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Improving A/D Converter Resolution
by Oversampling and Averaging—Part 3:
When Oversampling and Averaging Will Work

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The Noise Requirements
A Histogram Analysis
An Unsuitable System
Sample Code

by Leonard Staller, Applications Engineer,
Cygnal Integrated Products, Inc., Austin, Texas

In the last two installments of this article, we discussed oversampling and averaging as techniques that can boost the resolution and the signal-to-noise ratio (SNR) of an A/D conversion. In this third part of our ongoing ChipCenter tutorial, we'll present some guidelines to determine if oversampling and averaging will be effective. A sample of real-world coding is included.

As we've already discussed, we know that an A/D data conversion process can introduce noise, and we also have seen that that oversampling and averaging can reduce certain types of noise. As such, the techniques increase the SNR and the effective resolution of a data conversion.

But not all applications can benefit from oversampling and averaging. To understand which A/D converter measurements will benefit, you must understand the type and characteristics of the noise present in a given system.

The Noise Requirements
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Oversampling and averaging will work only if the A/D converter noise can be approximated as white noise. If the input signal changes randomly from sample to sample by amounts (amplitude) comparable to the code size (1 LSB), and the input signal has an equal probability of being anywhere between two adjacent codes, then the noise can be modeled as approximating white noise.

What is white noise? It's noise that's characterized as having a uniform power spectral density over a frequency band of interest. When noise can be approximated as white noise, then oversampling and averaging can improve the SNR and increase the effective resolution of your data.

If the overall noise isn't stationary (some systems may have some correlation due to feedback), then oversampling and averaging may not be effective. Additionally, if the quantization noise is comparable to sources of white noise (thermal and shot noise are small compared to quantization noise), then oversampling and averaging may not be effective.

This situation is typically encountered when using lower resolution A/D converters such as 8-bit types. In such cases, thermal noise doesn't have sufficient amplitude to cause the input signal to change randomly with equal probability between codes—the code width is too large. Some applications will inject noise into the signal or process intentionally to overcome this effect. This is referred to as dithering.

A Histogram Analysis
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Most applications that measure a signal using a 12-bit A/D converter will benefit from oversampling and averaging. A practical means of determining if the noise characteristics of your application are appropriate is to analyze the A/D converter's output data using a histogram.

The example histogram shown here depicts how many samples in a set from an A/D converter resulted in each A/D converter code. Note that if the input signal is a constant DC voltage value, the histogram will approximate a Gaussian probability distribution function (PDF) if the noise is white.

Figure 5 - A Histogram of A/D Converter Samples
that Shows DC input with White Noise

In the illustration note that the "bin" for code 1024 received the greatest number of samples because of the input voltage, while surrounding codes received some samples because of noise.

Because the histogram approximates a Gaussian PDF (the blue dotted line in Figure 5), the noise approximates white noise. This system can therefore benefit from the application of oversampling and averaging techniques.

In contrast, a system with insufficient noise (besides the quantization noise) will result in a histogram with all samples going to only one bin, or code. Oversampling and averaging may not be helpful in such a system.

An Unsuitable System
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If the noise is correlated, or the A/D converter's transfer function is nonlinear (because of power-supply noise, for example, or poor integral nonlinearity, or INL), the histogram may not approximate a Gaussian PDF. This is illustrated in Figure 6. In such cases, oversampling and averaging likely won't be helpful.

Figure 6 - A Histogram of A/D Converter Samples
that Shows a system that Isn't Optimal for
Oversampling and Averaging Techniques

If the combined sources of noise in the resulting A/D converter codes approximate white noise, a histogram of the samples will approximate a Gaussian PDF. Oversampling and averaging will then improve the SNR and increase the effective number of bits of your signal measurement.

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