# Definition of ENOB, SNDR for sigma-delta ADC

The general definition of each are the following:

$$\ENOB=\frac{SNDR_{max}-1.76}{6.02}\$$

Where

$$\SNDR_{max}=10 \log{\frac{S_{s,max}}{S_n}}\$$

And

$$\S_{s,max}\$$ : maximum signal power

$$\S_n\$$ : noise and harmonics power

In the context of a sigma-delta ADC, $$\S_n\$$ is easily found by integrating the PSD from 0 to half of the sampling frequency ( $$\f_s/2\$$ ). What I want to know is if $$\S_{s,max}\$$ is the power of the sinus with maximum amplitude that can be processed by the sigma-delta ADC or the power of a hypothetical sine with an amplitude equating the rail voltage. There is a big difference because in these ADCs, for stability reasons a margin should be left. For instance in a second order sigma-delta ADC, the maximum signal amplitude should not exceed 80-90% of the full scale.

The general meaning would be for a hypothetical signal with an amplitude equating the rails voltage. This works for any Nyquist rate ADC but for a sigma-delta ADC that would mean that SNDR and ENOB are actually not measurable since the circuit would become unstable (or marginally stable).

Anyone can give me his opinion? Maybe with a reference. Thanks!