# Integral nonlinearity

Integral nonlinearity (acronym INL) is the maximum deviation between the ideal output of a DAC and the actual output level (after offset and gain errors have been removed). The term is often used as an important specification for measuring error in a digital-to-analog converter (DAC).

The transfer function of a DAC should ideally be a line and the INL measurement depends on the ideal line selected. Two often used lines are the best fit line, which is the line that minimizes the INL result and the endpoint line which is a line that passes through the points on the transfer function corresponding to the lowest and highest input code. In all cases, the INL is the maximum distance between the ideal line selected and the actual transfer function.

## Formula

For the line through the endpoints, the INL of a DAC is

$\mathrm{INL} = \max_{0 \le c \le c_{\max}} \left| V_{\mathrm{out}}[c] - V_{\mathrm{out}}[0] - c \cdot m \right|$

where

$m = \frac{V_{\mathrm{out}}[c_{\max}] - V_{\mathrm{out}}[0]}{c_{\max}}$

is the slope of the line through the end points, and

$V_{\mathrm{out}}[c]$

is the output voltage at code c. This assumes that the minimum code is 0. This INL is measured in volts; one can divide it by the ideal LSB voltage to get the measurement in LSBs..