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IDNL/DNL characterization of the deviation for DAC

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FEM33

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Hello everyone,

For my internship I need to prove why at the midcode, the DNL is the maximum.
I'm designing a 10 bit DAC.
I need to express DNL and INL as a function of (sigmaI/I).
I_LSB = I_OUT_MAX/2^N -1
I found this on internet, maybe its true, but idk how to prove it
1686568332631.png


We need to start from the bottom with that equation :

DNL(k) =( (I(k) - I(k-1) )/I_LSB ) ) - 1

Thanks for all your answers :
 

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