I am trying to determine DC errors for ADC128S102QML-SP. More specifically, I am referring to the gain error, offset error, INL error, and DNL error. It is a 12 bit ADC with a supply voltage of 5V.

From the datasheet, I concluded the following:

1. Offset error is 2.3 LSB which I believe translates to an error of $$\left( \frac{2.3}{2^{12}} \right) \cdot 5 = 2.81mV.$$

2. INL is 1.4 LSB which I believe translates to an error of $$\left( \frac{1.4}{2^{12}} \right) \cdot 5 = 1.71mV.$$

3. DNL is 1.5 LSB which I believe translates to an error of $$\left( \frac{1.5}{2^{12}} \right) \cdot 5 = 1.83mV.$$

Does the above calculations make sense? Also, how I can calculate the gain error?

Given the standard definition of LSB as:

$$\text{LSB} = \frac{\text{FSR}}{2^N}$$

In this case:

\begin{aligned} \text{LSB} &= \frac{5\ \text{V}}{2^{12}}\\ \text{LSB} &= 0.0012207\ \text{V}\\ \text{LSB} &= 1.22\ \text{mV} \end{aligned}

So, yes, your calculations all look correct to me.

Regarding the calculation of "gain error", the linked datasheet contains a definition:

GAIN ERROR is the deviation of the last code transition (111...110) to (111...111) from the ideal (VREF - 1.5 LSB), after adjusting for offset error.

This is the standard definition. Gain error is the amount of deviation between the midpoint of the last step of the ideal ADC transfer (LSB) from the midpoint of the last step of the actual ADC transfer (LSB), after compensation for offset error.

The implication of this definition of gain error is the following:

• If saturation occurs before the input voltage reaches the maximum, then there is a positive gain error.
• Conversely, if the ADC fails to measure a full-scale value when the input voltage reaches the maximum, then there is a negative gain error.

So, you can think of gain error simply as the full-scale error minus the offset error.

The full-scale error (FSE) is defined in the datasheet as being a maximum of 2 LSB at 5 V. Since you also have the offset error defined as being a maximum of 2.3 LSB at 5 V, you can conclude that the gain error will be a maximum of 0.3 LSB at 5 V, which is equivalent to about 0.37 mV.