This paper describes the uncertainty improvements obtained by evaluating the agreement between the voltage and resistance ratios of a direct current (DC) high-voltage divider. Because of the high level of uncertainty in the voltage or resistance ratios of a high-voltage divider currently available internationally, the equivalence of these ratios must be proved to be below that uncertainty level. Thus, the error factors that can occur in the ratio measurement, such as the input resistance effect of the
digital multimeter (DMM), the system leakage effect, the gain error of the DMM due to low-voltage measurement below 100 mV, the parallel resistance leakage effect by the supporting insulator and the contamination of the high-voltage arm of the high-voltage divider, and the leakage effect between the high-voltage arm and the system ground should be evaluated and calibrated.

First, to investigate the effect of the input resistance of a digital multimeter (DMM) in the case where the low-voltage arm of the divider was as high as 1 MΩ in a voltage-ratio measurement, two standard resistors and a 20 V reference voltage were used to evaluate the input resistance of two models, an
Agilent 3458A and a Fluke 8508A, and the results obtained were 1012 and 1013 Ω, respectively. The results were used to correct the measured values. The uncertainty of the input resistance effect was consequently found to be negligible.

When the low-voltage arm of the divider was as low as 15 kΩ in a voltage-ratio measurement, it was not easy to calibrate a low voltage of less than 100 mV measured across the low-voltage-arm resistor by conventional methods. Therefore, we devised a method using a Zener voltage standard and a volt-ratio box. Using this method, the linearity and stability of the DMM were directly evaluated for voltage calibration below 100 mV to an uncertainty level of 0.2×10?6 or better.

Next, we investigated the effects of the leakage resistance of the measurement system and the direct shunting-leakage of the Teflon resistance supporting a divider. The leakage resistance effect on the measurement system was negligible because in this experiment, the low-voltage arm resistance was less than 1 MΩ, whereas the measured system insulation resistance was more than several tens of TΩ. The Teflon resistance effect was investigated by connecting the known high resistance to the high-voltage arm in parallel, and the effect obtained was less than 0.3×10?6. The result was applied to the voltage ratio and the leakage resistance effect on the ratio was evaluated to be a negligible uncertainty.

In addition,
the Korea Research Institute of Standards and Science (KRISS)-made modified Wheatstone bridge method, which is advantageous for high-resistance measurements because of a negligible leakage effect, was used in the resistance ratio evaluation. By measuring the total resistance RX at the same time with this method, the resistance ratio uncertainty was largely reduced to 0.38×10?6 and 0.39×10?6,
respectively, compared with measuring with the conventional methods which the constituent resistances of the high-voltage arm resistance(RX) having 225 and 675 MΩ are partially measured and combined.

As mentioned above, the error factors for the voltage and resistance ratios were tested and evaluated through analysis, and the two ratios were measured and analyzed for various dividing ratios (15,000:1, 13,500:1, 6750:1, 2250:1, and 675:1). It was proved that the two ratios agreed with each other within the range of 0.3×10?6 ∼ 0.5×10?6. In addition, the cumulative uncertainty could be improved in the evaluation of the voltage coefficient by single-step procedure instead of the seven-step procedure applied in the binary step-up method used
in the previous study. This resulted in a significant improvement in the measurement uncertainty, from 4.19×10?6 to 0.69×10?6, for measurements up to a supply voltage of 100 kV.

By comparing the evaluation results of the voltage and the resistance ratios of a divider, it was demonstrated that the two ratios agreed with each other within 0.5×10?6.
It was also confirmed that the evaluation result of the ratios was traceable to the national standards of both the Josephson voltage and quantum Hall resistance at an uncertainty level of 0.4×10?6. From the result, it is suggested that for high-voltage measurements, either a voltage ratio or a resistance ratio can be used as the reference dividing ratio within 0.5×10?6,
regardless of which of the ratios is used. Additionally, the measurement uncertainty at 1 MV that has been announced so far is at the 10×10?6 level; thus, the uncertainty of one module should be much smaller. It is expected from this study for the agreement and uncertainty of the two ratios to be within 1×10?6, which will make an important contribution to ultrahigh voltage measurements at the MV level with a smaller and more accurate uncertainty.