# INL and DNL error measurement for DeltaSigma ADC

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#### engrMunna

Hi,
I have searched alot but I couldn't find INL and DNL measurement related to Sigma-Delta ADCs. In normal ADC u can plot the digital output vs the analog input and calcualte INL and DNL, but in Sigma Delta Converters, even for a static input the digital input is not constant as it keeps changes between different levels so that the avrgae value of the digital output equal the analog input, and not the instantaneous digital value. In this case how to measure INL and DNL when you dont have a constant digital output for a static input???

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engrMunna

### engrMunna

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#### JoannesPaulus

A sigma-delta ADC is a dynamic chaotic system therefore the DNL/INL do not make much physical sense since they do not represent the static transfer function of the ADC. Of course you can use the histogram method, as suggested by erikl, for comparison with other ADCs but it won't have much meaning.

#### engrMunna

Thanks @erikl I did not know about the histogram method. It helped me alot! thanks again!

@JoannesPaulus Yes I also read somewhere that inl and dnl dont make much sense for delta sigma adc's. If I understood your reasons correctly is it because there is no concept of "instantaneous digital output" of sig-del adc rather its is the average of the digital values over time which correspond to the average of the analog input over time?

#### FvM

##### Super Moderator
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I don't agree to the see SD- and conventional ADC that opposite. A conventional high speed ADC will show output noise as well, even the signal source does, so you need to refer to averaging/statistical methods. The chaotic (but not purely random) noise generated by a SD will be reduces to an acceptable level with appropriate decimation filters, so you can apply classical measures like INL/DNL, and SD datasheets usually do. Frequency domain quantities like spurious free dynamic range should supplement it.

#### JoannesPaulus

Yes I also read somewhere that inl and dnl dont make much sense for delta sigma adc's. If I understood your reasons correctly is it because there is no concept of "instantaneous digital output" of sig-del adc rather its is the average of the digital values over time which correspond to the average of the analog input over time?
Yes and no. The simplest way to see the difference is using a DC input. The Nyquist ADC will output one digital value (provided the device and input noises are less than 0.5LSB). The SD ADC will output two values, due to the fact that the SD loop will try to stay around the signal. No static behavior can be observed and therefore the DNL/INL curves are not meaningful (this is of course my view of this performance measure, there is no clear explanation in literature that I am aware of).

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I don't agree to the see SD- and conventional ADC that opposite. A conventional high speed ADC will show output noise as well, even the signal source does, so you need to refer to averaging/statistical methods. The chaotic (but not purely random) noise generated by a SD will be reduces to an acceptable level with appropriate decimation filters, so you can apply classical measures like INL/DNL, and SD datasheets usually do. Frequency domain quantities like spurious free dynamic range should supplement it.
As I understand it, a large number of samples is used to find the thresholds where the digital output will switch from code n to code n+1 when the analog input increases (I am not sure this corresponds to averaging). The DNL is then calculated as the difference of these thresholds to the ideal thresholds, using your preferred methods (the INL is the cumulative sum of these differences). This will repeat always exactly the same in a Nyquist ADC.
In a SD ADC the DNL/INL might vary slightly with each experiment.

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