Systematic errors in the correlation method for Johnson noise thermometry: residual correlations due to amplifiers

TL;DR

This paper presents a hybrid analytical and numerical method to accurately evaluate residual correlation errors in Johnson noise thermometry, improving the precision of temperature measurements by better modeling amplifier noise.

Contribution

It introduces a combined analytical-numerical approach for modeling residual correlations in JNT, enhancing accuracy and efficiency over traditional methods.

Findings

The proposed method accurately estimates residual correlation errors.

Application to an ultralow-noise amplifier demonstrates effectiveness.

The approach simplifies the evaluation process for complex amplifier circuits.

Abstract

Johnson noise thermometers (JNT) measure the equilibrium electrical noise, proportional to thermodynamic temperature, of a sensing resistor. In the correlation method, the same resistor is connected to two amplifiers and a correlation of their outputs is performed, in order to reject amplifiers' noise. Such rejection is not perfect: the residual correlation gives a systematic error in the JNT reading. In order to put an upper limit, or to achieve a correction, for such error, a careful electrical modelling of the amplifiers and connections must be performed. Standard numerical simulation tools are inadequate for such modelling. In literature, evaluations have been performed by the painstaking solving of analytical modelling. We propose an evaluation procedure for the JNT error due to residual correlations which blends analytical and numerical approaches, with the benefits of both: a rigorous and accurate circuit noise modelling, and a fast and flexible evaluation with an user-friendly commercial tool. The method is applied to a simple but very effective ultralow-noise amplifier employed in a working JNT.