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How to measure ADC's offset, gain error

22 May 2014  | Abhijan Chakravarty, Sambhav Jain

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You can determine parameters by comparing the ADC's actual transfer function with its ideal transfer function. The actual transfer function of any ADC can be measured by two methods—the end-point method and the best-fit-line method. For this discussion, we consider a typical 12bit SAR (successive approximation register) ADC with single-ended input.

End point method
By this method, actual transfer function of ADC is a straight line between first and last transition points. Because of practical limitations described above, we take points close to the first and last transition to make a straight line. For offset-error calculation, we apply a voltage corresponding to 8 LSB (resolution), so that the distribution of the converted codes is Gaussian in nature and we could get correct average converted code. In our ADC setup, we saw that at 8 LSB, we see no hits of zero code, which ensures the Gaussian nature of the measurement. For accuracy, we measure the voltage applied at the input pad, as there may be some drop from voltage source to pad.

Next, we applied

Note that this is the offset error at 8 LSB.

For full-scale error, these same steps mentioned above should be followed for 4085 LSB voltage.

Again, here the full-scale error is measured at 4085 LSB.

Gain Error can be calculated as the difference of offset error from full scale error.

By doing this, however, we're neglecting the INL (integral non-linearity), which adds up to 8 LSB and is present in the above calculation of offset error. This shows that the above calculated offset error is actually the sum of offset error and INL added up to 8 LSB. This non-linearity effect can be minimised if we can find out offset error at ½ LSB instead of 8 LSB.

Let's now look at the Best Fit Line methodology and its advantages.

Best fit line method
The best-fit-line method is the mathematical procedure for finding the best-fitting curve to a given set of points by minimising the sum of the square of the offset (residuals) of the points from the curve. A line of best fit is a straight line that is the best approximation of the given set of data as shown in figure 4.

Figure 4: Best Fit Line drawn through a scatter plot lets you neglect the effect of integral non-linearity.

The best fit line associated with the n points (x1, y1), (x2, y2), ..., (xn, yn) has the form y=mx+c where,

Where y' and x' are mean values of y and x, respectively.

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