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Get Your 12-bits One Way or Another

By Bonnie C. Baker,
Senior Applications Engineer, Data Acquisition Products Division,
Burr-Brown Corporation

For most process control applications, a digital representation that is one part out of 4096 is enough. By definition, the digital output of a 12-bit ADC has 4096 different digital combinations. This makes it look like a perfect fit. So why have so many ADC options with differences in number of bits for the same application? The trick in these types of circuit applications is not the number of digital codes, but the analog voltage magnitude of the system LSB (Least Significant Bit). It is easy to calculate and design with the ADC converter's LSB size (FSR/ 2ˆn), but the system LSB size is a different story. Take for instance, an RTD (Resistive-Temperature Device) temperature-sensing circuit. A platinum RTD sensor, such as the PR-100, has measurable resistance changes with temperature. If it is excited with a current source, the voltage drop across it can be sensed and converted to a digital word with the ADC.

Now, the characteristics of this type of temperature sensor are common knowledge. For instance, the resistance of a PT-100 sensor is 100 ohms at 25 ıC and increases fairly linearly at 38.5 ohms for every 100 ıC. With a 400 ıC change in the environment, the RTD resistance will change 154 ohms. For this discussion, the temperature range of interest is from -100 ıC to 300 ıC, meaning the RTD will change in resistance from 61.5 ohms to 215.5 ohms. If this temperature range is converted into 4096 parts, the system LSB size in terms of temperature is 0.09766 ıC, or approximately 0.1 ıC.

So now that we have defined the system LSB size as 0.1 ıC and the full scale range of 400 ıC, the rest of the design should be easily implemented with a 12-bit converter!

PLAN A - Working the Obvious Solution

The first order for business is to power up the RTD with a current source of some sort. What's enough? If you are thinking of using a 12-bit converter with a 5-V input range and no analog gain stage, you might think of applying 23 mA through the RTD. This means that when the RTD is exposed to 300 ıC, the voltage drop will be 5 V. The bad news is that the voltage drop across the RTD in a -100 ıC environment is 1.43 V. Taking the difference of these two voltages, you can calculate a loss of dynamic range of about 28.5%. This brings the system accuracy down to 11.5 bits.

What are the design alternatives? Add additional circuitry to create a pedestal voltage that equals 1.43 V. First, this pedestal voltage can be applied to the inverting input of a differential-input 12-bit converter. The voltage from the positive side of the RTD can then be applied to the non-inverting input. 12-bit differential input ADCs are easy enough to find making this a viable alternative. Second, the input range of the ADC must be reduced down to 3.57 V. There are numerous 12-bit converters on the market that have an adjustable input range. Their input range is adjusted by changing the voltage reference to the ADC. There are fewer 12-bit ADC with the combination of differential inputs and adjustable input ranges, but they do exist.

Another alternative would be to use a higher resolution ADC. This is the option that I would vote for because it requires fewer support chips. Only 13-bits are needed and there are plenty of 14-bit and 16-bits converters on the market. With this alternative, the pedestal voltage and the differential input ADC is not required. Additionally, the input range of the converter can remain 0 V to 5 V, which is a common configuration. Although you throw away some of the dynamic range of the converter the number of total possible bits, given the voltage range from the RTD, is a little better than 12-bits.

Unfortunately, the downfall of this application solution is that the RTD is running too hot. It becomes a victim of self-heating and its linearity and reliability are compromised. At best, this RTD should be powered with less than 1 mA, actually, the lower the better. If the RTD is excited with a 500-ıA current, the voltage output range of the RTD has also been changed to a range from 30.75 mV to 107.75 mV. This redefined voltage output range of the RTD now excludes the 12-bit, 14-bit and the 16-bit converter from this simple application. This loss of gain across the RTD has to be put back into the system some place. The alternatives discussed above can still be used, but an analog gain cell prior to the ADC is now absolutely required.

PLAN B - Get Fancy with the Obvious

Since the current through the RTD must be small enough to keep self-heating to a minimum, the addition of an analog gain stage seems like a viable solution. In reviewing the gain, input swing, output swing and precision limitations of these types of analog stages, a differential input instrumentation amplifier makes the most sense. If power for the supply for the system is a single 5 V supply, it makes things a little bit more complicated, but not impossible. With most instrumentation amplifiers on the market, a discrete resistor is used to customize their gain.

Now if the current through the RTD is set to 500 ıA, an instrumentation amplifier with a gain of 64.8 V/V will make a good substitute for the reduction in current through the RTD. Sounds like an easy fix, but the subtleties may take you by surprise. If you are trying to design with the circuit with 5 V supplies, the analog instrumentation amplifier will not be able to swing completely to the positive rail or to ground for that matter. Because of this limitation you may be forced to reduce the gain of the instrumentation amplifier and once again use a 14- or 16-bit converter to finish the job.

PLAN C - The Not So Obvious, Simple Solution

Let's re-group. The LSB size of our measurement is 0.1 ıC. The full-scale range of our measurement is 400 ıC. The LSB size of the RTD is 38.5 mohms. The full-scale range of the RTD is 154 ohms. If we excite the RTD with 500 ıA, the LSB size of the system at that point is 19.25 ıV and the full-scale range is 77 mV. Forget the analog gain stage. Find a converter that can reliably digitize the analog signal down to the 19.25 ıV LSB size. In the past, analog designers were encouraged to use the full dynamic range of the parts in the signal path whenever possible. This generalization was sound in terms of keeping the noise floor of the devices under control. But now, with the arrival of high-resolution converters this design guideline has been relaxed.

If the converter has a full-scale range of 5 V, a true 18-bit converter will give the desired results. There is some specmanship that needs to be applied when using a high-resolution converter. For instance, if you expect a reliable result with every digital output word, the understanding of the terms r.m.s. and peak-to-peak are critical. You will find in the specifications that r.m.s. implies a calculated one-standard deviation using several hundred samples. A peak-to-peak specification predicts that the probability a sample will fall into an expected range is 99.9% (2 x Crest Factor of 6.6). Imagine that the system you are designing needs a guaranteed output resolution of 18-bits. This would imply that the r.m.s. resolution would be approximately 20.723-bits. A good ADC for this type of performance uses the Delta-Sigma topology.

Analog is Mixing with the Digital Domain

A 12-bit application may not always need a 12-bit converter. It is actually the system that dictates the real dynamic range. The last circuit discussed here may give you heartburn because you are throwing away all of that dynamic range. But not to worry. In this market, bits and dynamic range are like memory; they are getting cheaper and cheaper.

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