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# Which LSB unit is chosen for DNL/INL measurements? Ideal or measured LSB?

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#### dirac16

##### Member level 5
The DNL/INL measurement in the following exemplary 3b ADC shows different results depending on which LSB unit is chosen. For the case of the Actual_LSB unit we get DNL=0 and INL=0 for all codes. This tells me that the actual TF has no linearity errors! However, for the case of the Ideal_LSB unit the DNL and INL take on non-zero values, where DNL[k]=-0.75 Ideal_LSB and INL[k]=-(k-1)*0.75 Ideal_LSB for k=1,2,...,6. Though DNL is greater than -1 Ideal_LSB and apparently causes no missing codes, the INL grows up as a function of the code in this particular example. This tells me that the actual TF is very nonlinear! So which DNL/INL measurement is actually correct?

Solution
Actual TF is linear only when input is less than Vfs/2, however you are loosing on your max SNR by 6dB as the full scale has reduced to Vfs/2. Linearity does mean that you will not see any harmonic sticking out of the noise floor against expectation. But you do see the noise floor itself raised compared to the ideal TF, with respect to the signal tone. All the above arguments are true if you assume that the input signal is not crossing the new full scale (i.e Vfs/2).

But, an important thing to note is that, if the input tone crosses Vfs/2, then the output code is always at full scale output code. This is a huge non-linearity and you see huge third/fifth harmonic sticking out killing your SNR further.
--- Updated ---

Hi,

DNL...

#### KlausST

##### Super Moderator
Staff member
Hi,

My opinion:
--> Use the actual LSB value.
So for code_independet unlinearities (not influenced by digital code pattern) you get the same DNL/INL value for both cases.
E.g. DNL of 0.8LSB

Klaus

#### dirac16

##### Member level 5
Hi,

My opinion:
--> Use the actual LSB value.
So for code_independet unlinearities (not influenced by digital code pattern) you get the same DNL/INL value for both cases.
E.g. DNL of 0.8LSB

Klaus
Hi, I think I didn't get your answer. If the actual LSB value is chosen then it does not give me any indication of the converter's errors such as gain error. Only a perfect converter has zero DNL and INL values. The actual TF shown above clearly does not resemble a perfect converter.

#### KlausST

##### Super Moderator
Staff member
Hi,

DNL and INL tell you - as the names say - nonlinearity errors.
Neither gain error means nonlinearity, nor offset means nonlinearity.

If you have perfect equal step size (does not matter what size), DNL as well as INL should be zero.

Klaus

#### Dominik Przyborowski

All answers can you find in standards, for ADC it is IEEE Std 1241.
To calculate nonlinearity you should use end point method.

#### dirac16

##### Member level 5
Hi,

DNL and INL tell you - as the names say - nonlinearity errors.
Neither gain error means nonlinearity, nor offset means nonlinearity.

If you have perfect equal step size (does not matter what size), DNL as well as INL should be zero.

Klaus
I got it! Thanks so much for further clarification.
--- Updated ---

All answers can you find in standards, for ADC it is IEEE Std 1241.
To calculate nonlinearity you should use end point method.
It is a very interesting read. Thank you for sharing! I must give it a read.

#### KlausST

##### Super Moderator
Staff member
Hi,

@Domink.

I don't have the standard by hand.
If you have, can you please correct if my estimation is wrong.

Klaus

#### AMS012

##### Full Member level 4
Actual TF is linear only when input is less than Vfs/2, however you are loosing on your max SNR by 6dB as the full scale has reduced to Vfs/2. Linearity does mean that you will not see any harmonic sticking out of the noise floor against expectation. But you do see the noise floor itself raised compared to the ideal TF, with respect to the signal tone. All the above arguments are true if you assume that the input signal is not crossing the new full scale (i.e Vfs/2).

But, an important thing to note is that, if the input tone crosses Vfs/2, then the output code is always at full scale output code. This is a huge non-linearity and you see huge third/fifth harmonic sticking out killing your SNR further.
--- Updated ---

Hi,

DNL and INL tell you - as the names say - nonlinearity errors.
Neither gain error means nonlinearity, nor offset means nonlinearity.

If you have perfect equal step size (does not matter what size), DNL as well as INL should be zero.

Klaus
DNL and INL can look like gain/offset error depending on the absolute values of them.

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