Delta-sigma ADCs in a nutshell, part 3: the digital/decimator filter

-February 21, 2008

Following the modulator in the delta-sigma ADC is a digital/decimator circuit. This circuit samples and filters the modulator stream of 1-bit codes. At the modulator output, high-frequency noise and high-speed sample rates are problems. However, because the signal now resides in the digital domain, you can apply a digital-filter function to attenuate the noise and a decimator function to slow the output data rate. Designers often intertwine the digital filter and decimator functions in the same silicon.

Figure 1 shows the signal as it travels through the digital/decimator-filter functions. The digital-filter function operates at the same rate as the modulator sampling rate (Figure 1a). Notice that the 24-bit code-train resembles the original signal (reference 1 and reference 2). In the time domain, it looks like the digital-filter function is responsible for the low noise and high resolution of the delta-sigma converter. However, this function provides a second-order impact on the system noise by rejecting higher frequency noise, where the noise shaping from the modulator dominates noise reduction in the lower frequency band (Figure 1b).

Read all of Bonnie Baker's Baker's Best columns.

The digital-filter function provides a digital version of the input, but the data rate is still too fast to be useful. Although it might appear that you have an abundance of high-quality, multibit samples at a high sampling rate, you don’t need most of this data.

The second function of the digital/decimator filter is the decimator. Decimation is the process of reducing a digital signal’s output rate to the system’s Nyquist frequency. One simple way to implement a decimating function is to average together groups of 24-bit codes (Figure 1c). The decimator accumulates these high-resolution data words, averages several words together, outputs the average results, and dumps the data for the next average. A more economical way to implement a low-power decimator function is to simply pick out a 24-bit word every Kth sample without performing additional averaging. (K is equal to the oversampling or decimation ratio.)

Almost all delta-sigma converters incorporate a class of averaging filters called sinc or FIR filters, named for their frequency response. Many delta-sigma devices use other filters with sinc filters for two-stage decimation. Low-speed industrial delta-sigma ADCs usually use only a sinc filter.

In the frequency domain, you can see that this digital/decimator filter simply applies a lowpass filter to the signal (Figure 1b). In so doing, the digital/decimator filter has attenuated the higher frequency-modulator quantization noise. With the reduced quantization noise, the signal re-emerges in the time domain.

  1. Baker, Bonnie, “Delta-sigma ADCs in a nutshell,” EDN, Dec 14, 2007, pg 22.

  2. Baker, Bonnie, “Delta-sigma ADCs in a nutshell, part 2: the modulator,” EDN, Jan 24, 2008, pg 24.

  3. Baker, R Jacob, CMOS Mixed-Signal Circuit Design, J Wiley & Sons, ISBN 0471227544.

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