The 6010 Resistance Bridge is used in most cases to determine the value of an unknown resistor Rx from the ratio Rx/Rs (or Rs/Rx) where Rs is a reference resistor with a known value and uncertainty. The program (software) has a resistor menu where the values and uncertainties of up to 40 resistors can be entered by the user and stored by the program.The number 40 corresponds to the number of the available channels of 2 scanners that can be connected to the bridge and chosen automatically by the running program in any possible way to use one resistor as Rx and any other one as Rs. If required, the running measurement program can update the resistor menu by changing the value and uncertainty of the actual Rx in accordance to measurement results. It is obvious that if the ratio of 2 resistors has been measured and it is equal to Rx/Rs, then Rx = ratio x Rs. On the other hand, if the ratio = Rs/Rx, then Rx = Rs/ratio. The formulas to calculate uncertainties are much more complicated and need more explanation. When the program is running - not only the graph and the grid (showing the ratio Rx/Rs and the value of Rx) are continously updated; there are also three boxes on the left hand side of the screen labelled:
Mean Std. Dev. Uncert.
Nothing is shown in them until the 2nd measurement of the program is done. Then they are updated over and over again, and the formulas to calculate the values shown in them are as follows. After the K-th measurement (K = 2,3, .., N) the program performs the following calculations:
The RATIO_AVERAGE appears in the Mean box, and STD_DEV_PPM is displayed in the Std. Dev Box.
The uncertainty is calculated according to the formula: where SD_Rs is the standard deviation of Rs taken from the table of the resistor menu.
The UNC calculated this way appears in the Uncert. Box on the screen after each measurement.
All the calculations described above are performed after each measurement. If the user has set the auto-update option of the resistor Rx to Yes in the menu, then after execution of the program, the Rx value in the table of the resistor menu will be equal to the Average, and the standard deviation will be equal to the R_Value_SD calculated with the help of the above formulas. However, if the autoupdate of the resistor Rx has been chosen No, then Rx and SD_Rx will remain unchanged as they were before the measurement program started. In that case neither the Average nor the R_Value_SD will appear on the screen, although the value in the Mean Box will be equal to the Average.
If the running program the required number of measurements is greater than the number used for statistics, the average value displayed under the graph is calculated for the latest set of measurements equal to the number for statistics as soon as the measurement number exceeds that one for statistics. The final results for the unknown resistor (auto-update) are also calculated on the latest measurements equal to that number.
where SD_Rs is the standard deviation of Rs taken from the table of the resistor menu.