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Oversample to the Extreme
By Jon Titus, Contributing Writer -- Design News, November 2, 2008
My previous Tips column, “Oversample on Purpose,” (DN 10.20.08, http://designnews.hotims.com/22267-523), explained how averaging oversampled data can improve the resolution of an analog-to-digital converter (ADC). A delta-sigma converter also uses oversampling to produce results with as many as 32 bits, a resolution thought impossible not long ago. (Engineers often use “delta sigma” and “sigma delta” interchangeably to describe this type of ADC). A delta-sigma ADC includes a modulator section, which, in turn, comprises a difference amplifier, an integrator, a comparator and a 1-bit digital-to-analog converter. Those components form a closed loop that integrates the sum of an unknown signal and the DAC’s +Vref or -Vref signal. A comparator controls the DAC based on the voltage from the integrator and a reference voltage at the comparator. (For more operational details, see Useful Links, below right).
The modulator produces a “weighted” string of 1’s and 0’s. So, oversampling the signal at, say, 64 times the signal’s highest frequency component yields a string of 64 bits. The more 1’s in the string, the higher the voltage and the more 0’s, the lower. But the 64-bit stream doesn’t mean you get a 64-bit ADC! Digital circuits create a data value from the bit stream. Those values then go to a digital low-pass filter that removes noise that comes from several sources. In some converters, the filter will produce a sinc response, [sin(πx)]/πx, that helps attenuate power-line noise and harmonics.
At the end of the digital-filtering process the ADC has more values than you need. If you oversample a signal at 64 times the Nyquist frequency, you won’t need 64 values to reconstruct it. So, a decimation step eliminates, say, three out of four or seven out of eight values. Thus, the ADC produces values at 16 or eight times the Nyquist frequency. Typically, delta-signal converters offer high resolution, but they operate best with low-frequency signals. Texas Instruments’ ADS1282 ADC, for example, produces either 24- or 32-bit results at either a 4,000 or 250 samples/sec rate.
The modulator portion of a delta-sigma converter acts like a low-pass filter for the unknown signal and as a high-pass filter for quantization noise. (Remember, the converter has discrete voltage steps). So, the modulator provides some “noise shaping” capabilities. But the simple first-order delta-sigma modulator described here doesn’t offer enough noise shaping to allow for high-resolution results. Thus, IC manufacturers include from second- to fifth-order modulators that increase a converter’s signal-to-noise ratio. The TI ADS1282 noted earlier provides a fourth-order modulator. For more on modulators, go to http://designnews.hotims.com/22267-524.
Because a delta-sigma ADC oversamples at a high rate, the frequency of its Nyquist limit increases, too. This means the converter can often use an inexpensive and simple R-C anti-alias filter to remove high-frequency signal components.
Useful Links
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Find an excellent non-math introduction to delta-sigma converters: http://designnews.hotims.com/22267-525
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“An Overview of Sigma-Delta Converters:” http://designnews.hotims.com/22267-526
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“Are ΣΔ ADCs Greek to You?” http://designnews.hotims.com/22267-527
