# How to design anti-aliasing filter for a non-ideal oversampled SAR

If we want to go by text-book anti-aliasing filter design for an ADC, we would have $$\A(f_{samp}/2)\ge-20*log(2)*N\$$ dB attenuation at the Nyquist frequency, where $$\A(f)\$$ is the magnitude vs frequency function, $$\f_{samp}\$$ is the sampling frequency, and N is the ADC's resolution. For example, if a 12 bit ADC is sampling at 100kHz, we should have $$\-12*6.02dB\$$ attenuation at 50kHz to avoid any aliasing effects.

However, what happens when we're dealing with non-ideal ADCs and the ENOB is actually 10 bit? Can we reduce the attenuation requirements to $$\-10*6.02dB\$$? What happens, if we're oversampling the signal to introduce 4extra bits and sample at 25.6MHz? Would we need to have stronger attenuation to $$\-14*6.02dB\$$? Would this extra 4 bits be added to the ENOB or the ideal resolution of the ADC?

• The filter requirements are not based on the ADC properties but what you need in the application. And if you oversample by N, the ADC sampling rate is also N times higher, so filter requirements go down respectively. You then have to digitally filter and downsample by N to end up with your non-oversampled digital signal. Commented Dec 29, 2022 at 15:06
• @Justme Yes, I understand that but this is a generic question from the perspective of the ADC. Here I assume that the input BW is infinite and my BW of interest is <50kHz out of this spectrum. Commented Dec 29, 2022 at 15:10

However, what happens when we're dealing with non-ideal ADCs and the ENOB is actually 10 bit? Can we reduce the attenuation requirements to −10∗6.02dB?

Yes you can. All the AA filter does is try to get the aliasing below the noise floor. If your ENOB is 10 bits then your noise floor is 60 dB so that's all you need.

What happens, if we're oversampling the signal to introduce 4extra bits and sample at 25.6MHz? Would we need to have stronger attenuation to −14∗6.02dB?

Yes, but 14 bits attenuation at the oversampled frequency is actually a much simpler filter than 10 bits at the original sampling rate. So rather than stronger attenuation most people would refer to that as a cheaper filter.

In fact one of the main uses of oversampling is to avoid the need to design expensive anti-alias filters. For highly oversampled systems, often the AA filter is a simple capacitor.

Would this extra 4 bits be added to the ENOB or the ideal resolution of the ADC?

You seem really hung up on ENOB which is just a convenient unit for SNR. Remembering that 1 bit is equal to 6dB of SNR, perhaps it would be more clear if you converted to dB. If you average enough measurements that you increase your SNR by 24 dB (6 dB times 4), then you have simply increased your SNR by that amount, but you haven't changed anything about the ADC.