# Comparator input offset voltage

This is an example about input offset of a comparator in Analog Integrated Circuit Design by Tony Chan Carusone (page 414).

Could anyone explain why the plot in Fig 10.1 is a normal distribution?

## 2 Answers

There are two parameters in a Normal Distribution, the mean and σ, the standard deviation.

The mean here is +3.0 mV and the standard deviation is shown for the probability of a logic 1 output. The inverse curve would be the probability of a logic "0" output.

This Normal distribution curve of a transition or the "Bell curve" would indicate the probability than any threshold transition would occur.

The Cumulative Function of the Normal distribution is the integral of the area under the curve across the range of inputs was what was actually shown. ref Wiki

The curve shown is the cdf of the normal distribution. It is probably used in the comparator data sheet (as opposed to the pdf "bell curve") because it follows directly from the test data collected during manufacturing. To go from the cdf to the pdf you simply need to differentiate the cdf curve. This is not easy to do for a Gaussian distribution but there are tables that allow you to quickly make probability calculations using one if you have the other.