Selection of spectral distortion models for electronic measurement of the Boltzmann constant

Published

March 21, 2017

Author(s)

Kevin J. Coakley, Jifeng Qu

Abstract

In the electronic measurement of the Boltzmann constant based on Johnson noise thermometry, the ratio of the power spectral densitiesof thermal noise across a resistor and pseudo-random noise synthetically generated by a quantum-accurate voltage-noise source is distorted due to mismatch between transmission lines. We model this distortion as an even polynomial function of frequency. For any given frequency range, defined by the maximum frequency $f_{max}$, we select the optimal polynomial distortion model with a cross-validation method and estimate the conditional uncertainty of the constant term in the spectral distortion model in a way that accounts for both random and systematic effects associated with imperfect knowledge of the model with a resampling method. We select $f_{max}$ by minimizing this conditional uncertainty. Since many values of $f_{max}$ yield conditional uncertainties close to the observed minimum value on a frequency grid, we quantify an additional component of uncertainty associated with imperfect knowledge of $f_{max}$. We apply our methods to both experimental and simulated data.

Citation

Metrologia

Volume

54

Pub Type

Journals

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DOI Link

Keywords

Boltzmann constant, cross-validation, Johnson noise thermometry, model selection, resampling methods, spectral distortion

Citation

Coakley, K. and Qu, J. (2017), Selection of spectral distortion models for electronic measurement of the Boltzmann constant, Metrologia, [online], https://doi.org/10.1088/1681-7575/aa5d21 (Accessed October 6, 2024)