AOCV path based variations

[chevuturi]

Can anyone explain the below statement : How random variation would tend to cancel each other in path based aocv?
In the case of distance is fixed and path depth increases, systematic variation would be constant but the random variation would tend to cancel each other. Therefore as path depth increases the derate factor would decrease

 

[ThisIsNotSam]

it is simple statistics. at some point, you are unlikely to get unlucky on every single gate. Some are gonna behave like fast. Some are slow. But it is rare that they are all slow (from the point of view of local process variation. global is another story)

AOCV looks at the depth of the path and applies a correction coefficient for your silicon luck, basically.

 

[chevuturi]

So is it because of cells behavior the random variation would cancel each other ? correct me if i am wrong

 

[ThisIsNotSam]

Kind of. AOCV is not about canceling random variation, is about assuming that a really really really bad scenario is unlikely.

Think about it this way. I have a path with 2 inverters. Each inverter has a nominal delay of 10ps, plus or minus 1ps due to variation. You can get a path delay in the range of 18-22ps. This is a normal distribution centered around 20ps. It is relatively easy to get a delay of 22ps, you only need to get "unlucky" on 2 cells.

Now think of a path with 10 inverters. By the same logic, the delay would be in the range of 90-110ps. However, it is a freaking miracle of nature if you get 110ps delay. You have to get unlucky 10 times in a row. In a way, AOCV makes this a distribution centered around 100ps but the tail ends have a very low probability.

You can open an AOCV file in a text editor and inspect. You will see how the delays are derated according to the number of stages.

 

[chevuturi]

Sure Professor understood , Thank you ! I have one more doubt

For any design is it good or bad to have more common clock path ?