Viewpoint News, June 2010

Calibration for Accurate Measurements

by James Campbell - jac@viewpointusa.com

Accurate measurements are obviously a worthy goal. Are your measurements spread all over the place, as shown in Figure 1 or almost all the same value as in Figure 2. Do you know which is better? Would you do something different to calibrate your equipment in each of these situations?

Figure 1. Scattered

Figure 2. Grouped

Why Calibrate?

Measurement equipment changes with operating conditions, over time, with use, and so on. To maintain accuracy, equipment needs to be checked periodically against a known answer, or a standard, to assure that it measures the correct value. Also, with the ever-increasing prevalence of traceability requirements for test systems due to regulations or best practices, the need for accurate measurements in your company may be dictated rather than simply encouraged.

What is Calibration?

Just so everyone is on the same page, calibration is a method for assuring accurate conversion of a physical parameter value into a measured value.

In the past, this might have been a direct conversion, such as using a ruler to measure distance, with a particular ruler being compared to a known, calibrated length scale. Thus, the distance measured by the ruler, d_r, would be converted into a calibrated value by a calibration curve (or equation) such as d_c = d_r*m+b, where m and b are the calibration coefficients which account for any scale and bias in the ruler.

Today, calibration almost always involves and includes the scaling of a physical parameter into a voltage (or current) value that is measured by a digitizing device, such as a DMM or an oscilloscope or a Spectrum Analyzer or a data acquisition card. Thus, the calibration curve might be d_c = V_r*p+q, where V_r is the voltage output of the sensor and p and q are the calibration coefficients.

A calibration curve is created by measuring the sensor output at a number of points of sensor condition and associated output. Typically, there are at least 2 points in the curve, for a linear slope and offset curve, but some sensors, e.g., accelerometers, use one for slope (and assume the offset is zero) and others, e.g., thermocouples, use many. The number of calibration coefficients or calibration values can change as well as the form of the curve changes with common types of calibration curves being linear, polynomial, functional, spline, and even table-driven.

Two Basic Approaches

The best approach to calibrate the measurement equipment in a test system is to calibrate the entire system! The next best, but very common, approach calibrates the sensors and measurement equipment separately. Both approaches require that the sensor be placed in a known condition and the output be measured.

Calibrate the Total System

The total system approach measures the sensor in-situ with the output being measured by the system measurement equipment. This approach accommodates changes to the sensor signal by cable length, temperature effects, measurement equipment accuracy (or lack of accuracy), and so on.

Pros and cons when using this approach are listed next.

• This in-situ approach benefits from a calibration performed in a situation that is identical, or as close as possible, to the typical measurement usage. However, the in-situ approach is not supportable when the sensor cannot be placed in a desired condition. A typical scenario is that a calibrated source is unavailable. For example, you don’t have a calibrated way to supply a known pressure in a pipe to activate a pressure sensor mounted in that pipe. Note that, in this situation, you may be able to use another calibrated measurement device as a proxy to audit the sensor condition as a means of reporting to the test system the actual value of the physical parameter being measured. In the example above, you might have an audit pressure port so that you can directly measure the pipe pressure with a calibrated sensor nearby the sensor needing calibration.

• You may need to develop the test system to accommodate any required proxy measurement devices. And, you may need to purchase these proxy auditing devices.

• Cost may be prohibitive to accommodate placing the sensor in a variety of conditions to perform the calibration.

• You have to stop using the test system during calibration.

Calibrate the Sensor and Equipment Separately

The separate calibration of sensor and equipment is widely-used since it is convenient and easily traceable. In the typical approach, all sensors and equipment that can be calibrated are removed from the test system and sent to a calibration lab. Each sensor is usually returned with a calibration curve or an audit report, prepared by lab, showing as-found (before) and as-left (after) performance for the conversion of the physical condition to voltage (or current). Each measurement device is returned calibrated and sometimes with an audit report.

Pros and cons when using this approach are listed next.

• Any new sensor calibration curves may need to be reflected in the measurement software so that any new sensor behavior is properly accounted in the conversion of measured voltage to physical parameter.

• When using this approach, be aware of temperature effects or voltage loss in wires since these conditions may be different than used during sensor and device calibration. For example, some DMMs will have as much as additional 10 ppm accuracy reduction for every 1 degree C away from the temperature at which the DMM was calibrated.

• You need replacement sensors and devices while the test system equipment is being calibrated or else the test system is unavailable during calibration. However, if you have enough replacement sensors and devices, the test system can be returned to operational status usually more quickly than the in-situ approach, since it usually takes less time to replace than to calibrate equipment.

Calibration Accuracy and Precision

Any calibration is only as good as the accuracy and precision of the calibrated source. Referencing the Figures above, the accurate source is shown in Figure 1, since the average value is centered on the bull-eye. Many people confuse Figure 2 as being more accurate since the points are clustered more tightly. The points in Figure 2 are more precise, but, since they do not surround the bulls-eye, they are not accurate. A device with stable output is a precise device. Stability does not imply a correct value. In technical terms, Figure 1 has a larger standard deviation (SD) than Figure 2, but a correct average, or mean, value.

For proper calibration, your calibration source needs a mean value closer to correct than the inherent accuracy of the measurement device. In addition, it would be nice if your calibration source has a smaller inherent SD than the measurement device, although you can accommodate a larger SD by averaging many measurements.

As a caveat, beware of long-term drift. Some calibration sources might be very accurate just after they themselves are calibrated but their accuracy drifts with time. A good calibration might result in a bad audit the following month.

Some Good Rules Worth Remembering

A good rule to remember is that the measurement device should be able to make a measurement 10 times more accurate than the accuracy at which you wish to measure. This rule is based on the observation that one extra decimal point will enable proper averaging of multiple readings, thus giving even more accurate readings with averaging without worrying about quantization effects. This rule implies that the calibration source is even more accurate. I’ve seen calibration houses use calibration sources that are 4X better, but I prefer at least 10X if possible. Note that, for some very accurate devices, the cost of a calibrated source which is 10X better than the device to be calibrated can be very expensive. In these cases, sometimes it is less expensive to purchase a very accurate measurement device to use as a proxy of the actual value used in the calibration. For example, calibrating a DAQ device which needs a 10 ppm source can be accomplished with a less accurate source and a 10 ppm DMM for 5X to 10X less money.

Another good rule to remember is that the precision of an averaged measurement decreases by a factor of 1/sqrt(N), where N is the number of measurements. For example, averaging 100 measurements from a device that reads to a precision of +/- 1 mA will give averages that are precision to +/- 0.01 mA. Use averaging to achieve the desired precision levels during calibration.

Another good rule to remember is that +/- 3 SDs encompass about 99.7% of all measurements, so essentially all results will be within +/- 3 SDs. See the Confidence Interval table at http://en.wikipedia.org/wiki/Normal_distribution for other SD ranges. Many calibration labs calibrate to 95% confidence which is about +/- 2 SDs.

Reporting Device Accuracy

Even if your measurement device is treated to a super precise and accurate calibration source, you will still have variations in the measurements from the correct answer. Deviations are unavoidable. If you perform a system calibration, review the ways to determine the uncertainty of your device. One good reference is http://physics.nist.gov/Pubs/guidelines/TN1297/tn1297s.pdf. If you rely on a calibration house, have them tell you the uncertainty. And ask them how many SDs the +/- uncertainty range equals.

Conclusion

A total system calibration approach is best from an accuracy standpoint, but requires forethought in system design to allow all the sensors to be calibrated in-situ. In the event that complete in-situ is not available, partial usage is still better than nothing. However, system downtime during calibration and difficulty or cost in designing for calibration can justify the “sensor and device” approach as more effective.

More information about calibration in general is found at http://www.itl.nist.gov/div898/handbook/mpc/section3/mpc3.htm.

Finally, we will review the concepts behind accuracy and precision in more detail in the next article.