Define DNL (Differential Nonlinearity) and INL (Integral Nonlinearity) in ADCs.

Differential Nonlinearity (DNL):

Differential Nonlinearity refers to the deviation of the actual step size between consecutive digital output codes from the ideal step size of 1 LSB (Least Significant Bit). In other words, it measures the variation in the size of the digital output change that corresponds to a 1 LSB change in the analog input. Mathematically, DNL is calculated as the difference between the actual step size and 1 LSB, expressed in LSBs:

DNL = (Actual Step Size - Ideal Step Size) / LSB

A DNL value of 0 indicates perfect linearity, meaning that the ADC's output codes are changing exactly by 1 LSB as the input voltage changes. Positive DNL values indicate that the ADC is producing larger-than-expected output steps, while negative DNL values indicate smaller-than-expected steps.

Integral Nonlinearity (INL):

Integral Nonlinearity represents the cumulative deviation of the actual digital output codes from the ideal transfer function over the entire input range of the ADC. It quantifies the overall linearity error throughout the entire input range. Mathematically, INL is the sum of all DNL values up to a certain code point in the ADC's output range:

INL = Σ(DNL) for all codes

INL is typically expressed in LSBs or as a percentage of the full-scale range. An INL value of 0 indicates perfect linearity, while non-zero values indicate deviations from the ideal transfer function. INL considers the accumulated effect of DNL errors and is a more comprehensive measure of linearity compared to DNL alone.

Both DNL and INL are critical parameters for assessing the accuracy and quality of an ADC's output. A well-designed ADC should exhibit low DNL and INL values to ensure accurate conversion of analog signals into digital codes.