Electronic measurement of the Boltzmann constant with a quantum-voltage-calibrated Johnson noise thermometer

Currently, the CODATA value of the Boltzmann constant is dominated by a single gas-based thermometry measurement with a relative standard uncertainty of 1.8 × 10 − 6 [P.J. Mohr, B.N. Taylor, D.B. Newell, CODATA recommended values of the fundamental physical constants: 2006, Rev. Mod. Phys. 80 (2008) 633–730]. This article describes an electronic approach to measuring the Boltzmann constant that compares Johnson noise from a resistor at the water triple point with a pseudo-random noise generated using quantized ac-voltage synthesis. Measurement of the ratio of the two power spectral densities links Boltzmannʹs constant to Planckʹs constant. Recent experiments and detailed uncertainty analysis indicate that Boltzmannʹs constant can presently be determined using Johnson noise with a relative standard uncertainty below 10 × 10 − 6 , which would support both historic and new determinations. To cite this article: S. Benz et al., C. R. Physique 10 (2009).