Offset and Gain Error
Zero-Scale Errors and Full-Scale Errors can be used to calculate Offset and Gain Errors. These terms are used to define the performance on many industry-standard ADC’s but the definitions used vary and can be misleading or inconsistent.
- Offset Error (EO), Adjusted Offset, or Zero-Scale Offset is the difference between the actual and ideal first transition voltages. This is the same definition as Zero-Scale Error. The term offset; however, implies that all conversions are off by an equal amount. In the case of a strong non-linearity near the Zero-Scale Value, this definition may be misleading, and the less ambiguous Zero-Scale Error term is preferable.
- Best-Fit Offset is the difference between the Best-Fit Straight-Line Transfer Function and the Ideal Straight-Line Transfer Function at VREFL. Some definitions define the offset point at the center-conversion ((VREFH – VREFL) /2) instead of at VREFL. This offset is virtually impossible to measure in the application and is therefore only a laboratory curiosity. Since this yields optimistic results and is not measurable in the application, it can be misleading and will not be used.
- Full-Scale Offset is the difference between the actual and ideal last transition voltages. This is the same definition as Full-Scale Error, and is misleading for the same reason that Offset is misleading with respect to Zero-Scale Error.
- Gain Error (EG) or Adjusted Gain Error is the difference in the slope of the Actual and the Ideal Straight-Line Transfer Functions. The error is not measured as a slope but rather as the difference in the total available input range from the first to the last conversions between the Ideal and Adjusted Straight-Line Transfer Functions. It is can also be expressed by: EG = EZS – EFS. Gain Error is not directly measurable and the term has been inconsistently defined in the literature. Additionally, if there are strong non-linearities at the endpoints, this definition of Gain Error may be misleading, so the less ambiguous Full-Scale Error term is preferred provided a simple gain calculation (above) is possible.
- Best-Fit Gain Error is the difference in the slope of the Best-Fit and Ideal Straight-Line Transfer Functions. The error is not measured as a slope but rather as the difference in the total available input range from the first to the last conversions between the Ideal and Best-Fit Straight-Line Transfer Functions. Since the Best-Fit Straight-Line Transfer Function will result in an optimistic Gain Error and is virtually impossible to measure in the application, it can be misleading and will not be used.
Consistency with previous Freescale documents can be achieved by replacing references to Offset Error with Zero-Scale Error and Gain Error with the difference between of Zero Scale Errors and Full-Scale Errors.
Differential Non-Linearity (DNL)
Differential Non-Linearity (DNL) is the maximum of the differences in the each conversion’s Current Code Width (CCW) and the Ideal Code Width (ICW). DNL is the most critical of the measures of an ADC’s performance for many control applications since it represents the ADC’s ability to relate a small change in input voltage to the correct change in code conversion. DNL is defined as:
Code DNL = CCW – ICW
DNL = Max (Code DNL)
Some literature defines DNL using the Adjusted Code Width (ACW), which means Zero- and Full-Scale Error have been adjusted for. For relatively accurate ADC’s, the difference with respect to DNL is negligible, but using the ACW complicates defining and testing DNL. Additionally, this definition is only valid if the application has trim capability.
Related to DNL are two critical figures of merit used in defining ADC operation.
These are:
- Missing Codes — An ADC has missing codes if an infinitesimally small change in voltage causes a change in result of two codes, with the intermediate code never being set. A DNL of –1.0 LSB indicates the ADC has missing codes (DNL measured by this definition cannot be less than –1.0 LSB).
- Monotonicity — An ADC is monotonic if it continually increases conversion result with an increasing voltage (and vice versa). A nonmonotonic ADC may give a lower conversion result for a higher input voltage, which may also mean that the same conversion may result from two separate voltage ranges. Often, the transfer function will completely miss the lower code until after the higher code is converted (on an increasing input voltage).
Some literature suggests that a DNL of greater than 1.0 LSB may indicate nonmonotonicity. Non-monotonicity is usually accompanied by large, positive DNL (>1.0 LSB), although a non-monotonic situation can be coincident with a DNL of less than 1.0 LSB.
