Linearity of a DAC

The bit depth (16 or 24) of a DAC is a nominal value.
It is not a performance metric.
All it says is that the DAC accepts samples with a 16 or a 24 bit word.
Not to be mistaken for being able to resolve this sample to the last bit.

 

Assuming the output is ± 2V max then the range is 4V
16 bits =  65536 discrete steps
4/65536=0.00006104V
24 bits = 16777216 discrete steps
4/16777216 = 0.00000024 V

Even at 16 bits the step is very small indeed.

 

A perfect DAC would have no linearity error.

As you can see in the graph, this DAC tested starts to deviate at -70 dBFS.
As 70/6=11.6 this DAC is more or less able to reproduce 12 of the 16 bits perfect.

Often a margin of ±2 dB is used.
Using this margin this DAC can resolve 13 bits. As CD audio is 16 you will miss 3.

 

 

At ±2 dB this DAC resolves 19 bits.

The first dip is just slightly less  then – 2dB. At this point this DAC can resolve 22 bits.
At -145 the +2 dB is transgressed. At this point this DAC can resolve 24 bits.

 

Obvious DACs do differ in their ability to resolve the bits. The simple ones can’t resolve CD quality.
Obvious at $150, $1000 and $4000 they also differ in price tag.

DAC parameters - HITEQUEST (2002)