Johnson Noise Thermometer Research Articles

Sound-card-based Johnson noise thermometer

This article presents a Johnson noise thermometer with a signal acquisition system based on a sound card. The thermometer uses a simple analogue circuit to measure the Johnson noise on a resistor. No external hardware or power supply is necessary, except for a reference multimeter. Data processing is performed in real time on a personal computer using LabView software. The results show that the developed thermometer has an expanded uncertainty (k = 2) of 0.8 ℃ over a temperature range from − 196 ℃ to 300 ℃, with a measurement time of 5 min.

Progress towards in-situ traceability and digitalization of temperature measurements

Autonomous control systems rely on input from sensors, so it is crucial that the sensor input is validated to ensure that it is ‘right’ and that the measurements are traceable to the International System of Units. The measurement and control of temperature is widespread, and its reliable measurement is key to maximising product quality, optimising efficiency, reducing waste and minimizing emissions such as CO2 and other harmful pollutants. Degradation of temperature sensors in harsh environments such as high temperature, contamination, vibration and ionising radiation causes a progressive loss of accuracy that is not apparent. Here we describe some new developments to overcome the problem of ‘calibration drift’, including self-validating thermocouples and embedded phase-change cells which self-calibrate in situ by means of a built-in temperature reference and practical primary thermometers such as the Johnson noise thermometer which measure temperature directly and do not suffer from calibration drift. All these developments will provide measurement assurance which is an essential part of digitalisation to ensure that sensor output is always ‘right’, as well as providing essential ‘points of truth’ in a sensor network. Some progress in digitalisation of calibrations to make them available to end-users via a website and/or an Application Programming Interface is also described.

Ultrasensitive Calorimetric Measurements of the Electronic Heat Capacity of Graphene.

Heat capacity is an invaluable quantity in condensed matter physics and yet has been completely inaccessible in two-dimensional (2D) van der Waals (vdW) materials, owing to their ultrafast thermal relaxation times and the lack of suitable nanoscale thermometers. Here, we demonstrate a novel thermal relaxation calorimetry scheme that allows the first measurements of the electronic heat capacity of graphene. It is enabled by combining a radio frequency Johnson noise thermometer, which can measure the electronic temperature with a sensitivity of ∼20 mK/Hz1/2, and a photomixed optical heater that modulates Te with a frequency of up to Ω = 0.2 THz. This allows record sensitive measurements of the electronic heat capacity Ce < 10 -19 J/K and the fastest measurement of electronic thermal relaxation time τe < 10 -12 s yet achieved by a calorimeter. These features advance heat capacity metrology into the realm of nanoscale and low-dimensional systems and provide an avenue for the investigation of their thermodynamic quantities.

Linearity measurements of critical Johnson noise thermometer components with low-distortion multitones from a Josephson arbitrary waveform synthesizer

Quantum-based and low-distortion multitone signals from a Josephson arbitrary waveform synthesizer are used to calibrate critical noise thermometer components between 8 and 240 kHz at increased input noise levels. The example signal path includes a 24-bit ΣΔ analog-to-digital converter (ADC) and a prototype amplifier for Physikalisch-Technische Bundesanstalt’s new noise thermometer. The signals consist of odd harmonics of the pattern repetition frequency with growing tone spacing, minimizing the influence of intermodulation distortion during calibration. After a detailed description of the calibration procedure, we compare the multitone spectra with growing tone spacing to ones with equally spaced tones. For the example signal path, gain nonlinearities better than ±2 µV V−1 at input rms noise levels between 9.7 and 465 µV are experimentally demonstrated. Furthermore, we investigate the effect of dither and applied offset voltage on the non-linearity of the ADC.

Fabrication and Characterization of a Quantum Voltage Noise Source Chip for a Johnson Noise Thermometer

A Johnson noise thermometer (JNT) determines the thermodynamic temperature through cross-correlation measurement of the Johnson noise in a sense resistor at an unknown temperature. In the quantum voltage calibrated JNT system, a superconductive quantum voltage noise source (QVNS) is required to produce artificial pseudo-random noise to calibrate the gain of the cross-correlation electronics. In this paper, we present the design, fabrication, and characterization of the QVNS chip. Compared with our previous design, a new straightforward mirror symmetric layout is implemented. For this layout, the coplanar waveguides (CPWs) have the same lengths and transmission parameters. Equal pulse magnitudes are delivered to each Josephson junction array under the same output settings of the bipolar pattern generator. The modified QVNS chip is thereby enhanced because the quantum locking range is enlarged. A copper foil shielding package is used to eliminate crosstalk in this design. The first spectral comparison of two Josephson junction (JJ) arrays of with and without shielding is presented in this paper. The comparative results demonstrate that the shielding is effective. The abovementioned improvements enable us to synthesize both single and multitone waveforms with good spectral results, such that the chip satisfies the requirement of a QVNS-based JNT system for temperature measurements.

Developments towards an industrial Johnson noise thermometer

In this paper we present new developments in our practical, drift-free Johnson noise thermometer as it moves from a proof-of-principle prototype towards a practical implementation to become a viable primary thermometer for industrial applications. We will discuss bandwidth optimisation to obtain the lowest possible uncertainty of temperature measurements. The concept of weighting the cross-correlation frequency bins to improve the uncertainty will be introduced and it will be shown that this can decrease the measurement uncertainty in our system by 28%. Weighting fundamentally changes the optimum bandwidth calculation such that information from higher parts of the measured spectrum can always contribute to a reduction in total measurement noise. We will present the design approach used to provide extreme immunity to electromagnetic interference, a problem that has severely degraded previous efforts. We describe the results of tests by a third-party test laboratory demonstrating immunity up to field strengths of 10 Vm−1, as required in standards for equipment operating in heavy industrial environments. We have also looked at interference at frequencies that could directly interfere with our thermometer that are not covered in the standards. The latest test results will be presented showing a five-fold improvement in accuracy on an extrapolation to absolute zero compared with the original proof-of-principle prototype with similar measurement parameters. Developments in techniques for providing traceability of the thermometer’s calibration to electrical rather than temperature national standards will be presented.

Development of a driftless Johnson noise thermometer for nuclear applications

Existing temperature sensors such as thermocouples and platinum resistance thermometers suffer from calibration drift, especially in harsh environments, due to mechanical and chemical changes (and transmutation in the case of nuclear applications). A solution to the drift problem is to use temperature sensors based on fundamental thermometry (primary thermometers) where the measured property is related to absolute temperature by a fundamental physical law. A Johnson noise thermometer is such a sensor and uses the measurement of the extremely small thermal voltage noise signals generated by any resistive element to determine temperature using the Johnson-Nyquist equation. A Johnson noise thermometer never needs calibration and is insensitive to the condition of the sensor material, which makes it ideally suited to long-term temperature measurement in harsh environments. These can include reactor coolant circuits, in-pile measurements, nuclear waste management and storage, and severe accident monitoring. There have been a number of previous attempts to develop a Johnson noise thermometer for the nuclear industry, but none have achieved commercialization because of technical difficulties. We describe the results of a collaboration between the National Physical Laboratory and Metrosol Limited, which has led to a new technique for measuring Johnson noise that overcomes the previous problems that have prevented commercialization. The results from a proof-of-principle prototype that demonstrates performance commensurate with the needs of nuclear applications is presented, together with details of progress towards the commercialization of the technology. The development partners have effected a step change in the application of primary thermometry to industrial applications and seek partners for field trials and further exploitation.

Measurement of the Melting Point of Gallium Using a Johnson Noise Thermometer

We measured the thermodynamic temperature of the melting point of gallium $T_{\mathrm {Ga}}$ using a Johnson noise thermometer (JNT) with an integrated quantum voltage noise source (IQVNS) as a reference. $T_{\mathrm {Ga}}$ was calculated using the fundamental constants recommended by the Committee on Data for Science and Technology (CODATA) for the revision of the International System of Units (SI). The measured $T_{\mathrm {Ga}}$ is consistent with the value defined in the International Temperature Scale of 1990.

The Boltzmann Constant: Evaluation of Measurement Relative Uncertainty Using the Information Approach

The purpose of this work is to prove that only by applying a theoretically sound information approach to developing a model for measuring the Boltzmann constant, one can justify and calculate the value of the required relative uncertainty. A dimensionless parameter (comparative uncertainty) was proposed as a universal metric for comparing experimental measurements of Boltzmann constant and simulated data. Examples are given of applying the proposed original method for calculating the relative uncertainty in measuring the Boltzmann constant using an acoustic gas thermometer, dielectric constant gas thermometer, Johnson noise thermometer, Doppler broadening thermometer. The proposed approach is theoretically justified and devoid of the shortcomings inherent in the CODATA concept: a statistically significant trend, a cumulative value of consensus or a statistical control. We tried to show how a mathematical-expert formalism can be replaced by a simple, theoretically grounded postulate on the use of information theory in measurements.

Development of quantum voltage noise source chip for precision measurement of Boltzmann constant

The Johnson noise thermometer is used to precisely measure Boltzmann constant by comparing the thermal noise caused by charge movement and the quantized voltage reference noise synthesized by the quantum voltage noise source (QVNS). The QVNS signal is synthesized based on quantized voltage pulses produced by two channels of superconducting Josephson junction arrays, which are designed for cross-correlation electronics. The Nb/NbxSi1-x/Nb Josephson junction is used as a core device of QVNS chip in this work for its non-hysteretic current-voltage (I-V) characteristics and conveniently adjustable barrier parameters.In this paper, we present the design consideration, fabrication process, and measurement results of the QVNS chip. The QVNS chip contains two Josephson junction arrays, each consists of four 6 μm×12 μm junctions and is embedded in a 50 Ω coplanar waveguide transmission line. The random noise in signals from the two driven channels is eliminated by cross-correlation, and then an accurate quantum noise is obtained. Test chips with different areas of Josephson junctions are also designed on the same mask, aiming at estimating the variation range of Ic. The typical fabrication process for voltage standard chips in our laboratory is used for preparing the QVNS chip.The sample is measured at 4.2 K. The DC I-V curve shows that the critical current Ic is 6.1 mA. The I-V characteristics of the junctions under 5 GHz microwave radiation are measured. For a series array of four junctions, a 41.44 μV one-stage Shapiro step is observed. Calculation shows that the error between the measurement and theoretical value of 41.36 μV is about 1.9‰, which means that the QVNS chip performs well under microwave radiation and can be used for synthesizing the AC quantum voltage reference noise.A single-frequency 100 kHz sinusoidal waveform is synthesized by the QVNS chip under pulse driven signal. A spectrum of the synthesized sinusoidal waveform shows a single peak, which means that the digital pulse signal is perfectly filtered by Josephson junction arrays and the synthesized signals possess quantum accuracy. The results indicate that our chip has good dynamic response and works well in synthesizing a single-frequency AC quantum voltage signal. This work can provide core devices for the noise thermometry system and support the precise measurement of Boltzmann constant as well as redefinition of Kelvin in future. As a next step, the design and package will be further improved, and the probe module will be optimized to reduce the measurement uncertainty.

The Development of a Practical, Drift-Free, Johnson-Noise Thermometer for Industrial Applications

Johnson noise thermometers measure a phenomenon that is directly linked to thermodynamic temperature by a fundamental physical law. The measurement of Johnson noise therefore offers the prospect of realizing a drift-free thermometer. Despite previous attempts to produce a practical Johnson noise thermometer for industrial applications, the technique is currently used only in niche research applications to explore discrepancies between practical temperature scales and thermodynamic temperature, or to determine Boltzmann’s constant. This has largely been due to the historical use of switched correlators to measure Johnson noise, which limits the sense resistance and measurement bandwidth that can be employed. This constraint limits the Johnson noise signal to levels near the limits of measurement. A new technique that eliminates switching and thereby allows the use of much higher sense resistances and bandwidths to increase the Johnson noise signal is presented. The signal power achieved is significantly higher than for systems using a switched correlator. Results so far indicate that measurement performance is compatible with the requirements of industrial applications. Specifically, uncertainties of \({<}0.3 \, {^{\circ }}\hbox {C}\) (95 % confidence) were demonstrated for measurements near ambient temperature with a measurement time of only 7 s.

Improved electronic measurement of the Boltzmann constant by Johnson noise thermometry

The unit of thermodynamic temperature, the kelvin, will be redefined in 2018 by fixing the value of the Boltzmann constant, k. The present CODATA recommended value of k is determined predominantly by acoustic gas-thermometry results. To provide a value of k based on different physical principles, purely electronic measurements of k were performed by using a Johnson noise thermometer to compare the thermal noise power of a 200 Ω sensing resistor immersed in a triple-point-of-water cell to the noise power of a quantum-accurate pseudo-random noise waveform of nominally equal noise power. Measurements integrated over a bandwidth of 575 kHz and a total integration time of about 33 d gave a measured value of k = 1.3806513(53) × 10−23 J K−1, for which the relative standard uncertainty is 3.9 × 10−6 and the relative offset from the CODATA 2010 value is +1.8 × 10−6.

Self-validating contact thermometry sensors for higher temperatures

The measurement of high temperatures in industry is often accompanied by harsh environments and suboptimal measurement conditions. Typically used thermocouples often suffer from unavoidable drift effects which constrain the required improvement of process efficiency and control. A technique for overcoming drift effects and allowing the self-validation of thermocouples usable in industrial processes was tested and the application of combined thermocouple-noise temperature sensors was investigated in the temperature range between 1000 °C and 1450 °C. Fixed points of the International Temperature Scale of 1990 (ITS-90) were used to check the noise temperatures measured for their accuracy (according to the ITS-90 temperature). In this way a traceable and independent method to evaluate the long-term stability of the combined sensors and noise thermometer electronics was established. Relative measurement uncertainties by using the Johnson noise thermometer of about 0.1% were achievable which would be sufficient to determine and correct for unavoidable thermocouple drifts in the order of 1–2 K.

A Microkelvin Magnetic Flux Noise Thermometer

Due to its non-driven nature, noise thermometry intrinsically is the method of choice when minimal heat input during the temperature measurement is required. Our noise thermometer, experimentally characterized for temperatures between 42 \({{\upmu }}\)K and 0.8 K, is a magnetic Johnson noise thermometer. The noise source is a cold-worked high purity copper cylinder, 5 mm in diameter and 20 mm long. The magnetic flux fluctuations generated by the electrons’ Brownian motion is measured inductively by two dc-SQUID magnetometers simultaneously. Cross-correlation of the two channels leads to reduction of parasitic noise by more than one order of magnitude which allows for measuring the tiny noise powers at microkelvin temperatures.

Flat Frequency Response in the Electronic Measurement of Boltzmann's Constant

A new quantum-voltage-calibrated Johnson noise thermometer was developed at the National Institute of Metrology to demonstrate the electrical approach that determines Boltzmann's constant <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> , by comparing electrical and thermal noise power. A measurement with an integration period of 19 h and a bandwidth of 638 kHz results in a relative offset of 1 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> , from the current Committee on Data for Science and Technology value of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> , and a type A relative standard uncertainty of 17 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> . Closely matched noise powers and transmission-line impedances were achieved, and consequently, the quadratic fitting parameters of the ratio spectrum show flat frequency responses with respect to the measurement bandwidth. This flat response produces a dramatically reduced systematic error compared to that of the National Institute of Standards and Technology measurement of <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</i> , in which the relative combined uncertainty was dominated by this error.

Reduced Nonlinearity Effect on the Electronic Measurement of the Boltzmann Constant

The National Institute of Standards and Technology has developed a quantum-voltage-noise-source-calibrated Johnson noise thermometer (JNT) to provide a new electronic measurement technique for determining the Boltzmann constant. Improvements in electronics and synthesized noise waveforms have led to reduced uncertainty in the measurement. Recent investigations have shown that some of the distortion in the present electronics arises in the differential stage of both the preamplifier and the analog-to-digital converter (ADC). The distortion can be reduced by compensating the direct current offset of the signal at the inputs to the differential stage. A four-channel cross correlation JNT with optimized preamplifiers and new ADCs is being assembled. The improvements are on track to reach the goal of an electronic measurement of the Boltzmann constant at a relative uncertainty of 6 × 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> .

An electronic measurement of the Boltzmann constant

The Boltzmann constant k was measured by comparing the Johnson noise of a resistor at the triple point of water with a quantum-based voltage reference signal generated with a superconducting Josephson-junction waveform synthesizer. The measured value of k = 1.380 651(17) × 10−23 J K−1 is consistent with the current CODATA value and the combined uncertainties. This is our first measurement of k with this electronic technique, and the first noise-thermometry measurement to achieve a relative combined uncertainty of 12 parts in 106. We describe the most recent improvements to our Johnson-noise thermometer that enabled the statistical uncertainty contribution to be reduced to seven parts in 106, as well as the further reduction of spurious systematic errors and electromagnetic interference effects. The uncertainty budget for this measurement is discussed in detail.

Short Communication: Improvements to INRIM Johnson Noise Thermometer

This paper presents a progress report for the Johnson noise thermometry experiment which is under development at the Istituto Nazionale di Ricerca Metrologica. In order to aim at an uncertainty level better than 10−5 and to reduce the measurement time, a new setup has been developed. In particular, several modifications have been applied to the experiment described by Callegaro et al. (Metrologia 46: 409, 2009) to improve the traceability to voltage, resistance and frequency standards, and new amplifiers have been designed in order to expand the working frequency range up to 20 kHz, with a sensing resistor of 1 kΩ, while maintaining amplifier induced systematic errors to an acceptable level.

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 Boltzmann's constant to Planck's constant. Recent experiments and detailed uncertainty analysis indicate that Boltzmann's 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.

A Johnson noise thermometer with traceability to electrical standards

The paper presents an absolute Johnson noise thermometer (JNT), an instrument to measure the thermodynamic temperature of a sensing resistor, with traceability to voltage, resistance and frequency quantities. The temperature is measured in energy units, and can be converted to SI units (kelvin) with the accepted value of the Boltzmann constant kB; or, conversely, it can be employed to perform measurements at the triple point of water and obtain a determination of kB. The thermometer is composed of a correlation spectrum analyzer and a calibrator. The calibrator generates a pseudorandom noise (at a level suitable for traceability to an ac voltage standard) by digital synthesis, scaled in amplitude by a chain of electromagnetic voltage dividers and cyclically injected in series with the Johnson noise. First JNT measurements at room temperature are compatible with those of a standard platinum resistance thermometer within the estimated combined uncertainty of 60 µK K−1 of both instruments. A path towards future improvements of JNT accuracy is also sketched.