To create an intrinsic quantum-based electronic temperature standard to support the NIST Chemical Science and Technology Laboratory efforts toward reducing uncertainty in the ITS-90 temperature scale and to develop a novel method for determining the Boltzmann constant.
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Sae Woo Nam tests the cross-correlation electronics for the Johnson noise thermometry system. A gallium triple-point cell at 302.916 K is behind him. |
Existing precision thermometry methods use gas-based and fixed-point methods to achieve the lowest uncertainties below parts in 105. Unfortunately, these methods are limited to specific fixed temperatures and require considerable effort. Another method that compares electrical and thermal noise power, called Johnson noise thermometry (JNT), would provide a novel approach to precision thermometry and, through the use of quantum-based voltage standards, has the potential to improve the realization of the Kelvin Thermodynamic Temperature Scale, especially with regard to linearity.
In addition, a quantum-based JNT system would also provide a novel route to a re-determination of the Boltzmann constant, k. This latter goal is particularly timely because there are plans to redefine in 2011 four of the SI units (including the kelvin in terms of k) in terms of fundamental physical constants so that they are universal, permanent, and invariant in time. The NIST quantum-based JNT approach to create an “electronic kelvin” is analogous to the watt-balance program to realize an “electronic kilogram,” which compares electrical and mechanical power for the determination of Planck’s constant, h.
Our customers and collaborators include the NIST Chemical Science and Technology Laboratory, temperature calibration laboratories including other national measurement institutes, and industrial applications that require long-term temperature stability or have temperature sensors in difficult or remote locations.
In order to meet these customer needs and fundamental metrology goals, we created a quantum-based electronic temperature standard that is unique in the world by developing new technology in a number of different areas. Most importantly, we constructed the world’s first quantum voltage noise source (QVNS) as well as state-of-the-art low-noise cross-correlation electronics, which is calibrated by the QVNS. We developed pseudo-noise voltage waveforms and synthesis techniques for comparison with the voltage noise of resistors in triple point cells of both gallium and water. We also devised a novel ratiometric method that uses the QVNS to compare the voltage noise of resistors at different temperatures.
The goal of the NIST Johnson noise thermometry program is to build an electronic temperature standard based on the quantized voltage pulses of superconducting Josephson junctions.
In a JNT system, the temperature T is inferred from measurement of the Johnson noise voltage VT across a calibrated resistance R. The mean-squared voltage noise is given by the Nyquist formula VT2 = 4kTR Δf, where Δf is the measurement bandwidth. Cross-correlation techniques are typically used to measure these extremely small voltages to remove the error introduced by amplifier noise. In 1999, John Martinis realized that the Josephson Arbitrary Waveform Synthesizer being developed by the Quantum Voltage Project might be able to produce a stable, accurate, pseudo-noise voltage to provide a better means of calibrating the low-noise cross-correlation electronics. A stable, programmable, and intrinsically accurate noise source, based on the quantum accuracy of Josephson junctions, would provide a number of key advantages: (1) direct calibration of the cross-correlation electronics, (2) matching of the calibration voltage noise to that of the sense resistor, while (3) simultaneously matching the source impedance to both the sense resistance and the output transmission-line impedance. These features, which are mutually exclusive using conventional methods, reduce the measurement uncertainty, increase the measurement bandwidth, and decrease the measurement time for the entire JNT system.
During the JNT development program, the Quantum Voltage Project developed a QVNS that is ideally suited for these measurements and is based on digital-to-analog waveform synthesis techniques. The QVNS superconducting integrated circuit is based on technology and research developed for ac Josephson voltage standards. However, development of the QVNS also provided new insights and precision measurement expertise that improved and benefited the ac Josephson program.
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Sam Benz optimizes the operating margins for the Josephson arbitrary-waveform synthesizer. |
Our goal is to achieve uncertainties of better than a few parts in 105 for temperatures in the range of a several hundred kelvin. At these temperatures the noise signals are small, on the order of 1 nV/Hz½ for a 100 ohm resistor. In order to achieve small measurement uncertainties for such low-voltage signals, the noise power spectral density must be integrated for a long time and over a wide bandwidth. Thus the QVNS must be stable for long integration times but does not need to generate large voltages. We devised a special method of biasing the QVNS that meets these requirements and allows it to be much simpler than the Josephson arbitrary waveform synthesizer, where the primary focus is to obtain the highest possible voltages.
We also constructed custom cross-correlation electronics for the JNT program. Two pairs of voltage leads are measured with separate low-noise amplifier channels. Each signal is first measured with an ac-coupled differential FET, followed by an anti-alias filter with a cutoff frequency at 2 MHz. The resulting amplified and filtered signals are digitized at 50 MHz by a 14-bit analog-to-digital converter. Field-programmable gate arrays (FPGAs) at the output of the digitizers then digitally filter the signal with a low-pass frequency of 100 kHz. The digitally filtered data are transmitted via a 50 megabit/s optical link to a custom PCI card installed in a computer. Each channel transmits 2.08333 million samples per second which is the effective sampling frequency of the signal. In the present system, a dual-CPU computer is used to calculate two 221 point fast Fourier transforms (FFTs) in real-time (less than one second). The cross-correlation and auto-correlation power spectra are then calculated, accumulated, and stored for later analysis.
Sae Woo Nam, Wes Tew (NIST Chemical Sciences and Technology Laboratory),
and Sam Benz have performed many comparisons between the Johnson noise voltage
of resistors at known temperatures and the synthesized pseudo-noise waveforms
of the quantum voltage noise source. The resistor temperatures are controlled
using either a gallium fixed-point cell or a water triple point cell. Measurements
are made using the custom built cross-correlation electronics system. The
computer-controlled optically interfaced system correctly samples, stores,
and processes the waveforms in real time. This correlation electronics is
different from other systems because it digitally processes the signal in
an FPGA before sending it to a computer. This is necessary to reduce the
data rate to the computer.
Paul Dresselhaus fabricated numerous circuits specifically to improve
the performance and optimize the circuits for the JNT program. Benz has
tested the circuits with appropriate pseudo-noise waveforms and demonstrated
proper cross-correlation using an HP FFT spectrum analyzer. Benz also
performed extensive measurements of input-output coupling for the JNT
circuits and devised a novel unipolar bias method to decrease the coupling
by about 40 dB. Other improvements include novel QVNS circuits with
smaller common mode signals and implementation of Charlie Burrough’s flip-chip on flex
packaging. These results allowed us to take the next step and measure the
arrays at much smaller voltages and higher bandwidth using Nam’s cross-correlation
electronics.
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Log-log plot showing the measured spectrum of a QVNS-synthesized pseudo-noise waveform. The spectrum was measured with the JNT cross-correlation electronics and shows the power (V2) spectrum Sxy of the 1258 tones synthesized by the QVNS. Each bin has a width of 1 Hz and is an average of 200 samples. The power spectrum is in arbitrary units based on the digitizer bins. |
Nam, Benz, Dresselhaus, and Charlie Burroughs, in collaboration with Wes Tew of the Chemistry Laboratory, have continued development of the Johnson noise thermometry system, especially with regard to improvements in the measurement circuits and electronics. Unwanted distortion was observed when the accurate QVNS signal was measured with the cross correlation electronics. This distortion was significantly reduced by using inductive chokes on the input of the electronics. The cause of the distortion appeared to be mixing in the first FET amplifier from the high-frequency, 100-400 MHz, quantization tones in the QVNS waveform. Other major sources of distortion that were uncovered through measurements of the accurate QVNS synthesized waveforms were due to poor contacts and interconnections between the signal sources and the amplifiers; poor interfaces rectify the waveform and produce measurable harmonic distortion. Unique waveforms, with either odd-only or even-only harmonics, were developed to elucidate and remove these errors. By constructing a second QNVS system, and making comparisons between them using both inputs to the JNT electronics, we were able to remove all distortion within the dynamic range of the electronics.
Comparisons between different QVNS cryoprobes also increased our understanding of the high-frequency transfer function characteristics. Calculations showed that small differences in the transfer functions of the QVNS probes were caused by different transmission line leads. Calculations showed that this effect could not account for the transfer function differences between the QVNS and noise resistor probes. We finally realized, and confirmed through further calculations, that there is a fundamental difference between the QVNS and resistor output circuits that results in a significantly higher effective capacitance in the resistor circuits that progressively mismatches the two transfer functions at high higher frequencies. By increasing the QVNS output resistance by about 65%, we successfully matched the transfer functions of the QVNS and resistor circuits up to about 600 kHz. This truly matches the transmission lines for the first time, contrary to our original assumptions about impedance matching at the start of this program.
Having greatly reduced the errors from distortion and transmission lines, we can now investigate voltage noise over a much wider frequency range. In preliminary measurements we’ve demonstrated that we can closely match the two transmission lines of the Josephson and triple-point resistor sources, causing the ratio to remain flat over most of the measurement bandwidth. Control of the ratio’s frequency dependence is shown in Figure 4, where the grey data points show the ratio when the transmission lines are nearly matched. In this measurement, the absolute error in measuring temperature or determining “k/h” was approximately 50 ppm. This is 3-times better than previous temperature measurements. These preliminary results suggest that with only a 10-fold further improvement in the measurement uncertainty, we can have an impact on Boltzmann’s constant at a few parts per million.
The next step toward lower uncertainty involves improving the measurement electronics to reduce intrinsic nonlinearities, lower the noise floor, and extend battery lifetime. These improvements will allow the measurement electronics to complete much longer integration times (>2 days). We also must perform extensive measurements and calculations to model the transmission line effects. We also plan to investigate improvements in common mode rejection of the front amplifier stage and in the switching network.
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Measured power spectral density ratios vs. frequency (kHz) showing control of the frequency dependence. The blue points show the large frequency dependence in the ratio when the transmission lines (between the noise sources and the correlation electronics) are mismatched. The red points show a nearly constant ratio up to 600 kHz with matched transmission lines. |
This year we plan to make significant improvements to the cross correlation electronics, including better preamplifiers and battery chargers that allow us to make longer continuous measurements.
With further improvements and removal systematic errors for the electronics, transmission lines and measurement circuits, we hope to reduce our measurement uncertainty to less than 20 parts per million.
We are collaborating with Weston Tew and John Labensky of the Process Measurements Division (836) in the NIST Chemical Science and Technology Laboratory.
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Sae Woo Nam, Wes Tew, and Sam Benz with the quantized voltage noise source. |
Dr. D. Rod White from the Measurement Standards Laboratory in Lower Hutt, New Zealand is also consulting and collaborating with us, bringing many years of expertise in Johnson noise thermometry.
W.L. Tew, J.R. Labenski, S.W. Nam, S.P. Benz, P.D. Dresselhaus, and C.J. Burroughs, “Johnson noise thermometry near the zinc freezing point using resistance-based scaling,” submitted to the Sixteenth Symposium on Thermopysical Properties, 30 July–4 Aug. 2006, Boulder, CO, USA.
J.R. Labenski, W.L. Tew, S.W. Nam, S.P. Benz, P.D. Dresselhaus, and C.J. Burroughs, “Resistance-based scaling of LF- and MF-band thermal noise powers,” 2006 Conference on Precision Electromagnetic Measurements Digest, presented 10–14 July 2006, Torino, Italy, pp. 404-405.
W. L. Tew, S. W. Nam, S. P. Benz, P. Dresselhaus, John Martinis, and H. M. Hashemian, New Technologies for Noise Thermometry with Applications in Harsh and-or Remote Operating Environments, Presented at The 51st International Instrumentation Symposium in Knoxville Tennessee, The Instrumentation, Systems and Automation Society, May 2005.
S. Nam, S. Benz, P. Dresselhaus, C. Burroughs, W. L. Tew, D. R. White, J. M. Martinis, “Johnson Noise Thermometry using a Quantum Voltage Noise Source for Calibration,” IEEE Transactions on Instrumentation and Measurement, Vol. 54, No. 2, pp. 653-657 (April 2005).
S. Nam, S. Benz, P.D. Dresselhaus, and J. Martinis, “Johnson noise thermometry measurements using a quantized voltage noise source for calibration,” IEEE Transactions on Instrumentation and Measurement, Vol. 52, No. 2, pp. 550-554 (April 2003).
S.P. Benz, P.D. Dresselhaus, and J. Martinis, “An ac Josephson source for Johnson noise thermometry,” IEEE Transactions on Instrumentation and Measurement, Vol. 52, No. 2, pp. 545-549 (April 2003).
S. W. Nam , S. P. Benz, J. M. Martinis, P.D. Dresselhaus, W. L. Tew, and D. R. White, “A ratiometric method for Johnson noise thermometry using a quantized voltage noise source,” Temperature: Its Measurement and Control In Science and Industry, Vol. 7, Part 1, pp. 37-42, Edited by Dean C. Ripple, Proceedings of The Eighth International Temperature Symposium, (AIP Conference Proceedings Vol. 684: Melville, New York 2003).
S. P. Benz, J. M. Martinis, S. W. Nam, W. L. Tew, and D. R. White, “A new approach to Johnson noise thermometry using a Josephson quantized voltage source for calibration,” in Proceedings of TEMPMEKO 2001, the 8th International Symposium on Temperature and Thermal Measurements in Industry and Science, B. Fellmuth, J. Seidel, and G. Scholz, Eds., Berlin: VDE Verlag, April 2002, pp. 37-44