Publication date: 18 March 2008
Particularly in the field of delta sigma analog to digital converters (ADCs) , resolutions and speeds are increasing. These high resolution ADCs can now provide cost effective solutions in many applications. Often however, designers see the ’24 bit’ headline number on the datasheet and are lured into thinking that the ADC can provide better performance in terms of resolution and accuracy than it actually can.
This article will look at the term resolution, what it really means and the various ways in which it is defined. It will then explore the term accuracy and show that a high degree of resolution doesn’t necessarily imply a similar degree of accuracy, a point often not well understood.
Resolution is most commonly used as a measure of the repeatability of measurement, or the degree of noise present in a set of measurements. In other words, if we measure the same input many times, what is the spread in the results that are obtained. A low spread implies a low noise and a high resolution.
Resolution is normally quoted in ADC datasheets as effective resolution, or effective number of bits (ENOB). Resolution is measured by comparing the root mean squared (RMS) noise in a set of measurements from a fixed input, with the full scale range of the ADC to establish the signal to noise ratio (SNR), normally expressed in dB. The effective resolution, or ENOB, is calculated from the expression:-
ENOB = SNR (in dB)/6.02
In many applications this is fine. The ENOB is a measure of the power in the noise to the power in the signal and is just what would be required for an application such as a spectrum analyzer However there are also many applications where this isn’t a good measure of performance. A good example is a weight scale. We don’t expect the reading from a weight scale to be constantly changing and to be told its accuracy in grams RMS. We expect a constant, noise free reading from a weight scale and to be told the accuracy in grams. We need to be clear that the effective resolution or ENOB figure in the datasheet is not the same as the noise free resolution that many applications require.
Fortunately, if we make the assumption that the noise from an ADC has a Gaussian distribution (which is normally true), then we can get a good estimate of the noise free resolution from the effective resolution, or ENOB. To do this we assume that the peak to peak noise is 6.6 times the RMS noise. This is the equivalent of 2.7 bits, or approximately 3 bits. We then simply subtract 3 bits from the effective resolution, or ENOB, to get the noise free resolution.
Although resolution, either effective or noise free, is normally highlighted in datasheets expressed in bits, this is actually a meaningless figure unless we know the size of a bit, normally expressed as the least significant bit (LSB) size. A better measure of ADC resolution is input referred noise. This directly relates the noise generated by the ADC to the input signal applied to it. The input referred, RMS noise, can be calculated from the ENOB figure using the expression:-
Input referred noise (rms) = Full scale signal/10 ENOB x 6.02/20 = Full scale signal/2ENOB
This expression clearly shows one of the pitfalls of working in terms of bits when comparing different ADCs. Two parts can have the same effective resolution or ENOB when measured in bits, but if one part has a full scale range of 2.5V and the other has a full scale range of 5V, the first part has half the input referred noise of the other. This discussion becomes even more complex when we take into account the fact that many delta sigma ADCs incorporate a programmable gain amplifier (PGA), which effectively reduces the full scale by whatever gain is selected by the PGA. Some careful reading of the datasheet may be required.
It is instructive to look at an example from a real datasheet, in this case using the ADS1256 from Texas Instruments as an example. Table 1 details the input referred noise in uVrms :-
If we assume a 100sps data rate and a PGA gain of 1, then the input referred noise is 0.875uVrms.
This ADC requires a 2.5 reference (Vref) and its full scale range is +/-2Vref, or 10V. The signal to noise ratio (SNR) is therefore :-
SNR = 20log10(10/0.875 x 10-6) = 141.2dB
From this we can calculate an effective resolution of 141.2/6.02 = 23.4 bits. This agrees with figure in table 2 for the same data rate and PGA gain :-
Assuming a ratio of 6.6 between the peak to peak and RMS noise we would expect a noise free resolution of 23.4 – 2.7 = 20.7 bits. Tables 3 in fact shows a figure of 20.9 bits. The discrepancy between the expected 20.7 bits and the reported 20.9 bits here is actually the result of using a small datasheet for these slow speed measurements. At higher data rates the difference between ENOB and noise free bits is the expected value of 2.7.
Let us now rework these calculations using the same data rate but increasing the PGA gain from 1 to 8.
From table 1, the input referred noise is now 0.305uV. The input full scale however has changed from 10V to 1.25V (because of the PGA of 8), so the SNR is therefore:-
SNR = 20log10(10/0.305 x 10-6) = 132.3dB
The effective resolution is now 132.3/6.02 = 22 bits and the noise free resolution is 22 – 2.7 = 19.3 bits.
This clearly illustrates the problem of talking about resolution in bits. Between a PGA gain of 1 and a PGA gain of 8, the effective resolution fell from 23.4 bits down to 22 bits, which implies a decrease in performance. The input referred noise, however, fell from 0.875uV down to 0.305uV, which is an increase in performance. What actually happened here was that the input referred noise fell but the LSB size fell by a greater amount, resulting in more noise bits, but where each bit was smaller.
Hopefully it is now clear what is meant by resolution and what figures should be used from the datasheet to establish this. It might, at this point, be tempting to think that resolution has something to do with the accuracy of the ADC. This is not the case.As stated earlier, resolution is a measure of repeatability. An ADC with a high resolution gives results with good repeatability but could be repeatedly giving the wrong result. Its resolution would be good even although the accuracy was poor.
As can be seen, a real ADC has three significant sources of error which are offset error, gain error and integral linearity error (INL). Associated with each of these are also drift terms over temperature and time.
To use the ADS1252 as an example, this is a 24 bit, delta sigma ADC with 19 bits of effective resolution. But how accurate is it?
From the datasheet, the offset error is given as +/- 200ppm of full scale. Given that full scale is 224 codes, that’s an error of 3355 codes and since its an offset error has to be applied to every reading, whatever the signal amplitude. The gain error is given as +/-1% of full scale, which is the equivalent of 167,772 codes. This scales with the signal amplitude, so is half of this at a half full scale signal. Clearly these figures don’t give anything like the accuracy that might be expected by simply looking at the 19 bits of effective resolution headlined on the first page of the datasheet.
All of this isn’t to detract from the ADS1252. This part was designed for good AC performance and has a DC accuracy comparable with most 16 bit ADCs. If greater accuracy was required then clearly some form of calibration would be required to remove the offset and gain errors.
Some parts, such as the ADS1256 from Texas Instruments do in fact incorporate such offset and gain calibration internally to the part, which changes the situation significantly. For this part, the offset error, after calibration, is quoted as being at the level of the noise, clearly it is not possible to achieve better than this and gives an offset error that directly relates to resolution. The gain error, after calibration, is +/-0.005%, or about +/- 800 codes, again a much better fit to the level of resolution.
It should be clear by now why high resolution isn’t the same as high accuracy and that for very high resolution ADCs, high accuracy is only going to be achieved with some form of offset and gain calibration.
Having removed offset and gain errors, then the term that still remains is INL, the curve of the transfer slope. While offset and gain errors can be calibrated out without too much difficulty, in practice INL is very difficult to remove and is rarely, if ever, done by an ADC user. Few people have the equipment or the time to perform the multipoint calibration that would be required for this.
Clearly, then it is INL that ultimately will set the limits to accuracy for most users. For a part such as the ADS1256 the INL is 0.001% of full scale, or +/-167 codes. This matches well with the level of accuracy that might be expected from its resolution.
