# Theoretical hits for sine wave input

Question asked by EricBecker on Aug 11, 2016
Latest reply on Aug 25, 2016 by EricBecker

I am evaluating the AD9681 and using a sine-wave input for measuring DNL and INL using the histogram method. Looking through evaluation procedures, I have come across the equation:

p(n) = (1/pi)*[asin((VFS*(n-2^(N-1)))/(A*2^N))-asin((VFS*(n-1-2^(N-1)))/(A*2^N))],

where p(n) is the probability of ADC code n occurring in the sine wave, VFS is the voltage swing, and A is the amplitude. At least, that is what I have interpreted based on this document: http://www.analog.com/library/analogDialogue/archives/39-06/Chapter%205%20Testing%20Converters%20F.pdf .

The issue I am running into is that when I plot the above equation (5.16 in the document), I do not see a plot like that shown in Figure 5.41, nor do I see that when I generate the histogram using the ADC and an FPGA. The measured histogram (picture attached) looks like Figure 5.41, which is great, but I'm still left unsure about the theoretical number of hits i should be getting. I should mention that I am also using the amplitude estimation method in equation 5.20 as the value for A in equation 5.16. Attached are photos of the theoretical number of hits and the actual number of hits per ADC code that I am getting. Am I interpreting variables incorrectly? Am I using the equations incorrectly?

Any help is greatly appreciated!