[SOLVED] Meaning of mac_device parameter 'Mismatch_Sigma'?

erikl said:

Yes, sigma is the same as std (standard deviation), see here.

Click to expand...

flyingRabbit said:

I think setting Mismatch_Sigma as 3 is too rigorous ...

Click to expand...

Standard deviation - Wikipedia said:

If a data distribution is approximately normal then about 68 percent of the data values are within one standard deviation of the mean (mathematically, μ ± σ, where μ is the arithmetic mean), about 95 percent are within two standard deviations (μ ± 2σ), and about 99.7 percent lie within three standard deviations (μ ± 3σ). This is known as the 68-95-99.7 rule, or the empirical rule.

Click to expand...

erikl said:

Sure, but this depends on what you need: σ=1 will cover 68.2% of all possible cases, whereas σ=3 covers 99.73% , see below.
**broken link removed**

The trustability or confidence interval is determined by the number of probes (MC runs in your case). A confidence interval (CI) means that the confidence level (CL) of a measuring (or MC run) result will be 1-(1/√N) , if N is the number of measurements (runs) - if you repeat them very often. I.e. e.g. CL=68% for 10 runs or 90% for 100 runs.

Now what does this mean in practice? If you just want a quick overview over the distribution to be expected, you'd use σ=1 and remember there could still be 32% more results outside of the number of cases you got - with 90% confidence level if you run 100 times.

If you want to buy a million chips, you'd want to see more exactly how many of them you'd have to chuck away: you'd use σ=3 and will know that there still will be 2700 bad ones to be expected in the lot - with a confidence level of 96,8% at 1000 runs.

HTH!

Click to expand...

flyingRabbit said:

Let's say our PDK defines transistor's std of threshold voltage as 5mV and average as 300mV at given size. I think if I set Mismatch_Sigma as 3, the monte-carlo simulation picks random threshold voltage values from the Gaussian distribution of N(Mean,1-Sigma)=N(300mV,15mV), not from N(300mV,5mV).

Click to expand...

flyingRabbit said:

That's the reason why I think setting Mismatch_Sigma as 3 is "too rigorous" since now the 99.73% of random threshold voltages will come from -255mV~345mV, not from 285mV~315mV.
I would like to know that my thinking about Mismatch_Sigma is right.

Click to expand...

erikl said:

Yes, that's what I think, too.



No, I don't think so. I'd think 99.73% of random threshold voltages will come from mean±15mV (not ± 3*15mV).
Why? I think the Mismatch_Sigma declaration corresponds to how many sigmas of the standard deviation should be used (for the MC runs).

To get this straight - this is a contradiction to the above statement, that the std value corresponds to the Mismatch_Sigma value, but it's possible that the simulator shows this erroneously.

But I'm not sure, however. Why not try and plot a threshold voltage histogram?

Click to expand...

flyingRabbit said:

I found that Mismatch_Sigma is a constant that is multiplied to the random seed generated from N(0,1).

Click to expand...