Mismatch simulation for offset of an OTA

[rocky.king07]

Suppose I am simulating offset of an OTA having 8 transistors. I have given 3 sigma mismatch in all transistors and I have run monte carlo simulation for 30 runs. So I will get 30 offset values. Is this offset value will be Gaussian in nature. If yes, should I consider offset maximum and minimum value or 3 sigma of offset curve (Gaussian distribution curve of offset).

 

[checkmate]

1. The distribution of the offset will depend on the function on which the offset is computed. You can refer to the wikipedia article on "Normal Distribution" under the section titled "Related distributions".
2. Normally, we run MC to guarantee a certain yield in production. One way of specifying yield is in percentage terms, ie we want 99% of offsets to fall within specifications. Another way is to specify in sigma count, ie a 3-sigma design translates to a 99.87% yield for a parameter distribution assumed to be Gaussian.
3. As MC simulations creates a sample population, any mean or std computed from this sample population are merely estimates of the actual statistical parameters, with a more accurate estimate requiring a larger population (Refer to any statistical texts).

In other words, you seriously don't expect to be able to obtain accurate estimates of meeting a 3-sigma yield based on only 30 samples. Try 1000 instead.

 

[name_n16]

If you are simulating a differential OTA only mismatch will cause offset in your circuit. For mis-match you can refer to your model file for the parameter that MC simulation will vary with 3 Sigma deviation and gaussian as distribution.

I think most of the foundry in their MC characterisation data sheet recommends 30 iteration. As per my experience it is hell lot of difficult to meet specification with mis-match for 500 iteration

 

[leehying]

Hi,
In HSPICE, we use variation block to define the input parameter, including std. (sigma) and ...
When monte carlo analysis is performed, the sigma parameter has nothing to do with the sim output.
Which means you have to do the statistics yourself.
LEE