Application of Statistical Tools to Optimize a Dual Source Electrical High Dc Resistance Bridge

Abstract

At the Istituto Nazionale di Ricerca Metrologica (INRIM), a commercial dual source high resistance bridge has been optimized by means of the application of statistical tools and of the analysis of measurements distributions. These tools help to achieve the best precision for resistance ratio measurements in the range 10 TΩ ÷ 100 TΩ. A measurement procedure consisting of multiple steps, in which at each one the value of the resistor under calibration is updated and has been considered the best one. With this procedure, at the third step, the lowest standard deviation of the mean and the measurements distribution approximately normal are obtained regardless of the settle time, of the resistance ratio, of the measurement voltages and of the resistors under comparison. This comes from the achievement of the white noise regime and from a bridge balance close to the ideal. This measurement procedure therefore allows also to achieve the lowest measurement uncertainty due to the minimization of the type A uncertainty. The Allan variance and the power spectral density were used to identify the white noise analyzing the detector readings. Strict triangulation rules were also established and applied to validate both the measurement process and the chosen model to extrapolate the values of the standard resistors at low voltages.