by Leonard Staller, Applications Engineer,
Cygnal Integrated Products, Inc., Austin, Texas
Oversampling and averaging are techniques you can use to boost the resolution and signal-to-noise ratio
when you're doing an A/D conversion. You can also increase the resolution of a measurement when using one of
today's highly integrated data acquisition chips—without resorting to the cost and complexity of expensive
off-chip A/D converters.
Many designs involve making measurements using analog-to-digital (A/D) converter chips.
Such applications have resolution requirements based on (1) a signal's dynamic range, (2) the smallest change
in a parameter that must be measured, and (3) the desired signal-to-noise ratio (SNR). For these reasons,
many system designers choose to use higher resolution standalone A/D converters.
However, there are techniques that can be used to achieve higher resolution measurements and SNR.
Oversampling and averaging are two such approaches that can increase the resolution and SNR of A/D
conversion.
Today, oversampling and averaging can also increase the resolution of a measurement system based
on a highly integrated data acquisition chip—without resorting to the cost and complexity of
expensive off-chip A/D converters.
Let's discuss how to increase the resolution of A/D converter measurement by oversampling and
averaging. Then we'll take a more in-depth analysis of A/D converter noise, and discuss the types of
A/D converter noise that are optimal for oversampling techniques. We will look at how oversampling
and averaging can improve the SNR ratio for "white" noise, and see why oversampling and averaging
can improve SNR and measurement resolution, but at the cost of increased CPU utilization and
reduced throughput.
In a subsequent installment of this article, we'll provide some example software, including a
sample code listing for implementing oversampling and averaging.
Sources of Data-Converter Noise
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What are typical sources of data-converter noise? Thermal noise, shot noise, and noise from
variations in the supply voltage and variations in the reference voltage are a few sources.
Phase noise due to sampling-clock jitter and noise due to quantization error are two additional
sources. The latter is commonly referred to as quantization noise.
The noise power from these sources can also vary. You can reduce noise by means of thoughtful
circuit-board layout, and by using bypass capacitors on reference-voltage signal traces.
However, A/D converters will always have quantization noise. As such, the best SNR of a data
converter of a given number of bits is defined by the quantization noise with no oversampling.
Under the correct conditions, oversampling and averaging will reduce noise and improve the SNR,
which will effectively increase the number of bits of a measurement's resolution.
A typical system, shown in the block diagram of Figure 1, can be implemented with an on-chip
A/D converter and a software routine that takes a set of samples and averages (or filters) them
for a result.
Figure 1 - Oversampling and Averaging to Increase Measurement Resolution by "w" bits
Increasing Resolution
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Many applications measure a large dynamic range of values, yet require fine resolution to measure
small changes in a parameter. For example, an A/D converter may measure a large temperature range, yet
still have to respond to changes of less than one degree. Such a system could require a measurement
resolution of 16 bits.
Rather than resorting to an expensive off-chip 16-bit A/D converter, oversampling and averaging using
an on-chip 12-bit A/D converter, such as the type provided in one of Cygnal Integrated Products'
data-acquisition chips, can measure a parameter with 16 bits of resolution.
Other applications need A/D converters to analyze signals with higher frequency components, and these
systems can also benefit from oversampling and averaging. Indeed, the required sampling frequency in
accordance with Mr. Nyquist's theorem is the Nyquist frequency, derived as shown in Equation (1).
where fm is
the highest frequency component of interest in the input signal.
Sampling frequencies ( fs ) above fn
is called oversampling, and will increase the resolution of a measurement.
Calculating The Requirements
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To increase the effective number of bits (ENOB), a signal is oversampled, that is, it is sampled
by the A/D converter at a rate that's higher than the system's required sampling rate,
fs. The required sampling rate may be determined by
how often a system requires that a parameter be measured (the output word rate), or it may be the Nyquist
frequency, fn.
For each additional bit of resolution, the signal must be oversampled by a factor of four:
where w is the number of
additional bits of resolution desired, fs is the
original sampling frequency requirement, and fos is
the oversampling frequency.
Assume a system is using a 12-bit A/D converter to output a temperature value once every second (1 Hz). To
increase the resolution of the measurement to 16 bits, you can calculate the oversampling frequency as follows:
fos = 44 · 1 (Hz) = 256 Hz.
If you oversample the temperature sensor at fs = 256 Hz, you
will collect enough samples within the required sampling period to average them. You can then use 16 bits of the
output data for a 16-bit measurement.
Accumulate and Dump
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To do so, you accumulate (add 256 consecutive samples together), then divide the total by 16 (or right-shift the total
by four bits). Such a process is commonly referred to as decimation. This technique results in 16 bits of useful data.
Such an operation is referred to as an accumulate and dump.
Once you calculate the result of 256 samples (in our example), you can store or process the data, and begin collecting data
for the next output word. Note that the memory location used to accumulate the oversampled data, and to perform the divide,
must have enough bytes to prevent overflow and truncation error.
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