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{{Short description|Electromechanical weight measuring instrument}}
[[File:NIST-4 Kibble balance.jpg|thumb|The [[National Institute of Standards and Technology|NIST]]-4 Kibble balance, which began full operation in early 2015, measured the [[Planck constant]] to within 13 parts per billion in 2017, which was accurate enough to assist with the [[2019 revision of the SI|2019 redefinition]] of the [[kilogram]].]]

A '''Kibble balance''' (also formerly known as a '''watt balance''') is an electromechanical [[measuring instrument]] that measures the [[weight]] of a test object very precisely by the [[electric current]] and [[voltage]] needed to produce a compensating force.  It is a [[Metrology|metrological]] instrument that can realize the definition of the [[kilogram]] unit of [[mass]] based on [[Physical constant|fundamental constants]].<ref name="The watt or Kibble balance: A techn">{{cite journal |doi=10.1088/0026-1394/53/5/A46 |title=The watt or Kibble balance: A technique for implementing the new SI definition of the unit of mass |journal=Metrologia |volume=53 |issue=5 |pages=A46–A74 |year=2016 |last1=Robinson |first1=Ian A. |last2=Schlamminger |first2=Stephan |pmid=35023879 |pmc=8752041 |doi-access=free |bibcode=2016Metro..53A..46R }}</ref><ref>
{{cite news
 | last= Palmer
 | first= Jason
 | title= Curbing the kilogram's weight-loss programme
 | publisher= [[BBC News]]
 | date= 2011-01-26
 | url= https://www.bbc.co.uk/news/science-environment-12276822
 | accessdate= 2011-02-16
 | work= BBC News
}}</ref>

It was originally known as a watt balance because the weight of the test mass is proportional to the product of current and voltage, which is measured in [[watt]]s.  In June 2016, two months after the death of its inventor, [[Bryan Kibble]], metrologists of the [[Consultative Committee for Units]] of the [[International Committee for Weights and Measures]] agreed to rename the device in his honor.<ref name="NPL">
{{cite web
 | title = The Kibble Balance
 | work = Education
 | publisher =UK National Physical Laboratory website
 | date = 2016
 | url = http://www.npl.co.uk/educate-explore/kibble-balance/
 | format = 
 | doi = 
 | accessdate = 15 May 2017
}}</ref><ref>Consultative Committee for Units (CCU),
[http://www.bipm.org/utils/common/pdf/CC/CCU/CCU22.pdf Report of the 22nd meeting (15-16 June 2016)], pp. 32-32, 35</ref>

Prior to 2019, the definition of the kilogram was based on a physical object known as the [[International Prototype of the Kilogram]] (IPK).
[[Alternative approaches to redefining the kilogram|After considering alternatives]], in 2013 the [[General Conference on Weights and Measures]] (CGPM) agreed on accuracy criteria for replacing this definition with one based on the use of a Kibble balance. After these criteria had been achieved, the CGPM voted unanimously on November 16, 2018, to [[2019 revision of the SI|change the definition of the kilogram and several other units]], effective May 20, 2019, to coincide with [[World Metrology Day]].<ref name="NPL"/><ref>{{cite journal |doi=10.1126/science.356.6339.670 |pmid=28522473 |title=Plot to redefine the kilogram nears climax |journal=Science |volume=356 |issue=6339 |pages=670–671 |year=2017 |last1=Cho |first1=Adrian }}</ref><ref name=Milton16>{{cite web |url=http://www.sim-metrologia.org.br/docs/2016Presentations/BIPM%202016.pdf#page=10 |page=10 |title=Highlights in the work of the BIPM in 2016 |first=Martin |last=Milton |date=14 November 2016 |access-date=1 September 2017 |archive-url=https://web.archive.org/web/20170901031605/http://www.sim-metrologia.org.br/docs/2016Presentations/BIPM%202016.pdf#page=10 |archive-date=1 September 2017 |url-status=dead }}</ref><ref>[http://www.bipm.org/en/committees/cipm/meeting/105.html Decision CIPM/105-13 (October 2016)]</ref><ref>{{Cite news|url=https://www.nist.gov/news-events/news/2018/11/historic-vote-ties-kilogram-and-other-units-natural-constants|title=Historic Vote Ties Kilogram and Other Units to Natural Constants|last=Materese|first=Robin|date=2018-11-16|work=NIST|access-date=2018-11-16|language=en}}</ref> There is also a method called the [[joule balance]]. All methods that use the fixed numerical value of the [[Planck constant]] are sometimes called the Planck balance.

== Design ==
[[Image:Ampere balance 1927.jpg|thumb|Precision ampere balance at the US [[National Bureau of Standards]] (now [[National Institute of Standards and Technology|NIST]]) in 1927. The current coils are visible under the balance, attached to the right balance arm. The Kibble balance is a development of the Ampere balance.]]

The Kibble balance is a more accurate version of the [[ampere balance]], an early [[Electric current|current]] measuring instrument in which the [[force (physics)|force]] between two current-carrying coils of wire is measured and then used to calculate the magnitude of the current. The Kibble balance operates in the opposite sense; the current in the coils set very precisely by the [[Planck constant]], and the force between the coils is used to measure the weight of a test kilogram mass.  Then the mass is calculated from the weight by accurately measuring the local [[Earth's gravity]] (the net acceleration combining gravitational and centrifugal effects) with a [[gravimeter]]. Thus the mass of the object is defined in terms of a current and a [[voltage]]&mdash; allowing the device to "measure mass without recourse to the IPK ([[International Prototype Kilogram]]) or any physical object".<ref>{{Cite news|url=https://www.nist.gov/si-redefinition/kilogram-kibble-balance|title=Kilogram: The Kibble Balance|last=Materese|first=Robin|date=2018-05-14|work=NIST|access-date=2018-11-22|language=en}}</ref>

== Origin ==
The principle that is used in the Kibble balance was proposed by [[Bryan Kibble]] (1938-2016) of the UK [[National Physical Laboratory, UK|National Physical Laboratory]] (NPL) in 1975 for measurement of the [[gyromagnetic ratio]].<ref>{{Cite book |doi=10.1007/978-1-4684-2682-3_80 |chapter=A Measurement of the Gyromagnetic Ratio of the Proton by the Strong Field Method |title=Atomic Masses and Fundamental Constants 5 |pages=545–551 |year=1976 |last1=Kibble |first1=B. P. |isbn=978-1-4684-2684-7 }}</ref> In 1978 the Mark I watt balance was built at the NPL with Ian Robinson and Ray Smith.<ref>{{cite journal|journal=Cal Lab: The International Journal of Metrology|volume=Apr May Jun 2016|title=In Memory of Dr. Bryan Kibble, 1938-2016}}</ref><ref>{{cite web|url=https://www.npl.co.uk/people/ian-robinson|accessdate=21 May 2022|title=NPL website}}</ref> It operated until 1988.<ref>{{cite web|url=https://www.bipm.org/documents/20126/28432564/working-document-ID-11315/8532173e-8bae-2bdf-b74a-cb48296b4e67|title=NPL 17th Meeting of CCM|date=17 May 2019|accessdate=23 May 2022}}</ref>

The main weakness of the ampere balance method is that the result depends on the accuracy with which the dimensions of the coils are measured. The Kibble balance uses an extra calibration step to cancel the effect of the geometry of the coils, removing the main source of uncertainty. This extra step involves moving the force coil through a known magnetic flux at a known speed. This was possible by setting of the conventional values of the [[von Klitzing constant]] and [[Josephson constant]], which are used throughout the world for voltage and resistance calibration. Using these principles, in 1990 Bryan Kibble and Ian Robinson invented the Kibble Mark II balance, which uses a circular coil and operates in vacuum conditions .<ref>{{cite journal |doi=10.1088/0026-1394/27/4/002 |title=A Realization of the SI Watt by the NPL Moving-coil Balance |journal=Metrologia |volume=27 |issue=4 |pages=173–192 |year=1990 |last1=Kibble |first1=B. P. |last2=Robinson |first2=I. A. |last3=Belliss |first3=J. H. |bibcode=1990Metro..27..173K |s2cid=250829915 }}</ref> Bryan Kibble worked with Ian Robinson and Janet Belliss to build this Mark Two version of the balance. This design allowed for measurements accurate enough for use in the redefinition of the SI unit of mass: the kilogram.<ref>{{cite web |url=https://www.npl.co.uk/famous-faces/bryan-kibble |title=NPL Famous faces |accessdate=23 May 2022 }}</ref>

The Kibble balance originating from the National Physical Laboratory was transferred to the [[National Research Council of Canada]] (NRC) in 2009, where scientists from the two labs continued to refine the instrument.<ref>{{cite web|url=http://www.npl.co.uk/engineering-measurements/mass-force-pressure/mass/research/npl-watt-balance|title=Kibble balances : Research : Mass & Force : Science + Technology : National Physical Laboratory|website=www.npl.co.uk}}</ref>
In 2014, NRC researchers published the most accurate measurement of the [[Planck constant]] at that time, with a relative uncertainty of 1.8{{e|-8}}.<ref>{{cite journal |doi=10.1088/0026-1394/51/2/S5 |title=A determination of Planck's constant using the NRC watt balance |journal=Metrologia |volume=51 |issue=2 |pages=S5–S14 |year=2014 |last1=Sanchez |first1=C. A. |last2=Wood |first2=B. M. |last3=Green |first3=R. G. |last4=Liard |first4=J. O. |last5=Inglis |first5=D. |bibcode=2014Metro..51S...5S |s2cid=120813510 }}</ref> A final paper by NRC researchers was published in May 2017, presenting a measurement of the Planck constant with an uncertainty of only 9.1 parts per billion, the measurement with the least uncertainty to that date.<ref>{{cite journal |doi=10.1088/1681-7575/aa70bf |title=A summary of the Planck constant determinations using the NRC Kibble balance |journal=Metrologia |volume=54 |issue=3 |pages=399–409 |year=2017 |last1=Wood |first1=B. M. |last2=Sanchez |first2=C. A. |last3=Green |first3=R. G. |last4=Liard |first4=J. O. |doi-access=free |bibcode=2017Metro..54..399W }}</ref> Other Kibble balance experiments are conducted in the US [[National Institute of Standards and Technology]] (NIST), the Swiss [[Federal Office of Metrology]] (METAS) in Berne, the [[International Bureau of Weights and Measures]] (BIPM) near Paris and [[Laboratoire national de métrologie et d’essais]] (LNE) in [[Trappes]], France.<ref>{{cite journal |author-last1=Mohr |author-first1=Peter J. |author-first2=Barry N. |author-last2=Taylor |author-first3=David B. |author-last3=Newell |year=2008 |issue=2 |title=CODATA Recommended Values of the Fundamental Physical Constants: 2006 |url=https://www.nist.gov/pml/div684/fcdc/upload/rmp2006-2.pdf |journal=[[Reviews of Modern Physics]] |volume=80 |doi=10.1103/RevModPhys.80.633 |pages=633–730 |bibcode=2008RvMP...80..633M |arxiv=0801.0028 |archive-url=https://web.archive.org/web/20171001121533/https://www.nist.gov/sites/default/files/documents/pml/div684/fcdc/rmp2006-2.pdf|archive-date=2017-10-01}}</ref>

== Principle ==
A conducting wire of length <math>L</math> that carries an [[electric current]] <math>I</math> perpendicular to a [[magnetic field]] of strength <math>B</math> experiences a [[Lorentz force]] equal to the product of these variables. In the Kibble balance, the current is varied so that this force counteracts the [[weight]] <math>w</math> of a mass <math>m</math> to be measured. This principle is derived from the ampere balance.  <math>w</math> is given by the mass <math>m</math> multiplied by the local [[gravitational acceleration]] <math>g</math>. Thus,
: <math>w = mg = BLI.</math>  
The Kibble balance avoids the problems of measuring <math>B</math> and <math>L</math> in a second calibration step. The same wire (in practice, a coil) is moved through the same magnetic field at a known speed <math>v</math>. By [[Faraday's law of induction]], a [[potential difference]] <math>U</math> is generated across the ends of the wire, which equals <math>BLv</math>. Thus 
: <math>U = BLv.</math> 
The unknown product <math>BL</math> can be eliminated from the equations to give
: <math>UI = mgv</math>
: <math>m = UI/gv.</math>
With <math>U</math>, <math>I</math>, <math>g</math>, and <math>v</math> accurately measured, this gives an accurate value for <math>m</math>. 
Both sides of the equation have the dimensions of [[power (physics)|power]], measured in [[watt]]s in the International System of Units; hence the original name "watt balance". The product <math>BL</math>, also called the geometric factor, is not trivially equal in both calibration steps. The geometric factor is only constant under certain stability conditions on the coil.<ref name="The watt or Kibble balance: A techn"/>

== Implementation ==
[[File:Kibble-balance-in-weighing-mode.png|thumb|Weighing mode]]
[[File:The-Kibble-balance-in-moving-mode.png|thumb|Moving mode]]
The Kibble balance is constructed so that the mass to be measured and the wire coil are suspended from one side of a balance scale, with a counterbalance mass on the other side. The system operates by alternating between two modes: "weighing" and "moving". The entire mechanical subsystem operates in a vacuum chamber to remove the effects of air buoyancy.<ref>
{{cite journal
 |url=https://www.researchgate.net/publication/308735982
 |last1=Robinson |first1=Ian
 |last2=Schlamminger |first2=Stephan
 |date=2016
 |title=The watt or Kibble balance: A technique for implementing the new SI definition of the unit of mass
 |journal=Metrologia
 |volume=53
 |issue=5|pages=A46–A74
 |pmid=35023879 |pmc=8752041 |doi= 10.1088/0026-1394/53/5/A46 |doi-access=free
 |bibcode=2016Metro..53A..46R
}}</ref>

While "weighing", the system measures <math>I</math>. The system controls the current in the coil to keep the electromagnetic force on the coil balanced with the force of gravity. Coil position and velocity measurement circuitry uses an [[interferometer]] together with a precision clock input to determine the velocity and control the current needed to maintain it. The required current is measured, using an [[ammeter]] comprising a [[Josephson junction]] voltage standard and an integrating voltmeter.

While "moving", the system measures <math>U</math> and <math>v</math>. The system ceases to provide current to the coil. This allows the counterbalance to pull the coil (and mass) upward through the magnetic field, which causes a voltage difference across the coil. The velocity measurement circuitry measures the speed <math>v</math> of movement of the coil. This voltage is measured, using the same voltage standard and integrating voltmeter.

A typical Kibble balance measures <math>U</math>, <math>I</math>, and <math>v</math>, but does not measure the local gravitational acceleration <math>g</math>, because <math>g</math> does not vary rapidly with time. Instead, <math>g</math> is measured in the same laboratory using a highly accurate and precise [[gravimeter]]. In addition, the balance depends on a highly accurate and precise frequency reference such as an [[atomic clock]] to compute voltage and current. Thus, the precision and accuracy of the mass measurement depends on the Kibble balance, the gravimeter, and the clock.

Like the early atomic clocks, the early Kibble balances were one-of-a-kind experimental devices and were large, expensive, and delicate. As of 2019, work is underway to produce standardized devices at prices that permit use in any [[metrology]] laboratory that requires high-precision measurement of mass.<ref>
{{cite news
 |url=https://www.sciencenews.org/article/tabletop-device-turns-quantum-definition-kilogram-real-mass
 |title=This tabletop device turns the quantum definition of a kilogram into a real mass
 |first=Emily |last=Conover
 |date=June 3, 2019
 |website=ScienceNews
}}</ref>

As well as large Kibble balances, microfabricated or [[MEMS]] watt balances (now called Kibble balances) have been demonstrated<ref>{{cite journal |doi=10.1088/0957-4484/14/12/009 |title=Accurate analytical measurements in the atomic force microscope: a microfabricated spring constant standard potentially traceable to the SI |journal=Nanotechnology |volume=14 |issue=12 |pages=1279–1288 |year=2003 |last1=Cumpson |first1=Peter J. |last2=Hedley |first2=John |pmid=21444981 |bibcode=2003Nanot..14.1279C |s2cid=2500055 }}</ref> since around 2003. These are fabricated on single silicon dies similar to those used in microelectronics and accelerometers, and are capable of measuring small forces in the nanonewton to micronewton range traceably to the SI-defined physical constants via electrical and optical measurements. Due to their small scale, MEMS Kibble balances typically use electrostatic rather than the inductive forces used in larger instruments. Lateral and torsional<ref>{{cite journal |doi=10.1088/0957-4484/24/33/335706 |title=A compact torsional reference device for easy, accurate and traceable AFM piconewton calibration |journal=Nanotechnology |volume=24 |issue=33 |pages=335706 |year=2013 |last1=Portoles |first1=Jose F. |last2=Cumpson |first2=Peter J. |pmid=23892516 |bibcode=2013Nanot..24G5706P |s2cid=43451479 }}</ref> variants have also been demonstrated, with the main application (as of 2019) being in the calibration of the [[atomic force microscope]]. Accurate measurements by several teams will enable their results to be averaged and so reduce the experimental error.<ref>{{cite web|title=NPL Kibble Balance|url=https://www.npl.co.uk/kibble-balance|accessdate=23 May 2022}}</ref>

== Measurements ==
{{More citations needed section|date=May 2019}}
Accurate measurements of electric current and potential difference are made in [[conventional electrical unit]]s (rather than SI units), which are based on fixed "[[conventional electrical unit|conventional values]]" of the [[Josephson constant#KJ-1990|Josephson constant]] and the [[von Klitzing constant#RK-1990|von Klitzing constant]], <math>K_\text{J-90}</math> and <math>R_\text{K-90}</math> respectively. The current Kibble balance experiments are equivalent to measuring the value of the conventional watt in SI units. From the definition of the conventional watt, this is equivalent to measuring the value of the product <math>K_\text{J}^2 R_\text{K}</math> in SI units instead of its fixed value in conventional electrical units:
: <math>\frac{1}{K_\text{J}^2 R_\text{K}} = \frac{1}{K_\text{J-90}^2 R_\text{K-90}} \frac{\{mgv\}_\text{W}}{ \{UI \}_{W_{90}}}.</math>
The importance of such measurements is that they are also a direct measurement of the [[Planck constant]] <math>h</math>:
: <math>h = \frac{4}{K_\text{J}^2 R_\text{K}}.</math>

The principle of the electronic kilogram relies on the value of the Planck constant, which is as of 2019 an exact value. This is similar to the [[metre]] being defined by the [[speed of light]]. With the constant defined exactly, the Kibble balance is not an instrument to measure the Planck constant, but is instead an instrument to measure mass:
: <math>m = \frac{UI}{gv}.</math>

== Effect of gravity ==
[[File:Michelson Interferometer Laser Interference Fringes-Red.jpg|thumb|left|The local gravitational acceleration ''g'' is measured with exceptional precision with the help of a laser interferometer. The laser's pattern of [[Interference (wave propagation)|interference fringes]]—the dark and light bands above—blooms at an ever-faster rate as a free-falling [[Retroreflector|corner reflector]] drops inside an absolute [[gravimeter]]. The pattern's frequency sweep is timed by an atomic clock.]]

Gravity and the nature of the Kibble balance, which oscillates test masses up and down against the local gravitational acceleration ''g'', are exploited so that mechanical power is compared against electrical power, which is the square of voltage divided by electrical resistance. However, ''g'' varies significantly—by nearly 1%—depending on where on the Earth's surface the measurement is made (see ''[[Earth's gravity]]''). There are also slight seasonal variations in ''g'' at a location due to changes in underground water tables, and larger semimonthly and diurnal changes due to tidal distortions in the Earth's shape ([[earth tide]] and [[polar motion]]) caused by the Moon and the Sun. Although ''g'' is not a term in the ''definition'' of the kilogram, it is crucial in the process of measurement of the kilogram when relating energy to power in a kibble balance. Accordingly, ''g'' must be measured with at least as much precision and accuracy as are the other terms, so measurements of ''g'' must also be traceable to fundamental constants of nature. For the most precise work in mass metrology, ''g'' is measured using dropping-mass absolute [[gravimeter]]s that contain an iodine-stabilised [[helium–neon laser]] [[Interferometry|interferometer]]. The [[Interference (wave propagation)|fringe-signal]], [[Chirp|frequency-sweep]] output from the interferometer is measured with a rubidium [[atomic clock]]. Since this type of dropping-mass gravimeter derives its accuracy and stability from the constancy of the speed of light as well as the innate properties of helium, neon, and rubidium atoms, the 'gravity' term in the delineation of an all-electronic kilogram is also measured in terms of invariants of nature—and with very high precision. For instance, in the basement of the NIST's Gaithersburg facility in 2009, when measuring the gravity acting upon Pt{{nbhyph}}10Ir test masses (which are denser, smaller, and have a slightly lower center of gravity inside the Kibble balance than stainless steel masses), the measured value was typically within 8&nbsp;ppb of {{val|9.80101644|u=m/s2}}.<ref>R. Steiner, ''Watts in the watt balance'', NIST, Oct 16, 2009.</ref><ref name="Jiang Pálinkáš Francis Baumann 2013 pp. 452–471">{{cite journal | last1=Jiang | first1=Z | last2=Pálinkáš | first2=V | last3=Francis | first3=O | last4=Baumann | first4=H | last5=Mäkinen | first5=J | last6=Vitushkin | first6=L | last7=Merlet | first7=S | last8=Tisserand | first8=L | last9=Jousset | first9=P | last10=Rothleitner | first10=C | last11=Becker | first11=M | last12=Robertsson | first12=L | last13=Arias | first13=E F | title=On the gravimetric contribution to watt balance experiments | journal=Metrologia | publisher=IOP Publishing | volume=50 | issue=5 | date=2013-09-06 | issn=0026-1394 | doi=10.1088/0026-1394/50/5/452 | pages=452–471| bibcode=2013Metro..50..452J | s2cid=122057426 }}</ref><ref name="Liard Sanchez Wood Inglis 2014 pp. S32–S41">{{cite journal | last1=Liard | first1=J O | last2=Sanchez | first2=C A | last3=Wood | first3=B M | last4=Inglis | first4=A D | last5=Silliker | first5=R J | title=Gravimetry for watt balance measurements | journal=Metrologia | publisher=IOP Publishing | volume=51 | issue=2 | date=2014-03-31 | issn=0026-1394 | doi=10.1088/0026-1394/51/2/s32 | pages=S32–S41| bibcode=2014Metro..51S..32L }}</ref>

== See also ==
* {{section link|Alternative approaches to redefining the kilogram|Kibble balance}}
* [[Gouy balance]]

== References ==
{{Reflist}}

== External links ==
* {{cite journal |doi=10.1088/0026-1394/42/5/014 |title=Towards an electronic kilogram: An improved measurement of the Planck constant and electron mass |journal=Metrologia |volume=42 |issue=5 |pages=431–441 |year=2005 |last1=Steiner |first1=Richard L. |last2=Williams |first2=Edwin R. |last3=Newell |first3=David B. |last4=Liu |first4=Ruimin |bibcode=2005Metro..42..431S |s2cid=14976336 |url=https://repositorio.unal.edu.co/handle/unal/82624 }}
* {{cite journal |doi=10.6028/jres.106.028 |pmid=27500039 |pmc=4862827 |title=Hysteresis and related error mechanisms in the NIST watt balance experiment |journal=Journal of Research of the National Institute of Standards and Technology |volume=106 |issue=4 |pages=627–40 |year=2001 |last1=Schwarz |first1=J.P. |last2=Liu |first2=R.M. |last3=Newell |first3=D.B. |last4=Steiner |first4=R.L. |last5=Williams |first5=E.R. |last6=Smith |first6=D. |last7=Erdemir |first7=A. |last8=Woodford |first8=J. }}
* [http://www.bipm.fr/en/scientific/elec/watt_balance/ Bureau International des Poids et Mesures]
* [https://web.archive.org/web/20070810224138/http://www-optics.unine.ch/former/metrology/Watt_balance/Watt_balance.html Swiss Federal Office of Metrology]

{{DEFAULTSORT:Kibble Balance}}
[[Category:Measuring instruments]]
[[Category:Weighing instruments]]