# Kibble balance

The NIST-4 Kibble balance, which began full operation in early 2015, measured Planck's constant to within 13 parts per billion in 2017, which was accurate enough to assist with the 2019 redefinition of the kilogram.

A Kibble balance or 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 metrological instrument that can realize the new definition of the kilogram unit of mass based on fundamental constants,[1][2] termed an electronic or electrical kilogram.

The name watt balance comes from the fact that the weight of the test mass is proportional to the product of current and voltage, which is measured in units of watts. In June 2016, two months after the death of the inventor of the balance, 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.[3][4]

Since 1889, the definition of the kilogram was based on a physical object known as the International Prototype of the Kilogram (IPK). In 2013, accuracy criteria were agreed upon by the General Conference on Weights and Measures (CGPM) 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 change the definition of the kilogram and several other units, effective May 20, 2019, to coincide with World Metrology Day.[3][5][6][7][8]

## Design

Precision Ampere balance at the US National Bureau of Standards (now 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 current measuring instrument in which the force between two current-carrying coils of wire is measured and then used to calculate the magnitude of the current. In this new application, the balance will be used in the opposite sense; the current in the coils will be measured using the new standard definition of the Planck constant to "measure mass without recourse to the IPK or any physical object."[9] The balance determines the weight of the object; then the mass can be calculated 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, as described below—an "electronic kilogram."

## Origin

The principle that is used in the Kibble balance was proposed by Bryan Kibble of the UK National Physical Laboratory (NPL) in 1975 for measurement of the gyromagnetic ratio.[10]

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 method has an extra calibration step in which the effect of the geometry of the coils is eliminated, removing the main source of uncertainty. This extra step involves moving the force coil through a known magnetic flux at a known speed. This step was performed in 1990.[11]

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.[12] In 2014, NRC researchers published the most accurate measurement of the Planck constant at that time, with a relative uncertainty of 1.8×108.[13] A final paper by NRC researchers was published in May 2017, presenting a measurement of Planck's constant with an uncertainty of only 9.1 parts per billion, the measurement with the least uncertainty to date.[14] 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.[15]

## Principle

A conducting wire of length L that carries an electric current I perpendicular to a magnetic field of strength B 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 w of a standard mass m. This principle is derived from the ampere balance. w is given by the mass m multiplied by the local gravitational acceleration g. Thus,

${\displaystyle w=mg=BLI.}$

The Kibble balance avoids the problems of measuring B and L in a second calibration step. The same wire (in practice, a coil) is moved through the same magnetic field at a known speed v. By Faraday's law of induction, a potential difference U is generated across the ends of the wire, which equals BLv. Thus

${\displaystyle U=BLv.}$

The unknown product BL can be eliminated from the equations to give

${\displaystyle UI=mgv.}$

With U, I, g, and v accurately measured, this gives an accurate value for m. Both sides of the equation have the dimensions of power, measured in watts in the International System of Units; hence the original name "watt balance".

## Measurements

Accurate measurements of electric current and potential difference are made in conventional electrical units (rather than SI units), which are based on fixed "conventional values" of the Josephson constant and the von Klitzing constant, ${\displaystyle K_{\text{J-90}}=2e/h}$  and ${\displaystyle R_{\text{K-90}}=h/e^{2}}$  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 KJ2RK in SI units instead of its fixed value in conventional electrical units:

${\displaystyle K_{\text{J}}^{2}R_{\text{K}}=K_{\text{J-90}}^{2}R_{\text{K-90}}{\frac {mgv}{U_{90}I_{90}}}.}$

The importance of such measurements is that they are also a direct measurement of the Planck constant h:

${\displaystyle h={\frac {4}{K_{\text{J}}^{2}R_{\text{K}}}}.}$

The principle of the electronic kilogram relies on the newly agreed-upon value of the Planck constant similar to the metre being defined by the speed of light. In this case, the electric current and the potential difference are measured in SI units, and the Kibble balance becomes an instrument to measure mass:

${\displaystyle m={\frac {UI}{gv}}.}$

Any laboratory that has invested the (very considerable) time and money in a working Kibble balance will be able to measure masses to the same accuracy as they formerly measured the Planck constant via the IPK.

In addition to measuring UI, the laboratory must also measure v and g using experimental methods that do not depend on the definition of mass. The overall precision of m depends on the precision of the measurements of U, I, v and g. Since there are already methods of measuring v and g to very high precision, the uncertainty of the mass measurement is dominated by the measurement of UI, which is the value measured by the Kibble balance.

## References

1. ^ Robinson, Ian A.; Schlamminger, Stephan (2016). "The watt or Kibble balance: A technique for implementing the new SI definition of the unit of mass". Metrologia. 53 (5): A46–A74. doi:10.1088/0026-1394/53/5/A46.
2. ^ Palmer, Jason (2011-01-26). "Curbing the kilogram's weight-loss programme". BBC News. BBC News. Retrieved 2011-02-16.
3. ^ a b "The Kibble Balance". Education. UK National Physical Laboratory website. 2016. Retrieved 15 May 2017.
4. ^ Consultative Committee for Units (CCU), Report of the 22nd meeting (15-16 June 2016), pp. 32-32, 35
5. ^ Cho, Adrian (2017). "Plot to redefine the kilogram nears climax". Science. 356 (6339): 670–671. doi:10.1126/science.356.6339.670. PMID 28522473.
6. ^ Milton, Martin (14 November 2016). "Highlights in the work of the BIPM in 2016" (PDF). p. 10.
7. ^ Decision CIPM/105-13 (October 2016)
8. ^ Materese, Robin (2018-11-16). "Historic Vote Ties Kilogram and Other Units to Natural Constants". NIST. Retrieved 2018-11-16.
9. ^ Materese, Robin (2018-05-14). "Kilogram: The Kibble Balance". NIST. Retrieved 2018-11-22.
10. ^ Kibble, B. P. (1976). "A Measurement of the Gyromagnetic Ratio of the Proton by the Strong Field Method". Atomic Masses and Fundamental Constants 5. pp. 545–551. doi:10.1007/978-1-4684-2682-3_80. ISBN 978-1-4684-2684-7.
11. ^ Kibble, B. P.; Robinson, I. A.; Belliss, J. H. (1990). "A Realization of the SI Watt by the NPL Moving-coil Balance". Metrologia. 27 (4): 173–192. doi:10.1088/0026-1394/27/4/002.
12. ^
13. ^ Sanchez, C. A.; Wood, B. M.; Green, R. G.; Liard, J. O.; Inglis, D. (2014). "A determination of Planck's constant using the NRC watt balance". Metrologia. 51 (2): S5–S14. doi:10.1088/0026-1394/51/2/S5.
14. ^ Wood, B. M.; Sanchez, C. A.; Green, R. G.; Liard, J. O. (2017). "A summary of the Planck constant determinations using the NRC Kibble balance". Metrologia. 54 (3): 399–409. doi:10.1088/1681-7575/aa70bf.
15. ^ Mohr, Peter J.; Taylor, Barry N.; Newell, David B. (2008). "CODATA Recommended Values of the Fundamental Physical Constants: 2006" (PDF). Reviews of Modern Physics. 80 (2): 633–730. arXiv:0801.0028. Bibcode:2008RvMP...80..633M. doi:10.1103/RevModPhys.80.633. Archived from the original (PDF) on 2017-10-01.