Finally … managed to pull together esotheric mathematics related to data converters gathered over 18 years and different places around the globe into something that – to me at least – feels coherent.

The output spectrum of a finite resolution DAC including arbitrary DNL profile is expressed as a sum over all DAC output levels. The result is exact, allowing excel based fast numerical evaluation, short-ciruiting the normal route of time domain computation followed by Fourier transformation. It even contains a “Master formula,” an equation so compact and rich in consequences, encoding a connection between analog and digital, that it deserves that name. Enjoy!

The pdf file: DAC_finite_resolution_spectrum_v23

As an experiment, I add here the excel file that was used to compute the numbers and create the plots for the numerical examples in the paper: dac_spectrum_v13_8bit_64bins