# Calculate Absolute Accuracy of Dynamic Signal Acquisition Devices

## Visão geral

This article explains how to calculate the absolute accuracy of an NI Dynamic Signal Acquisition (DSA) board.

## Introduction

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:

• Gain Error
A measure of the deviation of the gain of an amplifier from the ideal gain. Expressed in dB or % of a reading, it can be viewed as the deviation m from the voltage transfer function of mx+b.
• Offset Error
A constant error added to a measurement along the whole transfer curve. In mx+b, the offset error is b.
• Flatness
A term expressed in dB to specify the limits within which the amplitude of a signal varies across a given frequency range. It measures the "frequency response" of the board. It is referenced to a measurement on a 1 kHz signal. It does not apply to DC signals. It only applies to waveform tones.

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:

• Warm-up Time
The highly linear Analog to Digital Converter (ADC) that the NI DSA devices use is a Sigma-Delta type converter.  One inherent property of this type of ADC is that it is very sensitive to temperature changes.  By allowing the card to reach a steady state temperature, this sensitivity can be reduced.
• Self Calibration
Once the NI DSA device has come to a steady temperature state, a self calibration should be performed to eliminate any differences since the last calibration.  This is important because the constant sources of error may be slightly different since the last calibration.  The specifications used below assume a self calibration was performed within 24 hours and ±5°C of the measurement. Refer to the NI 4461/4462 Calibration Procedure for more information.

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

## Analog Output

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.