Though it seems counterintuitive, it is possible to increase the effective resolution of an analog to digital beyond the converter’s native resolution by taking advantage of noise. For example, you could get nine or more bits of effective resolution out of an 8-bit converter using this technique. As you might expect, there are some caveats and compromises involved, but it is a useful trick to have up your sleeve.
An ADC converts an analog signal that can have an infinite range of values to a set of discrete codes, effectively “bracketing” a range of input voltages into each code. The resolution of the converter determines the number and width of these ranges. An 8-bit converter, for example, divides the input range into 256 levels and a 10-bit converter divides it into 1024 levels.
Figure 1 shows a section of the input/output characteristic of a typical ADC. The analog voltage (on the vertical scale) can take any value, but the output code must take one of the discrete values on the horizontal axis. The voltage represented by the code N for example, corresponds nominally to voltage VN, but also to any voltage within the ±½LSB range shown.
An ADC’s output code must take a discrete value, so a range of input voltages correspond to each one. The number and width of these ranges is a factor of the ADC resolution.
If the input voltage is right at the edge of the range, say half-way between VN and VN+1 (shown dotted in red) it will be right on the transition voltage between the codes N and N+1, however it must take one value or the other since the resolution of the converter does not permit any intermediate value. If the signal was constant and ADC was perfect the code would be the same every time we take a sample.
However, if we have some noise on the signal, as shown in Figure 2, the samples we take will sometimes result in code N and sometimes in code N+1. Assuming the average value of the noise is zero, and the noise is uncorrelated with the sampling, we should see half the samples fall either way. On average then, we would get a value of N+½ effectively giving us an intermediate value corresponding to higher resolution. We have created extra precision by taking multiple samples and combining them into one new sample.
By adding noise and oversampling, you can calculate intermediate values that have the effect of increasing the resolution of the ADC beyond its nominal level.
To put a bit of rigour around this explanation we need to dip a toe briefly into the deep pool of sampling theory. The Nyquist-Shannon theorem states that to correctly reconstruct a signal in the digital domain we need to sample that signal at a rate equal to (or greater than) twice the maximum frequency component present in the signal. This frequency is called the Nyquist frequency, and if we don’t the sample at or above this rate signal will contain aliasing and will not be a faithful representation of the original.
If we want to use the noise technique to increase ADC resolution, we have to calculate a new result at the Nyquist frequency. In other words, we have to sample at K times faster than the Nyquist frequency if we want to average K samples (or put more concisely we have to oversample the input by a factor of K).
The maths shows that the number of bits of additional resolution we can achieve is given by the relationship K = 4b where b is the number of additional bits and K is the oversampling factor. So, oversampling by a factor of 4 will result in an extra bit of resolution, and oversampling by a factor of 16 will result in an extra two bits of resolution and so on.
I mentioned above that there were a few caveats to this technique. First, the amplitude of the noise must be at least ±1/2 LSB for this to work. In fact, designers often deliberately add “dither” to a signal if the amplitude of the naturally occurring noise is not high enough. The noise must also average to zero and be uncorrelated with the sampling rate. Finally, as we have already mentioned, your ADC has to run faster than it otherwise would, impacting power consumption and perhaps requiring a faster part.
Bibliography
“AVR121: Enhancing ADC Resolution by Oversampling,” n.d. https://ww1.microchip.com/downloads/en/appnotes/doc8003.pdf.
“AN5537-How-to-Use-Adc-Oversampling-Techniques-to-Improve-Signaltonoise-Ratio-on-Stm32-Mcus-Stmicroelectronics.Pdf.” Accessed February 10, 2025. https://www.st.com/resource/en/application_note/an5537-how-to-use-adc-oversampling-techniques-to-improve-signaltonoise-ratio-on-stm32-mcus-stmicroelectronics.pdf.
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Andrew Levido (andrew.levido@gmail.com) earned a bachelor’s degree in Electrical Engineering in Sydney, Australia, in 1986. He worked for several years in R&D for power electronics and telecommunication companies before moving into management roles. Andrew has maintained a hands-on interest in electronics, particularly embedded systems, power electronics, and control theory in his free time. Over the years he has written a number of articles for various electronics publications and occasionally provides consulting services as time allows.
