Measurement time and statistics for a noise thermometer with a synthetic-noise reference

Abstract

This paper describes methods for reducing the statistical uncertainty in measurements made by noise thermometers using digital cross-correlators and, in particular, for thermometers using pseudo-random noise for the reference signal. First, a discrete-frequency expression for the correlation bandwidth for conventional noise thermometers is derived. It is shown how an alternative frequency-domain computation can be used to eliminate the spectral response of the correlator and increase the correlation bandwidth. The corresponding expressions for the uncertainty in the measurement of pseudo-random noise in the presence of uncorrelated thermal noise are then derived. The measurement uncertainty in this case is less than that for true thermal-noise measurements. For pseudo-random sources generating a frequency comb, an additional small reduction in uncertainty is possible, but at the cost of increasing the thermometer's sensitivity to non-linearity errors. A procedure is described for allocating integration times to further reduce the total uncertainty in temperature measurements. Finally, an important systematic error arising from the calculation of ratios of statistical variables is described.

Progress in Noise Thermometry at 505 K and 693 K Using Quantized Voltage Noise Ratio Spectra

“…The statistical uncertainties for the a 0 parameters in the four fitted spectra vary between 22 µK · K −1 and 26 µK · K −1 . These are approximately three times greater uncertainties than what would be expected in this model, averaging time, and bandwidth [6]. This statistical inflation is caused by distortion in the QVNS waveforms from small non-linear effects in the amplifiers [14].…”

“…The values of a 0 − 1 from the relative-mode spectra represent differences in the relative temperature difference or ε Zn − ε Sn . If the ITS-90 value for the Sn freezing point (505.078 K) was assumed to be thermodynamically correct, then ε Sn = 0 IRFR infrared filter radiometry, RR-JNT relative resistance-based Johnson noise thermometry, RQ-JNT relative quantized voltage-based Johnson noise thermometry a Adjusted by +10 µK · K −1 from as-published value due to a statistical offset [6] and the relative noise temperature for the Zn freezing point would be equivalent to a 0 − 1 (i.e., derived from Table 4). In contrast, we make a correction to the ITS-90 using the best available thermodynamic determination of that temperature which is the AGT result from Strouse et al [16].…”

Present Estimates of the Differences Between Thermodynamic Temperatures and the ITS-90

“…Therefore, various other data [34][35][36][37] have been included to take into account the older relative radiation thermometry exhibiting low uncertainties. The result of Edler [25] is excluded from the averaging process due to a recently detected statistical bias [38].…”

Johnson-noise thermometry based on a quantized-voltage noise source at NIST

“…The signals are amplified, low-pass filtered, and measured with an analog-to-digital converter (ADC) so that digital processing can produce the cross-correlated signal. It is important for the bandwidth to be large to decrease the integration period [7]. Our system typically amplifies by 10 4 with a bandwidth of 650 kHz.…”