Count Your Effective BitsCount Your Effective Bits

When you buy a data-acquisition (DAQ) board or system that includes, say, a 20-bit analog-to-digital converter (ADC), you expect to get 20 bits of resolution. Chip manufacturers produce highly accurate ADCs, but a DAQ board usually includes amplifiers, multiplexers and filters in the analog-signal path plus many digital circuits. All those supporting devices can slightly degrade an analog signal, so the 20-bit converter might offer only 18 "effective" bits. But don't assume you should ditch the 20-bit converter and replace it with an 18-bit DAQ board.

The effective number of bits (ENOB) indicates system performance, which depends to a great extent on circuit characteristics, types of components and so on. Unlike dc-error specs such as integral nonlinearity or differential nonlinearity, an ENOB value depends on dynamic (ac) tests. Thus, results can vary depending on a test signal's amplitude and frequency. Unfortunately, ENOB values don't get much attention.

No test directly produces a value for ENOB; instead you calculate it from a DAQ board's signal-to-noise-plus-distortion ratio, or SINAD, expressed in decibels. Although ADC-chip and DAQ-board specifications may list a SINAD value, you should measure it yourself to determine its value under your local conditions. It's unlikely your lab duplicates the "clean" test environment in which a DAQ-board supplier makes its measurements.

To calculate an ENOB value, you connect a low-distortion sine-wave source to one of your DAQ-board's inputs and acquire samples at the maximum rate. Because you will run an FFT on the data, choose a frequency that will not "fold" high-order harmonics into FFT results and apply a window, such as a Blackman-Harris function, to the data before you run the FFT. The FFT results show the energy at the fundamental frequency (signal) and the energy at all other frequencies (noise + distortion). You can plug these values into the equation:

SINAD = 20log (E_signal/E_{noise+distortion}) and then into:

ENOB = (SINAD - 1.76 dB)/6.02 dB

You can use at least one other measurement technique that performs a best least-squares fit to the sine wave in the time domain. I'll list below several references that explain ENOB measurement techniques in more detail and the math behind the calculations.

Now, back to the 20-bit DAQ board with ENOB = 18. The ENOB value does not mean you should toss out the ADC's two least-significant bits. ENOB simply represents a measure of overall system-performance that will help you better understand how system characteristics affect measurements. If you do eliminate the two LSBs, you simply increase your system's quantization error fourfold, from plus or minus 1/2 x 1/2²⁰ to plus or minus 1/2 x 1/2¹⁸.