Increasingly, it's not enough to measure a data acquisition (DA) board's performance by checking DC, or time-domain, specifications (e.g., linearity, relative accuracy, and monotonicity). With signal and data conversion rates on the rise, AC, or frequency-domain, characteristics play a growing role in determining overall accuracy.

If you evaluate a board solely on the accuracy specification, you're seeing only part of the performance story. Relative accuracy is defined as "the deviation of the analog value at any code from its theoretical value after the full-scale range has been calculated." For an analog input subsystem, the maximum deviation from the theoretical value of the full range determines the relative accuracy. This is considered a time-domain specification because it is typically measured at slow speeds, using one analog input channel.

Although this condition may cover some applications, most multifunction DA boards are used to monitor a variety of analog inputs at rates from 1

Photo 1. To determine the effective number of bits for a data acquisition board, a bipolar, full-scale sine wave was connected to channel 1, and channel 2 was connected to analog ground. The board was configured for differential inputs, and a gain of 1 was used. Data was acquired at a 1 Msps aggregate rate, or 500 Ksps per channel. The graph shows the results of a 1K FFT that was performed on the sine wave input.

reading per second to 1 million readings per second. At higher speeds, in multichannel acquisitions, the relative accuracy specification may no longer be a good indicator of a board's performance.

Only when you characterize performance using the frequency domain can you be sure that the acquired data will be as accurate as you need them to be. Fortunately, a figure of merit called effective number of bits (ENOB) makes it easy to specify a DA board's AC accuracy and performance (see Photo 1).

Derived from a board's SNR, ENOB specifies the overall accuracy of the A/D transfer function. With it, you can evaluate by simple numeric comparison a sampling A/D converter's transfer function over frequency—in other words, how closely the digitized output sine wave matches the ideal.

For example, multichannel systems often use a multiplexer to switch sampling from channel to channel. One mistake in assessing the accuracy of such a system is to evaluate the accuracy based on measurements made on just one channel. In particular, the mistake is to ignore errors caused by the input channel's settling time. Settling time provides a better measurement of the AC performance of an analog input subsystem than the accuracy specification. However this still doesn't take into account linearity or the total harmonic distortion (THD) of the signal.

Settling time is the result of source impedance, the parasitic input of the multiplexer, and the capacitance at the output (caused by parallel switches). In addition, the instrumentation amplifier adds its own settling time. If channels are switched before the input from the previous channel has settled to zero, a residual value is added to the measurement of the next channel.

Specifically, it takes nine resistor-capacitor time constants for a signal to settle to 0.01% of its initial value. Thus, with 1 k source impedance and 100 pF output capacitance, one time constant is 100 ns. Nine times that is almost 1 µs. If the prior channel was at 10 V and you don't allow enough settling time, a portion of the 10 V will be added to the next channel's value. This would be the case with a 250-Ksps channel scan rate, which reads a new channel every 4 µs. Yet no amount of DC testing on just one channel reveals this source of error.

Even DC tests valid for one channel are losing their significance with the development of new data conversion techniques. For example, in a typical test, a DA board is calibrated with ± full-scale signals applied and then checked for accuracy at the zero-input level. For successive approximation and other conversion methods, checking the zero or mid-scale point represents a worst-case test. That's because you are comparing the weight of the most significant bit (MSB)—worth half the full-scale value—to the sum of the remaining bits, which is one least significant bit less than the MSB.

Although for years this has been an accepted test, the results are less significant for new architectures, such as folding and - A/D converters. In addition, the architecture of a converter may itself have a fast settling time and good DC characteristics but introduce errors because of a high harmonic distortion instability caused by heat generated during high-speed operation.

THD and other nonlinear error sources lower a board's SNR (with this specification, a higher value is desired). ENOB gives a simple measure of a board's SNR, which can be compared with an ideal value to determine a board's dynamic accuracy. In fact, the ENOB is derived from the theoretical definition of SNR. For a sine wave input signal, the theoretical SNR is:

   SNR = (6.02N + 1.76) dB 1
   where N is the resolution

Solving for the resolution, (N):

In the ideal case, a 12-bit converter has a 74 dB SNR; a 16-bit converter, 98 dB SNR. By measuring the actual SNR, you can derive the ENOB of an analog subsystem. The resolution of an analog input subsystem represents the theoretical ENOB. In practice, the ENOB never reaches the actual resolution of the A/D converter; however, the closer the ENOB is to the resolution of the board, the better the performance. For a sine wave input at a given frequency, the ENOB calculated from the actual (measured) SNR is:

   ENOB = (SNR actual – 1.76)/6.02

Thus, the ENOB gives a comprehensive measure of dynamic accuracy based on one parameter. That makes it an excellent test of an analog input subsystem's ability to acquire and faithfully encode dynamic signals across the input frequency range of interest.

The SNR is a measure of the broadband noise introduced in a signal. The SNR is the ratio of the rms sum of the fundamental frequency to the rms sum of all the harmonics below the Nyquist frequency, excluding DC. [Strictly speaking, the result is actually the ratio of the signal-to-noise and distortion, S/(N+D), which is a generally accepted definition of SNR.] The measured SNR is then used to calculate the board's ENOB.

What if you aren't using a DA board with a high ENOB specification? Can oversampling and averaging give you the accuracy that the board may be lacking? Mathematics can help, but it can't overcome all the errors introduced by a poor design.

If, for example, you are monitoring thermocouples or other inputs with significant noise, averaging can improve the subsystem's overall accuracy. Most thermocouples are not very accurate (a standard Type J thermocouple might have an accuracy of 0.75%, or 2.2°C.) If you were to acquire 100 samples and then average the results, you would eliminate a lot of the noise and inaccuracies of the thermocouple. However, if you are monitoring higher speed signals over a wider voltage range, averaging may not help as much. And if the input section of the DA board has poor linearity or distortion, averaging cannot compensate for the errors.

Slowing down the sampling rate can improve the performance of a board if it suffers from poor settling time. However, this technique greatly reduces the bandwidth of the board and your ability to accurately digitize high-speed signals.

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