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The NRC Watt Balance Planck Constant Determination
Barry Wood
Carlos Sanchez
FC 2015 Eltville, Germany February 4, 2015
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Outline • Principles • Underlying Measurements and Uncertainties • Results • Recent Corrections
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I
B
m
F = mg = BLI HeNe Laser
Position
Coil Position Servoed to z=0
Principle – weighing phase
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B v
V = vBL
Vc +
-
HeNe Laser
Velocity & Position
Beam Moved with a secondary coil and magnet and servoed for
constant velocity
v
Principle – moving phase
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Voltage
Resistance
Combining both phases
h90
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The NRC watt balance
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The NRC watt balance Subsections
Control
Beam control – position, velocity, acceleration, limits Mass control – raising and lowering mass and tare Temperature control, vibration isolation, electrical isolation, vacuum, heat flow …
Measurement
Voltage Resistance, Velocity and position and synchronization Mass Gravity Alignment
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PJVS array supplied by
PTB
Voltage
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Programmable Josephson
array
3458 DVM
VR - +
nV amplifier
B I R Raising or Lowering the mass causes the coil
current to reverse
Coil Position Servoed to z=0
Position
Voltage – weighing phase
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Programmable Josephson
Array
Two 3458 DVMs Vc - +
nV amplifier
B v
Synchronized measurements of coil
voltage and coil velocity.
Coil Servoed for constant velocity (~ 10ppm)
PJVS tracks so amplifier does not overload
Velocity & Position
Voltage – moving phase
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Voltage uncertainties (parts in 109)
Microwave frequency 0.2
Filter leakage < 0.1
Nanovoltmeter gain 0.3
Voltmeter non-linearity 1.6
Combined 1.63
Voltage Uncertainties
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The watt balance 50 ohm resistors are calibrated in-situ with a portable QHR and CCC at the operating currents.
NRC V0054a : 0.32K : 10µA
0
3
6
9
12
15
0 2 4 6 8 10 12Magnetic Induction (T)
Res
ista
nce
(kΩ
)
Resistance
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Resistance uncertainties (parts in 109)
Measurement vs QHR 3
Sample dissipation 3
Resistor stability 5
Resistor power coefficient (1 kg) 2
Combined 6.9
Resistance Uncertainties
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The laser is calibrated in-situ through an optical fiber link to the NRC time and frequency lab.
B
He-Ne Laser
v
Frequency counter
Operation at constant velocity means detector rise times do not cause an error.
Velocity
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HP 3458
HP 3458
Frequency Counter
Interferometer signal
Input TTL logic
Coil voltage
Gate
Trigger position
Gate
Ext trigger
DVM 1
DVM 2
nV Amplifier
Voltage – Velocity – Position Synchronization
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He – Ne gain curve
Old laser – polarization stabilized
∆f = 640 MHz
Error caused by second mode leaking into the interferometer
∆f = 0.5 MHz
6101 −×≈∆ff
New laser – transverse Zeeman stabilized
9101 −×≈∆ff
Polarization leakage
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Velocity uncertainties (parts in 109)
Laser wavelength 0.8
Mode leakage < 0.1
Diffraction correction 0.2
Retroreflector imperfections 0.2
Beam shear 0.3
Frequency measurement 0.1
Index of refraction correction 0.1
Synchronization < 0.1
Position error 0.9
Combined 1.3
Velocity Uncertainties
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NRC M-one vacuum mass comparator
•Pt-Ir mass calibrated at BIPM •Vacuum-Air difference evaluated •Test masses measured in vacuum
Mass
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Mass uncertainties for 1 kg (parts in 109)
BIPM calibration uncertainty 7.2
Transport stability 3.5
Balance uncertainties 2
Stability of reference mass 2.8
Pressure dependence 1
Corrections
Sorption on reference 2
Center of gravity < 0.1
Weighing range sensitivity 0.2
Combined 9.0
Mass Uncertainties
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•Three isolated gravity pads. •3D Mapping of variations within
lab •Modeling of variations with
balance in place •Tide program, polar motion… •Seasonal variations ~ 3ppb •Gravity re-measured in July 2013
and Jan 2014 •Gravimeter compared with NIST
and NRCan with good agreement
J. Liard, C. Sanchez, B Wood, D. Inglis and R. Silliker, Gravimetry for watt balance measurements, Metrologia 51 S32–41, 2014
Gravity
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Gravity uncertainties (parts in 109)
Absolute measurement 2.7
Horizontal transfer 2.5
Vertical transfer 3
Corrections
Balance attraction 1
Earth tide < 0.1
Polar motion 0.1
Ocean loading 0.3
Atmospheric pressure 0.3
Seasonal changes 3
Combined 5.7
Gravity Uncertainties
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C. Sanchez and B. Wood, Alignment of the NRC watt balance: considerations, uncertainties and techniques, Metrologia 51 S42–53
•Horizontal forces: Fx , Fy ≈ 0 •Horizontal velocities: vx , vy ≈ 0 •Torques: τx , τy , τz ≈ 0 •Angular velocities: ωx , ωy , ωz ≈ 0. •Optical alignment (laser beam vertical, Abbe offset) •Mass pan position
All alignment related quantities are measured in vacuum.
Alignment
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Alignment
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Alignment uncertainties, m1 ( x 10-9)
Fxv’x 0.4
Fyv’y < 0.1
τxωx 0.2
τyωy 0.7
Abbe offset correction 3.9
Mass pan alignment 0.2
Laser vertical 0.8
Horizontal displacement 2.8
Vertical displacement 2.8
Change in θz 1.3
Change in θx and θy 0.5
Combined 5.9
Alignment Uncertainties
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1. Stretching of the coil support
( )NNµ018.0238.0 ±+=Initial correction
Solution • Modification of the coil support • Adjustment of the beam center of mass
NnN1<Error reduced to
The coil is servoed to z=0, so if the coil support stretches then beam will tilt.
Systematic Effects - Mass Exchange Errors
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2. Tilting of the balance base
Initial correction
Solution • Modification of the mass lift
The coil is servoed to z=0 so if the beam platform tilts the angle between the beam and the platform changes.
( )NNµ056.0636.0 ±−=
NnN7.1<Error reduced to
Systematic Effects - Mass Exchange Errors
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• Change of coil position / orientation between moving and weighing phases
• Knife-edge hysteresis • Voice coil coupling • Dielectric absorption
These effects were found to be smaller than 3 ppb
Other Tests for Systematic Effects
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Miscellaneous uncertainties ( parts in 109)
Mass-exchange errors 1.7
Knife-edge hysteresis 1.0
Buoyancy correction 0.1
Asymmetric magnetization 0.1
Mass magnetic susceptibility 0.1
Combined 2.0
Other Uncertainties
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1 kg AuCu
0.5 kg Si
0.5 kg AuCu
0.25 kg Si
Type A: 3 – 6 parts in 109
Original Results – All Data Points
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h Results from Each Mass
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Have we considered ALL systematic effects that can have a significant influence?
Apparently Not!
Any Other Systematic Effects ??
The IPK has only been taken out of its vault three times (1948, 1990, 2013) since it was originally stored in 1889.
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During the Extraordinary Calibration against the IPK conducted by the BIPM in 2014, it was discovered that the as-maintained mass unit of the BIPM has been drifting with respect to the IPK since about the year 2000. Corrections for the mass calibrations of NRC’s mass standards were received in mid-December 2014 and they impact the NRC Planck determination of 2014. The resulting corrections for the NRC Planck determination are 35 ppb in value and a reduction in the mass traceability uncertainty from 7.2 ppb to 3 ppb.
Another Systematic Effect
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0.15
0.17
0.19
0.21
0.23
Sep Oct Nov
AuCu 1kg
Si 500g
AuCu 500g
Si 250g
h/h
90 -1
x 1
0-6
h Results from Each Mass – Mass Corrected
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– 1 = (189 ± 18) × 109 h
h 90
NRC-14
h NRC-14 = 6.626 070 11(12) × 10-34 Js
NRC Combined Result – Mass Corrected
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0
6.8 7.0 7.2
[ h/(10-34 Js) - 6.6260 ] x 105
NPL-12
IAC 2015 corrected
NRC-14 corrected
NIST-15 corrected
NIST-98
IAC-11 corrected
METAS-11
NIST-14
CODATA 2014 ??
LNE 15
PTB-91
NPL-90
~ 12 ppb
NMI-89 10-7 h
BR = 1.12
Planck - February 2015
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Ian Robinson Stuart Davidson James Berry
NPL
Luis Palafox Ralf Behr
PTB
Dave Inglis Jacques Liard Richard Green Alan Madej Brent Young
NRC
Acknowledgements
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Thank You