# Resistance bridge calibration

Temperature measurement is one of the most demanding applications of resistance measurement. It requires the measurement of resistance ratios to accuracies of better than 1 part in 10^{7}, sometimes better than 1 part in 10^{8}. While dc resistance standards are sometimes available at this level, ac resistance standards are generally not. So how can we show that our resistance and temperature measurements are accurate as we claim?

One simple method for checking the linearity of a resistance bridge is to measure a pair of resistors individually, and then measure the two in series. Ideally the series measurement should equal the sum of the two individual measurements. If not, then the measurements give us a little bit of information about the errors in the bridge readings. Another check is to measure the ratio of two resistances, say *R*_{1}/*R*_{2}, then swap the resistors and measure the reciprocal ratio (or complement), *R*_{2}/*R*_{1}. Ideally the product of the two measurements should equal 1.0 exactly, if not, the measurements give us more information on the bridge errors. Most importantly, for both of these tests we do not need to know exactly values of the resistors to make this test work. All that is necessary is for them to be stable for the duration of the measurements and for the formation of the series combination to be accurate.

The Resistance Bridge Calibrator exploits the same principles as the linearity and complement check. It uses a network of four stable four-terminal resistors that can be connected in 35 different series and parallel combinations. By measuring each combination in the two different ways (as with the complement check) up to 70 different measurements can be made. Since the RBC has just four unknown resistance values, we obtain 66 independent measurements containing information about the errors in the bridge readings. With the appropriate analysis and modelling we can estimate the errors in the bridge readings. This 'combinatorial' calibration method is particularly powerful because it is not necessary to know the actual values of the four resistors, or their frequency dependence for ac measurements. This means we can calibrate any ac or dc bridge to any accuracy, so long as the four resistors are stable for the duration of the measurements and they are combined accurately in the various series and parallel combinations.

The patent for the Resistance Bridge Calibrator was filed in 1994, the first commercial RBC was produced in 1997, and the RBC won and R&100 award in 1998. RBCs are now in use in most national measurement institutes around the world. Rod White won the 1998 Royal Society Cooper medal for developing the RBC.

**Caption**: The four four-terminal resistors in the RBC can be connected in 35 different series and parallel combinations. The figure shows the *R*_{1} + *R*_{2} combination.

Current research on the RBC is focused on making an automatic RBC with a USB interface. At this point we have overcome the three big engineering problems associated with the automation and 5 prototypes are under test.

The principles underlying the RBC can be applied to many different indicating instruments, and we have developed calibration schemes based on the ‘combinatorial method’ to calibrate mass balances, weighbridges, and optical detectors.

For further information contact **Rod White**

### Key Publications

D R White, K Jones, J M Williams and I E Ramsey, “A simple resistance network for the calibration of resistance bridges”. *IEEE Trans. Instrument. Meas*. **IM-46**, 1068-1074, 1997

D R White and J M Williams, “A resistance network for verifying the accuracy of resistance bridges” Proc. CPEM ’96, *IEEE Trans. Instrument. Meas*. **IM-46**, 329-332, 1997

D R White “A Method for calibrating resistance bridges”. Proc. TEMPMEKO ’96 (Ed P. Marcarino: Levrotta & Bello, Torino) pp129-134, 1997

D R White, “Contribution of Uncertainties in Resistance Measurements to Uncertainty in ITS-90”, in *Temperature: its Measurement and Control in Science and Industry*, Vol 7 (Ed. D. C. Ripple: AIP) pp321-326, 2003

D R White, M. T. Clarkson, P. Saunders, and H. Yoon, “A general technique for calibrating indicating instruments”, *Metrologia*, **45**, 199-210, 2008.