Tags: ADC, differential nonlinearity DNL, education, theory


          Differential Nonlinearity DNL is defined as “the difference between the actual code width of a converter and the ideal case” [1] (underline of the word “width” is author’s):

DNL = actual step width – ideal step width [1]

          The transfer curve of an ideal 3-bit ADC and the corresponding DNL error is presented in Fig. 41. As it is seen, in the ideal case DNL error value is equal to 0 V or 0 LSBs for each conversion step. The transfer curve of a nonideal 3-bit ADC and the corresponding DNL error is presented in Fig. 42. The DNL errors for each step for an ideal and nonideal ADCs are gathered in Table 8.


Table 8: DNL errors of transfer curves from Fig. 41 and 42.

table 1 - dnl


To what values can DNL be equal to?

Minimum possible value is -1. DNL equal to -1 means that the step width is equal to 0. That is, there is no step corresponding to a given digital code. Thus, the digital code is missing.

DNL maximum value can be equal to any number. However, DNL equal to 2.0, 2.5 or 3.0 does not mean there is a missing digital code. DNLs of the rest codes can be equal to -0.5, -0.8, -0.9 or -0.99 and all the codes would exist. Only DNL equal to -1 means that there is a missing code.


DNL ideal plot

Figure 41: DNL of an ideal 3-bit ADC.


DNL plot non-ideal

Figure 42: DNL of a nonideal 3-bit ADC.



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