Tags: ADC, education, INL, integral nonlinearity, theory
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There are three approaches, that can be found on websites and in books, to measure Integral Nonlinearity INL error.
The first approach defines INL as a difference between the transfer curve of an ADC and the ideal straight line of the ideal conversion [9] as is illustrated in Fig. 43. The red dots in this and following figures indicate middles of conversion steps.
Figure 43: INL of a 3bit ADC calculated in regards to the line representing the ideal conversion.
The second approach defines INL as a difference between the transfer curve of an ADC and the straight line that connects the middles of the first and last steps of an ADC transfer response [10]. This is illustrated in Fig. 44. The minimum value is now bigger, the maximum value moved down and consequently the maximum absolute INL error is smaller than in the first approach.
Figure 44: INL of a 3bit ADC calculated in regards to the line that connects the end points of the conversion.
The third approach defines INL as a difference between the transfer curve of an ADC and the bestfit straight line that interpolates the transfer points [11]. In this approach, the INL errors are centered around xaxis the most, as presented in Fig. 45. Consequently, in the third approach, the maximum absolute INL error is the smallest from all the INL definitions.
Figure 45: INL of a 3bit ADC calculated in regards to the interpolation line of the conversion.
The transfer curve and the corresponding INL errors for an ideal 3bit ADC are presented in Fig. 46. In this case, all the above definitions of the INL result in the same straight line. In the ideal case, INL error is equal to ± 0.5 LSB.
The INL errors for transfer curves from Fig. 4346 are gathered in Table 9.
Figure 46: Transfer curve and the corresponding INL errors for an ideal 3bit ADC.
Table 9: INL errors comparison of transfer curves from Fig. 4346.
References:

Baker R. Jacob, CMOS Circuit Design, Layout, and Simulation, 3^{rd} Edition, 2010, John Wiley & Sons

Norsworthy S.R., Schreier R., Temes G.C., Deltasigma Data Converters Theory, Design, and Simulation, 1997

http://en.wikipedia.org/wiki/Deltasigma_modulation
Deltasigma modulation (link available 2015.06)

http://pdfserv.maximintegrated.com/en/an/AN634.pdf
Maxim Integrated Products, Inc., TUTORIAL 634: Pipeline ADCs Come of Age, Nov 20, 2001 (link available 2015.06)

http://pdfserv.maximintegrated.com/en/an/TUT810.pdf
Maxim Integrated Products, Inc., TUTORIAL 810: UNDERSTANDING FLASH ADCS, (link available 2015.05)

http://www.asdlib.org/onlineArticles/elabware/Scheeline_ADC/ADC_ADC.html#ADCMain
Scheeline Alexander, Analog to Digital Conversion, (link available 2015.05)

http://www.cypress.com/?id=4&rID=32117
Document titled “Definitions of INL and DNL in an ADC” (link available 2015.05)
Direct link to document: http://www.cypress.com/?docID=32695 (link available 2015.05)

http://www.maximintegrated.com/en/appnotes/index.mvp/id/283
Maxim Integrated Products, Inc., TUTORIAL 283: INL/DNL Measurements for HighSpeed AnalogtoDigital Converters (ADCs) (link available 2015.05)

http://www.maximintegrated.com/en/appnotes/index.mvp/id/1023
Maxim Integrated Products, Inc., TUTORIAL 1023: Understanding Pipelined ADCs (link available 2015.05)

http://www.maximintegrated.com/en/appnotes/index.mvp/id/1870
Maxim Integrated Products, Inc., TUTORIAL 1870: Demystifying DeltaSigma ADCs (link available 2015.06)