Are ADCs repeatable? In other words, will it always convert to the same digital number given the exact same voltage?
Short answer, no. There is always the possibility of thermal influence on the output. Any variation in reference voltage will be reflected in the output. Obviously manufacturers seek to minimize such, but with varying degrees of success.
Looking at a 24-bit 20kHz TI ADC I see:
Gain sensitivity to Vref 1:1
PSRR 70-80dB
Either of these mean the possibility of variation in the output code/input voltage.
its quite hard to make 24 bit dynamic range analog electronics in the full audio bandwidth
Johnson/thermal and Shot noise are physical limitations that the best circuitry can only approach asymptotically with lower impedance, higher circuit power dissipation
no monolithic ADC manages 24 bit/144 dB S/N in its analog internal electronics over audio bandwidths
some DC/low frequency measurement chips do manage better than 20 bits in restricted 10 Hz bandwidths
but best in class audio ADC today can do a good job to better than 100 dB dynamic range by all relevant measures of ENOB, SFDR, THD, and flat audio bandwidth noise
but its hard to find any that do all measures of resolution/accuracy to as good as 120 dB
Johnson/thermal and Shot noise are physical limitations that the best circuitry can only approach asymptotically with lower impedance, higher circuit power dissipation
no monolithic ADC manages 24 bit/144 dB S/N in its analog internal electronics over audio bandwidths
some DC/low frequency measurement chips do manage better than 20 bits in restricted 10 Hz bandwidths
but best in class audio ADC today can do a good job to better than 100 dB dynamic range by all relevant measures of ENOB, SFDR, THD, and flat audio bandwidth noise
but its hard to find any that do all measures of resolution/accuracy to as good as 120 dB
DC has some different concerns - offset V, thermal and aging drift of passives, op amps, Vrefs and ADC DC specs
and upper bandwidth makes a difference too
audio ADC aren't designed, speced for DC performance - you need to look at "industrial" ADC
but obviously it is possible for slow measurements - just look at benchtop 6 digit multimeters such as Agilent or Keithley
https://www.google.com/#q=6+1/2+digit+multimeters
you do have some work to do to become informed and probably need several prototyping iterations to "onion peel" all the issues if you really want to design and build your own, even starting with a ADC chip with good DC specifications
and upper bandwidth makes a difference too
audio ADC aren't designed, speced for DC performance - you need to look at "industrial" ADC
but obviously it is possible for slow measurements - just look at benchtop 6 digit multimeters such as Agilent or Keithley
https://www.google.com/#q=6+1/2+digit+multimeters
you do have some work to do to become informed and probably need several prototyping iterations to "onion peel" all the issues if you really want to design and build your own, even starting with a ADC chip with good DC specifications
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