Best-Fit Transfer Function
Some ADC’s exhibit low Zero- and Full-Scale Errors but still have significant non-linearities. In cases where these linearities tend to be in one direction (for example, a significantly “bowed” function) the best application results may be obtained if the errors are compared to a Best-Fit Transfer Function. The Best-Fit Straight-Line Transfer Function is the line from which the average deviation of all conversions is minimum. Computing this function requires that the entire Actual Transfer Function be recorded, which is impractical in most applications. Therefore, any performance parameters calculated against the Best-Fit Transfer Function are not useful to the user. Unfortunately, many automatic evaluation packages (software and hardware) assume this type of curve.
Zero-Scale Error and Full-Scale Error
The non-linearities at the endpoints are considered special cases due to the ease with which they are measured and corrected. The non-linearity at the beginning of the Actual Transfer Function is called the Zero-Scale Error (EZS) and the non-linearity at the top end of the function is called Full-Scale Error (EFS). The Zero- and Full-Scale Errors have the following definitions:
NOTE: The Ideal Code Width for the zero code is ½LSB for ADC’s with ½LSB compensated quantization.
Representing this error is by code widths: EZS = CCW(0) – ICW(0)
Or, in the case where the first “x” codes are missing, EZS = CCW(x) – sum(i=0 →x)[ICW(i)]
NOTE: The Ideal Code Width for the last code is 1½LSB for ADC’s with ½LSB compensated quantization.
Representing this error by code widths:
EFS = CCW(last) – ICW(last)
Or, in the case where the last “x” codes are missing,
EFS = CCW(last-x) – sum(i=x→last)[ICW(i)]
References:
Some ADC’s exhibit low Zero- and Full-Scale Errors but still have significant non-linearities. In cases where these linearities tend to be in one direction (for example, a significantly “bowed” function) the best application results may be obtained if the errors are compared to a Best-Fit Transfer Function. The Best-Fit Straight-Line Transfer Function is the line from which the average deviation of all conversions is minimum. Computing this function requires that the entire Actual Transfer Function be recorded, which is impractical in most applications. Therefore, any performance parameters calculated against the Best-Fit Transfer Function are not useful to the user. Unfortunately, many automatic evaluation packages (software and hardware) assume this type of curve.
Zero-Scale Error and Full-Scale Error
The non-linearities at the endpoints are considered special cases due to the ease with which they are measured and corrected. The non-linearity at the beginning of the Actual Transfer Function is called the Zero-Scale Error (EZS) and the non-linearity at the top end of the function is called Full-Scale Error (EFS). The Zero- and Full-Scale Errors have the following definitions:
- Zero-Scale Error (EZS) is the difference between actual first transition voltage and the ideal first transition voltage (if the first transition is not from $000 to $001, then use the difference between the actual and ideal $001–$002 transition voltages, and so on).
NOTE: The Ideal Code Width for the zero code is ½LSB for ADC’s with ½LSB compensated quantization.
Representing this error is by code widths: EZS = CCW(0) – ICW(0)
Or, in the case where the first “x” codes are missing, EZS = CCW(x) – sum(i=0 →x)[ICW(i)]
- Full-Scale Error (EFS) is the difference between the actual last transition voltage and the ideal last transition voltage (if the last transition is not from $3FE to $3FF, then use the difference between the actual and ideal $3FD–$3FE transition voltages, and so on).
NOTE: The Ideal Code Width for the last code is 1½LSB for ADC’s with ½LSB compensated quantization.
Representing this error by code widths:
EFS = CCW(last) – ICW(last)
Or, in the case where the last “x” codes are missing,
EFS = CCW(last-x) – sum(i=x→last)[ICW(i)]
References:
- J. Feddeler and Bill Lucas, 8/16 Bit Division Systems Engineering, Austin, Texas, Aplication Note AN2438/D 2/2003, Frescale Semiconductor, Inc, Motorola 2003, www.freescale.com
- http://en.wikipedia.org
