Accurate calibration of resistance ratios between 1 MΩ and 1 GΩ using series resistors
As shown in high-resistance key comparisons carried out by the Consultative Committee for Electricity and Magnetism (CCEM), Inter-American Metrology System (SIM) and European Association of National Metrology Institutes (EURAMET), the accuracy of 10 MΩ and 1 GΩ resistances depends on ratio values between the reference resistance and unknown resistance and the accuracy of the reference resistance, which is determined with a quantized Hall resistance standard. This paper presents a method for calibrating 10:1 ratios in a high-resistance bridge using series resistors simply and accurately. By applying the 10:1 ratio errors determined using the presented method, the combined relative standard uncertainty for 1 GΩ resistance measurements using a modified Wheatstone bridge was estimated to be on the 1 × 10−6 level. The method was also applied to 1 GΩ resistance measurements using a direct-current comparator resistance bridge. It was found that the 1 GΩ resistances determined by the two bridges agreed within 2.4 × 10−6 Ω/Ω. We expect that the presented method can also be used to calibrate arbitrary resistance ratios.