Defining Data Accuracy

Fred R. Schraff, IOtech, Inc.

Data acquisition (DA) devices come in a variety of forms and configurations, making it difficult to compare products. One specification worthy of close attention is accuracy. To what degree is a given device error-free? Making this determination requires some know-how.

DA device manufacturers use various methods and terms to describe accuracy. But device accuracy is best defined as the sum of three components stated

Figure 1. Accuracy varies within a measurement range. Measurements at the low end of the scale are less accurate than those at the high end. The first step to getting the accuracy you want is to determine the upper and lower limits of a measurement.

in terms of the reading, range, and least significant bit (LSB). When you compute and sum all three components, the device accuracy (or uncertainty) will be larger than 1 LSB. A single-term statement, such as "0.075% of range," oversimplifies reading accuracy.

Generally, accuracy is not constant over an entire measurement range; it varies with the reading magnitude—you'll find larger errors at the low end of the scale and more accurate results at the high end. When comparing different DA devices, the most practical approach is to compute the stated spec sheet accuracy for a given voltage measurement and then define the upper and lower limits (see Figure 1). The device with the smallest voltage window is the most accurate for a voltage measurement at that level.

Figure 2. To determine a DA system's overall accuracy, combine all sources of error using the square-root-of-the-sum of-the-squares method.

Error introduced by input signals also affects system accuracy. While ideal input signals would have zero output impedance and negligible noise, real signals contain noise and have nonzero output impedance. Both these undesirable aspects of signals and the internal limitations of DA devices reduce accuracy. No sensor is perfect, and no installation is noise-free; so every measurement application will have some uncertainty that you cannot control or predict.

DA devices generally have signal-conditioning circuitry between the signal source and the ADC. The circuitry contributes such sources of inaccuracy as offset, gain error, and noise. Offset voltage is the nonzero value delivered to the ADC when the device input is zero. Gain error is the difference between ideal gain and actual gain. Noise comes in the form of thermal noise in resistors, conducted or induced RFI originating in DC/DC power supplies or digital circuitry, and AC power line noise. To screen out most noise, DA devices with individual channel signal conditioning can include low-pass filtering in each channel. However, devices that multiplex a group of channels through a common programmable gain amplifier path can not use low-pass filtering without losing necessary bandwidth.

Another source of error is aliasing. If an ADC converts a signal containing frequency components at or near the A/D conversion frequency, aliasing occurs. Aliasing causes an ADC to deliver misleading low-frequency data. You can generally prevent aliasing by limiting the bandwidth of input amplification circuitry to less than one-half the A/D conversion frequency. Manufacturers often include low-pass, or antialiasing, filters to eliminate this source of error.

The second, more common cause of aliasing is too low a sampling rate relative to the input signal. You can easily avoid this by raising the sampling rate.

Dual-slope integrating ADCs are slower (1000 readings/sec or less), but the individual readings have the benefit of integration, which reduces the impact of input noise. Medium-speed data loggers and digital multimeter-based scanners most frequently use integrating-type ADCs. These devices can often operate at higher speeds with lower resolution and lower speeds with higher resolution.

To verify the accuracy of an ADC used for high-speed applications, connect a high-speed DA device to a fixed voltage. You should see a variation in the returned digital value on consecutive conversions. There will be a range of values that when sorted into vertical number-of-occurrences columns, form a Gaussian histogram centered on the closest average value. The difference between this average value and the actual applied value is the accuracy of the ADC.

Figure 3. To test the accuracy of an ADC, feed a fixed voltage into the device. Sort the returned digital values obtained in consecutive conversions into vertical number-of-occurrences columns, which form a Gaussian histogram centered on the closest average value. The accuracy of the ADC is the difference between the average value and the actual applied value.

The width of the histogram in counts (or discrete steps) is the peak-to-peak noise. If the system is out of calibration, the histogram can look the same in terms of noise counts, but the average value will be farther from the actual value (see Figure 3).

It may occur to you that taking 100,000 readings a second and then averaging them in groups of 100 is no better than taking 1000 readings more slowly. But high-speed readings let you digitize faster signals more fully or digitize more channels in the same amount of time. The noise counts are a natural consequence of the conversion speed because the input bandwidth is high enough to pass the noise and the converter is fast enough to digitize it.

Device flexibility is the issue here. Filtering a noisy signal with software can convert the output of a high-speed ADC in a multiplexed device into useful data. Using the same filtering in hardware (in the main signal path) will so limit the ADC bandwidth as to remove most of the value of the high-speed, multiplexed device. Instead, use hardware low-pass filtering in the individual channel paths prior to the multiplexing stage to effectively reduce noise. However, the overall flexibility requirement of operating a single channel at full device bandwidth requires provisions for bypassing low-pass channel filters.

It's impractical to select fixed value components for the input amplification stages to an ADC and expect to attain acceptable accuracy beyond 8 bits. For 12-bit systems, manually adjustable components can deliver good results within a nominally narrow range of operating temperatures. For 16-bit systems, manual calibration settings are fairly difficult.

Software-controlled hardware calibration methods can use D/A converters (DACs) to cancel offset voltages and gain errors before the A/D conversion

If you know what noise is not inherent in your signal, you will know what you can post-filter without losing information you might want.

takes place. Alternatively, software correction constants can be applied to the digital data after A/D conversion, based on previously established calibration look-up tables.

If you calibrate the system on a per-channel basis, the corrections can also cover channel-to-channel variations. For systems operating in varying temperature environments, autozeroing techniques can cancel the effects of offset drifts originally set for one environment.

Most ADC devices require external standards, though, for high-accuracy recalibration, but these standards can cause unexpected problems. For example, DC voltage calibrators have low bandwidth and can exhibit output transients when connected to a time-varying load, such as a multiplexed input channel. Such a transient can result in a lower voltage being delivered to the ADC than that indicated by the calibrator dial settings.

Always follow the DA device manufacturers' recommendations regarding remote sensing and decoupling capacitors at the point of connection. Some voltage calibrators have high-frequency noise components in their output voltage. This noise—which is inherently averaged to zero by the integrating ADCs on digital voltmeters—can sometimes be a problem to a high-speed ADC in a DA system. If a calibrated system delivers incorrect data, the calibration source and the DA device may not be compatible.

Incorrect calibration can reduce data accuracy in another unexpected way. Most DA devices multiplex a number of channels into a signal amplification path to the ADC. Some multiplexing devices can disturb the signal source if the source impedance is over a few hundred ohms. This can lead to disturbing and seemingly inexplicable results, particularly when the DA device has recently been calibrated and is presumed accurate. If the signal sources are not known to be low in output impedance, select a device system with buffered inputs to the multiplexer stage.

If you know your signal is noisy, you can be sure the noise will show up on the output. Likewise, if you know what noise is not inherent in your signal, you will know what you can post-filter without losing information you might want.

Home | Contact Us | Advertise © 2009 Questex Media Group, Inc.. All rights reserved. Reproduction in whole or in part is prohibited. Please send any technical comments or questions to our webmaster.