Differential non-linearity

Representation of the differential non-linearity in an ADC

Differential non-linearity , DNL for short , is a characteristic value of analog-to-digital converters (ADC) or digital-to-analog converters (DAC) in electronic devices .

Typically, the desired transfer function is as linear as possible, in the case of a DAC a series of points on a straight line, in the case of an ADC a staircase with a constant width of the steps. The desired grid dimension is denoted by. With real converters, the distances are only approximately constant. ${\displaystyle U_{\text{LSB}}}$

The differential non-linearity of a DAC can be calculated by the following equation:

${\displaystyle DNL_{n}={\frac {U_{n+1}-U_{n}}{U_{\text{LSB}}}}-1}$

Successive codes are numbered in it . The transfer function is monotonic if none occurs. A lack of monotony can become problematic in control loops because negative feedback can become positive. ${\displaystyle n}$ ${\displaystyle DNL_{n}<-1}$

ADCs can also be non-monotonic (decreasing code with increasing analog value). In this case, 1 must be added in the above formula instead of subtracted. However, the phenomenon of missing codes is more common with ADCs: Despite a slow increase at the input, the code increases by more than 1. The DNL at such a point has a jump height of -1.

The DNL of the converter is usually given as the maximum of over all transitions, with the gain error already balanced or taken into account in the value of . ${\displaystyle DNL_{n}}$ ${\displaystyle U_{\text{LSB}}}$

Web links

• Article at elektronikpraxis (accessed: May 6, 2009)
• Article in Maxim (accessed March 28, 2012)

See also

• Non-linearity
• Integral non-linearity