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Jacki

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how to find the worst case directly instead of Monte Carlo simulation?
Feb 24^th, 2016, 7:03am

Hi,

I am thinking how to find the worst case directly instead of many runs of Monte Carlo simulation if I am not interested in the distribution, only want to find the worst case.
About the mismatch variation, is it possible that I just add the threshold voltage mismatch directly? For example 50 mV for 65 nm CMOS technology.
About the process variation, I think it is the most serious case. Normally we can choose fnsp or snfp for the worse case analysis. But is it possible to have the case in a differential Circuit, one branch has "snfp" and another branch has "fnsp". I know the variation on the same wafer within a small distance cannot be very large. Just wondering if it could happen or how we shall analyze the worst case directly.
Thank you.

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Geoffrey_Coram

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Re: how to find the worst case directly instead of Monte Carlo simulation?
Reply #1 - Feb 24^th, 2016, 12:02pm

If the statistics are Gaussian, then there's a small (but non-zero) chance of getting a VT mismatch that's larger than say the 3-sigma point, so what do you mean by "worst case"?

I heard about one company that does what I think they called "Hadamard sampling": rather than picking the value for each mismatch parameter from the Gaussian distribution, they pick each one at �σ or �3σ. Then you're arguably more likely to get the worst case, since you're not doing all the runs with parameters close to nominal.

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If at first you do succeed, STOP, raise your standards, and stop wasting your time.

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Jacki

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Re: how to find the worst case directly instead of Monte Carlo simulation?
Reply #2 - Feb 25^th, 2016, 12:26am

Geoffrey_Coram wrote on Feb 24^th, 2016, 12:02pm:

If the statistics are Gaussian, then there's a small (but non-zero) chance of getting a VT mismatch that's larger than say the 3-sigma point, so what do you mean by "worst case"?

I heard about one company that does what I think they called "Hadamard sampling": rather than picking the value for each mismatch parameter from the Gaussian distribution, they pick each one at �σ or �3σ. �Then you're arguably more likely to get the worst case, since you're not doing all the runs with parameters close to nominal.

Hello Geoffrey_Coram,

Thank you very much for your reply. The worst case I mean is which can give me the largest mismatch and process variation. Currently, a single run takes me around 12 hours with liberal accuracy. If I try to find the case for �σ or �3σ, I still need to do a lot of run first. I just Wonder if I can avoid the Monte Carlo simulation, and based on the common experience to find the possible one or several worst cases, and run them directly.

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Geoffrey_Coram Senior Fellow Offline Posts: 1998 Massachusetts, USA	Re: how to find the worst case directly instead of Monte Carlo simulation? Reply #3 - Feb 25^th, 2016, 12:49pm If you're using Gaussian without truncation, then there is no worst case: the statistics can choose an arbitrarily large shift.
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