MC908QY8CDWE Datasheet, PDF (45/232 Pages) Freescale Semiconductor, Inc – Addendum to MC68HC908QB8, rev. 3

Functional Description
3.3.4.4 Code Width and Quantization Error
The ADC10 quantizes the ideal straight-line transfer function into 1024 steps (in 10-bit mode). Each step
ideally has the same height (1 code) and width. The width is defined as the delta between the transition
points from one code to the next. The ideal code width for an N bit converter (in this case N can be 8 or
10), defined as 1LSB, is:
1LSB = (V_REFH–V_REFL) / 2^N
Because of this quantization, there is an inherent quantization error. Because the converter performs a
conversion and then rounds to 8 or 10 bits, the code will transition 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 ± 1/2LSB in 8- or 10-bit mode. As a consequence,
however, the code width of the first ($000) conversion is only 1/2LSB and the code width of the last ($FF
or $3FF) is 1.5LSB.
3.3.4.5 Linearity Errors
The ADC10 may also exhibit non-linearity of several forms. Every effort has been made to reduce these
errors but the user should be aware of them because they affect overall accuracy. These errors are:
• 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 (1/2LSB). Note, if the first
conversion is $001, then the difference between the actual $001 code width and its ideal (1LSB) 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 (1.5LSB). Note, if the last conversion is $3FE, then the
difference between the actual $3FE code width and its ideal (1LSB) 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.
• Integral Non-Linearity (INL) — This error is defined as the highest-value the (absolute value of the)
running sum of DNL achieves. More simply, this is the worst-case difference of the actual transition
voltage to a given code and its corresponding ideal transition voltage, for all codes.
• Total Unadjusted Error (TUE) — This error is defined as the difference between the actual transfer
function and the ideal straight-line transfer function, and therefore includes all forms of error.
3.3.4.6 Code Jitter, Non-Monotonicity and Missing Codes
Analog-to-digital converters are susceptible to three special forms of error. These are code jitter,
non-monotonicity, and missing codes.
• Code jitter is when, at certain points, a given input voltage converts to one of two values when
sampled repeatedly. Ideally, when the input voltage is infinitesimally smaller than the transition
voltage, the converter yields the lower code (and vice-versa). However, even very small amounts
of system noise can cause the converter to be indeterminate (between two codes) for a range of
input voltages around the transition voltage. This range is normally around ±1/2LSB but will
increase with noise.
• Non-monotonicity is defined as when, except for code jitter, the converter converts to a lower code
for a higher input voltage.
• Missing codes are those which are never converted for any input value. In 8-bit or 10-bit mode, the
ADC10 is guaranteed to be monotonic and to have no missing codes.
MC68HC908QB8 Data Sheet, Rev. 3
Freescale Semiconductor
43