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Montecarlo simulation on matched devices

Senan

Hello,

Suppose the verification of simple MOS current mirror using Montecarlo (MC) simulation.  Now the MC module used in the simulation have the statistical process variation, where at some samples one of the transistors has the maximum threshold voltage and the other minimum. Hence a maximum deviation between the mirror outputs is expected at this sample and can be monitored in the simulation.

However, in practical implementation, these transistors are matched, suppose matched very well with layout matching techniques, so such a process variation should not be effective as MC tell.

In this case I wonder if the MC from post layout simulation is already considering the matched transistors, and how it knows those transistors are matched.

Thank you in advance for your help

Regards 

  • in reply to Senan

    Dear Senan,

    Senan said:
    That is why I think I need to know the optimum number of fixed samples to reach certain sigma with certain confidence level.

    If we limit the discussion to a normally distributed parameter, there is a relationship between the sample size, the computed standard deviation of that sample size and the actual (population) standard deviation.

    Using this relationship, one can determine the sample size required to determine a standard deviation that falls below some value with a given confidence interval. I assembled a Microsoft Excel workbook that will allow you to enter your sample size and sample standard deviation and it will compute the actual range of the standard deviation for a given confidence interval. For example, suppose you run a MC simulation with 50 samples and find a standard deviation of your parameter of interest is 3.5. With a 95% confidence interval, as shown in FIgure 1 from the workbook, the actual standard deviation falls between 2.924 and 4.362.

    Now, you would like to guarantee that the standard deviation fall below 4.0 with a 99% confidence interval. A few iterations (or using Solver) on the sample size to provide a maximum population standard deviation of less than 4.0 shows a sample size of 210 is required (Figure 2). Hence, if you re-run your MC simulation using greater than 210 samples and enter the resulting sample standard deviation with a confidence interval of 99%, there is a reasonable chance the maximum population standard deviation will be less than your objective of 4.0.

    If you are interested, I have attached the Microsoft Excel file.

    I hope I understood your question and this is somehow useful!

    Shawn

    sigma_confidence_interval_vs_sample_size_sml_071123.xlsx

  • in reply to ShawnLogan

    Dear Shawn,

    I am very grateful to you for your rich information, It is really interesting for me.

    I have also downloaded the Excel file and I tried it.

    1. I would like to ask you practically, what is the standard set for the confidence level, is it 95%?, I mean for design for manufacturing and industry.

    2. The difference between minimum and maximum population standard deviation reduces as we increase the number of the samples with respect to the chosen confidence level. Ideally the difference becomes zero if very huge (just for example) number of samples is selected. I also proved it from your excel file.

    As a practically I am asking, how much difference I should target to say ok this number of samples should be enough. 

    Best Regards

     

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