Information

31.6.2.4 Code width and quantization error

The ADC quantizes the ideal straight-line transfer function into 65536 steps (in 16-bit

mode). Each step ideally has the same height (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 (in this case N can be 16, 12, 10, or 8), defined as 1 LSB, is:

LSB

Figure 31-66. 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.

31.6.2.5 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 should be aware of them because they affect

overall accuracy. These errors are:

• Zero-scale error (E

) (sometimes called offset): This error is defined as the

difference between the actual code width of the first conversion and the ideal code

width (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

): This error is defined as the difference between the actual code

width of the last conversion and the ideal code width (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.

Application information

K20 Sub-Family Reference Manual, Rev. 2, Feb 2012

630 Freescale Semiconductor, Inc.