Matching A/D Converter Performance with Application (Part I)
A fundamental understanding of precision and accuracy, and how they relate to ADC specifications to enable the designer to quickly choose the right ADC for their application.
Understanding ADC performance, especially as it relates to system requirements, is not always a straightforward task. Take, for example, a customer designing what they thought was a simple, low-end test system for one of their products. The customer needed to develop a test system with an accuracy of 1% so decided to use a 12-bit resolution ADC integrated with their MCU. The reasoning for using the integrated ADC was that they had more than enough margin to meet the accuracy requirement with the 12-bit ADC. Which, it turns out, was not a correct assessment. Their first mistake was they did not understand how to correctly assess the accuracy needed.
The initial manufacturing run for their test system showed a 2% reject rate due to inaccuracy of the system level measurement. This led them down a path of upgrading their MCU so they could implement additional digital processing to improve system accuracy. This was their second mistake. They incorrectly diagnosed the root cause of the 2% rejection rate and exacerbated their first mistake by applying additional digital processing. The result was their next production run had a reject rate as high as 5% with higher variability.
How did the customer design a system that failed when they thought they had much more accuracy than they needed? The customer failed to interpret key specifications of the ADC and apply them to the system requirements needed.
Let’s review the decision process to assess how they ended up in this situation. The first mistake made by the customer was confusing resolution with precision and accuracy, which is a common mistake. The second mistake was failing to identify the true source of error that led to the high reject rate. This in turn led to a solution that increased the reject rate even further.
ADC Resolution
Resolution is the first and most widely searched parameter for ADCs. The customer looked at the ADC resolution and assumed it matched the accuracy and precision of the ADC. The problem is that resolution, precision and accuracy are not always related – and can vary significantly on a given ADC.
The resolution of the ADC only refers to the number of bits or codes the ADC outputs. It does not give a qualitative indication of the precision or accuracy of the data coming out of the ADC.
All 12-bit ADCs are not created equal. You must dig deeper to understand what performance the ADC is providing.
This can be accomplished by looking at qualitative indicators of resolution such as Effective Resolution (bits), Effective Number of Bits (ENOB) and noise (volts). These attributes are used to define resolution in slightly different ways.
Effective resolution is simply the useable ADC resolution considering the noise of the ADC with respect to a full-scale input. Effective resolution is typically used as a qualitative figure of merit to indicate the effects of DC RMS (Root Mean Square) noise, i.e., ADC readings that are one standard deviation from the mean. For example, if you take 100 readings from a 12-bit ADC and calculate the standard deviation from the 100 readings to be 2-bits, then the effective resolution of the ADC is 10-bits.
ENOB is like effective resolution but it is a qualitative figure of merit for AC RMS noise in terms of bits.
Noise is another way to represent the effective resolution of an ADC but it is quantified in volts.
Noise is useful when trying to compare the performance of an ADC in terms of the signal referred to the input, whereas bits are useful when trying to understand the noise of the ADC as it relates to the full-scale code range of the ADC. For example, let’s compare an ADC with 12-bit effective resolution and an ADC with 10-bit effective resolution. The ADC with 12-bit effective resolution has a full-scale range of 5 V and has input referred noise of (5V/2^12) = 1.2mV. The ADC with 10-bit Effective Resolution has a full-scale range of 1 V and has input referred noise of (1V/2^10) = 0.98mV. The 12-bit effective resolution ADC has higher input referred noise, so the best RMS precision is 1.2mV, but it has a wider input range. The 10-bit effective resolution has lower input referred noise but has a smaller input range.
Which is the better ADC? The answer depends on your application needs.
Precision
Precision is the ability of a measurement to be consistently reproduced or in other words, the repeatability of a measurement. The more precision in your measurement, the more you can discern small differences. High precision is good.
Accuracy
Accuracy is the ability of the measurement to match the actual value being measured. It’s needed when trying to measure a specific value. High accuracy is VERY good.
Which Matters More – Precision or Accuracy?
Let’s say I buy a set of arrows and go to an archery range to demonstrate precision and accuracy using three systems.
Figure 1 shows System 1, which is an example of a precise system. Notice that the arrows are tightly grouped, which indicates the method of launching the arrows is very repeatable. However, they are not close to the intended target of the bullseye, which means the performance of the launcher or the arrow is not capable of accuracy.
Figure 2 shows System 2, an example of a precise, accurate system. Again, notice that the arrows are tightly grouped, which indicates the method of launching the arrows is very repeatable. Also notice that they are grouped on the bullseye, which indicates high accuracy.
Figure 3 shows System 3, an example of a system that is neither precise nor accurate. There is no tight grouping of arrows and there is low accuracy.
Which matters more, precision or accuracy?
To answer that question, let’s look at the three systems again.
What happens if a month later, a new set of arrows is manufactured and I use those on the archery range? I would expect the groupings in System 1 to remain tight, but since the new arrows differ from the old arrows the grouping may have moved to a different location on the target. I would also expect the groupings in System 2 and System 3 to stay the same as before.
What happens if the next day the temperature, humidity or wind changes direction on the archery range? Again, I would expect the groupings in System 1 to remain tight, but the grouping will have moved to a different location on the target. Also, I would expect the groupings in System 2 and System 3 to stay the same as before.
What happens if I launch a newly-manufactured set of arrows with changing environmental conditions every day? After about 30 days, System 2 would look the same as it did on day one, but System 1 and System 3 would start to look the same. Over time, a precision system without accuracy starts to look like a system with neither precision nor accuracy since the accuracy will vary based on internal variations (manufacturing) and external variations (environmental).
That is what happened to the customer in the example at the beginning of the article. They thought they had accuracy but realized they did not. Then they tried to improve precision to compensate, but the system shifted so they lost both precision and accuracy and had to redesign their system.
Now that we have a good understanding of resolution, precision and accuracy, we can apply this understanding to our ADC. In part two, we will continue exploring the customer example to understand ADC parameters that define precision and accuracy. This will ultimately allow us to achieve the system accuracy that meets our requirements.
To read continued articles on this matter: