^{1}, C. J. Burroughs

^{1}and S. P. Benz

^{1}

### Abstract

We have performed a variety of precision measurements by comparing ac and dc waveforms generated by two independent ac programmable Josephson voltage standard (ACPJVS) systems. The objective of these experiments was to demonstrate the effectiveness of using a sampling digital voltmeter to measure small differences between Josephson waveforms for frequencies up to . The low uncertainties that we obtained confirm the feasibility of using this differential sampling method for high accuracy comparisons between ACPJVS waveforms and signals from other sources.

We thank Tom Nelson and Bryan Waltrip, NIST Gaithersburg, for advice regarding sampling techniques and customization of the DVM to implement the external clock reference. We are grateful to Paul Dresselhaus, Yonuk Chong, Nicolas Hadacek, Burm Baek, and Michio Watanabe for helping develop the stacked junction fabrication process used for our PJVS chips. We thank Jonathan Williams of NPL for helpful conversations and support regarding the bias electronics.^{18} We also thank Ralf Behr and Luis Palafox of PTB for collaborative discussions regarding ac waveform synthesis using Josephson arrays. Rod White suggested helpful approaches to elucidating the systematic deviations observed in the higher frequency differential measurements.

I. INTRODUCTION

II. SAMPLING METHOD

III. DIFFERENCE MEASUREMENTS WITH TWO IDENTICAL ACPJVS CHIPS

A. Type A uncertainty

B. Deviation from ideal Josephson value

IV. DIFFERENCE MEASUREMENTS WITH DIFFERENT ACPJVS CHIPS

A. Time alignment between the two synthesized waveforms and the sampling DVM

B. Operating margins and dither-current flat spot

C. Accuracy of the difference measurements

V. DVM GAIN AND LINEARITY ANALYSIS

A. Gain and linearity on the range

B. Gain and linearity in the null detector configuration

VI. CONCLUSION

### Key Topics

- Electric measurements
- 50.0
- Josephson effect
- 28.0
- Error analysis
- 16.0
- Josephson junctions
- 10.0
- Microwaves
- 9.0

## Figures

Schematic of the differential sampling configuration used for comparing the voltages synthesized by two ACPJVS systems. All the generated clock input signals are locked to the same reference (not shown).

Schematic of the differential sampling configuration used for comparing the voltages synthesized by two ACPJVS systems. All the generated clock input signals are locked to the same reference (not shown).

Time-dependent voltage plot showing the sampling windows for a waveform containing 16 samples at an rms amplitude of . In this example waveform, alternating gray and white time slices represent different time integration windows of the sampling voltmeter. The gray zones are free of transients and therefore sample only the parts of the waveform where the voltage is accurately established. We discard the white sampling zones that contain the transients where the voltage is changing between steps.

Time-dependent voltage plot showing the sampling windows for a waveform containing 16 samples at an rms amplitude of . In this example waveform, alternating gray and white time slices represent different time integration windows of the sampling voltmeter. The gray zones are free of transients and therefore sample only the parts of the waveform where the voltage is accurately established. We discard the white sampling zones that contain the transients where the voltage is changing between steps.

Sampled voltages from a differential waveform containing 64 steps with peak amplitude for five different frequencies. The inset shows the stepwise voltages for a full waveform period and the rectangle illustrates the data range presented in the main frame, namely, steps 43 through 51.

Sampled voltages from a differential waveform containing 64 steps with peak amplitude for five different frequencies. The inset shows the stepwise voltages for a full waveform period and the rectangle illustrates the data range presented in the main frame, namely, steps 43 through 51.

Difference between the expected Josephson voltage and the measured voltage, for 64 sample waveforms of different frequencies. Step numbers 43–51 are presented here. The uncertainties are clearly independent of the differential amplitude (, , and ) of the waveform and dependent on the waveform frequency. Thus, the uncertainty depends primarily on the sampler’s aperture time.

Difference between the expected Josephson voltage and the measured voltage, for 64 sample waveforms of different frequencies. Step numbers 43–51 are presented here. The uncertainties are clearly independent of the differential amplitude (, , and ) of the waveform and dependent on the waveform frequency. Thus, the uncertainty depends primarily on the sampler’s aperture time.

Type A uncertainty (, averaged over the number of samples) measured for amplitude waveforms with various sample numbers (4, 32, and 64) as a function of the waveform frequency.

Type A uncertainty (, averaged over the number of samples) measured for amplitude waveforms with various sample numbers (4, 32, and 64) as a function of the waveform frequency.

Measured Type A uncertainties (for differential waveforms) as a function of the aperture time of the voltmeter. The dashed line shows slope as a guide to the eye.

Measured Type A uncertainties (for differential waveforms) as a function of the aperture time of the voltmeter. The dashed line shows slope as a guide to the eye.

Standard deviation (for differential waveforms) as a function of the voltmeter aperture time. The line slope gives the general trend of the data dependence for this aperture time range.

Standard deviation (for differential waveforms) as a function of the voltmeter aperture time. The line slope gives the general trend of the data dependence for this aperture time range.

Expected step voltage differences (calculated) between a chip and a chip (both generating rms sine waves), for (a) 32 and (b) 64 samples plotted vs the sample number for one complete waveform period.

Expected step voltage differences (calculated) between a chip and a chip (both generating rms sine waves), for (a) 32 and (b) 64 samples plotted vs the sample number for one complete waveform period.

The upper part of the figure [(a)–(c)] schematically shows how the sampling windows shift (, 0%, and ) relative to the center of each ACPJVS waveform step. (d) Difference between the reconstructed rms voltage and the expected ideal rms voltage for array B ( chip, rms) as a function of the relative time alignment with the sampling voltmeter. Array A ( chip) provides the voltage reference levels for reconstructing the rms voltage of array B. Both plots (60 and ) use 32 samples.

The upper part of the figure [(a)–(c)] schematically shows how the sampling windows shift (, 0%, and ) relative to the center of each ACPJVS waveform step. (d) Difference between the reconstructed rms voltage and the expected ideal rms voltage for array B ( chip, rms) as a function of the relative time alignment with the sampling voltmeter. Array A ( chip) provides the voltage reference levels for reconstructing the rms voltage of array B. Both plots (60 and ) use 32 samples.

Difference between the reconstructed rms voltage and the expected ideal rms voltage for array B ( chip, rms) as a function of the dither current flowing in array B. Array A ( chip) provides the rms reference for reconstruction of the rms voltage of array B. Measurement results are shown for two different waveforms with 32 and 64 samples. The upper plot shows a 100 times smaller voltage range.

Difference between the reconstructed rms voltage and the expected ideal rms voltage for array B ( chip, rms) as a function of the dither current flowing in array B. Array A ( chip) provides the rms reference for reconstruction of the rms voltage of array B. Measurement results are shown for two different waveforms with 32 and 64 samples. The upper plot shows a 100 times smaller voltage range.

Difference between the reconstructed measured rms voltage and the expected ideal rms voltage for array B ( chip, rms) at different frequencies. Array A ( chip) provides the voltage reference for reconstructing the rms voltage of array B. Waveforms with both 32 and 64 samples were synthesized at each frequency. Both plots (a) and (b) show the same voltage difference, but on different voltage scales. The combined uncertainty of the measurement is only shown in (b).

Difference between the reconstructed measured rms voltage and the expected ideal rms voltage for array B ( chip, rms) at different frequencies. Array A ( chip) provides the voltage reference for reconstructing the rms voltage of array B. Waveforms with both 32 and 64 samples were synthesized at each frequency. Both plots (a) and (b) show the same voltage difference, but on different voltage scales. The combined uncertainty of the measurement is only shown in (b).

Voltmeter gain and linearity on the range in (a) dc mode, and (b) the sampling mode, with 32 sample triangular waveforms. . The plotted uncertainties correspond to the standard deviation of the mean with (a) three measured points and (b) 500 measured points.

Voltmeter gain and linearity on the range in (a) dc mode, and (b) the sampling mode, with 32 sample triangular waveforms. . The plotted uncertainties correspond to the standard deviation of the mean with (a) three measured points and (b) 500 measured points.

Voltmeter gain and linearity in the null detector configuration ( amplitude voltages) in (a) dc mode and (b) sampling mode, with 32 sample triangular waveforms. . The plotted uncertainties correspond to the standard deviation of the mean with (a) three measured points and (b) 500 measured points.

Voltmeter gain and linearity in the null detector configuration ( amplitude voltages) in (a) dc mode and (b) sampling mode, with 32 sample triangular waveforms. . The plotted uncertainties correspond to the standard deviation of the mean with (a) three measured points and (b) 500 measured points.

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