Integral nonlinearity (acronym INL) is a commonly used measure of performance in

digital-to-analog In electronics, a digital-to-analog converter (DAC, D/A, D2A, or D-to-A) is a system that converts a digital signal into an analog signal. An analog-to-digital converter (ADC) performs the reverse function. There are several DAC archit ...

(DAC) and

analog-to-digital In electronics, an analog-to-digital converter (ADC, A/D, or A-to-D) is a system that converts an analog signal, such as a sound picked up by a microphone or light entering a digital camera, into a digital signal. An ADC may also provide ...

(ADC) converters. In DACs, it is a measure of the deviation between the ideal output value and the actual measured output value for a certain input code. In ADCs, it is the deviation between the ideal input threshold value and the measured threshold level of a certain output code. This measurement is performed after offset and gain errors have been compensated. The ideal transfer function of a DAC or ADC is a straight line. The INL measurement depends on what line is chosen as ideal. One common option is the line that connects the endpoints of the transfer function, in other words, the line connecting the smallest and largest measured input/output value. An alternative is to use a

best fit line In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is ca ...

, where one minimizes the average (or alternatively the mean squared) INL. While the INL can be measured for every possible input/output code, often only the maximal error is provided when reporting the INL of a converter.Johns, David A. and Martin, Ken. ''Analog Integrated Circuit Design'' (1997), Wiley. Page 456.

Formulas

INL of a DAC

The INL of a code

c

of a DAC with

N_c

output codes is defined as the absolute value of the difference of the real output voltage minus the ideal value: :

\mathrm_ = \left,  V_(c) - V_(c) \ = \left,  (V_ - V_)\frac - V_(c) \

where :

V_

and

V_

are the maximum and minimum ideal output voltages of the DAC.

INL of an ADC

For an ADC, the INL of a code

c

is defined as the deviation of the ''mid-points of the quantization steps'' between the ideal and real transfer function. :

\mathrm_ = \left,  V_(c) - V_(c) \

Maximum INL of a converter

When referring to the INL of a converter usually the maximum INL maximized over all codes is meant. For the line through the endpoints, the INL of a DAC is :

\mathrm_ = \max_ \mathrm_c

This INL is measured in volts; one can divide it by the ideal LSB voltage

V_

to get the measurement in LSBs: :

\mathrm_ = \frac

References

External links