Absolute accuracy is used to define the overall uncertainties of a measurement. For a DSA module, it can be computed with the following formula:
Absolute Accuracy = Gain Error + Offset Error + Flatness
This formula uses the three major sources of error in the system:
As an example, the Absolute Accuracy of the NI 4461 is calculated for both the Analog Input and Analog Output below. For Analog Input, we assume we are acquiring a 1 kHz sine wave with 10 V amplitude. For Analog Output, assume we are generating the same frequency signal.
Note: The values used in this article are the typical specifications, not the maximum error specifications. These values should be reasonable if the device has been setup properly. Specifically, it is important that the device has been allowed to warm up for the correct time and self calibrated within 24 hours of taking the measurements. The reasons for each of these factors are explained below:
To find the AI Gain Amplitude Accuracy, AI Offset and AI Flatness refer to the NI 4461/4462 Specifications.
For a 1 kHz sine wave with an amplitude of 10V, the following values apply:
AI Gain Amplitude Accuracy = ±0.03 dB max
AI Offset (with no Gain applied) = ±0.7 mV max
AI Flatness (with no Gain applied) = ±0.003 dB typical
Gain Error is calculated based on this Gain Amplitude Accuracy of a 1kHz input tone.
Gain Amplitude Accuracy = ±0.03 dB max
Gain Amplitude Accuracy(dB) = 20 log (1 + (Gain Error(%)/100))
±0.03 dB = 20 log (1 + (Gain Error(%)/100))
Gain Error(%) = 0.3460
Gain Error(V) = Input Voltage x Gain Error(%) = 10 x 0.003460 = 34.60 mV
Where the Input Voltage refers to the voltage range the device is configured for.
Flatness is converted to voltage in an identical manner.
Flatness = ±0.003 dB max
Flatness(dB) = 20 log (1 + (Flatness(%)/100))
±0.003 dB = 20 log (1 + (Flatness(%)/100))
Flatness(%) = 0.0345
Flatness(V) = Input Voltage x Flatness(%) = 10 x 0.000345 = 3.45 mV
From these two calculation the total AI Accuracy is calculated as follows:
AI Accuracy = AI Gain + AI Offset + AI Flatness
AI Accuracy = 34.60 mV + 0.7 mV + 3.45 mV
AI Accuracy = ±38.75 mV
The analog output accuracy can be calculated in the same way. See the following sample calculation:
AO Gain Amplitude Accuracy = ±0.04 dB max
AO Offset = ±1 mV max
AO Flatness = ±0.008 dB max
Gain Error (calculated using formula above) = 46.16 mV
Flatness (calculated using formula above) = 9.21 mV
The final calculation for the analog output accuracy is as follows:
AO Accuracy = AO Gain + AO Offset + AO Flatness
AO Accuracy = 46.16 mV + 1 mV + 9.21 mV
AO Accuracy = ±56.37 mV
Note: These accuracy numbers may seem poor, but it is important to put them in the context of the purpose of a Dynamic Signal Acquisition module: to obtain high accuracy spectral content, not necessarily temporal content. The frequency of a signal can be calculated two ways. The first and most obvious is with a reciprocal of the period. This method is good for repeating signals, but does not hold up well for changing or dynamic signals. The second method is by looking at the instantaneous slope (rise over run) of a signal. We can take the rise (amplitude change, dV) and divide by the run (time change, dt) and calculate instantaneous frequency. DSA modules have excellent clock signals to give a very accurate dt. This dt is also a very small value due to the oversampling nature of the DSA architecture. When we are looking at a difference in voltage, the absolute accuracy becomes less important.