Accuracy considerations in process control

The majority of process control applications require digital results that are accurate to one part in 4096. As the output of a 12-bit A/D converter matches this exactly, why do these applications use converters with a higher number of bits? It is important not to be pre-occupied with the number of digital codes or the full-scale input range of the converter, but instead to look at the system accuracy requirements or analogue voltage least significant bit (LSB) size. Using the A/D converter’s LSB to define the design is straightforward (full-scale range/2n), but using the system LSB size is not as easy.

For example, take an RTD (resistive temperature detector) temperature-sensing circuit. A platinum-RTD sensor, such as the PR-100, has a resistance of 100 ohms at 25°C, which increases by 38.5W every 100°C. A 1mA current source excites the sensor. The voltage drop across the sensor can be captured, conditioned, and converted. With a four hundred degree Celsius change in the environment, the RTD resistance changes by 154W. If the desired system LSB size is 0.1°C over 40°C, the granularity of the voltage across the RTD sensor is one out of four thousand, or four thousand 38.5mV steps. So now that we have defined the system LSB size as 0.1°C and the full-scale range of 400°C, it is easy to see that the design can be implemented with a 12-bit converter, right? Before we jump to this conclusion, let us look at some more numbers.

For a temperature range of 0°C to 400°C, the voltage range across the RTD element is 90.375mV to 244.375mV. If a 12-bit, single-supply A/D converter is used, an analogue gain stage is needed. In reviewing the gain, input swing, output swing and precision limitations, this gain problem can be solved with a dual, single-supply operational amplifier. In this application, the gain of the analogue amplifier stage should be approximately 20V/V. This sounds straightforward, but there are some subtleties hiding in the numbers. With a gain of 20V/V the output swing of the amplifier will be 1.8075V to 4.8875V. With this voltage range, the 12-bit A/D converter will be under-utilised. It is possible to work around this problem quite easily. One solution uses a 12-bit A/D SAR converter that has a combination of differential inputs and adjustable input ranges.

There is an alternative way of dealing with the above specifications for the system. By finding a converter that can reliably digitize the analogue signal down to the 38.5mV divided by two, or 19.25mV, we can omit the analogue gain stage. If a high-resolution converter, such as a delta-sigma, is used, not only is there no need for an analogue gain stage, but there is the added luxury of being able to ignore unused bits. Let us look at how this works A high-resolution A/D converter with a full-scale range of 5V peak-to-peak and a noise accuracy of 18-bit will give the desired results. This is calculated with the following formula:

(# of bit) = 1.44 * ln (FSR/LSB).

Care needs to be taken with definitions and specifications when using high-resolution converters. For example, if a reliable, repeatable result is expected with every digital output word, it is very important to understand the terms rms and peak-to-peak. Rms implies a calculated, one standard deviation from several hundred samples. A peak-to-peak specification predicts the probability that one conversion result will fall into an expected range. If a crest factor of 3.3 is used to calculate the peak-to-peak LSB size (or effective number of bits), the converter’s results will be within a 99.9% window around the expected result (peak-to-peak = 2 x crest factor x rms). Imagine that the system needs a repeatable output resolution of 18 bits. This requires a converter with an rms resolution of 20.723-bits. Industrial quality delta-sigma A/D converters have this type of performance.

A 12-bit application may not always need a 12-bit converter. The system dictates the required dynamic range. Throwing away unused codes may seem wasteful because the full dynamic range is not being used, but this is compensated for by reduced chip count. In this market, bits and dynamic range are like memory; they are getting cheaper and cheaper.