Journal of Shandong University of Technology, Te Carlo Analysis Method and Electronic Circuit Simulation Chen Jianghua Department of Electronic Engineering, Shandong University of Technology, Jinan, Introduction Monte Carlo Elbow, 1 cent. The method is also known as random simulation method or statistical test method 〃. Belongs to a branch of experimental mathematics. It uses random numbers for statistical experiments, and uses the obtained statistical eigenvalues ​​such as mean probability as the question to be solved. Its founder is von Neumann 1 along such as 1. Its main idea is to simulate the actual on the computer. It has the advantage of being easy to implement. It can handle complex problems that other methods cannot handle, and it is easy to implement on a computer.
The Monte Carlo method has been widely used in the fields of solid-state circuit design and ecology of the atomic energy, especially in the computer. The Monte Carlo method is used to solve many theoretical and applied scientific questions, which can largely replace many Large-scale complex experiments that are difficult to realize, such as the use of circuits, taxes, and zero-person tools. The Monte Carlo analysis method that contains millions of transistors and 1 electronic circuit. In the field of circuit, people, if you know all the circuit parameters According to this distribution law, the component parameters are randomly extracted multiple times, and the computer simulation of the randomly extracted circuit can be used to estimate the statistical distribution law of the circuit performance. This is the Monte Carlo method of circuit analysis. The process 1. Using Monte Carlo method to solve the actual electronic circuit. Generally speaking, the following aspects are given: 31 The topology of the electronic circuit is given. The component parameters and the statistical distribution rules of the component parameters, such as the central value of the component parameters and the 77 difference 21, produce a uniformly distributed pseudo-random number sampling sequence; Distributed pseudo-random number sampling sequence to establish a random sampling sequence of the distribution specified by the electronic circuit component parameters; use a circuit simulation tool to sequentially simulate the circuit composed of the circuit group parameters of the random sampling of the circuit group; statistical analysis of the simulation results Calculate the statistical law of the circuit, the center value variance of the circuit performance, and the pass rate of the circuit, etc.
Date of collection 19 pockets 4916 2 Random number generation To realize Monte Carlo analysis method on the computer, we must first generate random sampling values ​​of circuit component parameters, that is, on the condition that the statistical distribution of the component parameters is enough, Generate sampling values ​​that conform to its distribution law. This process is called random variable simulation. The simplest and most important random variable wall is the random variable distributed on the mountain average. Almost all other distributed random variables can be obtained by transforming one or more uniformly distributed random variables. Therefore, how to generate sample values ​​of uniformly distributed random variables is the basis of the Monte Carlo analysis method on a computer.
In the Monte Carlo analysis method of the circuit, the number of component parameters of the general circuit is large, and the number of sampling points of the Monte Carlo analysis is also large, so the period of the random number generator is required to be long enough, and the randomness is good, otherwise Will affect the accuracy of Montero analysis. For the component parameters that are not asked. To get different pseudo-random number sequences, it depends on setting the initial value. It should also be especially noted that before using the generated pseudo-random numbers, they must be statistically tested, including the parameters, the remaining groups, and the uniformly distributed random numbers such as the length of the independence of the Tengyan number, the independence period should meet Statistical characteristics 4.
The most common way to define a function from distribution density to generate uniformly distributed random numbers is the congruence method. Its formula is among them. Children integer. Given the initial price, the mountain type 2 gives an integer sequence knife. For each. , Make a transformation 〃; =, add, it is a random function sequence of 0, 1 ratio. If you pass the statistical test, you can use, as a random function of the uniform distribution of 1.
Congruence algorithms include multiplicative congruence algorithms and hybrid congruence algorithms. In formula 2, if 0, then the algorithm is called the multiplication congruence algorithm, it is the reason. 1. First proposed in 1949 and used to generate random numbers; if, then the corresponding algorithm is called a hybrid congruence algorithm, from, 1 trance 61. In 1961, the multiplication congruence algorithm was generalized to 56. Generated by 2 After the length is reached, there will be a cyclical phenomenon, that is, it may be composed of repeated occurrences of several sub-columns.
The shortest length of this repeated sub-column is called the period of. Obviously, this periodicity and randomness are contradictory, so only one cycle can be taken as the available random number sequence. In addition, the period for generating a sufficient number of random numbers should be as large as possible, which can be appropriately selected to achieve. Generally speaking, when book = 2, the maximum period is 7 2 so the random number generated by mathematical method is a random number sequence. That is, the random number implemented on the computer is listed as a pseudo-random number sequence. But in practical applications, as long as these pseudo-random number sequences pass a series of statistical tests, they can be used as random numbers.
3 Sampling of random variables After obtaining uniformly distributed random numbers, they can be transformed to obtain random numbers of other statistical distribution laws, so various transformation methods from average 9 random numbers to random numbers of a given distribution are called Various sampling methods for the city. Frequently used sampling methods for random variables include transformation methods and selection sampling methods. Let's look at the implementation of the transformation method. For other random variable sampling methods, please refer to the relevant literature 3.
It is assumed that the random variable 1 is uniformly distributed between 0 and 1 Hun, and the distribution density function is as follows: v = gU. Transform 1 into a random variable with a distribution density as wide as 7. The idle number is, according to the summary. Basically set 1! In other words, its 2 households present, that is, 1 is the number of anti-1 water. The special case of the inversion method 5 in random sampling. That is, if there are already 0, 1 uniform random variables between bait, the distribution function is 0, the random product of 0 is +7, then the inverse transformation formula for generating fire is that if 0, 1 is given, the variable 1 Value, then = factory is the value of the continuous random variable of distribution function 3;
4 The application of Monte Carlo method in circuit simulation solves the problem of sampling pseudo-random numbers and electronic circuit component parameters on the computer, and then Monte Carlo performs statistical analysis. In addition, statistical characteristics such as the mathematical mean square error of the circuit performance and the standard deviation of the pass rate of the circuit can be obtained. At present, many commercial circuit simulators of 0-person companies have Monte Carlo analysis functions, such as the results of simulation, and the calculated maximum and minimum variances of circuit performance after a specified sub-sampling simulation and the statistical distribution histogram of circuit performance oblique. If the constraints of circuit performance are specified, the qualification rate of the circuit and the deviation of the qualification rate can also be calculated, which brings great convenience to the production of the circuit. The 2 band-pass filter circuit of this method is also given by a 5-foot text file input method, milk 1.1., 5 0, heart Monte Carlo analysis of the output node AC small signal voltage amplitude, total analysis Calculated ten times, the first time for nominal value analysis, and the next nine times for Monte Carlo analysis. (1) The output of the Montenegro output of the filter is given by the waveform.
The Monte Carlo analysis method is an effective method to simulate the actual manufacturing situation of the circuit. The performance function of the circuit is 1 yes. Monte Carlo analysis requires multiple circuit simulations, and its juice-to-cost ratio is very high. The requirements for computer storage resources are also very high. In particular, time-domain Gitero analysis and frequency-domain Montero analysis, for each sampling circuit, circuit simulation should be performed at each time point in the time domain or at each frequency-frequency sampling point, and the simulation results should be stored to calculate the The storage capacity may be very large. For example, the machine memory we use is 12 rivers. It is acceptable to perform ten Monte Carlo analysis, but the core enters the hall ten times Monte Carlo analysis and fails. In addition, if the circuit model is not accurate, it becomes the component parameter. The distribution of the juice is inaccurate. Accurate pieces of Tecaro analysis will be heard. In 1. Monte Carlo analysis, the total number of sample points is 1 Zhu Benren. Introduction to the Monte Carlo method. Jinan Shandong University Press, 1987.12 2 Fang Zaigen. Computer simulation and Monte Carlo method. Beijing Beijing Institute of Technology Press, 1988.15 3 Wang Hui, Wang Zhihua. Computer aided analysis and design methods of electronic circuits. Beijing Tsinghua University Press, 1996.202 4 Tu Zhongji. Monte Carlo method. Shanghai Shanghai Science and Technology Press, 1985.121
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