Data Acquisition

A/D board can divide the input range into (2 12 = 4096) discrete levels, each 1/4096 the size ofthe input voltage range.Together, the resolution, input range, and input amplifier gain available on the A/D board,determine the smallest detectable voltage change in the signal input. For an ideal A/D boardwith a resolution of n-bits, this is calculated using the formula:smallest detectable change = input rangeamplifier gain × 2 nFor example, on a 12-bit A/D board, with a 0 V to +10 V input range, and the amplifiergain set to 1, the smallest detectable voltage change would be 10/(1 * 4096) = 2.44 mV.Therefore, each 2.44 mV change at the input would change the output of the A/D converterby ± l LSB or ± 0 × 001h. 0 V would be represented by 0 × 000h, while the maximumvoltage, represented by 0 × FFFh would be 9.9976 V. Due to the staircase nature of the idealtransfer characteristic of an A/D converter, a much smaller change in the input voltage canstill result in a transition to the next digital output level, but this will not reliably be the case.Changes smaller than 2.44 mV will not therefore be reliably detected. If the same 12-bit A/Dconverter is used to measure an input signal ranging from –10 V to +10 V, then the smallestdetectable voltage change is increased to 4.88 mV. This value represents the voltageequivalent of 1 LSB, of the full-scale voltage, and for A/D boards, is termed code width.The resolution figure quoted only provides a guide to the smallest detectable change thatcan be reliably distinguished by the A/D board, since the value calculated is based on theideal performance of all components of the analog input circuitry. The effects of noise, nonlinearitiesin the A/D converter, and errors in the other components of the analog inputcircuitry, can mean that the true resolution of an A/D board can be as much as 2 bits lowerthan the manufacturer’s specification. This means that a 16-bit A/D board may be accurate toonly 14-bits.5.4.3System accuracyThe system accuracy, or how closely the equivalent digital outputs match the incominganalog signal(s), is another very important criteria, especially where the analog signalcontains a lot of information, or where a small part of the signal range is to be examined indetail. As has been demonstrated, the functional components of the analog input circuitry (i.e.multiplexer, amplifier, sample-and-hold and A/D converter) of A/D boards are not ideal. Thepractical performance limits and errors in each of these components influence the overallperformance and accuracy of the system as a whole.The specification known as system accuracy usually refers to the relative accuracy of theA/D board and indicates the worst-case deviation from the ideal straight-line transferfunction. Relative accuracy is determined on an A/D board by applying to the input a voltageat minus full-scale, converting this analog voltage to a digital code, increasing the voltage,and repeating the steps until the full input range of the board has been covered. Bysubtracting the theoretical analog voltage, which should cause each code transition from theanalog input voltage that actually resulted in the code transition. The maximum deviationfrom zero is the relative accuracy of the A/D board. Board manufacturers usually quote thesystem accuracy in terms of LSB, since an absolute voltage value would only have meaningrelative to the selected input voltage range. For example, where ‘n’ = 2, the system accuracyof a 12-bit A/D board is 2/4096 (±0.048%), while for a 16-bit A/D board the accuracy is2/65536 (±0.003%).The tendency of analog circuits to change characteristics or drift, with time andtemperature, requires that A/D boards be periodically calibrated to maintain accuracy withinthe specified range. Manufacturers specify the offset voltage and gain accuracy to be