NXP Semiconductors K32 L2A Series, Reference Manual, Page: 225 / 1379

11.6.2.4 Code width and quantization error
The ADC quantizes the ideal straight-line transfer function into 65536 steps in the 16-bit
mode.. Each step ideally has the same height, that is, 1 code, and width. The width is
defined as the delta between the transition points to one code and the next. The ideal code
width for an N-bit converter, where N can be 16, 12, 10, or 8, defined as 1 LSB, is:
LSB
Equation 3. Ideal code width for an N-bit converter
There is an inherent quantization error due to the digitization of the result. For 8-bit, 10-
bit, or 12-bit conversions, the code transitions when the voltage is at the midpoint
between the points where the straight line transfer function is exactly represented by the
actual transfer function. Therefore, the quantization error will be ± 1/2 LSB in 8-bit, 10-
bit, or 12-bit modes. As a consequence, however, the code width of the first (0x000)
conversion is only 1/2 LSB and the code width of the last (0xFF or 0x3FF) is 1.5 LSB.
For 16-bit conversions, the code transitions only after the full code width is present, so
the quantization error is -1 LSB to 0 LSB and the code width of each step is 1 LSB.
11.6.2.5 Linearity errors
The ADC may also exhibit non-linearity of several forms. Every effort has been made to
reduce these errors, but the system designers must be aware of these errors because they
affect overall accuracy:
• Zero-scale error (E
ZS
), sometimes called offset: This error is defined as the difference
between the actual code width of the first conversion and the ideal code width. This
is 1/2 LSB in 8-bit, 10-bit, or 12-bit modes and 1 LSB in 16-bit mode. If the first
conversion is 0x001, the difference between the actual 0x001 code width and its ideal
(1 LSB) is used.
• Full-scale error (E
FS
): This error is defined as the difference between the actual code
width of the last conversion and the ideal code width. This is 1.5 LSB in 8-bit, 10-bit,
or 12-bit modes and 1 LSB in 16-bit mode. If the last conversion is 0x3FE, the
difference between the actual 0x3FE code width and its ideal (1 LSB) is used.
• Differential non-linearity (DNL): This error is defined as the worst-case difference
between the actual code width and the ideal code width for all conversions.
Chapter 11 Analog-to-Digital Converter (ADC)
K32 L2A Reference Manual, Rev. 2, 01/2020
NXP Semiconductors 225