The delta-sigma advantage to anti-aliasing filters


My last post introduced the concept of signal aliasing and how it manifests itself in data-acquisition systems. When out-of-band signals alias into the passband, they overlap lower frequency content and mask the true signals you’re trying to measure. To help filter any signals beyond the bandwidth of interest, you can add an anti-aliasing filter just before the inputs of your analog-to-digital converter (ADC).

Designing an anti-aliasing filter can be challenging and costly depending on the filter response your application needs. In this post, I’ll highlight two distinguishing features in delta-sigma ADCs that relax the requirements on your anti-aliasing filter and simplify the design. 

Figure 1: Anti-aliasing filters can kick back and relax in front of delta-sigma ADCs

ADC Architecture: SAR vs. delta-sigma ADCs

We now know that an ADC must sample the input signal slightly faster than the Nyquist rate to properly represent it in the digital domain. Before you begin designing your anti-aliasing filter, you must first understand the architecture of the ADC that it’s used for. This will dictate how close to the Nyquist rate your ADC will convert and therefore the response your filter needs.

Successive approximation register (SAR) ADCs sample the input at a frequency, fS, that is typically just beyond the required Nyquist rate. Frequency signal content begins to repeat at the Nyquist frequency (fS/2), so, to be effective, a SAR ADC’s anti-aliasing filter must have a sharp, high-order roll-off just before the Nyquist frequency to prevent any signals from aliasing. Creating this kind of response often requires using operational amplifiers as active filters, perhaps in multiple stages, which can be very challenging and expensive to design.

Oversampling data converters like delta-sigma ADCs sample the input much faster than the Nyquist theorem requires. Not only does oversampling push the delta-sigma ADC’s quantization noise away from the bandwidth of interest, it also moves the Nyquist frequency further away and allows for a more gradual anti-aliasing filter roll-off.

Figure 2 below illustrates the difference in the anti-aliasing filter response needed for a SAR ADC (Figure 2a) versus a delta-sigma ADC (Figure 2b). 

                       Figure 2a: Anti-aliasing filter response for SAR ADCs                                              Figure 2b: Anti-aliasing filter response for delta-sigma ADCs

 

Digital decimating filter

What really sets the delta-sigma ADC apart, however, is the digital decimating filter. In delta-sigma ADCs, the input sampling rate is not the same as the output data rate! As the delta-sigma ADC’s modulator (over)samples the input at the frequency, fMOD, the data is decimated and passed through a digital filter before being output at a much slower data rate, fDR. The ratio of fMOD to fDR is known as the oversampling ratio (OSR). The higher the OSR, the more separation between fMOD and the passband. Many of TI’s delta-sigma ADCs allow you great flexibility in choosing an OSR that meets your application needs. For example, in the ADS1262, you can set the OSR as low as 24 or as high as 368,640!  

The passband of the digital filter ends around fDR/2 or earlier depending on the filter’s frequency response. In between the passband and fMOD is a lot of unwanted signal content that could alias into the passband, such as the quantization noise from the modulator. This is where the digital filter really shines. The stopband of the digital filter provides significant attenuation from fDR/2 all the way until fMOD where the filter response repeats.

With the digital filter in place, the requirements placed on the anti-aliasing filter become even more relaxed! Instead of needing to filter everything beyond the Nyquist frequency as in SAR ADCs, the anti-aliasing filter for delta-sigma ADCs only needs filter out unwanted frequency content around multiples of fMOD.  This allows for an even more gradual filter roll-off that is much easier to design with a few discrete, passive components. Typically, a single-pole RC filter is all that is required, but you may need a second-order filter for lower OSRs.

Figure 3 shows the filter response for a third-order sinc filter. As you can see, the digital filter is supplemented by the anti-aliasing filter to achieve an overall response with low in-band noise and very little signal aliasing.

 

Figure 3: Combined responses of anti-aliasing and digital filters

In next month’s post, I’ll introduce several key guidelines to help you design the anti-aliasing filter that’s right for your application.

Additional resources

 

  • Dear Ryan Andrews :

           Your blogs are so detailed that I have learned a lot about the anti-aliasing filter for delta-segma ADCs!

           I have a question about that since the digital filter could not attenuate the nosie around the sampling rate of ADCs,as fMOD,so the front-end anti-aliasing filter is necessary!Thus, the anti-aliasing filter is at the front of ADCs,and the quantizing noise is produced by modulation of ADCs after the filter,so my question is how the front filter to attenuate nosie produced later?

  • Hello user4372489,

    Thanks for your question! I'm glad the blogs are useful to you. :)

    The quantization noise produced by the delta-sigma modulator is mostly filtered by the digital filter, not the analog antialiasing filter at the inputs. As you can see in Figure 3, the quantization noise is shaped until fMOD/2, where it reaches its peak magnitude. This falls directly in the stopband of the digital filter and becomes heavily attenuated.

    Best Regards,

    Ryan

  • Hey Ryan,

    Thanks for the blog post! I have been reading several e2e forum posts and blog articles that you have wrote besides another literatures about anti-aliasing filter design for delta-sigma ADC's. But I still in doubt about how much attenuation my anti-aliasing filter must provide and where. For example, in traditional SAR ADC's the AA filter must provide, theoretically at least, 6.02*N + 1.76 dB of attenuation in Fsample/2 in order to reduce out-of-band noise at quantization noise level order, or below noise floor. But I don't know how to determine mathematically how much attenuation my anti-aliasing filter must provide and in which frequency this attenuation must be. I have read several times that oversampling delta-sigma ADC's relaxes the requirements of AA filter, but I never found a consistent guideline in order to calculate AA filter parameters so that I can design a AA filter using Butterworth or another filter approximation. In most literatures, the information is that a simple RC passive filter is enough, just it. Can you help-me?

  • Hi Otavio,

    Thanks for reading!

    How much attenuation your antialiasing filter (AAF) should provide really depends on your application. I think the theoretical target you mentioned holds true for any ADC architecture - that is, your AAF should attenuate the noise seen after the first Nyquist frequency to a level which is insignficant when compared to the ADC's inherent quantization and thermal noise. For a SAR, this attenuation level must be reached very close to Nyquist. However, for a delta-sigma ADC, this attenuation is really necessary closer to the modulator sampling frequency (fMOD). Between the data rate Nyquist frequency (fDATA / 2) and fMOD, the digital filter stopband will suppress most of the out-of-band noise.

    The signal bandwidth of interest determines the passband that you need for your filters (AAF and digital). The difference in frequency between the signal bandwidth and the aliasing band determines the type of AAF and the response you need. Ideally, your AAF and digital filter should remain relatively flat throughout your bandwidth of interest. For low-speed applications where the bandwidth is only a few hundred hertz, a first- or second-order RC filter may be enough since the modulator of the ADC is often running at frequencies greater than hundreds of kilohertz. Conversely, a high-speed application with hundreds of kilohertz of signal bandwidth may need a high-order active filter to reach the attenuation target before a modulator frequency of a few megahertz.

    I don't know of any new filter design tools out there, but we used to promote this FilterPro Webench tool (see link below). This may help you as a starting point for active filter design.

    Best Regards,

    Ryan