How Do I Calculate Absolute Accuracy Or System Accuracy?Hardware: Multifunction DAQ (MIO)
Problem: How do I calculate the absolute accuracy of my components and the system accuracy of my entire measurement? Solution: There are three steps when calculating the system accuracy of a measurement:
First, determine how each component is connected to the system and identify all pertinent variables that will affect the calculated accuracy. For this example, we'll assume an SCXI1125 isolation module is cascaded using the SCXI1352 cable to an SCXI1141 filter module. This filter module is then connected to an NI 6052E DAQ device. SCXI 1125 » SCXI 1141 » NI 6052E Assume the following:
Next, calculate the Absolute Accuracy for each component. For any individual device with gain (either an amplifier or attenuator), for a specified nominal range, National Instruments provides an absolute accuracy specification in millivolts. Depending upon the presentation of different errors, there are three different equations to use to calculate the accuracy. All equations are listed below: Equation 1 Absolute Accuracy = ± [(VoltageReading x GainError) + (VoltageRange x OffsetError) + NoiseUncertainty]
Where,
GainError = ResidualAIGainError + (GainTempco x TempChangeFromLastInternalCal) + (ReferenceTempco x TempChangeFromLastInternalCal)]
OffsetError = [ResidualAIOffsetError + (OffsetTempco x TempChangeFromLastInternalCal) + INL_Error]
for a coverage factor of 3 σ and averaging 100 points
You can obtain the parameter values in the above equation by looking at the specifications found in each component's catalog or user manual. Equation 2 Absolute Accuracy = ± [(InputVoltage x %OfReading) + (Range x %OffsetOfTheRange) + SystemNoise + TemperatureDrift]
TemperatureDrift = ± [(InputVoltage x %OfReading/ °C + %Offset/ ° C)]
Temperature effects are already accounted for in the specification values unless your ambient temperature is outside of the 15°C to 35°C range. For instance, if the ambient temperature of your measurement system is at 45°C, you must account for 10°C of temperature difference. In this case, since the temperature is assumed to be 25°C, we don't have to add in anything for Temperature Drift. Please note that terminal blocks or connector blocks are not considered gain stages unless they have attenuation circuitry. Modules or DAQ devices that do not have amplifiers are also not considered gain stages.
You can obtain the parameter values in the above equation by looking at the specifications found in each component's catalog or user manual.
Equation 3 Absolute Accuracy = ± [(InputReading x GainError) + (Range x OffsetError) + InputNoise
C Series Modules provide concise specifications for users to determine their accuracy throughout the entire operating temperature range (Calibrated Maximum 40 to 70). This accuracy entry accounts for temperature variations, worst case component tolerances, thermal hysteresis, etc.
Figure 1: NI 9209 Accuracy Specifications
Step 3: Calculate the system accuracy and system accuracy RTI
Finally, we will use the Absolute Accuracy from each component to calculate the System Accuracy and System Accuracy RTI. Like the Pythagorean Theorem, the System Accuracy is equal to the square root of the sum of the squares of each component's Absolute Accuracy.
The System Accuracy Relative To Input (RTI) is calculated as follows: System Accuracy Example Calculations for the above setup: Here are the absolute accuracy calculations for each component of our system: Absolute Accuracy of the SCXI1125
Absolute Accuracy = ± [(InputVoltage x %OfReading) + Offset + SystemNoise + TemperatureDrift] Absolute Accuracy = ± [(10 V x 0.002478) + 0.01 V + 0.0191 V + N/A]
Absolute Accuracy = ± 54.88 mV
Absolute Accuracy of the SCXI1141 Absolute Accuracy = ± [(InputVoltage x %OfReading) + Offset + SystemNoise + TemperatureDrift] Absolute Accuracy = ± [(5 V x 0.0002) + 0.0006 V + 0.00142 V + N/A]
Absolute Accuracy = ± 3.02 mV
Absolute Accuracy of the PCI6052E
Absolute Accuracy = ± [(InputVoltage x %OfReading) + Offset + SystemNoise + TemperatureDrift] Absolute Accuracy = ± [(5 V x 0.000071) + 0.000476 V + 0.000491 V + N/A]
Absolute Accuracy = ± 1.322 mV
System Accuracy System Accuracy RTI For more information, see the Using Calibration to Improve Measurement Accuracy document linked below. An application, DC Accuracy Calculator, is attached in order to calculate the accuracy of most C Series Modules. Related Links: White Paper: Using Calibration to Improve Measurement Accuracy White Paper: Understanding Instrument Specifications  How to Make Sense Out of the Jargon KnowledgeBase 3IHCT5LE: Absolute Accuracy of Dynamic Signal Acquisition Devices Attachments: DC Accuracy Calculator.zip
Report Date: 05/05/2003 Last Updated: 09/29/2017 Document ID: 2X4HGEBG
