SQNR vs SNDR (with regards to Delta Sigma Modulation)

Question

With regard to delta-sigma modulation, I understand that SQNR is the ratio of the signal power within our frequency bandwidth to the noise power within our bandwidth (in-band quantization noise). What I don't understand is how this is functionally different from SNDR (signal-to-noise distortion ratio). Is there even a difference or is this just a terminology quirk?

Answer 1

The difference is SNQR is the SNR due to quantization noise alone as a theoretical limit while SNDR (also referred to as SINAD) includes multiple distortion sources in addition to quantization. SINAD typically includes all distortion sources including harmonic distortion but excludes DC offsets.

For example, for a standard ADC without noise shaping, the SNQR is given by the well known expression:

$$SNQR = 6.02 \text{ dB/bit} + 1.76 \text{ dB}$$

Please see this other post where I explain how this formula is derived. This formula is then used again with $SNDR$ replacing $SNQR$ to come up with the Effective Number of Bits or ENOB:

$$ENOB = \frac{SNDR-1.76 \text{ dB}}{6.02 \text{ dB}}$$

So when we use $SNQR$ we are referring to the actual number of bits in the converter, and determining the theoretical noise due to quantization alone, while with $SNDR$ and $ENOB$ we are including additional noise sources and equating that to the perfect ADC that would provide similar performance.