# Calculating Uncertainty Using Digital Multimeter Ratio Measurement Techniques

Application Notes

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Introduction

Ratio measurements are used to compute the value and accuracy of an unknown input voltage relative to a known reference voltage. Ratio measurements can be easily performed using a modern digital multimeter (DMM) by measuring the unknown input and reference voltages and using their ratio to determine the exact value of the unknown input voltage.

This paper compares three DMM ratio measurement techniques for determining the traceable value and measurement uncertainty of unknown input. It also demonstrates how ratio measurement techniques can be used to achieve traceable measurement uncertainties that approach an instrument’s 24-hour stability or transfer accuracy specifications.

Overview

All DMMs perform a DC voltage measurement by comparing or ratio-ing the unknown voltage applied to its input terminals to the instrument’s internal, calibrated voltage reference. The instrument’s 90-day, 1-year, or 2-year accuracy specifications can be applied to the resulting measured value to determine its traceable uncertainty.

A “Ratio” measurement performs this same comparison but instead uses a second measurement of an external reference voltage that is generally known to have much greater precision than the DMM’s 90-day or longer accuracy specification. By doing so, the DMM is used only as a short-term stable transfer device and as such will contribute a much smaller error to the final measurement result.

If the DMM contributed zero error, then the accuracy of the unknown voltage would be exactly the same as the traceable uncertainty of the reference voltage used in the measurement. The DMM’s error contribution will generally dominate the final measurement uncertainty; however, this error can be significantly less than simply measuring the unknown voltage and applying the appropriate 90-day, or longer, DMM accuracy specification.

Some DMMs incorporate an “automated” measurement of the unknown input voltage and the applied reference voltage and then automatically calculate and display the resulting voltage ratio value. This measurement configuration is shown in Figure 1.

The DMM will automatically measure the two applied voltages using internal switching and then automatically calculate the resulting voltage ratio value from the two independent measurements.

Any DMM can be used to manually perform these two measurements as shown in Figure 2. The user will then manually compute the voltage ratio value from these two individual measurements.

Once the voltage ratio value is determined, the unknown value is calculated using Equation 1, independent of whether an “automated” or “manual” sequence of measurements were used to compute the voltage ratio value.