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A measurement of the Planck constant using the NPL Mark II watt balance
I A Robinson
An initial measurement of Planck's constant using the NPL Mark II watt balance
I A Robinson and B P Kibble
History and progress on accurate measurements of the Planck constant
Richard Steiner
Alignment of the NPL Mark II watt balance
I A Robinson
Simplified fundamental force and mass measurements
I A Robinson
Watt balance experiments for the determination of the Planck constant and the redefinition of the
kilogram
M Stock
A determination of Planck's constant using the NRC watt balance
C A Sanchez, B M Wood, R G Green et al.
The watt or Kibble balance: a technique for implementing the new SI definition of the unit of
mass
View the table of contents for this issue, or go to the journal homepage for more
2016 Metrologia 53 A46
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1. Introduction
Previously known as the moving-coil watt balance, the moving
coil Kibble balance was invented at the National Physical
Laboratory (NPL) by Bryan Kibble [1] in 1975 and it relates
virtual mechanical and electrical power. Dr Kibble passed
away in 2016 and the watt balance technique is now referred
to as the Kibble balance technique in his honour. Originally, it
was intended as a replacement for the current balance which
realised the ampere from its denition in terms of the mechan-
ical units [2, 3]. When combined with an SI ohm derived from
the calculable capacitor [4], the Kibble balance can be used to
realise the SI volt or SI ampere [5].
The discovery of the quantum Hall effect (QHE) by von
Kitzing in 1980 [6], in conjunction with the previously dis-
covered Josephson effect [7], led to the provision of highly
stable representations of the ohm and volt, respectively [8].
The results from the National Institute of Standards and
Technology (NIST) [9] and NPL Mark I [5] Kibble bal-
ance prior to 1990 contributed to the conventional values
for the Josephson and von Klitzing constants
KJ90−
and
RK90−
, respectively. By xing these constants in 1990, stable
quantum representations of the volt and ohm were provided to
the world. However, because they were xed using data taken
prior to 1990, they are close, but not equal, to the present best
estimates of the SI volt and ohm.
The combination of these quantum effects enable electrical
power to be measured in terms of the Planck constant h and
frequency (counts per unit time). This enabled the Kibble bal-
ance to relate macroscopic mass to h with sufciently low
uncertainty to contemplate redening the kilogram [10]. The
Kibble balance would then represent a route to the realisation
of the kilogram in the revised SI [11]. The existing proposals to
revise the SI in 2018 would x the values of h and the elemen-
tary charge e which would also x the values of KJ and RK,
within the SI, eliminating the need for
KJ90−
and
RK90−
[12].
Metrologia
The watt or Kibble balance: a technique
for implementing the new SI denition
of the unit of mass
IanARobinson1 and StephanSchlamminger2
1 National Physical Laboratory, Hampton Road, Teddington, Middlesex, TW11 0LW, UK
2 National Institute of Standards and Technology (NIST), 100 Bureau Drive Stop 8171, Gaithersburg,
MD 20899, USA
E-mail: ian.robinson@npl.co.uk
Received 9 May 2016, revised 18 July 2016
Accepted for publication 27 July 2016
Published 28 September 2016
Abstract
The redenition of the SI unit of mass in terms of a xed value of the Planck constant has
been made possible by the Kibble balance, previously known as the watt balance. Once the
new denition has been adopted, the Kibble balance technique will permit the realisation of
the mass unit over a range from milligrams to kilograms. We describe the theory underlying
the Kibble balance and practical techniques required to construct such an instrument to relate
a macroscopic physical mass to the Planck constant with an uncertainty, which is achievable at
present, in the region of 2 parts in 108. A number of Kibble balances have either been built or
are under construction and we compare the principal features of these balances.
Keywords: kilogram, watt balance, redenition, Kibble balance, Planck constant,
mass measurement
(Some guresmay appear in colour only in the online journal)
I A Robinson and S Schlamminger
The watt or Kibble balance: a technique for implementing the new SI definition of the unit of mass
Printed in the UK
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Metrologia 53 (2016) A46– A74
I A Robinson and S Schlamminger
A47
The Josephson and quantum Hall effects could then be used
to realise the SI volt, the SI ohm and, in combination, the SI
ampere.
1.1. Basic principles
The Kibble balance consists of a coil of wire which is sus-
pended from one arm of a balance and is placed in a strong
magnetic eld. The apparatus has two measuring modes:
weighing mode and moving mode, which are illustrated in
gures1 and 2, respectively. In the weighing mode, the weight
M g of a mass M is opposed by the vertical force Bl I generated
by a current I owing in a coil of wire of length l in a magnetic
ux density B giving M g = Bl I. In the moving mode, the mass
is removed and the coil is moved in the eld with a velocity u
which induces a voltage V = Bl u in the coil. If it is assumed
that the quantity Bl is unchanged between the weighing and
moving measurements, it can be eliminated giving:
VIMgu.=
(1)
As the measurements of force and current are separated from
those of velocity and voltage, this expression equates virtual
electrical to virtual mechanical power. Comparing virtual
power eliminates the effects of energy loss mechanisms such
as resistive losses, friction and eddy current losses, which
would severely hamper a direct comparison of power. This
makes it possible to achieve the extremely low overall uncer-
tainty (of the order of 1 part in 108) required for the redeni-
tion of the kilogram.
The simple derivation of equation(1) ignores many issues,
including the vector nature of the force generated by the coil,
but in the next sectionwe will show that equation(1) can be
made to hold exactly under carefully dened circumstances.
2. The Kibble balance
2.1. Theory
Over the last few years, it has been observed that under
some circumstances, the Kibble balance is immune to errors
arising from secondary forces and torques, non-vertical
motion of the coil, and electrical leakage effects [13, 14].
It was recognised in [14] that a Kibble balance which uses
a common mechanism for both weighing and moving can
act as a reciprocal system resulting in the cancellation of the
above mentioned errors. The conditions required for these
cancellations to occur in a virtual work system were derived
in [15]. This theory covers the design of a range of Kibble
balances and assumes that the motion of the coil is fully
determined by the vertical velocity of the mass pan. The coil
has coordinates (x, y, z) and its angles about the (x, y, z) axes
are
,,
xyz
( )θθθ
and it is threaded by a magnetic ux
Φ
. The
position of the mass pan along the vertical (z) axis is
z′
and
its vertical velocity is
uz′
.
The weighing mode of the balance is shown in gure1,
a current I is passed through the coil and the resultant of the
forces and torques produced by the coil oppose the weight
Mg. In the measuring phase corresponding to this mode of
operation, the current I is measured. The equilibrium condi-
tion for the balance is:
⎛
⎝
⎜
⎞
⎠
⎟
θ
θ
θ
θ
θ
θ
−−
∂Φ
∂
∂
∂+∂Φ
∂
∂
∂+∂Φ
∂
∂
∂
+∂Φ
∂
∂
∂+∂Φ
∂
∂
∂+∂Φ
∂
∂
∂=
′′′
′′′
Mg Ix
x
zy
y
zz
z
z
zzz
0.
x
x
y
y
z
z
(2)
To measure the relevant properties of the coil and magnet,
often referred to as the Bl product or geometric factor, the
mass is removed, the current switched off and the apparatus
is placed in moving mode as shown in gure2. The mass car-
rier moves with a vertical velocity
uz′
. This motion causes the
coil to move and rotate with velocities
uuu,,
xyz
( )
and angular
velocities
,,
xyz
( )ωωω
. These motions are related to the vertical
velocity by:
uuxz
x
z/=∂∂′
′
(3)
uuyz
yz
/=∂∂′
′
(4)
uuzz
zz
/=∂∂′
′
(5)
uz
xzx
/ωθ=∂∂′
′
(6)
uz
yzy
/ωθ=∂∂′
′
(7)
uz.
zzz
/ωθ=∂∂′
′
(8)
In the measuring phase associated with this mode, the velocity
uz′
and the voltage V generated by the coil are measured giving:
⎛
⎝
⎜
⎞
⎠
⎟
θωθωθω
=− ∂Φ
∂+∂Φ
∂+∂Φ
∂
+∂Φ
∂+∂Φ
∂+∂Φ
∂
V
xuyuzu
xyz
x
x
y
y
z
z
(9)
and, using (3)–(8),
⎛
⎝
⎜
⎞
⎠
⎟
θ
θ
θ
θ
θ
θ
=− ∂Φ
∂
∂
∂+∂Φ
∂
∂
∂+∂Φ
∂
∂
∂
+∂Φ
∂
∂
∂+∂Φ
∂
∂
∂+∂Φ
∂
∂
∂
′′′
′′′
′
Vu
x
x
zy
y
zz
z
z
zzz.
z
x
x
y
y
z
z
(10)
If the only signicant forces or torques are produced by gravity
g or the interaction of current and magnetic ux and the values
of the partial derivatives in (3)–(8) and the spacial derivatives
of
Φ
do not change during and between moving and weighing
modes (the stability conditions), then it is possible to combine
(2) and (10) to give the exact equation
Mgu VI.
z=
′
(11)
If the stability conditions are met, the Kibble balance can
relate its principal measurands without the need for precise
alignment. However, if the balance is not well aligned, motions
caused by misaligned forces and torques can invalid ate the
stability conditions. To ensure that these conditions are met,
all existing Kibble balances are carefully aligned. A technique
Metrologia 53 (2016) A46
I A Robinson and S Schlamminger
A48
Figure 1. The Kibble balance in weighing mode.
Figure 2. The Kibble balance in moving mode.
Metrologia 53 (2016) A46
I A Robinson and S Schlamminger
A49
has been proposed to overcome these limitations [16] which
should simplify the construction and operation of Kibble bal-
ances and is described in section 2.2.5. The existing NIST,
NPL/National Research Council (NRC) and Measurement
Standards Laboratory (MSL) Kibble balances use common
weighing and moving mechanisms employing pressure or
knife-edge balances which require care to reach the required
weighing sensitivity. An alternative is a exure-based bal-
ance which is extremely sensitive and does not display the
hysteresis problems inherent in knife edge balances. However,
existing exure-based balances cannot generate the large
excursions required in the moving mode of the Kibble balance
and, to overcome this problem, it is usually necessary to adopt
a separate mechanism for moving the coil which can make the
apparatus sensitive to parasitic forces, torques and motions as
illustrated below.
If it is assumed that the weighing mechanism in a exure-
based balance is sensitive only to vertical forces then equa-
tion(2) becomes:
MgI z./=− ∂Φ ∂
(12)
The other terms in equation(2) can be represented in terms
of torques (
,,
xy
z
ΓΓΓ
) and horizontal forces (
F F,
xy
) :
FIx
x/=− ∂Φ ∂
(13)
FI y
y
/=− ∂Φ ∂
(14)
I
xx
/θΓ=−∂Φ∂
(15)
I
yy
/θΓ=−∂Φ∂
(16)
I
zz
/θΓ=−∂Φ∂
(17)
using (13)–(17) equation(9) becomes
(
)
ωωω
=++
+Γ +Γ +Γ
VI Fu Fu Mgu
.
xx yy z
xx yy
zz
(18)
or
⎛
⎝
⎜
⎞
⎠
⎟
ωωω
=++
+Γ+Γ+Γ
VI
MguFu
Mgu
Fu
Mgu
MguMgu Mgu
1
.
zxx
z
yy
z
xx
z
yy
z
zz
z
(19)
Under these circumstances, the Kibble balance equationis
no longer exact and the power ratios in the bracket of equa-
tion(19) represent fractional errors which must be eliminated.
This is achieved by careful alignment of the balance to reduce
the unwanted forces, torques and motions to levels where their
products are either less than 1 part in 109 of the measured
virtual power M g uz or are known with this uncertainty and a
correction can then be applied.
The techniques used to align Kibble balances apply to all
existing balances and are discussed in section3.8.
To relate the kilogram to fundamental constants, the vir-
tual electrical power VI is measured using the quantum Hall
effect (QHE) and the Josephson effect. The Josephson effect
allows the voltage V to be determined in terms of a measured
microwave frequency f as V = h f /2e. The QHE generates a
resistance R = h/ne2 where n is a quantum number. By suit-
able scaling and in combination with the Josephson effect
(
Vhf e2/=
′′
) the current
IVRnef 2//==
′′
can be measured
in terms of e and frequency
f′
. The elementary charge e can-
cels in the product of voltage and current
VIhff n4/=′
and
so, via equation(11) or (19), mass can then be related to the
Planck constant h, the metre and the second.
2.2. Types of Kibble and joule balances
Since the original invention of the Kibble balance, a number
of different balances have been described and built by labo-
ratories around the world. Mostly, they differ in the details
of their construction such as: the size of the balance, mech-
anisms used for moving the coil, weighing the mass and other
details. However, there are some more signicant variations
which can be categorised into a relatively small number of
types. This sectiondescribes the major variant types and the
existing watt balances that exemplify each type. To conserve
space, the descriptions have been limited to the latest version
of each existing balance but, if previous versions exist, a refer-
ence has been made to them.
2.2.1. Conventional two-mode two measurement phase
Kibble balances. As described in section1, the original Kib-
ble balance [3] has two modes, a weighing mode and a mov-
ing mode, each of which is associated with a measuring phase
which collects either weighing or moving data. The Kibble
balances listed below, in alphabetical order of the institutes’
acronyms, use this operating principle.
Korea Research Institute of Standards and Science
(KRISS), Korea: The KRISS Kibble balance [17] uses
a circular coil in the radial eld of a permanent magnet.
The coil is suspended from a commercial weighing cell
and both are guided in moving mode by the ‘piston in a
cylinder’ technique pioneered by MSL (see below). The
balance operates in vacuum.
Laboratoire National de Métrologie et d’Essais (LNE),
France: The balance and coil of the LNE Kibble balance
are supported by a large exure bearing [18, 19] which is
designed to provide accurate vertical movement. The bal-
ance is a custom made exure balance which supports the
coil and is locked during the moving phase. The circular
coil is placed in the radial eld of a permanent magnet.
The apparatus can be operated in vacuum.
Federal Institute of Metrology (METAS), Switzerland:
Researchers at METAS have built two Kibble balances.
The rst is described in [20, 21]. The second, METAS
Mark II [22], uses an optimised exure stage [23] to
move a customised commercial weighing cell and the
circular coil. The magnet generates a radial eld and is
temperature compensated using a magnetic shunt. The
balance can operate in vacuum.
Measurement Standard Laboratory of New Zealand
(MSL): Researchers at MSL use a pressure balance for
Metrologia 53 (2016) A46
I A Robinson and S Schlamminger
A50
both the weighing and moving modes. The cylinder of the
pressure balance provides guidance for the coil in moving
mode and the normal operation of the pressure balance
allows the comparison of coil force with the weight of
the mass. To minimise the effects of ground vibration,
they intend to use an oscillatory motion of the coil in the
moving mode [24] rather than gathering data at a uniform
velocity as adopted by other balances.
National Institute of Metrology (NIM), China: The original
NIM joule balance technique is described in section2.2.2.
Recently the apparatus has been changed to use a conven-
tional magnet/electromagnet which makes the original
mutual inductance measurement technique difcult. To
measure the geometric factor, they have adopted a variant
of the methods used in the moving phase of the Kibble
balance (see section 3.3). Almost all the techniques
described in section3 are relevant to the operation of this
form of joule balance; where there are signicant differ-
ences these have been pointed out in the text.
National Institute of Standards and Technology (NIST),
USA: The rst three NIST Kibble balances used elec-
tromagnets, versions two and three a superconducting
magnet [25]. The NIST-4 balance uses a permanent
magnet [26] and a circular coil. The coil is suspended
from a wheel balance using a band of ne titanium wires.
It operates in vacuum.
National Physical Laboratory (NPL), UK: NPL has made
two Kibble balances the Mark I is described in [5]. The
Mark II balance employs a circular coil on a glass former
suspended in the eld of a permanent magnet. The coil
is suspended from the balance beam used in the Mark I
apparatus which employs knife edges. The balance oper-
ates in vacuum.
National Research Council (NRC), Canada: The NPL
Mark II Kibble balance was shipped to NRC in 2009.
Modications were made to the mass lift [27] and the
coil support system to eliminate problems identied by
NPL prior to shipment. Further modications have been
made to reduce the noise of the moving measurements
and allow alignments to be made while the apparatus is
under vacuum.
2.2.2. The original joule balance.
National Institute of Metrology (NIM), China: The original
NIM joule balance design [28] replaced the moving mode
of the Kibble balance with measurements of mutual
inductance [29] between two stationary coils: the coil
which generates the eld for the weighing mode (the
exciting coil) and the movable coil [30]. Each measure-
ment is made by applying a linear current ramp to the
eld generating coil which induces a constant voltage
in the stationary movable coil, similar to [31]. This
measurement is repeated for different positions of the
movable coil. Weighings are performed with constant
currents in the exciting and movable coils. The resulting
equationrelates virtual energies which gives rise to the
name of the technique. The rst generation joule balance
reported results in 2014 [28] but heating effects and
problems with mutual inductance measurement have
concentrated future work onto its successor which is
described in section2.2.1 and no longer measures mutual
inductance.
2.2.3. Single-mode one measurement phase Kibble balances.
Bureau International des Poids et Mesures (BIPM): The
BIPM introduced a variation to the Kibble balance
technique [32] whereby the two measurement modes
are combined into one and the two measurement phases
are carried out simultaneously. This has the advantage
that, as the weighing current is always owing in the
coil, changes in the magnetic eld of the magnet do not
affect the measurement but, in their original proposal, a
superconducting coil [33] was required to ensure that the
moving voltage could be measured accurately with the
weighing current owing in the coil. BIPM are presently
working on a room temperature implementation of the
technique.
2.2.4. Moving magnet balances.
Ulusal Metroloji Enstitüsü (UME), Turkey: Recently,
researchers at UME have proposed a Kibble balance
where the magnet is moved and oscillates about an equi-
librium position [34]. This technique separates the signal
in weighing mode and velocity mode in frequency space.
The weighing current is applied and measured mostly at
zero frequency, while the electromotive force is gener-
ated mostly at the oscillation frequency. If the eld is not
perfectly uniform, the signals will spill over in multiples
of the oscillation frequency. In principle, however, it is
possible to separate the resistive voltage drop across the
coil from the induced voltage. So far there is only a white
paper on this idea.
2.2.5. Single-mode two measurement phase watt balances.
National Physical Laboratory (NPL), UK: Recently, NPL
has proposed a technique [16] to make a Kibble balance
which does not require precise coil alignment. The tech-
nique employs a variant of the BIPM single weighing/
moving mode but the measurement phases are separated
in the manner of the original Kibble balance. By treating
the mass raised and mass lowered states of the balance as
two independent Kibble balances, the theory introduced
in section 2.1 can be applied to eliminate the need for
precise alignments.
The uncertainties achievable using this technique should
be equivalent to those achieved by existing Kibble bal-
ances but the advantage will be in simplied construction
and operation. Once the kilogram has been redened,
more laboratories will wish to have an independent
realisation of the unit of mass which will enable them
to contribute to a worldwide consensus mass scale [35].
Metrologia 53 (2016) A46
I A Robinson and S Schlamminger
A51
Cost, both to acquire and operate, is becoming an increas-
ingly important concern and this new idea may help to
address these issues.
3. Design and operation of Kibble balances
3.1. Magnets
3.1.1. Source of the magnetic eld and ux guides. In gen-
eral, a magnetic eld can be produced by a polarized fer-
romagnetic material or by a current. In the latter case, the
current can ow through either a conventional or a supercon-
ducting coil. All three types of sources have been used to build
Kibble balances. However, the most recent designs all use
permanent magnets to source the eld. Because designs with
permanent magnets are, generally speaking, cheaper, simpler,
and easier to use. The main disadvantage of systems with
permanent magnets is the fact, that the magnetic ux density
cannot be varied over a large range. It can be useful for the
experimenter to change the magnitude of the eld to study
systematic effects. Electromagnets on the other hand can be
easily changed to different values by adjusting the current in
the coils. As a consequence, they require a feedback system
to sufciently stabilize the current during normal operations.
This is not a trivial task, if a relative eld stability of 10−8 is
required.
Regardless of the source of the magnetic eld, the magnet
system can be designed with or without a yoke. A soft-iron
yoke concentrates the magnetic ux from the source into a
small volume which is swept through by the coil in moving
mode. Magnet systems with yokes use the magnetic energy
very efciently. Because the magnetic energy is directed to
the coil volume, referred to as the gap and very little magnetic
energy is wasted to other regions. In yoke-less systems, the
magnetic energy is usually spread out over a large volume.
A disadvantage of the yoke is that another, magnetically
non-linear, material is introduced to the system. Special atten-
tion needs to be paid to the effect of the weighing current on
the yoke [36, 37].
Halbach arrays [38] are an alternative to using a yoke to
achieve a magnetic eld in a conned region of space and mit-
igate the disadvantage of having to introduce a magn etically
non-linear material.
A big advantage of a yoke, that Halbach arrays cannot
deliver, is magnetic shielding. If designed correctly, a yoke
can effectively shield the coil from varying external magnetic
elds. The yoke can also shield the working mass from the
magnetic eld of the permanent magnet. Furthermore, the
yoke also allows the magnetic eld to be shaped. For example,
the shape of the gap can be modied by precision grinding,
allowing the magnet designer to manipulate the vertical pro-
le of the magnetic ux density.
3.1.2. The shape and direction of the eld. The direction of
the magnetic force is given by the cross product of the current
and the magnetic ux density for each line element along the
wire of the coil. Hence, it is immediately clear, in order to
produce a vertical force, the eld has to be horizontal.
The most efcient use of the wire is achieved by coiling it
up in a circle with a vertical area vector and by using a eld
that is perpendicular to the wire at each point, i.e. a radial
eld.
A beautiful cancellation of the dependence of the geometric
factor from the size of the coil, and hence the temperature,
can be achieved if the magnetic ux density falls off as 1/r.
This idea is credited to Olsen [39]. In this case, the product
of the ux density and the wire length remains the same inde-
pendent of thermal expansion and contraction. For example,
as the radius of the coil grows due to thermal expansion, the
magnetic ux density encountered by the coil is reduced by
the same relative amount as the wire length is increased.
Ideally, the geometric factor remains unchanged over the
length of the coil sweep, i.e. the magnetic ux density is inde-
pendent of z. In this case, for a xed velocity, the induced
voltage remains constant and is easy to measure. Also, the pre-
cise location of the weighing position does not matter. A con-
stant magnetic ux density with vertical position is practically
impossible to achieve due to the fringing elds at the ends
of the gap. Typically the eld varies by a part in 104 over the
10’s of mm swept by the coil and the designer of the magnet
systems tries to keep this eld variation as small as possible.
3.2. Considerations for the magnet system
Every current Kibble balance uses a magnetic eld for its
operation. The purpose of the magnet system is to provide
the magnetic eld at the weighing position of the coil and
a few centimetres above and below this position. As dis-
cussed above, in the ideal case, the eld is purely radial at
the weighing position, i.e. it has no vertical component Bz = 0
and the radial component Br is only weakly dependent of the
vertical coil position z, in the best case
Bz 0
r/∂∂=
.
Today, researchers around the world agree that a perma-
nent magnet system is the most efcient way to generate the
magnetic eld. A permanent magnet system is typically con-
structed of two different materials: an active magnetic mat-
erial, typically Samarium–Cobalt, and a material that guides
the ux, very often mild steel. The magnetic ux is concen-
trated into an annular gap that houses the coil. Currently all
existing Kibble balances use one or more circular coils with a
vertical axis of symmetry. The NPL/NRC Kibble balance uses
two circular coils mounted on a single former. The two coils
are connected in series opposition and are vertically displaced
in two different air gaps.
Four different arrangements of the yoke and the active
magnetic material are in use today, shown in gure 3. The
two designs pictured on the left of gure3, the NPL-design
and the LNE-design, allow access to the complete gap from
the top. The coil can easily be inserted into the gap. In the
BIPM and MSL designs, the coil is completely surrounded
by the magnet; therefore, holes in the top or bottom yoke
piece allow the penetration of rods that connect the coil to
the balance and stirrup system. After the coil has been placed
into the magnet-system during construction, it needs to be
closed. Different strategies are used to close the magnet. The
top plate of the original BIPM magnet consists of sectors.
Metrologia 53 (2016) A46
I A Robinson and S Schlamminger
A52
After the coil is placed in the gap, the sectors are put in place,
completing the magnetic circuit on the top. Using sectors
instead of a monolithic top plate keeps the magnetic forces at
a manageable level. The researchers at NIST completely split
the magnet in two parts, insert the coil and rejoin the magnet.
This procedure needs a dedicated sturdy device because the
magnetic forces can be quite large, in excess of 10 kN. The
BIPM and MSL designs achieve a at eld at the weighing
position because this position is in a horizontal plane of
mirror symmetry.
In the NPL and LNE design, a at eld can be achieved
by carefully engineering the width of the gap as a function of
vertical position [40].
Besides the arrangement of the active magnetic material
and yoke, other design parameters are: the useful height of
the gap, the width of the gap, the mean radius of the coil and
the strength of the magnetic ux density at the coil position.
Table 1 summarizes the design choices that have been made
by nine groups. Remarkably, the design parameters only vary
within small ranges: the magnetic ux density at the mean
radius of the coil varies from 0.42 T to 0.95 T. The gap width
ranges from 8 mm to 30 mm. The smallest usable height
of the coil is 34 mm, the largest 100 mm. The nominal coil
radius is between 72 mm and 215 mm. The geometric factor,
Bl z/=∂Φ∂
, approximately the product of the coil’s nominal
circumference, the magnetic ux density at this position, and
the number of turns. For the available data, the geometric
factor ranges from 300 T m to 1250 T m.
The atness of the eld at the weighing position,
Bz
r
z0
/∂∂|
=
,
is an important concern. Typically two measurements are per-
formed in the weighing mode, named mass off and mass on.
Depending on the compliance of the coil support and the
details of the balance control, the coil can be at two different
vertical positions for each of these two measurements. The
substitution measurement that is carried out during force
mode can be written in one equationas
IlBz IlBz Mg
OffOff On On
() ()=−
(20)
Instead of using the position of the coil coordinates during
mass on and mass off, we use the difference and mean values,
i.e.
zzz
1
2
On Off
¯
()=+
and zzz
1
2
On Off
()∆=−
. A similar trans-
formation can be made for the currents,
II
I
A
1
2
On Off
()=−
and
III
1
2
On Off
()δ=+
. Here,
IA
, the current amplitude, is a large
positive number and
Iδ
is a small number which indicates how
symmetric the mass on and mass off currents are about zero
a) NPL-type b) BIPM-type
c) LNE-type d) MSL-type
Figure 3. Schematic drawings of the four permanent magnet designs used in Kibble balances. All magnets exhibit rotational symmetry
around the dashed line in the centre. The grey shaded parts concentrate the ux and are typically manufactured of mild steel. The hatched
parts represent the active magnetic material. The arrows indicate a possible direction of the magnetic polarization of the material. (a) NPL-
type. (b) BIPM-type. (c) LNE-type. (d) MSL-type.
Metrologia 53 (2016) A46
I A Robinson and S Schlamminger
A53
current. Replacing these variables and solving equation(20)
for the weight of the test mass yields after expanding the result
in a Taylor series up to second order in
z∆
and
Iδ
,
(¯)(¯)
()
(¯)
¯¯
⎛
⎝
⎜
⎜
⎜
⎞
⎠
⎟
⎟
⎟
δ
≈+
∆
+
∆
∂
∂=
∂
∂=
MgIlB zI
I
z
Bz
z
Bz
21 1
2
.
B
zzz
B
zzz
A
A
22
2
(21)
The second term in the parenthesis on the right side of the
above equationcan be made zero by adjusting the currents
such that they are equal and opposite,
I0δ=
. In traditional
Kibble balances, the current offset
Iδ
is adjusted by adding
or removing a small amount of mass on the tare side of the
balance.
Assuming a nite
z∆
, the third term can only be made
zero if the second derivative of the radial eld with
respect to z is zero. The effect of the third term is usu-
ally negligible as it scales with the square of
z∆
, which
is small. Publications of watt balances report typical rela-
tive changes of the magnetic ux over the height of the
gap to be about 10−4. Assuming a quadratic prole and a
gap height of 8 cm,
BzB
22
//∂ ∂
is
0.125 m2
−
. Combining this
value with
z10∆=µ
m yields
6.31012
×−
for the third term
in the parentheses on the right side of equation(21). This
number is more than three orders of magnitude smaller
than the typical uncertainties achieved by Kibble balances.
In conclusion, the eld atness does not play a major role
in the weighing mode as long as the weighing currents are
symmetric about zero.
A at eld is also desired for the moving mode. The elec-
trical measurements benet if the induced electro motive
force (EMF) stays constant as a function of time. In this
case, an equal and opposite voltage can be added to the EMF
and a null measurement with high gain can be made. If the
prole is at, it is easy to achieve a constant EMF by moving
the coil with constant velocity. If the eld changes signi-
cantly over the region where measurements take place, the
coil velocity may have to be varied slightly to maintain a
constant EMF. This is not difcult but the variation can often
be absorbed by the dynamic range of the voltmeter used for
the measurement.
3.2.1. Effect of the weighing current on the magnetic ux
density. One important assumption for the two-mode
two-measurement-phase Kibble balances is that the geomet-
ric factor is the same in the weighing and the moving mode.
However, in the weighing mode the coil carries a current and
in the moving mode it does not. The current causes ohmic
heating and a magnetic eld. Both effects can change the B l
between the modes.
A popular model for the dependence of the magnetic eld
on the current has been introduced by researchers at NPL [46].
The magnetic ux density is written as
BI BII1.
o2
() ()αβ=++
(22)
Rewriting equation(20) to reect the change in B as a func-
tion of current is
IlBI IlBI Mg.
OffOff On On
() ()=−
(23)
Using
III
On A
δ=+
and
III
OffA
δ=−
yields
MglBI III2123 .
oA2A2
()αδ βδ β=+++
(24)
There are three corrections terms to the unbiased term,
BI2oA
.
The rst two terms are proportional to the current asymmetry.
These vanish, if the weighing current for the mass off state
is exactly equal and opposite to the current in the mass on
state. The nal term,
IA2
β
is proportional to the current ampl-
itude squared. This term can introduce a serious bias to the
Kibble balance experiment but its magnitude can be estimated
by using test masses with different mass values. For example,
the relative size of this effect would quadruple, if a 0.5 kg test
mass is replaced by a 1 kg test mass. Note, introducing another
odd term in equation(22) yields another term proportional to
Iδ
. Only even powers of I produce bias terms which depend
on
IA
.
While the methods above provide an experimental way
to estimate the magnet non-linearity, they do not provide a
reason for the effect. Several possibilities exist to provide an
explanation:
Demagnetization of the rare earth magnets. The current
in the coil adds or subtracts, depending on the sign of
the current, a magnetic eld to the demagnetizing eld
in the magnet. This shifts the working point along the
recoil curve of the material, see [44], which can change
the magnetic ux density in the gap of the permanent
magnet. By using a symmetrical design, two permanent
magnets or two coils, this effect can be reduced. This
effect is mostly proportional to I, since the recoil curve is
very linear for rare earth magnets.
Change of the reluctance of the yoke. The magnetic eld
produced by the coil adds to the magnetic eld produced
by the permanent magnet and can change the relative
permeability of the yoke material, which depends in a
non-linear function on the magnetic eld, see [36, 37].
Consequently the reluctance of the yoke changes, causing
a change in magnetic ux density in the air gap. This
effect is, to rst order, proportional to I2.
The reluctance force. An iron core gets pulled inside a
solenoid if it is energized, because in this position the
Table 1. Comparison of the magnet design of Kibble balances at
nine different laboratories.
Labora-
tory
Bg
(T)
gw
(mm)
gh
(mm)
rc
(mm)
z
∂Φ
∂
(T m) Type
Refer-
ence
BIPM 0.6 13 80 125
500≈
BIPM [41]
KRISS 0.73 25 60 208 462 BIPM [17]
LNE 0.95 9 60 134 536 LNE [40]
METAS 0.64 8 50 100 757 BIPM [42]
MSL 0.6 16 100 120 420 MSL [43]
NRC 0.42 24 102 170 300 NPL
NIST 0.55 30 80 215 710 BIPM [44, 45]
UME 0.55 10 34 72 1250 BIPM [34]
Note. The magnet designs of the latest Kibble balances as of spring 2016
are shown. The column labelled Bg gives the magnetic ux density along the
radial direction in the centre of the gap with a gap width gw and a gap height
gh. The mean coil radius is abbreviated with rc.
Metrologia 53 (2016) A46
I A Robinson and S Schlamminger
A54
magnetic energy of the system is minimal and so is the
reluctance of the eld path. The same is true for a coil
inside a yoke. It experiences a force towards the point
where the reluctance of the yoke completing the magnetic
circuit of the coil is minimal [44]. This effect does not
change Bl; instead it generates a force. This force is pro-
portional to I2; hence, it would cancel if the currents were
symmetric about zero. However, it is more complicated,
because the coil moves between the mass on and mass
off state due to the suspension’s nite spring constant.
Hence, this effect can produce a different force on the
coil, even if the current is absolutely symmetric.
Temperature change of the rare earth magnet. The ohmic
heating caused by the current passing through the coil
heats up the magnetic material. With increasing temper-
ature, the remanence of the material decreases causing
a decrease of the magnetic ux density in the air gap.
Sections3.2.2 and 3.2.3 provide two ways of mitigating
this effect: (1) by engineering a better magnet and (2) by
actively heating the magnet in moving mode to keep the
thermal load on the magnet constant during all modes of
the Kibble balance experiment. This effect is proportional
to the ohmic heating, i.e. I2.
Temperature change of the yoke material. This effect is
much smaller than the effect of changing the temperature
of the active magnetic material, but it is listed for com-
pleteness. A changing temperature of the magnet system
can change the reluctance of the yoke material and the
geometry of the yoke, e.g. the width of the gap, through
thermal expansion. Both effects change the magnetic ux
density in the gap. This effect is also proportional to I2.
3.2.2. Engineering of magnets with smaller temperature coef-
cients. The preferred active magnetic material is samarium–
cobalt, Sm2Co17, a rare earth magnet. A typical energy density
of this sintered material is about 250 kJ m−3. Double this
energy density is provided by neodymium-iron-boron mag-
nets. However, for neodymium magnets the Curie temper ature,
the temperature where a magnetic material loses its magnet-
isation, is low, about 310 °C. Consequently, it has a large
temperature coefcient of its remanence (of order 10−3 K−1).
In contrast, samarium–cobalt has a Curie temperature of about
800 °C and its temperature coefcient is about a third of that
of neodymium.
For a typical Sm2Co17 magnet the temperature coefcient
of the ux density is about
3104
− × −
K−1. If the magnet
changes its temperature by −1 mK, the magnetic ux density
changes by
310 7
×−
, a number that is about a 10 times larger
than the relative uncertainty reached with Kibble balances.
This is only acceptable, because the temperature drift is usu-
ally very slow compared to the cadence of taking data. By
using an appropriate data sequence and data analysis, most of
the drift can be rejected in the nal result.
In recent years, magnet designs with much smaller temper-
ature coefcients have been proposed. The data collected with
these magnets will be quieter and it is less probable that the
result includes a bias caused by temperature drift.
Researchers at METAS have designed a magnet system that
uses gadolinium samarium cobalt [47] instead of samarium
cobalt as the active magnetic material [42]. Alloying gado-
linium to the samarium cobalt reduces the temperature coef-
cient from
3104
− × −
K−1 to
1105
− × −
K−1 at the expense
of reducing the remanence by 30 %.
Besides using a better magnet alloy, another technique has
been implemented in the METAS magnet system: temper ature
compensation with a shunt. This idea has previously been sug-
gested by LNE [40]. The magnet system has a second return
path for the magnetic ux. In the rst path, the ux goes
through the air gap, in the second path the ux goes through
a magnetic shunt made from an iron nickel alloy with very
low Curie temperature. Both ux paths are in parallel to each
other. With rising temperature, the reluctance of the shunt
path increases, which forces a larger fraction of the magnetic
ux through the air gap. The thickness of the shunt can be
nely tuned such that the increase in ux through the air gap is
exactly equal and opposite to the loss of magnetization in the
magnetic material. Hence, the magnetic ux density in the air
gap remains constant, independent of the magnet temperature
provided that no signicant temperature gradients exist within
the magnet. With this technique, it seems possible to build a
magnet system with a relative temperature coefcient of the
magnetic eld in the gap within
10 K
61
±−−
.
3.2.3. Actively controlling the temperature. The relative
change of the magnetic eld inside the gap is the product of
the temperature coefcient and the temperature change. The
above sectionfocused on minimizing the temperature coef-
cient. However, a similar end result can be achieved by
reducing the temperature change of the magnet. A temper-
ature change that is coherent with the sequence of the Kibble
balance measurements is especially troublesome. Coherent
temper ature change can arise from several causes. For exam-
ple, there is ohmic heating by the weighing current in the force
mode, while there is none in the velocity mode. Hence,the
heating power is modulated in phase with the experiment.
Researchers at NPL have implemented a simple but effec-
tive way to cancel this possible systematic effect [48]. The
coil former carries a heater coil with the same resistance as
that of the moving coil. During moving mode, a current equal
to that of the weighing current is passed through the heater
coil. The heater is a bilar coil which does not generate an
external magnetic eld and therefore does not produce a force
on the coil former or an external magnetic eld.
Besides temperature changes due to power uctuations
inside the Kibble balance experiment, temperature changes
from the environment (laboratory) can couple into the meas-
urement, see section3.11 for more details.
3.3. Voltage measurements
Voltage measurements are vital for the successful operation of
both measurement phases of a Kibble balance. In the weighing
phase it is necessary to measure the 5 mA to 20mA current
in the coil by measuring the voltage drop across a resistor.
Metrologia 53 (2016) A46
I A Robinson and S Schlamminger
A55
Usually the resistor is chosen to be between 200
Ω
and 50
Ω
to generate a voltage of order 1 V. In the moving phase
most existing Kibble balances move the coil at approximately
1 mm · s−1. This speed is chosen to take a sufcient number
of voltage measurements over a practical moving range of
around
20±
mm. The voltage generated by the coil is usually
chosen to be around 0.5 V.
In the moving phase, ground vibrations affect the apparent
motion of the coil with respect to the magnet; this induces
noise voltages in the coil [49, 50]. The interferometer system
measures this motion and, in a well designed system, the
voltage and velocity will be precisely correlated. If the
measurements of both velocity and voltage are made with a
bandwidth greater than that of the interfering ground vibra-
tions, their ratio can be free of vibration generated noise.
This condition sets a lower limit to the bandwidth of the
input stage of the voltage measuring system of a few hun-
dred hertz to 1 kHz. Usually the velocity and voltage signals
are integrated over the same period and the ratio of average
voltage to average velocity is determined by least squares
data tting. The joule balance uses the same technique of
integrating the velocity and voltage signals over the same
time but extends the integration time to points at which the
coil is stationary.
For the weighing phase, there are no critical requirements
for measurement bandwidth and voltage averages obtained
by integration over a few seconds usually provide sufcient
resolution.
3.3.1. Measurement techniques. A conventional voltmeter
can measure voltages with an uncertainty of a few parts in
107. To relate the measured voltages to fundamental con-
stants with an uncertainty approaching 1 part in 109, the
measurements are usually made by connecting an accurate,
Josephson-effect-based reference voltage in opposition to
the majority of the voltage to be measured and measuring
the difference, either directly with a digital voltmeter or, to
reduce measurement noise, by a combination of a low noise
amplier and digital voltmeter. The voltmeter/amplier is
calibrated, at the expected values of the difference voltage
using the voltage reference. By measuring differences in
this way, the combination of voltmeter/reference can mea-
sure voltages which are stable at the 0.1%–1% level to a few
parts in 109.
3.3.2. Josephson reference. The Josephson effect [7] allows
the construction of extremely precise voltage references by
illuminating weak links between superconductors with micro-
wave radiation of frequency f. The voltage generated is a mul-
tiple of hf/2e. In carefully fabricated and operated devices,
the uncertainty of the voltage generated can be much better
than 1 part in 109. These references are commonly operated at
frequencies of either 16 GHz or 75 GHz with associated volt-
ages of 33
µ
V and 155
µ
V respectively. These voltages are too
small for practical use at room temperature. However, arrays
of these junctions, with output voltages up to 10 V, are avail-
able from several laboratories [51–54].
Two types of array have been used for Kibble balance work.
Hysteretic arrays The hysteretic array uses insulating junc-
tions and can be set to any multiple of hf/2e within its
operating range [55]. However, such an array is very
sensitive to electrical noise and interference which can
cause it to suddenly change its voltage to a different (usu-
ally lower) multiple of hf/2e requiring extreme care in its
use. Only one Kibble balance (the NPL Mark II [46]) has
made direct measurements using such an array.
Programmable arrays All existing Kibble balances either
use, or intend to use, the programmable Josephson array
[56–58] which consists of a string of Josephson junc-
tions with a normal metal substituted for the insulator.
Connections are made to the array to divide it into seg-
ments containing numbers of junctions that are usually
related in a binary manner. Bias currents of ± a few
milliamperes can be applied to individual segments
to generate positive or negative voltages equal to the
number of junctions in the segment multiplied by hf/2e.
This allows the array to generate any voltage up to ± its
maximum voltage in steps of hf/2e. Theoretically, a 75
GHz array can be set to match the voltage to be meas-
ured to within
155 280/≈µ
V requiring only a modest
linearity and accuracy of the voltmeter measuring the
difference.
The programmable array can change its voltage rapidly
and this property can be used to simplify the voltage
measurement procedure during the moving phase. A good
approximation to the voltage generated by the coil can be
calculated from the velocity of the coil and the magnetic
ux density. This allows the array voltage to be continu-
ously adjusted to null the input to the voltmeter during the
acceleration and deceleration of the coil. This eliminates
errors due to transient thermal EMFs generated by the
switches which would otherwise be necessary to protect
the voltmeter/amplier from overload.
The output voltage of the array is not well dened during
the time that it is switching from one voltage state to
another so, to ensure the accuracy of the measured
voltage, once the coil has reached its target speed [59],
the voltage from the array is xed and any changes are
measured via the voltmeter/amplier.
3.3.3. Voltmeter. As mentioned in section 3.3.2, in theory a
voltmeter of fairly modest linearity and stability could be used
to measure the difference voltages. In practice, the coil volt-
age noise is dominated by the effects of ground vibrations. In
the weighing mode, the resistor voltage contains noise comp-
onents from the servo system which keeps the balance in equi-
librium. These noise sources limit, to around 1000, the gain of
the amplier which amplies the difference voltage between
the voltage source and voltage reference. Therefore the volt-
meter must achieve part in 106 level calibration, linearity and
stability to achieve an overall measurement uncertainty of a
part in 109. Modern voltmeters can easily achieve this level
of performance but often need time for carrying out internal
‘autozero’ procedures to eliminate the effects of drifts in their
Metrologia 53 (2016) A46
I A Robinson and S Schlamminger
A56
circuitry. This is not a major problem in the weighing phase of
the measurement but does introduce problems in the moving
phase where it is desirable to measure the voltage and velocity
continuously over identical time intervals. The problem can
be addressed by the NIST technique [60] which uses three
voltmeters in a cyclic fashion where one is measuring, another
is performing auto zero functions and the third is preparing to
measure.
Another way of achieving the same end is to use a single
voltmeter preceded by a highly stable preamplier [48]. This
can eliminate the need for autozeroing as the effective drift of
the voltmeter is reduced by the gain of the preamplier which
becomes one part of the unavoidable linear temporal drifts in
the measurement system. The reversals inherent in the meas-
urement procedure allow such drifts to be removed from the
measurement in the postprocessing calculations. The only
problem with the use of a preamplier is that most preampli-
ers with nanovolt level drifts have low bandwidths which
may be incompatible with the need to eliminate noise from the
moving phase by correlation between the weighing and moving
measurements. This problem is addressed in section3.3.4.
3.3.4. Ampliers. Most highly stable nanovolt level DC
ampliers [61, 62] are intended for use in measurements tak-
ing many seconds and have low bandwidths. Integrated circuit
operational ampliers can have much higher bandwidths but
have unacceptable low frequency performance: they drift with
time. By combining the two types of amplier, it is possible to
assemble a composite amplier which has a bandwidth of sev-
eral hundred Hz and nV level drift [48]. This can be achieved
by using the low drift amplier to monitor the difference in
voltage between the inverting and non-inverting input pins of
the high bandwidth amplier. A simple servo loop feeding the
offset nulling input of the high bandwidth amplier drives the
input voltage to zero ensuring that the composite amplier is
close to the performance of an ideal amplier at low frequen-
cies. Extreme care must be taken to minimise the effects of
thermal EMF’s in critical parts of the circuit [48].
3.3.5. Synchronisation of the voltmeter and counter. To elimi-
nate correlated noise between the average voltage and average
velocity measurements in the moving phase, it is necessary
for the signals to be integrated over the same time and for the
bandwidths of both signal channels to be greater than the band-
width of the noise signal. The velocity signal is a frequency,
generated by the laser interferometer, which is measured using
a frequency counter. By using passive noise isolation tech-
niques, such as resilient pads in parts of the support structure of
the balance, it is possible to limit the bandwidth of vibrational
noise to a few hundred hertz. Under these circumstances, dif-
ferences in the integration times of less than 1 ms will have lit-
tle effect on the elimination of correlated noise. Many methods
of achieving this aim are possible and indeed have been imple-
mented. For illustration, we will describe a method similar to
the one used on the NPL Mark II balance [48] but employing
a different form of frequency counter. It provides simple and
accurate measurements of velocity and voltage with the caveat
that the integration times are not identical.
The technique uses a charge balance voltmeter and a time
interval analyser. Both of these instruments possess the great
advantage that they measure continuously. The charge bal-
ance voltmeter can be considered to be an integrator with
two inputs. The rst is connected directly to the voltage to be
measured, the second is connected alternately to positive and
negative reference voltages. The reference input polarity is
switched whenever the output of the integrator reaches one of
two xed limits. The times for which each reference is applied
are accumulated and, upon receipt of a trigger pulse, the ana-
logue-to-digital converter (ADC) waits until a whole number
of reference switching cycles has taken place and reports the
accumulated data. The average value of the input voltage can
be calculated from this data and calibration information. The
period of the reference switching cycle is chosen to be around
200
µ
s and varies about this value.
The time interval analyser counts events and notes the time
of the rst and last event. This allows the average frequency of
the events to be calculated but, as the last event of one meas-
urement corresponds to the rst event of the next, the counter,
like the voltmeter described above, measures its input contin-
uously. Whenever it notes a time it generates an output pulse.
This ‘gate pulse’ is used to trigger the voltmeter which will take
approximately 200
µ
s to respond so, on average, the times of
the integrals will be shifted by 100
µ
s with a jitter of
200±µ
s.
This may cause a slight decrease in the correlation between
voltage and velocity signals but both integrals will be correct.
There is a further advantage to the back-to-back data collec-
tion in that no part of either signal is lost and, if desired, the
integration time can be increased in post processing, giving
the ability to analyse and correlate the data at both higher and
lower frequencies.
3.3.6. Joule balance measurements. In its equivalent to the
Kibble balance moving mode, the joule balance adopts a simi-
lar measurement scheme to the Kibble balance except that the
integrals mentioned above are taken between points where the
balance is stationary. This reduces the velocity integral to a
simple difference in position of the coil. However, increased
care is required in the measurement of the coil voltage int-
egral. As the motion of the coil must be started and stopped
the reference voltage must be varied to keep the voltmeter in
its linear range. A programmable Josephson voltage reference
does not produce well dened transitions between voltages
(section 3.3.2) and this can increase the uncertainty of the
measurement. This problem is solvable and is presently under
investigation [63, 64].
3.4. Current generation and measurement
In weighing mode, a current is passed through the coil to
generate the electromagnetic force. The current continues
on through a resistor and the potential difference across this
resistor is measured precisely, in a four terminal geometry,
using the techniques described in section3.3. Figure4 shows
a simplied circuit diagram of a Kibble balance in weighing
mode. Typically, the electromagnetic force is half the weight
of the mass standard used in the experiment and the current is
Metrologia 53 (2016) A46
I A Robinson and S Schlamminger
A57
reversed, such that the difference of the two electromagnetic
forces corresponds to the weight of the mass. In this section,
we discuss the current sources, the measurement resistor, and
the process required to calibrate the measurement resistor
using the quantum Hall effect.
3.4.1. Current sources. Typical weighing currents range from
a few milliamperes to about 20 mA, given by the quotient of
the geometric factor (see column 6 of table 1) and half the
weight of the test mass. The current source needs to be able
to generate a bi-directional current, since the force reverses
between the mass-on and mass-off measurement. Properties
to consider designing a current source are: (1) the impedance
to ground, (2) the update rate, (3) the resolution of the digital
to analogue converter (DAC), and (4) the noise of the cur-
rent source. Details to each of these design considerations are
discussed below. Descriptions of current sources for Kibble
balances can be found in [48, 65].
The current source should be fully isolated to allow the
experimenter to choose the point at which the Kibble balance
measurement circuit will be connected to the mains ground
wire. If the circuit is connected to mains ground at more than
one point parasitic currents can ow which can introduce a
bias to the experiment if they ow through the coil or resistor,
but not both. For example, a current owing through the coil
but not through the resistor, will contribute to the electro-
magnetic force, but it will not be measured, resulting in a bias
in the experiment. In order to avoid such parasitic currents,
all elements of the electrical measurement circuit should have
a high resistance to ground. High in this context is approxi-
mated by dividing the resistance in the measurement circuit
by the maximum acceptable bias. For example, the current
measurement requires a relative uncertainty of 1 part in 109
and a 100
Ω
resistor, the resistance to ground should be more
than 100 G
Ω
and would usually be at least 1 T
Ω
. One possible
path of parasitic resistance is via the cables that carry the con-
trol signals from the control computer to the current source.
A good way to minimize this leakage path is to employ bre
optical communications between the controller and the current
source, e.g. see [66]. Another leakage path is via the power
supply for the circuit. This leakage can be eliminated either
by powering the current source with batteries or by using a
mains power supply which has been carefully isolated. Such a
supply is described in [67]. This is a general problem for the
Kibble balance and is further addressed in section3.11.4.
As a rule of thumb, the update rate of the current source
should be at least an order of magnitude faster than the closed
loop bandwidth. This reasoning gives a lower bound for the
update rate of the current source. The faster the update rate of
the current source the better. However, the closed loop system
in the weighing mode contains at least two low pass lters,
attenuating the effect of changes at the current setpoints at
high frequencies. The resonance frequency of the mechanical
system of the Kibble balance depends on the design but is in
the ball park of tenths of Hz to tens of Hz. This leads to an
attenuation of the quotient of balance position and coil cur-
rent at high frequencies. The second low pass lter is elec-
trical and is given by the inverse of the time constant of the
system composed of the self inductance of the coil and the
series resist ance of the measurement resistor and the coil, i.e.
LR/τ=
. For example, a self inductance of 1 H and a total
resistance of 100
Ω
yield a time constant of 10 ms. A Kibble
balance coil in a permanent magnet has typically an induct-
ance of a few henries. The total resistance is typically below
1 k
Ω
. Hence, this low pass lter attenuates the quotient of
coil current to applied voltage for frequencies above 1 kHz.
This effect can be modied by the internal feedback of the
current source.
The simplest design of the current source is a variable
voltage source followed by a transconductance amplier. In
this case, the resolution of the current source is given by the
resolution of the voltage source. Naively, one would think that
in order to measure the current with a relative uncertainty of
10−9, a resolution of 10−9 is required. However, this require-
ment calls for a digital-to-analogue converter (DAC) with
30 bit resolution, which is not commercially available. One
technique to obtain sufcient resolution is to add two volt-
ages together with a summing amplier, where one voltage
is attenuated by a voltage divider. In the NPL balance [48],
for example, two 16-bit DAC outputs are combined with a
relative gain of
2000 :1−
. In the NIST Kibble balance [65],
two 20 bit DAC outputs are combined with a ratio of
1000 :1
.
The ADC with the larger gain is used for coarse control of
the balance and the one with the smaller gain for ne con-
trol. Since the current source is in a closed loop feedback
system, a higher resolution than the nominal resolution will be
achieved, because the Kibble balance will average or integrate
the applied current with a time constant given by the differ-
ential equation of the balance. Hence the output rate multi-
plied with this characteristic time gives an effective increase
in resolution of the DAC.
The combination of the two DACs will not be linear to their
combined resolution but, if the control software is written
to minimise unnecessary changes in the output of the more
signicant DAC, the resolution will, for most of the time,
be equal to that of the less signicant DAC. When it is necessary
to change the more signicant DAC, it is set to centre the less
Figure 4. Typical circuit topology during force mode. The current
is passed through the coil, drawn as an inductive and a resistive
element and a measurement resistor. The voltage drop across
the measurement resistor is compensated with a programmable
Josephson voltage system (PJVS) and the residual voltage is
measured with a digital voltmeter (DVM).
Metrologia 53 (2016) A46
I A Robinson and S Schlamminger
A58
signicant DAC in its range; this increases the time to the next
change and its associated small glitch in the combined output.
The noise of the current source is one contribution to the
measurement noise in the weighing mode and ultimately
the type A uncertainty. However, this part is not likely to be
the dominating factor in the measurement noise. In this con-
text, it is best to think about the current noise in the frequency
domain. Depending on the frequency, the noise level of the
current source varies, achieving worst levels at low frequen-
cies due to 1/f noise. However, this is not a problem. The
critical time scale is given by the bandwidth of the weighing
servo. In weighing mode, the servo adjusts to keep the balance
position constant over many minutes without applying rapid
changes of current which would be seen by the measurement
system as noise. In practice, the bandwidth of the servo is of
the order of 1 Hz. The action of the servo eliminates the need
for excessive low frequency stability in the current source. For
some balances, e.g. METAS, BIPM, a xed current is required
and such circumstances often require a highly stable current
source. However, care should be taken to minimise the noise
of the current source at frequencies higher than the bandwidth
of the servo. As the weighing data is usually taken by a series
of averages, each lasting a few seconds, the sensitivity of the
integral used to form the average, to high frequency noise
drops linearly with the frequency of the noise. This indicates
that close attention should be paid to the noise of the source in
the region around 1 Hz to 100 Hz.
In a practical situation, the slow drifts in the balance due
to outgassing and temperature changes usually dominate over
random noise. If the dynamic range of the less signicant DAC
is chosen to ensure that it is many times the change expected
over the duration of a single weighing, the weighing current
should be glitch free during each measurement.
To further reduce the mid-range noise it is possible, once
the balance has stabilised, to reduce the bandwidth of the
more signicant DAC. As it, and its reference, will contribute
the majority of the current source noise, a signicant reduc-
tion in its bandwidth should result in a signicant reduction in
the critical mid-range noise.
3.4.2. The measurement resistor. The measurement resis-
tor in the Kibble balance is, typically, a conventional resis-
tor (wire wound or thin lm). This conventional resistor is
calibrated against a quantum Hall resistor (QHR) on a regular
basis (see next section). It is used in a four terminal congura-
tion: two terminals connect to the current leads and two con-
nect to the potential leads. The potential leads are connected
to a voltmeter with high input impedance. Ideally, no current
is owing in the potential lead, hence contact resistances in
the potential leads do not bias the measurement.
The measurement resistor is kept either in an air or an oil
bath with good temperature stabilization. Nevertheless, the
temperature of the bath must be carefully monitored. Most
resistors have a linear temperature coefcient of several
1
µΩΩ
−
K−1. For certain resistors, in addition to the linear
temperature coefcient, a quadratic temperature coefcient
must be considered. Besides the temperature dependence, the
resistance depends on the measurement current, mostly due
to self-heating. A power coefcient, i.e. the change in relative
resistance divided by the power dissipated in the resistor, is
used to quantify this effect. If the calibration current is dif-
ferent from the current used in the Kibble balance, a power
correction may become necessary. Some resistors, with a cer-
tain design, require an additional pressure correction which
includes changes in the atmospheric pressure and the hydro-
static pressure, exerted by the oil above the resistive element.
For these resistors, the ambient atmospheric pressure must
also be monitored.
In some cases, the resistor can cause local heating of the
oil surrounding it which can cause transient effects at the start
of the weighing mode. If the element is surrounded by a can,
the removal of the can may allow more efcient mixing of the
oil which may reduce the heating effect to acceptable levels.
Otherwise it may be possible to use isolated heaters, near the
resistance element, to keep the power dissipation in the oil
bath constant.
3.4.3. Resistance determination with the quantum Hall
effect. To link mass to the Planck constant the resistor used
in the Kibble balance measurement must be related to the
quantum Hall effect (QHE). A QHE measurement system
consists of a superconducting magnet, a QHE device and a
cryogenic current comparator bridge. The QHE device is held
in a low temperature probe in the 5 T to 14 T eld of the
superconducting magnet. The Hall resistance of the quantised
Hall sample is compared to that of the Kibble balance resistor
using a cryogenic current comparator [68, 69]. The voltages at
the potential terminals of the two resistors are adjusted to be
equal by passing different currents through them and the ratio
of the resulting currents is measured using a technique which
makes use of the Meissner effect. By this means, the Kibble
balance resistor can be measured with an uncertainty of a few
parts in 109.
As mentioned above the value of the resistor will depend
on the power dissipated in it. If possible, the resistor should be
calibrated at the currents that are used in the Kibble balance
measurements. If this is not possible, a power coefcient must
be measured which can then be used to correct the value of the
resistor to the operating power. The use of a power coefcient
will, in general, increase the uncertainty associated with the
resistor.
Ideally, the resistor should be measured in situ, either by
using cables [48] over tens of metres, or via a transportable
QHR measurement system [70]. If it is necessary to transport
the resistor to the quantum Hall effect system, extreme care
should be taken in the transport arrangements. Mechanical
shocks can alter the value of the resistor in an unpredictable
way and would increase the uncertainty assigned to the resist-
ance measurement. Extremely good temperature control and
monitoring is also required. A thermal shock to the resistor,
caused by changing thermal environments during transport,
could permanently change its value or its temporal drift. In
addition, if the temperature gradients in the enclosure varied
from the location of use to the location of measurement,
and this affected the temperature difference between the
monitoring thermometer and the resistor, the resistor value,
Metrologia 53 (2016) A46
I A Robinson and S Schlamminger
A59
corrected for temperature, would be different at the two loca-
tions. The magnitude of this problem can be investigated by
changing the temperature gradient across the resistor enclo-
sure at a constant temperature as seen by the monitoring ther-
mometer. There should be no signicant correlated changes in
the device resistance.
3.5. Velocity and position measurement
3.5.1. Interferometry. Laser interferometry is used to relate
the vertical velocity of the coil/mass pan to the metre and the
second and to monitor the position of the coil/pan. In some
Kibble balances, additional interferometers are used to moni-
tor the rotation of the coil.
3.5.2. Refractive index of air. The wavelength of light in air
air
λ
is altered from its vacuum value
vac
λ
such that
n
vacair
λ λ=
where n is the refractive index of air. If a Kibble balance is
operated in air, a correction must be made for the refractive
index of the air, which depends upon its temperature, pressure
and composition and is of the order of 300 parts in 106. How-
ever, most existing Kibble balances are operated in vacuum, at
a pressure of less than 0.1 Pa, which makes the this correction
and the correction for the effects of air buoyancy on the work-
ing mass (section 3.7.5) negligible.
3.5.3. Light source. All existing Kibble balances use visible
lasers to provide the length reference for interferometry. The
frequency of the light emitted by the laser needs to be stabilised
to achieve the uncertainties required. An excellent stabilisation
method involves locking the laser frequency to a line in the spec-
trum of molecular iodine [71]. Such iodine-stabilised lasers can
produce almost monochromatic radiation with frequency sta-
bilities far better than 1 part in 109 and, as many of the lines are
well characterised and recommended for the practical realisation
of the metre [72], such a laser can act as a primary standard of
length. Alternative schemes, such as Zeeman stabilisation [73]
are commonly used but require calibration against a primary
standard in intervals of months.
The light from the laser can be coupled into the interferom-
eter either by free space propagation or by use of an optical
bre. Free space propagation has the advantage that the verti-
cality of the beam can be checked and adjusted from outside
the vacuum chamber which houses the Kibble balance, but
has the disadvantage that the laser housing has to be main-
tained in alignment with the apparatus within the chamber,
a requirement which is often difcult and time consuming to
achieve. Fibre coupling frees the laser to be placed anywhere
in the laboratory and, if the bre is passed through a vacuum
seal into the chamber, avoids the need for optical windows in
the vacuum chamber wall. However, this requires that a pro-
cedure be established to ensure that the laser beam is vertical
within the chamber.
3.5.4. Types of interferometer. So far, two different types of
interferometers have been used in Kibble balances, Michel-
son and Fabry–Perot interferometers. Table 2 shows the
types of interferometer used in Kibble balances at different
laboratories.
Michelson In a Michelson interferometer, the light is split
into two arms, the measurement arm and the reference
arm. The length of each arm is the distance from the beam
splitter to a reector. The reector of the measurement
arm is mounted on the moving coil. The measured optical
distance is twice the displacement of the reector in the
measurement arm. This ratio of optical distance to actual
displacement can be increased using multiple passes.
Based on the frequency difference of the light entering
the two arms, a distinction between an homodyne and
heterodyne interferometer is made.
Homodyne In a homodyne interferometer, the optical fre-
quency of the light entering both arms is identical. Hence,
if the lengths of both measurement arms remain constant,
the interference signal at the output port has a constant
brightness. Moving the measurement reector will cause
the output port’s brightness to go through fringes, i.e.
change from dark to bright to dark. The period of this
signal change corresponds to a change in the optical
path length by one wavelength. A Michelson type inter-
ferometer has two output ports, referred to as dark port
and bright port. In a conventional beamsplitter energy
conservation requires the sum of the luminous uxes to
add to a constant, if one port is bright the other is dark
and vice versa. However, the beamsplitter used in the
NPL/NRC interferometer is deliberately made lossy to
allow the determination of the position of the coil at low
velocity [74]. Monitoring both ports allows rejection of
the intensity uctuation of the laser and the subdivision
of the fringes. If the measurement reector moves with
constant velocity the fringe crossing frequency is given
by the
Nv2/λ
, where v is the velocity of the coil and λ the
wavelength of the laser and N the number of passes.
Heterodyne In a heterodyne interferometer [75], light enters the
two arms with frequencies that differ by a modulation fre-
quency ranging from about 1 MHz to 50 MHz. If the reector
of the measurement arm is stationary, the interference signal
is at this frequency difference. If the reector moves with a
velocity v along the line of sight of the measurement beam,
the interference signal is Doppler shifted by
Nv2/λ
. The sign
of the frequency shift encodes the direction of motion.
The essential difference between a homodyne and a heter-
odyne interferometer is the detection frequency, which is
increased by the modulation frequency in the heterodyne
Table 2. Types of interferometers used in the latest Kibble balances
built by different laboratories.
Laboratory Mode Laser Type
BIPM Heterodyne Nd:YAG Michelson
KRISS Homodyne I2Michelson
LNE Heterodyne Nd:YAG Michelson
METAS Homodyne HeNe Fabry–Perot
MSL Heterodyne HeNe Michelson
NPL Homodyne I2Michelson
NRC Homodyne HeNe Michelson
NIST Heterodyne Nd:YAG Michelson
Metrologia 53 (2016) A46
I A Robinson and S Schlamminger
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interferometer. This is one point worth considering when
deciding between using a homodyne or an heterodyne
interferometer. The other important consideration is the
optical non-linearity [76]. In brief, optical non-linearity
occurs when light that is assumed to be in the measure-
ment arm leaks into the reference arm and vice versa. In
the homodyne case, the incident laser beam is, sometimes,
separated by the polarization state into the measurement
and reference arm and, hence, the optical non-linearity
is caused by polarization mixing. Polarization mixing
occurs if the polarizing beam splitter is not perfect. Part
of the light that should have been reected is transmitted
instead. Similarly, for a heterodyne interferometer, light
of the wrong frequency can leak into the other arm.
This effect is called frequency mixing. Another mech-
anism for frequency mixing to occur, is when the two
polarization directions have different frequencies and
some of the light not intended for part or all of the interfer-
ometer leaks into these areas due to imperfections in the
optical elements. Both optical non-linearities, frequency
and polarization mixing produce biases that are periodic
in displacement. The period is referred to as fringing
period. By averaging the data over a fringing period, this
error can be attenuated. The optical non-linearity can be
a limiting factor in the achievable signal-to-noise ratio of
the velocity mode measurement.
Fabry–Perot A Fabry–Perot interferometer requires only one
arm. Two mirrors in the arm are aligned such that they
form an optical resonator, commonly called a cavity. The
reection coefcient of the cavity changes periodically
with a period of
2/λ
. A photo diode measures the light
reected from the cavity. Similar to the homodyne detec-
tion the velocity signal produces a fringing frequency
of
v2/λ
. So far, only one National Metrology Institute,
METAS, is using a Fabry–Perot interferometer [21, 77].
The current Kibble balances that use Michelson interfer-
ometers employ corner cubes as reectors for the measure-
ment arm. The METAS Kibble balances use at mirrors to
form the Fabry–Perot cavity. Flat mirrors are much smaller
than corner cubes, an important factor if the mirror has to be
mounted inside the narrow air gap of a permanent magnet.
Systematic biases in the interferometric velocity measure-
ment can arise from restricted width of the beam and dist-
ortions of the wavefronts and angles between the reference
beam and the measurement beam. The wavefront distortions
are especially troublesome if the moving reector is subject
to parasitic motions, e.g., perpendicular to the measurement
direction, that may change the wavefront. A comprehensive
description of these biases can be found in [13, 78–80].
3.5.5. Alignment of the laser beam to the vertical. Correct
operation of a Kibble balance requires that only the verti-
cal velocity of the coil/mass pan is measured. This requires
that the interferometer’s laser beam is accurately vertical at
the point where it reects from the reector which is used
to measure the velocity. A simple way to achieve this is to
allow the laser to reect from the surface of a pool of liquid
inserted into the beam path. The centre of the surface of an
undisturbed liquid pool is horizontal. If the angle of the laser
beam is adjusted so that the incoming and outgoing beams
are exactly coaxial, the beams will be normal to the surface
and therefore vertical. A simple way to detect coincidence
of the beams is to observe the reected beam when it hits
the periphery of the entrance pinhole for the laser beam. The
angle of the beam is adjusted until the reected beam exits
through the pinhole. The adjustment can be made with a reso-
lution of about 0.1 mm. If the pinhole and reector are sepa-
rated by about 2 m, the beam can be aligned to the vertical
to about 25
µ
rad. If the beam is not vertical a cosine error
results. Using the expansion
cos12
2
() /αα≈−
, the term
2
2/α
must be below 1 part in 109. This requires that α is less
than 45
µ
rad. The simple technique described can full this
requirement. The verticality requirement described above is
relatively easy to achieve, since the measurement bias is pro-
portional to the angle squared. Another bias, can occur, when
the coil has a parasitic horizontal velocity, for example, uy. In
this case, if the laser beam deviates from vertical in the direc-
tion of the y axis by
x
α
, a measurement bias of
u
xy
α
occurs
[81].
A number of techniques have been used for this adjust-
ment; some substitute a tiltmeter and mirror for the liquid sur-
face to avoid problems with handling liquids [5]. If the laser
beam is introduced into the vacuum chamber from outside
and is not deviated before it is reected from the coil or mass
support, the verticality of the beam can be determined exter-
nally. If, however, the laser is introduced via a bre into the
chamber laser verticality must be measured [82] and adjusted
in vacuum or it must be ensured that evacuating the chamber
does not affect the verticality of the laser beam. Motorised mir-
rors can easily be used to adjust the beam angles. To measure
laser vertical, either of the general techniques described above
may be used but care must be taken to avoid liquid evapora-
tion in the vacuum chamber or changes in the sensitivity and
offset of a tiltmeter on transition from vacuum to air. A pos-
sible solution to using a liquid mirror open to vacuum without
evaporation problems was suggested in [83] using gallium
which when gently heated forms a liquid mirror with very low
vapour pressure.
3.5.6. The Abbe error. The laser beam retroreector is always
mounted so that, in moving mode, its angular velocities
x
ω
and
y
ω
about the horizontal axes x and y are minimised. If the
effective point of measurement of the velocity u is not on a
vertical line through the centre of mass but is offset from it by
distances rx and ry the angular velocity will be coupled into the
measurement of vertical velocity. For small angles, the mea-
sured velocity um can be approximated to be:
uurr.
mx
yy
x
ωω=− +
(25)
To achieve an overall contribution to the uncertainty of
the measurement of a part in 109 for angular velocities of
0.1
µ
rad s−1 and a coil velocity of 1 mm s−1, rx and ry must
each be less than 5
µ
m.
In an apparatus which uses a single interferometer, the
adjustment can be made by xing the balance beam and
Metrologia 53 (2016) A46
I A Robinson and S Schlamminger
A61
causing the arm of the balance containing the retroreector
to perform pendulum oscillations. The horizontal position
of either the centre of mass or the retroreector can then be
adjusted until there is no apparent vertical motion, as seen by
the interferometer, at the fundamental frequency of the pen-
dulum motion.
For balances which use three interferometers placed around
the periphery of the coil, the adjustment process is carried out
mathematically by weighting the contributions of the three
interferometers to the calculation of the velocity of the coil [84].
3.5.7. Synchronisation of velocity and voltage measure-
ments. To reduce the noise of the moving measurement, the
measurements of vertical velocity must be synchronised to
those of the voltage generated by the coil. The techniques for
achieving this are discussed in section3.3.5.
3.5.8. Provision of a time reference. The Kibble balance
requires a reliable and accurate time reference which is trace-
able to the SI. As this reference is needed at an uncertainty
better than a part in 109 and the primary clocks which main-
tain the SI unit of time operate at levels better than parts in
1016 this is not usually a problem [85].
Many NMIs have one or more Hydrogen Masers which are
referenced to primary clocks. The output of the maser is usu-
ally distributed as a 10 MHz signal via lab-wide optical bres
and coaxial cables. In addition, modern GPS-disciplined
oscillators, which take their long-term time reference from
visible GPS satellites, can be used, provided that the oscillator
which is controlled has excellent phase noise and sufcient
medium term stability to work properly when few satellites
are available [86, 87]. Rubidium oscillators can also be con-
sidered but their drift can be affected by helium in the atmos-
phere and they must be checked periodically against a primary
standard. Caesium clocks which are used to realize the deni-
tion of the second can be used directly. Such signals usually
drive the reference input of the critical counters/synthesisers
in the system (those for the velocity measurement and the fre-
quency reference for the microwave synthesiser which drives
the Josephson array).
In all cases, it is useful to have an indication of the cor-
rect operation of the standard and this is routinely provided
by high-quality GPS-disciplined oscillators. It is also prudent
to have a secondary mechanism for checking the frequency
references via an independent route to a primary standard.
A possibility for this is to use an off-air frequency standard,
which makes use of a low frequency radio signal whose car-
rier is locked to a primary standard. In general such standards
do not have the low phase noise required for direct use but, by
using measurement times of more than 1000 s, can provide a
valuable consistency check at relatively low-cost.
3.6. The local acceleration due to gravity
To derive the mass M from the weight Mg, which is measured
by the Kibble balance, it is necessary to know the value of
the acceleration due to gravity g at the centre of gravity of the
mass during the weighing phase of the measurement [88, 89].
A number of geophysical effects cause the value of g to vary
with time and position. In general, g is measured at a different
place and time than those required; therefore, the measured
value must be corrected to compensate for this.
An absolute gravimeter is necessary to measure g with an
uncertainty of a few parts in 109 which is necessary for a low
uncertainty in the overall measurement. Absolute gravimeters
are expensive instruments which are also time consuming to
set up and operate. Thus a number of procedures exist for
combining the measurements made by absolute gravimeters
with those made by the Kibble balance; this sectionwill dis-
cuss their relative merits.
3.6.1. Absolute gravimeters. Absolute gravimeters oper-
ate by dropping a mass in a vacuum and timing its fall. The
dropped mass can be either macroscopic [90] or atomic [91,
92]. At present, the most common gravimeter used with Kib-
ble balances drops a macroscopic reector. The reector is
incorporated into an interferometer and the passage of inter-
ferometer fringes caused by the fall of the object in vacuum
are timed. If the laser frequency and the time reference are
calibrated in SI units, the instrument measures g in SI units
with an uncertainty of a few parts in 109.
3.6.2. Relative gravimeters. As their name implies, relative
gravimeters [93–95] measure relative changes in g. They are
used for two main tasks: gravitational surveys to support the
transfer of the value of g from the gravimeter to the Kibble
balance and measuring changes in g with time to support less
frequent absolute measurements of g.
Many relative gravimeters measure changes in length of
carefully designed spring systems [96]. These instruments
are small, easy to move, easy to operate and are usually used
for three dimensional gravity surveys of Kibble balance
laboratories.
Superconducting relative gravimeters sense the movement
of a magnetically levitated niobium sphere and are costly,
extremely sensitive, highly reliable, but difcult to move [97].
They do have the advantages of relatively low maintenance
and, once set up, they are very easy to operate. These instru-
ments are useful to support the temporal interpolation of g
between measurements made with absolute instruments.
3.6.3. Methods of operation. The ideal way of measuring g
for use with a Kibble balance is to operate an absolute gra-
vimeter simultaneously with the weighing phase of the mea-
surement. Under these circumstances, the only corrections
needed are those which transfer the position of the measure-
ment, a correction for the speed of light, which is required by
the gravimeter, and possible corrections for the nite masses
of the gravimeter and watt balance. Whilst this method gives
good results, it increases the effective complexity of the sys-
tem and thereby decreases its reliability and increases its cost
to operate.
If a superconducting relative gravimeter is available, it can be
used to interpolate between infrequent absolute measurements
again needing only the same corrections as mentioned above.
If an interpolation instrument is not available and the absolute
Metrologia 53 (2016) A46
I A Robinson and S Schlamminger
A62
instrument is only available infrequently, it is necessary to use
the average value of g from the gravimeter measurements cor-
rected for the geophysical effects listed in section3.6.5. The
Kibble balance software calculates the instantaneous value of
g at the required time from estimates of these effects. On a well
characterised, properly instrumented, stable site, this technique
can yield a relatively modest added uncertainty to that of the
measurements of the average value of g.
3.6.4. Gravity surveys. Before a Kibble balance is constructed
on a new site, it is important to carry out a gravitational survey.
A minimal survey will determine the vertical and horizontal
gravitational gradients at the planned locations of the absolute
gravimeter and the Kibble balance mass pan and the horizontal
and vertical transfer corrections between these points. A more
thorough survey will provide a 3-dimensional map of the site
from which the optimum locations of the Kibble balance and
gravimeter can be determined [95, 98–100]. These are usually
at maxima or minima of the eld as a function of horizontal
position so that the corrections are insensitive to small posi-
tioning errors in either the Kibble balance or the gravimeter.
3.6.5. Corrections. A number of corrections must be con-
sidered when deriving an accurate value of g at the centre of
gravity of the mass from a set of raw measurements of g made
by an absolute gravimeter.
Speed of light correction This correction is applied in the
gravimeter software and reects the fact that, at the
required uncertainty of the measurement, the speed of
light cannot be considered to be innite with respect to
the velocity of the falling object.
Horizontal correction This correction is determined by the
survey discussed in section 3.6.4 and should be stable
unless signicant masses have been moved in the vicinity
of the gravimeter or Kibble balance. Ideally it should be
zero but in practice, due to the location of masses such as
room walls, it is often a few parts in 109.
Vertical correction Part of this correction arises from
gradients measured during the survey discussed in sec-
tion3.6.4. It is useful to design the Kibble balance so that
the height of the mass pan is close to part of the drop of
the gravimeter which reduces the height difference, the
size of the vertical correction and thereby its uncertainty.
The nal correction will depend on the value determined
from the survey, any change to the height of the reference
plane of the mass pan and the height of the centre of gravity
of the mass above the reference plane of the mass pan.
Atmospheric pressure The measured value of g will be
decreased if the mass of the part of the atmosphere above
the apparatus increases. This is reected in an increase
in the local barometric pressure. Usually a single coef-
cient is used to calculate the correction to g from the
measured barometric pressure. This assumes that the
pressure in the region a few kilometres around the Kibble
balance is uniform which is usually reasonable except
under storm conditions. Some modern laboratories have
air conditioning systems which raise the pressure inside
the laboratory. Under these circumstances, it is necessary
to ensure that the barometer used for the measurements is
recording the outside air pressure.
Solid earth tide corrections Changes in the relative positions
of the sun and the moon have a signicant effect on g.
These effects are known as the solid earth tides and are
modelled by considering the earth as a solid body which
is not deformed by the gravitational forces acting on it.
The geophysical community has carried out considerable
work on the modelling of the solid earth tides and they
can be predicted accurately, given input parameters of
the time and the location of the Kibble balance on the
surface of the earth. Real-time corrections can be made
either by incorporating solid earth tide prediction code
into the program controlling the Kibble balance or by
interpolating the correction from a tableproduced by a
stand-alone tidal prediction program. If real-time tidal
correction is not required, the same techniques can be
used in the post processing of the results.
Ocean loading corrections The earth is an elastic body and
further corrections can be made to take this into account.
As its name implies, the principal source of the correc-
tion is the change in height caused by the tidal motion of
sea water. The correction depends on the location of the
Kibble balance with respect to large bodies of tidal water.
In many cases the correction is small and can be ignored.
Earth rotational axis (polar motion) correction The rota-
tion of the Earth about its axis provides an acceleration
of the laboratory frame of reference which affects the
measured value of g. If the Earth rotated about a xed
axis, the effect would be constant. Unfortunately the point
at which the instantaneous rotational axis of the Earth
intersects the surface of the earth moves very slowly in
a spiral pattern. The location of this point is monitored
and its location is published on line by the international
earth rotation and reference systems service (IERS) from
which a correction can be calculated. This effect is also
referred to as polar motion.
Self-mass corrections Both the gravimeter and the Kibble
balance contain parts which have signicant masses. For
a typical gravimeter, the associated correction [101, 102]
of g is a few parts in 109 but for a Kibble balance the cor-
rection associated with the magnet can easily be 20 parts
in 109 and other parts of the apparatus will have smaller
effects. There are presently two ways to achieve a low
uncertainty on this correction. A nite element model can
be used to calculate the gravitational eld and its gradient
near the mass pan to allow the appropriate correction to
be applied at the centre of gravity of the working mass.
Alternatively, a relative gravimeter can be placed in the
area usually occupied by the mass pan to measure the dif-
ference in g from a local reference point and the vertical
gradient near the pan. This technique depends on having a
sufciently low magnetic eld in the vicinity of the mass
pan to operate the gravimeter and a large enough space to
accommodate the instrument.
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3.6.6. Verication of the correct operation of an absolute
gravimeter. An absolute gravimeter is a complex instrument
and, whilst care in its calibration and operation should achieve
low measurement uncertainties, the measurement results will
vary naturally because of local and global geophysical effects.
This makes it desirable to verify the operation of the instru-
ment and this is usually achieved by comparison with other
similar instruments in gravimeter comparisons [103, 104].
Participation in such comparisons is relatively expensive as
the gravimeter must be shipped to the site of the comparison
and operated there. However, successful participation in a
comparison provides independent evidence that the instru-
ment, which is a critical part of a Kibble balance, is both oper-
ating correctly and has a valid uncertainty budget.
3.7. Measurement of the working masses
Most conventional mass metrology is performed in air. If the
masses being compared have exactly the same density,
the effect of buoyancy due to the mass of air displaced by
the mass will be equal for both masses and will cancel. If a
Kibble balance is operated in air, the apparent weight of the
mass is compared to the force generated by the coil. Under
these circumstances, the effects of air buoyancy do not cancel
and the results must be corrected for its full effect which is
approximately 500 parts in 106 for a silicon mass. To achieve
their target uncertainties at a few parts in 108, the Kibble bal-
ances have to operate in vacuum to eliminate the signicant
uncertainty arising from the air buoyancy corrections. This
means that the measurements made in vacuum must be related
to those made in air and this can be done without the need
for buoyancy corrections [105]. On moving a mass from air
to vacuum, layers of molecules (mostly water) present on the
surface are removed and the desorbed mass must be taken into
account [11]. Considerable work has been carried out in this
area [106–108] and different techniques [109] exist to esti-
mate the mass change due to the removal of the sorption layer.
In an air-vacuum comparator, the test mass can be compared
to a sorption artefact which has the same mass, identical sur-
face properties but a known surface area several times that of
the test mass [110]. Differential changes in mass between the
two artefacts when moved between vacuum and air can be
used to measure the mass lost or gained per unit surface area
of the mass.
Another, more direct, way to compare a mass in vacuum to
a mass in air is via a mass comparator that has two mass pans,
one in vacuum and one in air that are connected via a magn-
etic coupler. Such a magnetic suspension mass comparator
(MSMC) has been built at NIST [111]. It will be interesting to
see what uncertainties can be achieved with such an MSMC.
The process of disseminating the unit of mass from a unit
of mass realized in vacuum is described in other articles in this
focus issue of Metrologia.
3.7.1. Substitution weighing. In the watt balance, the work-
ing mass is measured by substitution weighing. For reasons
described in section3.2, the balance is offset by half the weight
of the working mass. This requires a current to ow in the coil
to generate an upwards force of half the weight of the working
mass. This current is measured and the mass is lowered requir-
ing the current to be reversed to maintain the balance in equi-
librium. The weight of the mass is derived from the difference
in the two currents and the reversal makes the measurement
insensitive to constant thermal EMF’s in the measurement cir-
cuit. If the balance is not disturbed by the raising or lowering
of the mass, the technique can make extremely accurate mass
measurements.
3.7.2. Types of balance. A range of balance types are used
in Kibble balances their principal features are summarised in
table3.
NIST and NPL/NRC balances use knife edges which are
robust and allow the beam/wheel to rotate enough to move
the coil in the moving phase; however, they suffer from hys-
teretic effects [48, 115] which must be eliminated by moving
the beam/wheel in a damped sinusoidal manner. This sinu-
soidal motion is executed after every mass transfer to the mass
pan. The sinusoidal motion wastes time and can increase the
weighing noise.
MSL will use a pressure balance for weighing. The piston
of the balance provides precise vertical motion during the
moving phase.
The majority of Kibble balances use mass comparators
which are sensitive balances which use exures, i.e. thin metal
strips which are used as highly repeatable pivots. The ex-
ures provide high sensitivity and low hysteresis but to avoid
damaging them, their motion must be limited, so a separate
mechanism must be provided for the moving phase.
3.7.3. Alignment of the mass on the mass pan. For a beam
balance, the mass pan is suspended at the end of the beam by
a exure or a knife edge. If the mass is not centred on the mass
pan, a torque will be applied to this pivot. Due to the nite
stiffness of real pivots, a fraction of this torque is transmitted
to the beam. This parasitic torque can cause a measurement
bias, referred to as corner load error. This error can be reduced
by implementing multiple pivot points between the mass pan
and the beam. With each pivot point the amount of torque that
is transmitted up the linkage is substantially lowered.
The mass pan can be designed such that the mass is self
centring [116, 117]. Then the mass ‘walks’ to the centre of the
balance pan with each mass exchange. A couple of weighings
using such a design will reduce the corner loading effect.
A pendulum motion of the mass pan can increase the noise
of the watt balance, substantially increasing the number of
cycles required for the mass self-centring action described
above and possibly introduce a measurement bias. Therefore,
it is desirable to damp the pendulum motion of the mass pan.
An interesting possibility to damp the mass pan motion is to
use sloshing liquids in a sealed ring channel mounted to the
mass pan [118, 119].
3.7.4. Alignment of the mass comparator. For their correct
operation, the mass comparator needs to be aligned with
respect to vertical. Otherwise, the weighing cell is sensitive to
horizontal forces [58]. This sensitivity can be used to align the
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weighing cell, see [117]. So far two NMIs have built systems
with mass comparators, METAS [58] and BIPM [112]. Three
more NMIs are planning on using mass comparators, KRISS,
NIM, and UME.
3.7.5. Pressure effects. At a room temperature of 22 °C and an
atmospheric pressure of 100 kPa, the density of air is approxi-
mately 1.2 kg m−3 and the density of a silicon mass standard
(one of the lowest density mass standards) is 2300 kg m−3.
The correction that must be made to the measured mass to
allow for its buoyancy is over 500 parts in 106. This correc-
tion is difcult to make accurately because the density of the
air is dependent on its temperature, pressure and composition.
By reducing the air pressure to below 0.1 Pa, the buoyancy
correction is much less than 1 part in 109. Most Kibble bal-
ances are operated at such pressures to ensure that both the
buoyancy and refractive index corrections (section 3.5.2) are
negligible.
The reduction in pressure also effects the surface lms on
the mass and the resulting changes in mass are time dependent
and may exhibit hysteresis with variations of pressure. This
effect has been extensively investigated [120, 121].
3.7.6. Magnetic forces on the mass. All mass standards,
including platinum–iridium and stainless steel, have a nite
magnetic susceptibility [122, 123] which can affect their
apparent weight when in the spatially varying magnetic
eld of a Kibble balance. If the effect cannot be shown to be
negligible, it will require correction which can increase the
uncertainty of the measured mass. This has been addressed in
two ways. Many recent Kibble balances use magnets having
a closed magnetic circuit which reduces both the stray eld
and its gradient thereby reducing the effect considerably. Also
research has been carried out to nd materials with low magn-
etic susceptibilities which have the correct mechanical proper-
ties to make excellent mass standards. The application of both
of these techniques can reduce corrections for the magnetic
susceptibility to much less than 20 parts in 109.
3.7.7. Load locks and mass exchangers. The Kibble bal-
ance operates under vacuum and it takes many hours for a
freshly pumped balance to stabilise. The pumping can pro-
duce temperature changes in the magnet and the moving
parts of balance outgas at different, but slowly reducing, rates
both of which disturb the weighing measurements. If the bal-
ance has to be opened every time the working mass has to be
changed, much time can be lost via this mechanism. Some
Kibble balances [22] now incorporate mechanisms for storing
a number of working masses inside the vacuum chamber and
provide mechanisms for loading a selected mass into the bal-
ance. Such a mass exchanger allows many comparative invest-
igations to be carried out relatively rapidly.
It is also possible to t Kibble balances with load locks
which allow masses to be introduced into the balance chamber
and stored on the mass exchanger. This allows a large number
of masses to be measured by the Kibble balance in an ef-
cient manner which is a great advantage for routine operation.
The NIST Kibble balance is tted with both a mass exchanger
[124] and a load lock to aid its use in maintaining national
and international standards of mass. Both of these are likely
to become far more common features of Kibble balances in
the near future.
3.8. Alignment of the Kibble balance
All existing Kibble balances require precise alignment of
both the magnet and the coil [125–127]. The arguments in
section 2.1 show that, for balances which have a common
weighing and moving mechanism, the alignment require-
ments may be relaxed, due to the cancellation of the effects
of the derivatives of the ux with respect to the non vertical
directions [15]. The amount of this relaxation depends on
the details of their mechanical construction. If the guidance
of the coil is exible, such that horizontal torques and forces
on the coil cause it to move signicantly, then the coil needs
to be aligned to suppress such movements. This ensures that
the theory in section2.1 applies correctly, and the alignments
are carried out using the techniques described below [128].
An alternative is to guide the coil using elements which are
stiff enough to suppress motion and the effects of forces and
torques in all but the weighing direction. If the position and
orientation of the coil can be completely described in terms of
the vertical position of the mass pan then, during manufacture,
it may be possible to align the balance sufciently well and
operate the balance in a way which eliminates the need for the
regular, extremely precise, alignments described below.
3.8.1. Alignment of the magnetic eld. The axis of the magn-
etic eld should be aligned to be vertical but the required
accuracy of this alignment varies considerably. For most bal-
ances, any misalignment will be compensated by an opposing
change in the direction of the axis of the coil to ensure that the
force generated by the coil is vertical at the weighing posi-
tion. But in moving mode the sensitivity of the coil to angular
velocities will change as the coil moves vertically. Limits on
the requirements are discussed in [13]. A recent publication
by the BIPM group discusses different ways to check the eld
alignment with a dedicated instrument that combines a rotat-
ing tilt meter, a Hall sensor, and capacitive sensors [41].
3.8.2. Alignment of the weighing pan. The weighing pan
should be aligned such that the coil does not tilt or move,
when the mass is placed on the weighing pan. Note, this step
should be performed without current in the coil. The best way
to do this is to lock the balance at the weighing position. Using
Table 3. Balances at nine different laboratories.
Lab. Design Reference
BIPM Mass comparator [112]
KRISS Mass comparator [17]
LNE Flexure balance [113]
METAS Mass comparator [22]
MSL Pressure balance [43]
NIM Beam bal./mass comp. [114]
NRC Beam balance [70]
NIST Wheel balance [81]
UME Mass comparator [34]
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the mass lift, a mass is placed on the mass pan and the motion
of the coil is monitored. Ideally the mass pan and the coil
swivel about two independent gimbals. However, due to nite
stiffness or misalignment between the mass and coil gimbals,
there is a coupling and a movement of the mass pan can create
movement in the coil which can be corrected by moving the
mass pan gimbal with respect to the coil gimbal. The mea-
surement needs to be current-less, because if the coil carries a
current, which is reversed when the mass is added changes in
electromagnetic forces and torques can mask the effect.
3.9. Horizontal forces and torques
Horizontal forces,
F F,
xy
and torques,
,
xy
Γ Γ
, occur, when the
coil is not perfectly aligned with the magnetic eld. Horizontal
forces are caused by an angular misalignment of the eld with
respect to the coil. The presence of torques implies that the
line of action of the force produced by the coil does not pass
through the vertical line linking the centre of mass with the
point of suspension of the coil. One of many solutions to this
is to make the symmetry axis of the coil and the symmetry
axis of the magnet coincident with the line mentioned above.
The best way to infer these parasitic forces and torques is
by using one or more exible elements in the coil suspension.
These elements convert the forces and torques into linear and
angular displacements, which can be measured. The details
and the restoring forces and torques depend on the exact
design of the coil suspension.
Two coil suspensions are popular. The NIST and NPL
Kibble balances use a coil suspension similar to the operating
cross of a string puppet. The controlling cross is always par-
allel to the coil, but both can tilt together with respect to the
horizontal plane. In addition, the coil can displace horizon-
tally with respect to the controlling cross in a so called shear
motion. The shear motions are measures of the horizontal
forces on the coil, the tilt motions are measures of the torque.
In the LNE Kibble balance [129] and later the NRC Kibble
balance, the coil is suspended from vertically-separated,
double gimbals. The angular excursions of the upper gimbals
is exclusively given by the horizontal forces on the coil, the
excursions of the lower gimbals by a combination of the hori-
zontal forces and the torques on the coil. By measuring four
quantities (two in each of the direction x and y) the forces
and torques can be inferred [129]. Typically, the angles of the
lower gimbals and the horizontal displacements of the coil are
measured.
Various techniques are employed [130] to measure the
angular and linear displacements. An autocollimator, an
optical lever [131] or a differential interferometer can be
used to measure angular displacements. Linear displacements
can be measured by reecting a vertical laser beam from a
corner cube and monitoring the position of the reected beam
on a position sensitive detector. Capacitive sensors, reec-
tive optical sensors and interferometers can also be used to
detect horizontal motions. Typically, the techniques used can
sense linear motion to a fraction of 1
µ
m and angular motion
to about 1
µ
rad. To convert these sensitivities into force and
torque units the stiffness parameters of the coil suspension are
required. These should be given in the publications describing
each Kibble balance.
Horizontal forces arise if the coil is tilted with respect to the
magnetic eld. In the alignment procedure the current in
the coil is altered and the horizontal displacement of the
coil is monitored. If the horizontal displacement, and by
implication the associated horizontal force, is too large,
the tilt angle of the coil is changed and the process is
repeated until the horizontal forces have been suppressed
to the level desired. If the suspension of the coil is such
that it can tilt freely, then the easiest way to change the
tilt is to add a mass on the coil or a connected mechanical
structure and the coil will tilt into a new equilibrium posi-
tion.
Torques on the coil are created when the coil is not centred
in the magnetic eld, more specically, when the centre
of mass of the coil and the magnetic centre of the coil
magnet system are horizontally displaced. To measure
the torques, the current in the coil is reversed and the
corresponding coil motion recorded. The torque on the
coil can be minimized by three means, (a) the coil can be
displaced, (b) the magnet can be displaced, or (c) masses
on the coil can be moved to change the mass centre of the
coil. Typically, the third option typically changes the tilt
of the coil and should be avoided.
3.9.1. Parasitic motions in moving mode. In moving mode, the
coil should follow the ideal trajectory given by the mechanical
system, e.g. a perfect vertical motion for the wheel balance or
an arc-shaped course for a beam balance. Velocities present
during the moving phase that are not explained by the ideal
system are parasitic motions and stem from minor deviations
of the real mechanical system from the ideal system. Very
often these deviations can be trimmed away. In most cases,
the ideal motion of the coil does not include any horizontal or
angular velocities of the coil. Ideally the coil should translate
without changing its roll, pitch, or yaw. Any angular velocity
is a parasitic motion.
The parasitic velocities are measured by the same detectors
and instruments that sense the parasitic forces, see section3.9.
Horizontal velocities occur due to small misalignments in
the guiding mechanism. The root cause depends on the
detailed guiding mechanism used in each Kibble balance
and it is therefore impossible to give a general descrip-
tion of the methods used to minimize these velocities.
For example, in the classic beam balance, one horizontal
velocity is given by the angle of the at with respect to
the horizontal plane. By tilting the at, the horizontal
velocity can be changed and eventually minimized.
An easy way to measure horizontal displacement is the use
of a vertical laser beam directed into a corner cube mirror
mounted on the coil. The reected beam is monitored with
a position sensitive detector. It will move twice the distance
that the corner cube has moved. With this technique it is
possible to resolve horizontal motions below
1µ
m. Note,
the laser beam has to be vertical, otherwise the motion of
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the coil is optimized for the direction of the laser beam
and not local vertical. The same techniques described to
align the main interferometer to vertical, see section3.5.5,
can be used for this beam. Ideally, the interferometer beam
can also be utilized for this measurement, minimizing the
number of beams that have to vertically aligned.
Angular velocities of the coil in the moving mode have to be
minimized, as well. One culprit for such parasitic rota-
tions are the wires that connect the coil to the electronics.
Because of the motion of the balance, the torque produced
by these wires changes. If the coil suspension is compliant
to torque changes, the coil will rotate. Care must be taken
in routing the wires such that the torque produced by them
is small and, ideally, constant over the velocity sweep.
This can be done by using thin wires at small lever arms.
The wires can be made softer by heat treating them. In the
NIST Kibble balance, the coil can rotate around the ver-
tical axis. This degree of freedom is not compliant in most
other watt balances. To eliminate parasitic rotation around
the vertical axis in the weighing and moving mode, the
NIST researchers employ a feedback system that produces
an electrostatic torque on the coil suspension that keeps
the coil at constant azimuthal angle.
3.10.Verication
A Kibble balance is a complex, automated measuring instru-
ment and it can be difcult to diagnose problems and verify
its correct operation if it is treated as a monolithic device.
Problems of diagnosis and verication can be simplied by
the technique of splitting the watt balance into a number of
subsystems which can be tested individually. However, it is
important to ensure that the instrument can be split up without
changing the characteristics of its parts. For example, if the
correct operation of one part is being disturbed by the opera-
tion of another via an unexpected route, both parts may work
perfectly when separated but their operation may be affected
in subtle ways when both parts are installed to the apparatus.
Some ways of minimising such effects are discussed in sec-
tion3.11.4. In the following sections, it is assumed that the
parts have been designed to minimise unwanted interactions
and tests for such effects have been carried out where feasible.
3.10.1.Subsystem verication. The Kibble balance can be
broken into a number of independent subsystems. In many
cases, the correct operation of these subsystems can be veri-
ed independently of the main apparatus.
Resistor The resistor must be measured against a QHR and
this can be used to verify the stability of the resistor as
described in section3.4.2.
Josephson voltage reference This is often veried by com-
parison against another Josephson voltage reference [53,
132–134].
Voltmeter The operation of the voltmeter can be checked
using the Josephson voltage reference.
Laser This can be veried by comparison with an iodine
stabilised laser.
Time reference Verication of the time reference was
described in section3.5.8.
Software The software for the system should be subject to
tests. Individual software subsystems can be checked
independently but it is advantageous to be able to test the
whole system using synthetic measurement data either
with or without synthetic noise. This requires consider-
able effort especially as gravitational corrections are time
dependent and must be synthesised correctly. However, if
the data is synthesised at the lowest level of the system i.e.
at the level of voltmeter and interferometer output data, it
can be used to validate the whole of the data processing
system. This can include checks on the corrections which
are applied to the results either at the time of data acquisi-
tion or during post processing.
3.10.2.System verication. Many parts of the system can be
veried by setting carefully chosen parameters to values out-
side their usual range and by checking that the effect of the
change is as expected [14, 70].
The linearity of the system can be checked by weighing
masses of differing values and by making measurements at
differing coil velocities. This is a necessary, but not sufcient,
test for the accuracy of the apparatus because offsets which
are proportional to the quantity being changed will not be
detected [48].
The ultimate test of a Kibble balance is the comparison
of its results with those of independent balances. This should
be carried out in the manner of a formal comparison [135] so
that any problems that are discovered are properly identied
and corrected. A comparison of different Kibble balances and
of the two Avogadro spheres was carried out in 2016 [136] to
check for consistency before the revision of the international
system of units. Such comparisons will form the basis of the
global mass scale which needs to be derived from a large
number of independent primary measurements.
3.11. Environmental effects
A Kibble balance will always be sensitive to some environ-
mental effects for example: the conversion between force
and mass depends on the free-fall acceleration g which is
dependent on the position of the mass within the apparatus
and atmospheric pressure outside the laboratory to name
but two. However, the aim of the design of a Kibble balance
should be to minimise the the effect of the environment on
the balance.
3.11.1. Ground vibration. Ground vibration can affect both
weighing and moving phases, as described in section3.3. If
critical parts of the balance are constructed carefully to ensure
that the vertical velocity measurement is highly correlated
with the voltage produced by the coil, the effects of ground
vibration in the moving phase can be greatly reduced but is
difcult to eliminate them entirely. In common with precise
mass balances, most practical Kibble balances would benet
from being sited in an area with low ground vibration.
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Anti-vibration systems can be used to reduce the effects
of ground vibration but care has to be taken to ensure that the
angular stability of the anti-vibration system is sufcient to
minimise the overall noise of the balance.
3.11.2. External magnetic elds. Kibble balances are usually
sited far from signicant sources of magnetic elds; therefore,
the remaining sources of magnetic interference are: changes
in the magnetic eld of the earth and local line frequency
interference. The sensitivity of the Kibble balance to these
effects is strongly dependent on the design of the magnet. As
described in section3.2, most recent balances use variants of
the closed magnetic circuit design introduced by the BIPM.
This design provides good rejection of both changes in the
magnetic eld of the earth and local line frequency elds.
However, it is good practice to ensure that line frequency
elds are minimised by ensuring that no mains wiring loops
encircle the room containing the balance. For magnets which
are more sensitive to external elds, a sensitive magnetometer
and Helmholtz coil can be used to null temporal changes in
the eld of the earth as described in [48].
3.11.3. Temperature effects. As described in section 3.2,
some Kibble balances use magnets with temperature coef-
cients of approximately −400 parts in 106 · K−1 which, even
with vacuum isolation, required local temperature control at
the level of
4±
mK [48]. As described in section3.2, recent
designs have reduced this considerably but Kibble balances
still need sufcient temperature control to eliminate noise and
uncertainty caused by temperature gradients which can cause
changes in the arm lengths of the balance and variations of
thermal EMFs in critical parts of the measurement circuit.
3.11.4. Shielding and electrical isolation. The Kibble bal-
ance is a complex electrical measuring instrument which must
measure its principal electrical quantities with uncertainties
approaching 1 part in 109. To simplify the task of ensuring and
verifying that the measurement achieves these uncertainties, it
is advantageous to isolate the principal electronic instruments
of the measurement system to ensure that currents can only
ow through the system in a predictable way. This is achieved
by placing the entire apparatus in an electrostatic shield and
ensuring that each instrument is similarly shielded and that
there is a high level of both dc and ac isolation between each
instrument, the mains, and the controlling computer. This
eliminates uncontrolled ac or dc currents owing between
instruments, through critical parts of the measurement sys-
tem, via unintentional leakage paths to either the controlling
computer or the mains. Very high levels of isolation (greater
than 10 T
Ω
and leakage at line frequency less than 1 pA) can
be achieved, for example, by using the techniques described
in [67, 137].
4. Existing implementations and their results
At the time of this writing (spring of 2016) researchers at
ve laboratories have published results with Kibble balances
and researchers at one laboratory have published two results
with a joule balance, that has been substantially altered for
the second publication. Several laboratories are currently in
the process of designing or building a Kibble balance. At four
laboratories (METAS, NPL, NIM, and NIST), more than one
balance have been built. To distinguish the results from dif-
ferent iterations, we assign an incremental version number to
the Kibble balance at a given institute. However, one has to
be careful with this nomenclature. Typically, Kibble balances
are constantly improved and two results are rarely published
with exactly the same instrument. Very often the hardware is
changed, sometimes the alignment procedures, the measure-
ment protocol, or the data analysis. Assigning a new version
number to each of these incremental changes would lead to an
ination of version numbers and would ultimately render them
meaningless. We assign a new version number only when sub-
stantial changes were made. Examples for substanti al changes
are a redesigned magnet system or the addition of a vacuum
Table 4. List of published and ongoing joule and Kibble balance research.
Lab. Ver . h
10 Js
34
/()
−
h
h
σ
/ 10−91
h
h90
( )
− / 10−9Year Reference Comments
BIPM 1 [32] Undergoing improvements.
KRISS 1 [17] Under construction.
LNE 1 6.626 0688 302 −82015 [138] First result in air, ongoing.
METAS 1 6.626 0691 302 37 2011 [21] Final result.
METAS 2 [23] Ongoing.
MSL 1 [43] In design.
NPL 1 6.626 068 21 136 −97 1990 [5] In air, non radial eld.
NPL 2 6.626 071 23 200 359 2012 [48] Systematic found, before sending to NRC.
NRC 1 6.626 070 11 19 189 2014 [139] IPK correction applied, ongoing.
NIM 1 6.626 104 8900 5300 2014 [28] Air coil system.
NIM 2 6.626 069 2566 22 2016 [114] Iron free permanent magnet system.
NIST 1 6.626 070 39 1300 232 1989 [9] Solenoid to generate eld, in air.
NIST 2 6.626 068 39 87 8 1998 [140] Superconducting solenoid, in air.
NIST 3 6.626 069 36 57 77 2015 [141] In vacuum, IPK correction applied.
NIST 4 6.626 069 83 34 148 2016 [81] Permanent magnet, ongoing.
UME 1 [34] In planing.
Note. Several institutes have worked on different versions of the Kibble balance. If a result has been published the number can be found in the third column.
This is the latest number obtained from the version of the balance indicated in the second column. The result is published in the reference indicated in the
fth column.
Metrologia 53 (2016) A46
I A Robinson and S Schlamminger
A68
chamber. The early experiments were performed in air and
vacuum chambers were added later on.
Table 4 lists the joule and Kibble balances that have been
described in the metrological literature in the past 27 years.
The table has 16 rows describing balances in all stages of
completion, from the planning stage to completely disman-
tled. Eleven numerical values have been produced.
Some of the results listed in table 4 can be discarded
because new results from the same instrument have super-
seded older results. One example is the NPL-2 Kibble
balance. This balance was transferred to the Canadian
Metrology Institute (NRC) in 2009. A combination of two
systematic effects was discovered before the system was due
to be shut-down and dismantled. Unfortunately, there was
not enough time to carefully estimate the bias that these sys-
tematic effects introduced into the result. As a consequence,
the uncertainty budget had to be signicantly increased
from the originally estimated uncertainty of 36 parts in 109
to 200 parts in 109. Upon arrival in Canada, these effects
were carefully studied and the corresponding entries in the
uncertainty budget were considerably reduced. Hence, the
NRC result can be considered to effectively supersede the
NPL result.
In 2014, due to the extraordinary circumstances of the pos-
sible redenition of the kilogram in 2018, the International
Prototype of the Kilogram was taken out of the vault and
measured against the witnesses, the working standards at
BIPM, and several national prototypes. During this extraor-
dinary verication, an offset between the working standards
at the BIPM and the IPK was found [143–145]. It is now
believed that the use of a particular balance, with auto-
matic mass exchange, caused small amounts of wear on the
working standards thereby reducing their mass. Hence, a
difference of 35
µ
g between the mass unit as maintained
by the BIPM and the mass unit represented by the IPK was
found in 2014. After a careful analysis of the data, it could
be shown that this bias started building up from 2003 to
about 2014. As a consequence, the calibration of all masses
in this time interval had to be corrected. NIST and NRC
have published corrections to their measurements of h using
newly calculated SI values of their working masses [139,
141]. Table 4 shows the latest number, including the mass
correction.
Figure 5 shows the eleven results listed in table 4. The
horizontal scale is large making it difcult to compare the
most precise measurements with each other and the recom-
mended value by the Task Group on Fundamental Physical
Constants under the auspices of the Committee on Data for
Science and T