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The Monte Carlo method, also called Monte Carlo analysis, is a means of statistical evaluation of mathematical functions using random samples. This requires a good source of random numbers. There is always some error involved with this scheme, but the larger the number of random samples taken, the more accurate the result.
In its pure mathematical form, the Monte Carlo method consists of finding the definite integral of a function by choosing a large number of independent-variable samples at random from within an interval or region, averaging the resulting dependent-variable values, and then dividing by the span of the interval or the size of the region over which the random samples were chosen. This differs from the classical method of approximating a definite integral, in which independent-variable samples are selected at equally-spaced points within an interval or region.
The Monte Carlo method is most famous for its use during the Second World War in the design of the atomic bomb. It has also been used in diverse applications, such as the analysis of traffic flow on superhighways, the development of models for the evolution of stars, and attempts to predict fluctuations in the stock market. The scheme also finds applications in integrated circuit (IC) design, quantum mechanics, and communications engineering.
In uElectronic design you may use Monte Carlo to know how many percent of your chips will meet the requirements with a statistic variation in the parameters of the technology(process variation).
By example if you size your circuit (let's say an amplifier) to obtain a tolerable value for the maximum offset you will be interested to know if you have a systematic offset and what is it's maximum deviation.
Equally important you want to know how many samples will be in the accepted interval.
After a Monte Carlo simulation you can have an histogram for the values of the offset versus nb. of samples. So you have an idea of the robustness of your design against statistical process variation.
This kind of simulation should not be confused with corners simulation where all identics elements will be influenced in the same way (by example you put all NMOS or all resistors in a same "process state").
The main reason to use Monte Carlo analysis in electronics, RF and microwave engineering is that it helps to get some data about production yield. When you do such analysis you need to tell software what limits do you prefer for all parts and what goals for parameters you want to include for analysis. For example, you need to analyze simple LC matching circuit. You put the limits for parts variation, say +/-10% for L and +/-5% for C. Then put the goals, say S11<=-15 dB for frequencies from Fmin to Fmax and S21 >=-1 dB for the same band. Then you tell the program how many samples do you want to analyze and start the analysis. As an option you may select to show the plot of analysis. When it is done you will get the percentage number for units that should satisfy your goals. Try to do it with any available for you simulator and you will see how it works. When you need to know what is the worst case scenario you need to insert the maximum possible variations for the parts into circuit simulator and you will see what you can get for this maximal deviation. Very often it is better for RF performance characterization than Monte Carlo analysis.
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