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# Problem with defining DNL of Nyquist ADC

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#### neoflash

There is statement saying:

If DNL > 1LSB, there must be a missing code.

Why it is true? How many different definitions does DNL have?

If you apply one positive going ramp and check:

{code(i)-code(i+1)} in terms of lsb. then it should increase by 1-lsb. so, if you substruct 1-lsb from it then you get zero. it makes DNL(i)=0.

All definition has the same meaning, only diferent in approach.

for missing code(from positive ramp); if DNL<-1lsb.
then only you will miss your code.

DNL < -1LSB should not imply missing code.

I think they do not have direct relationship. If bit (i) DNL is -1.5dB, bit (i+1) DNL is 1dB, bit (i+2) DNL is 0.5dB, then the total INL induced is zero and there is no missing code. Code (i+1), (i+2) is still there.

DNL is not defined in dB.!!!.

sorry, should be LSB, typo...

The DNL it is the normalized deviation of the difference between two consecutive code transition levels, with respect to the ideal value, VLSB:
DNL(i)=(Vt[i+1]-Vt-VLSB)/VLSB=(Vt[i+1]-Vt)/VLSB-1
where Vt is the input voltage where the transition from code i-1 to i occurs.

Thus, when DNL=-1, we have Vt[i+1]=Vt, which means that code i does not exist -> missing code.

So, Shaber_Mezbah is right.

Rgds

### neoflash

Points: 2

DNL < -1LSB does not mean that a code is missing. But it implies that the converter is not monotonic. Which may be a serious matter in closed loop applications such as regulation.

ADC DNL shoud not be less than -1LSB

Hi,
In my view the definition is correct....although it is not the actual definition...but the definition implies this....you can go thru the folloing post ....a very good book...and hopefully convince on the matter....

sankudey

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