inner and outercoil are connected in antiseries to one voltmeter and the middlecoil to a second voltmeter. Both voltmeters are sampled at thesame time, while the GM coil is vertically moving through thegap of the magnet with a velocity of v = 2 mm/s. A value ofβ is estimated using

β ≈ Vo−i

Vm

rm

ro − ri. (12)

Fig. 12 shows the measurement for β around the symmetryplane of the magnet, β = −0.003. The negative sign indicatesthat the field drops faster than 1/r with increasing radius. Thesame value of β is obtained when the middle and outer coilor the inner and middle coil are combined. Since we cannotcompletely rule out other sources of induced electromotiveforce, we conservatively interpret the measured value as anupper limit for β, i.e., |β| < 0.003. Using this β, the changein flux integral due to a geometry change caused by e.g., coilheating, can be calculated. Changing the temperature of thecoil by �T causes a radial expansion of �r = rα�T , whereα = 16.6 × 10−6 K−1 is the linear coefficient of expansionfor copper. Note, that γ = α�T . According to (10) and (11)the relative change in flux integral is γβ = 5 × 10−8 K−1δT .In the current design of NIST-4, the power dissipation in theforce mode is about 8 mW (R = 130 � and I = 8 mA).Assuming a copper mass of 3 kg, the temperature of the coilwould rise by 0.026 K in 1 h. Note this estimation neglectslosses in thermal energy due to radiation to the environment.The corresponding relative change in the flux integral wouldbe 1.3 × 10−9. To further minimize this effect, a coil heatercan be installed as was done in the NPL watt balance [11]. Thedeviation from a 1/r field gets rapidly worse with increasingdistance of the coil to the symmetry plane of the magnet. At adistance of 2.2 cm, β is already ten times larger.

VII. MEASUREMENT OF THE RELUCTANCE FORCE

As discussed in [6], the reluctance force pulls the coilinto the center of an iron structure like the yoke of this

magnet regardless of the sign of the current in the coil.The force originates from the fact that a current carrying coilhas minimum energy in the center of the yoke. Note, this effectis independent of the magnetic field. If the Sm2Co17 rings werereplaced by magnetically inactive stainless steel rings (μr =1), the effect would still be present. The reluctance effect issimilar to the effect exploited by a solenoid actuator, where aniron slug is pulled into a solenoid after it has been energized.

The energy of the magnetic field produced by the coil isgiven by E = (1/2)L I 2. From the energy, the vertical forcecan be calculated using

Fz = dE

dz= 1

2I 2 dL

dz, (13)

assuming that the current in the coil is maintained at a constantlevel. To estimate this effect, the inductance of the coil,L has to be measured as a function of vertical position inthe magnet, z.

The measurements below were carried out by connecting aprecision 50 � resistor in series with the vertical GM coil.This time, the two coils on the GM coil were connected inseries to form effectively one coil with 928 turns. A sinusoidalvoltage with an amplitude of 2 V and frequency, f , wasapplied. Two Agilent 3458A voltmeters were used to simul-taneously measure the voltage across the 50 � resistor andthe coil. Fitting sines to both of these measurements yieldedthe amplitudes and the relative phase between these twomeasurements. From the amplitudes and the phase difference,the electrical resistance and the inductance of the coil couldbe reconstructed.

The inductance of the coil is measured at f, yielding L( f ).Since the watt balance operates near DC, we are interested inlim f →0 L( f ). We placed our GM coil in the center of themagnet and measured L( f ) using the procedure explainedabove. We found that for low frequencies ( f < 1 Hz) theinductance scales like L( f ) = a − b

√f , with a = 4.2 H and

b = 0.66 H/√

Hz. The same coil outside the magnet and faraway from any metal has an inductance L = 0.8 H, which isindependent of f for f < 100 Hz. The frequency dependence ofthe inductance of the coil inside the magnet is due to the skineffect [12]. In solid iron, the skin depth is very small since ithas a high conductivity and a high susceptibility. At 1 Hz, theskin depth is about 5 mm. Hence, in order for the field to com-pletely penetrate the inner yoke, f has to be below 0.6 mHz.

To obtain a good estimate for lim f →0 L( f ), themeasurement was carried out at f = 0.01 Hz. In this case, thedeviation from the DC value is at most 0.06 H and we foundno position dependence of this difference. L(z) was measuredfor every millimeter along the z direction. The result is shownin the top graph of Fig. 13. In the middle graph of the figure,dL/dz is plotted. This derivative is calculated from a fourthorder polynomial fit to the raw data. The second derivativeof the inductance is mostly independent of z and evaluates tod2L/dz2 = −346 H/m2 at the center of the magnet.

The spurious force signal to the watt balance experimentdue to the reluctance effect can be written as

F = 1

2I 2

ON

dL

dz

∣∣∣∣z=zON

− 1

2I 2

OFF

dL

dz

∣∣∣∣z=zOFF

(14)


Fig. 13. Top graph: measurement of the inductance, L , of the GM coil(928 turns). L(z) is measured at 10 mHz. Each point represents an averagevalue of two measurements. The error bars are obtained from the fit. Solidline: a fit to the data using a fourth-order polynomial. Middle graph: derivativecalculated from the polynomial fit. Bottom graphs: results of (15) for fourdifferent cases. For these calculations, I = 8 mA is assumed.

where IOFF, ION and zOFF, zON are the currents and positionsof the coil during the mass-off and mass-on measurement,respectively.

This equation simplifies in first order to

F ≈ 2δ I IAdL(z)

dz− (IA)2�z

d2L(z)

dz2 , (15)

where z = (1/2)(zON + zOFF), �z = (1/2)(zON − zOFF), δ I =(1/2)(ION + IOFF), and IA = (1/2)(ION − IOFF). Typically, awatt balance is operated such that ION ≈ −IOFF, hence δ I ≈ 0and IA ≈ ION. The results of the above equation for fourdifferent cases are shown in the lower plot of Fig. 13.

The spurious force needs to be compared with the force thatwill be generated by the watt balance, i.e., ≈10 N. To keep therelative contribution of the spurious force to the measurementbelow 10−8, a maximum force of Fm = 10−7 N is permitted.We will use 10−7 N as a benchmark for the analysis below.

The first term on the right of (15) can be made small, evenfor a finite δ I , by performing the watt balance experimentat the center of the yoke, where dL/dz = 0. The slope atwhich the spurious force changes with deviations from theideal position depends on the current mismatch, δ I , as isshown in Fig. 13. For a current mismatch of δ I = 4 µA,the range of operation where |F | < Fm is ±4.5 mm.

The second term remains approximately constant for differ-ent coil positions, since the second derivative of the inductancewith respect to z is largely independent of z. It evaluates to�z × 2.2 × 10−8 N/µm at the center of the magnet. To keepthe absolute value of this term smaller than Fm, the change incoil position, zOFF − zON must be smaller than 9 µm. Typically,in an experiment like NIST-4, the coil position between themass-ON and mass-OFF state can be maintained within a fewmicrometers of each other. In this case, the second term of (15)is about Fm/3. This number is certainly large enough tobe considered as systematic uncertainty of the experiment.However, it will not be a dominant effect.

We would like to emphasize that it is important to measurethe inductance of the coil at low frequency. We performedthe same measurement with f = 100 Hz. Using this data,

Fig. 14. Top plot: three components and the absolute magnitude of themagnetic flux density above the magnet as a function of the distance above thetop surface. Bottom graph: systematic force divided by the local accelerationcaused by the magnetic susceptibility and the magnetization of the weight. Forthis calculation, a 1 kg E1 weight was assumed with the maximum allowedvalues for the magnetic susceptibility, χ = 0.02 and magnetization, 2 A/m.Vertical dotted line: position of the mass during weighing.

one would calculate a reluctance force that is about ten timessmaller than the real reluctance force at DC.

An order of magnitude estimation of the reluctance forceis given in [6, eq. (10)]. Using this estimation to calculated2L/dz2, a value of −800 H/m2 is found. While the absolutevalue of this number is almost twice as large as the resultobtained from the measurement, the order of magnitude isright, as intended.

VIII. MAGNETIC FIELD OUTSIDE THE MAGNET

One concern of any magnet system being developed for awatt balance is the magnetic field at the location of the mass.The interaction between the field and the mass can create aspurious force that may lead to a systematic effect. In general,the vertical force on an object with a volume susceptibility χand permanent magnetization M is given by [13]

Fz = −μ0

2

∂

∂z

∫χH · HdV − μ0

∂

∂z

∫M · HdV . (16)

The three components of the flux density above thepermanent magnet system have been measured as a functionof distance from the top surface. This measurement wasperformed near the symmetry axis using a 3-D magnetore-sistive sensor. In Fig. 14, the three components and theabsolute magnitude are shown. At close distances, the verticalcomponent of the field is dominant. It decreases in a nearlylinear fashion with growing distance until it vanished at adistance of 350 mm. From there on, it decreases further tomatch the vertical component of the ambient field, about45 µT. The horizontal components are close to zero in thefirst 300 mm. At larger distances, they approach the ambientvalues.

To calculate the force from these measurements, few sim-plifications were made: a 1 kg stainless steel weight witha height of 69.1 mm and a diameter of 48 mm was assumed.The magnetic susceptibility was assumed to be constant over


the volume of the weight and independent of H , which isreasonable at these small fields. The magnetization is alsoassumed to be constant over the volume of the weight. Forsimplicity, we assumed two components of the magnetizationto be zero, i.e., Mx = My = 0. Ideally, NIST-4 is ableto realize mass using an E1 class weight. To calculate theworst case force on such a weight, we assume the maximumpermissible limits for the susceptibility and the magnetization.According to [14], χ = 0.02 and Mz = 2 A/m were assumed.

The bottom plot in Fig. 14 shows the calculated magneticforce for the two terms in (16). The first term gives the forcedue to the magnetic susceptibility of the mass. It depends onthe derivative of the squared magnitude of the magnetic field.Since the magnetic field has a minimum around 350 mm, thisterm changes sign at this point. The second term gives theforce due to a permanent magnetization of the mass. Thisforce depends on the derivative of the z-component of themagnetic field. The derivative is negative for the entire datastretch leaving a positive force on the mass. The magnitude ofthe force generated by the first term is smaller than 1 µg forz >300 mm and can be neglected. The second term producesa force that can be as large as 3 µg for the stainless steelmass in its weighing position. There are three strategies tomitigate this effect. First, a mass can be chosen that has asmaller permanent magnetization. As mentioned above, thiscalculation was performed with the maximum permissiblemagnetization for an E1 mass. Second, the magnetization termchanges sign as the mass is rotated upside down. If a masswith a magnetization of |Mz| ≥ 2 A/m has to be measuredin the new watt balance, the magnetic effect can be nulledby averaging two measurements with the mass rotated upsidedown in between. Third, two coils wired in series oppositioncan be installed above and below the mass generating amagnetic field gradient. By choosing the right current in thecoil, a vertical field gradient can be generated that cancels theexisting gradient. If the actual gradient at the mass is zero,both terms vanish.

In conclusion, the external field above the new permanentmagnet is sufficiently small such that stainless steel massescan be used in the new watt balance. If an E1 mass with anominal value of 1 kg is used, a worst case magnetic force of4 µg is expected.

IX. POWER SPECTRAL AMPLITUDE

OF A COIL INSIDE THE MAGNET

Another interesting measurement is the power spectralamplitude of the voltage across a coil at rest inside themagnet. To accomplish this measurement, the three coils ofthe radial GM coil were connected in series. Fig. 15 showsthe coil in the gap. The coil is supported by three pillars. Eachpillar is composed of two optical posts and one teflon spacerjoined together by brass set screws. The coil is concentricand vertically centered inside the air gap. This measurementwas performed with the magnet sitting on a pallet in storage.Hence, the vibrational environment for this measurement wasnot ideal. The power spectral amplitude was measured usinga Rhode and Schwarz UPV audio analyzer.

Fig. 15. Coil in the magnet. The coil is supported by three pillars, eachcomprised of two optical posts and one teflon spacer. Each pillar is attachedto the bottom of the coil with brass set screws. The teflon spacer centers thecoil in the gap and eliminates horizontal motion.

Fig. 16. Power spectral amplitude of terminal voltage of the radial GM coilin the precision gap of the magnet. This measurement was performed withthe magnet sitting on a pallet in storage. Hence, the vibrational environmentfor this measurement was not ideal leading to the vibrational peaks in thespectral amplitude.

Fig. 16 shows the measured spectra for both channelsof the analyzer. One channel was connected to the coil, whilethe other was shorted. Two observations on the spectrum of thecoil voltage are noteworthy. First, at the low frequency end, thespectral amplitude is below 1 µV/

√Hz. This is an important

figure of merit, since a white noise of smaller than 1 µV/√

Hzwould allow the determination of the flux integral Bl with arelative uncertainty of 10 × 10−9 in 10 000 s. Second, there isa lot of excess noise in the region between 10 and 500 Hz.This excess noise is mostly due to mechanical resonances inthe coil and the coil support. These peaks are from differentvibration modes of the coil, some of which we could identify.


The radial GM coil was not optimized for stiffness, sinceit was built to measure the radial gradient of the field. Thedesign of the coil for NIST-4 is currently ongoing. One focusin the design work is to dampen the vibration mode in thefrequency range from 10 to 300 Hz. Ultimately, NIST-4 willbe installed in an underground laboratory. This environmentwill have less vibration. In this environment, the peaks in thespectral amplitude should be greatly reduced.

X. CONCLUSION

The NIST-4 magnet has been successfully built. Initial mea-surements of the basic properties of the magnet were carriedout at NIST. A dedicated GM coil was built to measure thevertical gradient of the radial flux density. The measurementswith the GM coil enabled the manufacturer, EEC, to regrindthe gap improving the field profile. After delivery, it was foundthat the magnetic field profile could be further improved bychanging the magnetic working point of the iron yoke. Thiscan be accomplished by opening the magnet in a tilted fashion.Using this technique, the profile of the radial magnetic fluxdensity could be changed to have a nearly vanishing derivativewith respect to z at the symmetry plane of the magnet. Themagnetic flux density stayed within ±10−4 of its value in thecenter over a travel range of 5 cm.

The radial dependence of the radial magnetic flux densitywas measured using a radial GM coil. It was found that thefield follows a 1/r dependence closely and we expect anyrelative systematic error due to geometry changes of the coil ofabout 1.3 ×10−9. This effect can be reduced by incorporatinga heater in the coil.

We investigated the forces on the coil due to the reluctanceforce. This force can lead to a systematic error via twomechanisms: 1) a difference in the mass-on and mass-offcurrent and 2) a parasitic motion of the coil in these two states.It was determined that each of the two components producesa relative systematic error below 3 × 10−9 for reasonableassumptions.

The external magnetic field was measured above the magnet,i.e., where the balance and mass would be located. It wasfound that the field drops off rapidly reaching the earth’smagnetic field at about 600 mm above the top surface ofthe magnet. The spurious force on a stainless steel weight,class E1, was calculated using worst case assumptions detailedin OIML R111. In this case, the relative systematic effectproduced by the magnet is about 4 × 10−9. Hence, it ispossible to use a E1 stainless steel mass on the NIST-4watt balance without a substantial increase in uncertainty.This uncertainty can be reduced by installing bucking coils,using PtIr artifacts or numerically canceling the permanentmagnetization of the stainless artifact by measuring it upsidedown.

The power spectral amplitude of a coil in the magnet wasmeasured. The spectrum is currently dominated by mechan-ical resonances and vibrations in the frequency region from10 to 500 Hz. Assuming these resonances can be removed andthe vibrations damped, a measurement of Bl with a relativeuncertainty (type A) of 10 × 10−9 can be achieved with an

integration time of ≈3 h or less. This uncertainty may bereduced due to partial cancelation of the voltage noise withvelocity noise, which is likely to be highly correlated with thevoltage noise.

Adding the relative type B uncertainties mentioned abovein quadrature yields ≈ 5.2 × 10−9. This is a conservativeestimate of the uncertainty of the magnet system, because theimprovements outlined above would reduce this uncertaintyby approximately a factor of two. In conclusion, the knownsystematic effects from the magnet system are small enoughto allow the construction of a watt balance at the 1 kg levelwith a relative uncertainty of a few parts in 108.

REFERENCES

[1] I. M. Mills, P. J. Mohr, T. J. Quinn, B. N. Taylor, and E. R. Williams,“Adapting the international system of units to the twenty-first century,”Phil. Trans. Roy. Soc. A, vol. 369, no. 1953, pp. 3907–3924, Oct. 2011.

[2] R. Steiner, “History and progress on accurate measurements of thePlanck constant,” Rep. Progr. Phys., vol. 76, no. 1, pp. 1–46, Dec. 2012.

[3] B. P. Kibble, “A measurement of the gyromagnetic ratio of the proton bythe strong field method,” Atomic Masses and Fundamental Constants,vol. 5, J. H. Sanders and A. H. Wapstra, Eds. New York, NY, USA:Plenum, 1976, pp. 545–551.

[4] P. T. Olsen, W. D. Phillips, and E. R. Williams, “A proposed coilsystem for the improved realization of the absolute ampere,” J. Res.NBS, vol. 85, no. 4, pp. 257–272, Jul. 1980.

[5] S. Schlamminger et al., “Determination of the Planck constantusing a watt balance with a superconducting magnet system at thenational institute of standards and technology,” Metrologia, vol. 51,pp. S15–S24, Mar. 2014.

[6] S. Schlamminger, “Design of the permanent-magnet system forNIST-4,” IEEE Trans. Instrum. Meas., vol. 62, no. 6, pp. 1524–1530,Jun. 2013.

[7] M. Stock, “Watt balances and the future of the kilogram,” INFOSIMInform. Bull. Inter Amer. Metrol. Syst., vol. 9, pp. 9–13, Nov. 2006.

[8] R. M. Bozorth, Ferromagnetism, 1st ed. Piscataway, NJ, USA: IEEEPress, 1993.

[9] A. L. Eichenberger et al., “A new magnet design for the METAS wattbalance,” in Conf. Precis. Electromagn. Meas. Dig., pp. 56–57, Jul. 2004.

[10] P. Gournay, G. Geneves, F. Alves, M. Besbes, F. Villar, and J. David,“Magnetic circuit design for the BNM watt balance experiment,” IEEETrans. Instrum. Meas., vol. 54, no. 2, pp. 742–745, Apr. 2005.

[11] I. A. Robinson, “Towards the redefinition of the kilogram: Ameasurement of the Planck constant using the NPL Mark II wattbalance,” Metrologia, vol. 49, no. 1, pp. 113–116, Dec. 2011.

[12] G. R. Gonzales and A. Brambilla, “Frequency dependence of theresistance and inductance of solid core magnets,” IEEE Trans. Nucl.Sci., vol. 12, no. 2, pp. 349–353, Jun. 1965.

[13] R. S. Davis, “Determining the magnetic properties of 1 kg massstandards,” J. Res. Nat. Inst. Standards Technol., vol. 100, no. 3,pp. 209–226, May. 1995.

[14] International Recommendation on Weights of Classes E1, E2, F1, F2,M1, M2, M3, International Recommendation No. R111, OrganisationInternationale de Métrologie Légale, Paris, France, 1994.

Frank Seifert was born in Berlin, Germany. Hereceived the Dipl.-Ing. and Dr.-Ing. degrees in elec-trical engineering from Leibniz University, Han-nover, Germany, in 2002 and 2009, respectively.

He was with the California Institute of Technology,Pasadena, CA, USA, from 2009 to 2012, wherehe was involved in the frequency stabilization oflasers for high precision metrology. He is currently aGuest Researcher with the National Institute of Stan-dards and Technology, involved in the watt balancesNIST-3 and NIST-4.


Alireza Panna was born in Mumbai, India. Hereceived the B.S. degree in Electrical Engineeringfrom the University of Maryland, College Park, MD,USA, in 2013.

He is currently a Guest Researcher with theNational Institute of Standards and Technology,Gaithersburg, MD, USA, where he is involved withthe new watt balance NIST-4.

Shisong Li (S’14) received the B.S. degree fromNorth China Electric Power University, Beijing,China, in 2009. He is currently pursuing the Ph.D.degree with Tsinghua University, Beijing.

He was involved in the Joule Balance Project withthe National Institute of Metrology, Beijing, China.He has been a Guest Researcher with the NationalInstitute of Standards and Technology (NIST) NIST-4 Watt Balance Group, National Institute of Stan-dards and Technology, Gaithersburg, MD, USA,since 2013.

Bing Han was born in Zhangjiakou, China. Hereceived the Ph.D. degree from Tianjin University,Tianjin, China, in 2009.

He was a Post-Doctoral Researcher with theNational Institute of Metrology (NIM), Changsha,China, from 2010 to 2012, for the Joule BalanceProject, and a Guest Researcher with the NationalInstitute of Standards and Technology (NIST),involved in the magnetic system of NIST-4 wattbalance in 2013. He is currently at NIM, where heis involved in the magnetic system of joule balance.

Leon Chao received the B.S. degree in mechanicalengineering from the University of Maryland, Col-lege Park, MD, USA, in 2012.

He joined the National Institute of Standards andTechnology (NIST), Gaithersburg, MD, USA, in2012, and he serves as a Mechanical Design Engi-neer for the NIST-4 watt balance.

Austin Cao is currently pursuing the B.S. degree inmechanical engineering at the University of Mary-land, College Park, MD, USA.

He is currently a Guest Researcher with theNational Institute of Standards and Technology(NIST), Gaithersburg, MD, USA, where he wasinvolved in the mechanical design for the NIST-4watt balance.

Darine Haddad (M’09) received the Ph.D. degreein optics, optoelectronics and microwaves from theUniversity of Versailles, Versailles, France, in 2004,where she was involved in the research of opticalsensors and dimensional metrology.

She has been a Post-Doctoral Fellow with the Lab-oratoire National de Métrologie et d’Essais, Trappes,France, involved in watt-balance experiments tomeasure the Planck constant and realize the unit ofmass, the kilogram, and with the National Institute ofStandards and Technology, Gaithersburg, MD, USA,

since 2008.

Heeju Choi (M’02) received the B.S. degree fromChonnam National University, Gwangju, Korea, in1998, the M.S. degree from the Gwangju Instituteof Science and Technology, Gwangju, in 2000, andthe Ph.D. degree from North Carolina State Univer-sity, Raleigh, NC, USA, in 2005, all in mechanicalengineering.

He is currently a Senior Applications Engineerwith Electron Energy Corporation, Landisville, PA,USA, since 2005. He has extensive experience, ofmore than 15 years, in the design of electromechan-

ical systems, including motor, generator, magnetic bearing, magnetic coupling,Halbach assembly, energy harvesting, dynamometer, eddy current brakes,flywheel energy storage, and hybrid vehicles.

Dr. Choi is a member of ASME, ASM, and SAE.

Lori Haley received the certification as a Tool andDie Maker from the National Tool, Die and PrecisionMachining Association, Fort Wayne, IN, USA, in1981.

He has been with Electron Energy Corporation,Landisville, PA, USA, for the past 18 years, servingfirst as a Lead Toolmaker, and currently as a Man-ufacturing Engineer. His mechanical, metallurgical,and magnet expertise is instrumental to governmentand military permanent magnet projects, includinginvolvement with NASA, USAF, DOE, and DARPA.

His current research interests include optimizing custom permanent magnetdesigns, and designing and implementing processes for manufacturing perma-nent magnet assemblies.

Stephan Schlamminger (M’12) was born in Kel-heim, Germany. He received the Diploma degree inphysics from the University of Regensburg, Regens-burg, Germany, in 1998, and the Ph.D. degree inexperimental physics from the University of Zürich,Zürich, Switzerland, in 2002.

He was with the University of Washington, Seattle,WA, USA, where he was involved in the experi-mental test of the equivalence principle, from 2002to 2010. He is currently with the National Instituteof Standards and Technology (NIST), Gaithersburg,

MD, USA, where he is involved in the watt balances NIST-3 and NIST-4.

construction, measurement, shimming, and performance of

Documents