# How to find the Nyquist-/sampling frequency of a Sigma-Delta-ADC

I'm looking at the datasheet of an Analog Devices ADC (AD7124-4) and can't understand what is the relevant sampling frequency to use as a basis for calculating the anti aliasing filter.

Is the relevant frequency the clock frequency of 614.4kHz? Is it the maximum data rate of 19.2 kHz? Or does it depend on the specific data rate I'm using?

• It looks like the top sampling rate is 19200 Sps and this should be the clock that is always used to do raw signal sampling. Thereafter the data is properly decimated/resampled. Mar 18 at 13:09

## 2 Answers

This Sigma Delta converter uses over-sampling to obtain the resolution then decimation to reduce the signal BW which is $$\f_{ADC} /2\$$ maximum Nyquist rate. It has a built in SINC filter to notch desired grid e-field noise from unbalanced signals.

## Analog and digital anti-aliasing

A typical choice might be 64x oversampling, in which case the ADC will sample at 64 x fADC kHz. Then the digital Nyquist frequency is 1/2 of that . However the Analog anti-aliasing filter still needs to have its -3 dB rolloff at fADC/2 , but it does not need to be -97 dB down until 32 x fADC. That is a much easier filter to design. In fact, a 3-pole filter, easily and cheaply implemented with an op amp, is sufficient.

So the answer is the fADC /2 Nyquist Rate is your 3rd order Analog Filter. This is how almost all SD ADC 's work with oversampling and decimation with simpler requirements for the Nyquist filter. (Some RF types use the above Nyquist BW as the passband like old GHz scopes with stable sub-nanosecond samples to achieve GHz BW in a lower sampling rate than the signal..)

Enabling certain sampling rates with Zero Latency On achieves twice the signal BW while using the built-in SINC filter creates a harmonic notch filter at 4x the SPS (sample per second) ADC net rate. Certain combinations allow for notches at 50,60 or both line frequencies.

Therefore when you specify your signal BW and noise BW attenuation requirements with Passband ripple and group delay flatness BW, you can choose any filter to meet these requirements.

e.g. if fADC = fCLK/(4 × 32 × FS[10:0]). and you want a Bessel flat group delay response to fADC /2 or /3 choose that and the order, n of the filter depends on the n x 6 dB/ octave rejection slope in your Bandstop noise rejection to prevent aliasing.

If you need more rejection above ADC/2 rate use Chebychev and decide on acceptable PB ripple. There are other variations of filters that compromise ripple and GD determined by your specs.

Consider 20 SPS as your fastest fADC if you want to reject 60Hz and enable Zero Latency.

Define your S/N input and output spectral requirements first include. GD flatness and ripple. (Before designing anything)

• Whoever votes -1 without comments is evil and ignorant. Mar 18 at 13:33
• No, it is not I and just to prove it I shall downvote and reverse that downvote. Currently on -1 and soon to be -2 then, when you acknowledge, it will return to -1. Mar 18 at 13:47
• Tada at -2..... However, you are not addressing the question as far as I can see. It likely comes down to the fact that it samples at 19200 then digitally filters and decimates to a much lower frequency but, that still means the nyquist frequency is 9600 Hz because the digital filter does the business rather than lamely ignoring samples. Mar 18 at 13:47
• Tada and now at -1. Mar 18 at 13:52
• So you are saying at ADC 20 samples per second you can pass noise up to 9600 Hz without aliasing? Mar 18 at 13:58

what is the relevant sampling frequency to use as a basis for calculating the anti aliasing filter. ... does it depend on the specific data rate I'm using?

Yes, it depends upon the specific data rate your are using. See for example this document.

The sampling rate to use for determining the cutoff frequency of your anti-aliasing filter is the rate at which your data is actually reported to other parts of your system.

Aliasing occurs (in the normal case) when a signal of higher frequency appears as a signal of lower frequency after it is digitized. Anti-aliasing filters are designed to remove signals of higher frequency before digitization takes place.

With non-Delta-Sigma ADCs, the anti-aliasing low-pass filter needs to have a sharp cut-off, to ensure that high frequency signals that might be aliased are sufficiently attenuated. However, Delta-Sigma ADCs use "over-sampling" and decimation, which attenuate signals between the Nyquist frequency $$\f_B\$$ and the oversampling frequency $$\f_S\$$. As a result, a low pass filter with cut-off frequency at $$\f_B\$$, need not have as steep a cut-off, because it's real work begins at the higher $$\f_S\$$ frequency.

• Digital sampling is still sampling. :) Mar 18 at 13:20
• The question is about anti-aliasing filter. The anti-aliasing filter needs to filter out frequencies that might be aliased. That depends only on the data that is actually processed, not the data that might be converted but ignored. Mar 18 at 13:23
• More than likely, the digital filter actually does the business on removing the higher frequency stuff so that decimating will work without causing aliasing of signals. In other words (and likely), you can assume any anti-alias filter will be OK at 9600 Hz irrespective of what the decimation is set to. Mar 18 at 13:54
• This document distinguishes $f_s$, the "over-sampling" rate (used by the delta-sigma ADC), and $f_B$, the effective Nyquist frequency, and suggests that the anti-aliasing filter should cut-off at $f_B$, see figure 4. The roll-off in a delta-sigma need not be as steep as for other types of ADC/filter combos, but the cut-off frequency is still the same, as far as I know. Willing to be shown wrong, however. Mar 18 at 14:09