What does an ADC DNL specification mean, exactly?

Question

I'm looking at the differential non-linearity specification for an Analog-Digital converter. The spec sheet claims that the DNL ranges from -1LSB to +1LSB, with a typical value of $\pm$0.6LSB. What exactly does that mean? Is this some value that's taken statistically? Does this mean the 3$\sigma$ value is 0.6LSB? I.E., for any given code, the range of voltages over which it has jurisdiction is 99.7% likely to be no greater than 1.6LSB or less than 0.4LSB?

Suppose I wanted to model a 16-bit ADC with these specifications. How would I go about injecting DNL into the output codes? The spec sheet is completely unclear as to what 0.6LSB means. Is there some statistical convention? Or would it just be some random number which caps at $\pm$1LSB for every single code?

Answer 1

Differential non-linearity specifically is the deviation from ideal between successive bits. For an ADC, the ideal would be the converted signal will not transition to another bit value until the input deviates by 1 bit. If the DNL is greater than 1 bit, non-monotonic behavior could result (an linearly increasing input could result in some transitions actually going down).

If the spec claims ±1 bit, this is a absolute maximum limit and is therefore guaranteeing monotonic behaviour. The "typical" limits are not so stringent in what that means and you would need to ask the manufacturer directly, but in essence it is what you could typically expect, on average (so therefore could be the the mean of the absolute value of the deviation).

Similar to if I said I had a 9V battery that had a spec of +/-0.5V and provided 9V typical. The average is 9V, the peak limit that the manufacturer will guarantee is 8.5V to 9.5V; now as far as the statistics that is completely up to them in balancing yield at final test in what they will ship.

If I was to model this, I was first tempted to generate a Gaussian random sequence with a standard deviation of $\sigma = (0.6) 4/\pi$ and clamp it at $\pm 1$ since the mean of the absolute value of a Gaussian R.V. Is $(4/\pi)\sigma$... but the clamping reduces the mean, so increasing that to $\sigma = (0.7) 4/\pi$ results in a random (clamped Gaussian) distribution that never exceeds ±1 but also has an average magnitude (therefore typical) of 0.6.