Johnson Noise Thermometry Measurement of the Boltzmann Constant With a 200 <formula formulatype="inline"><tex Notation="TeX">$\Omega$</tex></formula> Sense Resistor

Abstract

In 2010, the National Institute of Standards and Technology measured the Boltzmann constant $k$ with an electronic technique that measured the Johnson noise of a 100 $\Omega$ resistor at the triple point of water and used a voltage waveform synthesized with a quantized voltage noise source (QVNS) as a reference. In this paper, we present measurements of $k$ using a 200 $\Omega$ sense resistor and an appropriately modified QVNS circuit and waveform. Preliminary results show agreement with the previous value within the statistical uncertainty. An analysis is presented, where the largest source of uncertainty is identified, which is the frequency dependence in the constant term $a_{0}$ of the two-parameter fit.