Voltage Measurement Accuracy, Self-Calibration, and Ratiometric

White Paper Code: 3WHITE PAPERVoltage Measurement Accuracy,Self-Calibration, andRatiometric Measurements815 W. 1800 N. Logan, Utah 84321-1784 (435) 753-2342 FAX (435) 750-9540Copyright (C) 2001 Campbell Scientific, Inc.

Voltage Measurement Accuracy, Self-Calibration, and Ratiometric MeasurementsSelf-CalibrationNational Institute of Standards and Technology (NIST) traceablecalibrator 1 . Sensor errors and/or external measurement noise cannotbe practically incorporated into a general purpose instrumentaccuracy specification. For example, individual samples of anoisy measurement may have errors that exceed the instrumentaccuracy specification, although the mean value of these measurementsshould be within the specified accuracy.The root-mean-square (rms) noise of a system with a constantinput is equivalent to the standard deviation, which can be determinedusing instructions available in CSI dataloggers 2 . The totalmeasurement uncertainty of a system can be obtained by combiningthe instrument accuracy, sensor accuracy, and measurementnoise. Measurement accuracy is usually expressed as peak-topeak,while noise is usually rms. For a Gaussian (normal) probabilitydistribution, 99% of all possible values are within ±2.5 standarddeviations of the mean. Consequently, a conversion oftenassumed is that the peak-to-peak value equals 2(2.5) = 5 times therms value. The instrument accuracy, sensor accuracy, and measurementnoise can be combined by adding the individual errorstogether. This gives a worst-case uncertainty, but it is an overlypessimistic estimate for uncorrelated error components that areunlikely to all be at their maximum value and same polarity at thesame time. A more realistic way to combine uncorrelated measurementerrors is to use the root-sum-of-squares method 3 . Thismethod takes the square root of the sum of the individual errors2 2 2squared I a + S a + M n .VxVoltageExcitationVrefVoltageReferenceRfRsCalibrationVoltagesVsH1L1H2L2HnVcal1 VcalmInputMultiplexingGainVrefAnalog-to-DigitalConverterDigitalOutLnFigure 1. Multiplexed Voltage Measurement System2 Copyright © 2001 Campbell Scientific, Inc.White Paper: 3 815 W. 1800 N., Logan, UT 84321 (435) 753-2342

Voltage Measurement Accuracy, Self-Calibration, and Ratiometric MeasurementsFig. 1 shows a block diagram of a multiplexed voltage measurementsystem with a voltage reference that is used for the analogto-digitalconverter (ADC) and also for generating the bridgeexcitation voltage. With CSI dataloggers, self-calibration voltagesare also derived from this measurement voltage reference and areused to remove gain errors for the different input ranges. Themeasurement voltage reference is factory calibrated to a traceableNIST voltage standard and provides a calibration source for theportable measurement system. This self-calibration is typicallydone between measurement scans. Self-calibration, a feature ofall CSI dataloggers, significantly improves measurement accuracyby compensating for gain stage and ADC temperaturedrift, and component aging.Campbell Scientific quotes accuracy figures for most productsthat take into account the combined effects of calibration, linearity,and drift error over an operating temperature range of -25° to+50°C. This should be considered when comparing products orselecting sensors where often (1) an accuracy figure at one temperature(2) a temperature drift figure and (3) a non-linearity figureare provided as separate specifications.Ratiometric MeasurementsThe accuracy of the measurement system using self-calibration islimited by the temperature drift of the measurement voltage reference.For some types of sensors, this inaccuracy is eliminated byusing a ratiometric measurement. In ratiometric measurements,the measured quantity is proportional to a ratio of two voltagesrather than an absolute voltage. When both voltages are proportionalto the same reference, the absolute value of the referencedoes not affect the ratio. Resistive bridge measurements are inherentlyratiometric, since the unknown sensor resistance is proportionalto a ratio of the sensor and excitation voltage (V s /V x ). Aratiometric resistive bridge measurement is illustrated in Fig. 1.The measured voltage is derived from the resistive voltage dividerasVs⎛ Rs= V⎜x⎝ Rs+ Rf⎞⎟⎠(eq. 1)Copyright © 2001 Campbell Scientific, Inc. 3815 W. 1800 N., Logan, UT 84321-1784 (435) 753-2342 White Paper: 3