Differential Nonlinearity: What happens when DNL = -1LSB

[Peter Alexander]

Homework Statement

Question is simple: what happens when $DNL = -1 LSB$ where DNL signifies differential nonlinearity and LSB stands for Least Significant Bit. It is also required to try and sketch such condition.

Homework Equations

Equation for differential nonlinearity: $$DNL(i) = \frac{V_{out}(i) - V_{out}(i - 1)}{\text{ideal LSB step width}} - 1$$

The Attempt at a Solution

I understand what DNL is, is represent a deviation between two analog values corresponding to adjacent input digital values (from Wikipedia). Ideally, two sequential digital codes should belong to analog values that are 1LSB apart, so the deviation from such step is called DNL.

At $DNL \leq -1LSB$, missing codes appear in the transfer function. Those are binary representations that have no such analog signal to cause them.

I am having troubles visualizing such case. What are the conditions that have to be met in order for this to occur? Is such case an example of bad analog-digital converter, or is it something that can happen to properly functional instruments as well?

 

[.Scott]

Are you dealing with an ADC or a DAC? You seem to be mixing them.

Missing codes occur with ADC devices - not DAC devices. You are always allowed to enter any code into a DAC.
But if the DNL(i) is less than -1, what does that mean when you step from input code i-1 to i as input to your DAC?
You would normally want the DAC output to be monotonic as the digital input is stepped from 0 to $2^n-1$.

If the device is spec'd for DNL > -1, then this would be a bad part.

Looking at your post again, I am suspecting that you were suppose to be looking at an ADC, but dug up a DAC wiki article instead. Isn't that the problem?