CN105303008A - Analog integrated circuit optimization method and system - Google Patents

Abstract

The embodiment of the present invention discloses an analog integrated circuit optimization method and system. The method simulates the new-generation population by using a circuit-level simulation program to obtain the circuit performance indicators of each individual in the new-generation population. The SPICE model and Gaussian process regression are used to perform Monte Carlo analysis and estimation on the new generation of populations using SPICE simulators to obtain yield estimates; so that in the process of population evolution, the performance index and yield of the circuit are used as constraints to participate in the evolutionary algorithm at the same time Among them, the problem of low yield rate in the final decision-making in the prior art is solved.

Description

An analog integrated circuit optimization method and system

technical field

The present invention relates to the technical field of Electronic Design Automation (EDA), more specifically, to an analog integrated circuit optimization method and system.

Background technique

With the continuous advancement of integrated circuit technology to nano-scale advanced node technology, the challenges faced by analog integrated circuit design are also more prominent. On the one hand, the application requirements require that the analog integrated circuit unit has more complex functions, better performance, smaller area and lower power consumption. For example, the radio frequency circuit unit used for 4G communication may need to be compatible with various standards such as LTE, GSM, and Bluetooth, and at the same time require a smaller area and lower power consumption. Therefore, designers need to consider multiple design goals with constraints at the same time, for example, these goals may include: circuit performance, power consumption and area (PPA) and so on. And some of these goals may be mutually exclusive. On the other hand, due to the process fluctuations, layout-dependent effects and interconnection parasitic effects in the manufacture of nanoscale integrated circuits, the designer has to face the gate length (L), gate width (W) and bias of the transistor in the design stage. In addition to design variables such as voltage and current, it is also necessary to consider the impact of process fluctuations on yield and the impact of layout-dependent effects on circuit performance.

For such a complex design, it is almost impossible to find the optimal design through the traditional design method based on experience and a large number of iterations, especially in the small-scale nanotechnology, its manufacturing process (such as photolithography, ion implantation, oxidation, Chemical mechanical polishing, etc.) precision control becomes very difficult. In the case of significant and unavoidable process fluctuations, failure to correctly evaluate the impact of process fluctuations on the circuit will lead to a decline in yield and delay in product launch. The above two challenges can be summarized as how to better and faster solve the constrained multi-objective optimization (MOO) problem based on a large number of design variables and process fluctuations, namely:

min or max

Restrictions $g_j\left(\stackrel{\&Right\; Arrow;}{x}\right)\≤0,j=1,2,...k$

in, and Represents a function related to the performance, area, yield, or power consumption of a circuit. x ₁ ... x _m represent design variables.

After analyzing the papers of ANewApproachforCombiningYieldandPerformanceinBehaviouralModelsforAnalogueIntegratedCircuits and AnAutomatedDesignMethodologyforYieldAwareAnalogCircuitSynthesisinSubmicronTechnology, the commonly used rapid design and optimization methods for analog integrated circuits in the prior art in solving constrained multi-objective optimization (MOO) problems based on a large number of design variables and process fluctuations can be summarized as Steps S101-S108, Step 101: Obtain the initial circuit netlist and transistor statistical model; Step S102: Analyze the initial circuit netlist and transistor statistical model to obtain design variables, optimization objectives and constraints; Step S103: According to the design The scope of the variable randomly generates an initial population; step S104: change the design variable, and generate a circuit netlist corresponding to each individual in the initial population according to the modified design variable, and the circuit netlist represents a new generation population; Step 105: Simulate the first-generation population by using a circuit-level simulation program (Simulation program with integrated circuit emphasis, SPICE), to obtain circuit performance indicators of each individual in the new-generation population, such as circuit performance, area, power consumption, etc.; step S106: According to the circuit performance index, the evolutionary algorithm is used to evolve the new generation population to obtain the next generation population; Step S107: According to the preset maximum evolution algebra, it is judged whether the evolution of the next generation population is over, and if so, execute step S108 , otherwise continue to execute step S104; step S108: generate the Pareto optimal solution set corresponding to the current population, perform Monte Carlo analysis on the obtained Pareto optimal solution set, and obtain the yield estimate; step S109: according to the Pareto optimal solution set Make decisions and validate.

When adopting the above-mentioned traditional method for circuit design optimization, since the yield rate design does not participate in the evolutionary algorithm in the above process, the yield rate on the Pareto optimal solution set is not necessarily optimal, and the resulting decision may be There will be a problem of low yield rate, so how to use the yield rate as an optimization constraint or optimization goal to participate in the evolutionary algorithm in the optimization process has become one of the technical problems to be solved urgently by those skilled in the art.

Contents of the invention

The purpose of the present invention is to provide an analog integrated circuit optimization method and system, which is used to make the yield rate as an optimization constraint condition or optimization goal participate in the evolutionary algorithm in the optimization process.

In order to achieve the above object, the embodiment of the present invention provides the following technical solutions:

A method for optimizing an analog integrated circuit, comprising:

Obtain initial circuit netlist and transistor statistical model;

Analyzing the initial circuit netlist and transistor statistical model to obtain design variables, optimization objectives and constraints;

Randomly generating an initial population according to the range of the design variables;

changing the design variable, and generating a circuit netlist corresponding to each individual in the initial population according to the modified design variable, the circuit netlist representing a new generation population;

The circuit performance index of each individual in the new generation population is obtained by simulating the new generation population by using a circuit-level simulation program, and the SPICE model and Gaussian process regression are used to perform Monte Carlo on the new generation population by using a SPICE simulator. Analyzing and estimating to obtain an estimated value of the yield rate, the estimated value of the yield rate includes the value to be predicted of the yield rate at each individual observation point in the population;

Evolving the new-generation population by using an evolutionary algorithm according to the circuit performance index and the estimated yield value to obtain the next-generation population;

Determine whether the evolution is over according to the preset maximum evolution algebra, if yes, generate the Pareto optimal solution set corresponding to the current population, make a decision and verify it according to the Pareto optimal solution set, if not, change the design variable, and then change it according to the changed The design variable generates the first circuit netlist corresponding to each individual in the initial population, and the first circuit netlist represents the new generation population until the Pareto optimal solution set corresponding to the current population is generated, and according to the Pareto optimal solution set The solution set is decided and verified.

Preferably, in the above analog integrated circuit optimization method, the SPICE model and Gaussian process regression are used to perform Monte Carlo analysis and estimation of the new generation of populations using SPICE simulators to obtain yield estimates, including:

Obtain the training point set (Y, X) of the current population, Y is the observed value of the yield of each individual observation point in the population, X is each individual observation point in the population;

According to the training point set (Y, X), the posterior distribution of the expected value y ^* of the yield of each individual observation point in the group calculated by formula (1) is $\left\{\begin{array}{c}{\mathrm{the\; y}}^{*}|x,Y,{\stackrel{\&Right\; Arrow;}{x}}^{*}~N({\stackrel{\&Right\; Arrow;}{\mathrm{the\; y}}}^{*},{\mathrm{\σ}}_{\mathrm{the\; y}*}^2)\\ {\stackrel{\‾}{\mathrm{the\; y}}}^{*}=K({\stackrel{\&Right\; Arrow;}{x}}^{*},x)K{(x,x)}^{-1}Y\\ {\mathrm{\σ}}_f^2=k({\stackrel{\&Right\; Arrow;}{x}}^{*},{\stackrel{\&Right\; Arrow;}{x}}^{*})-K({\stackrel{\&Right\; Arrow;}{x}}^{*},x)K{(x,x)}^{-1}K(x,{\stackrel{\&Right\; Arrow;}{x}}^{*})\end{array}\right.,$ Then determine the average value of the expected value of the yield of each individual observation point in the current population and its variance Judging the variance Whether it is within the allowable error range, if not, select a new individual x ^* in the current population, and perform Monte Carlo analysis to obtain the yield observation value y of the selected new individual x ^* , put (x ^* , y ) into the training point set (Y, X), and re-predict until the variance of the average value of the yield to be predicted for each individual observation point ${\mathrm{\σ}}_f^2$ All are within the allowable error range, y ^* is the expected value of yield;

Wherein, described formula (1) is: $\left[\begin{array}{c}Y\\ {\mathrm{the\; y}}^{*}\end{array}\right]~N(0,\left[\begin{array}{cc}K(x,x)& K(x,{\stackrel{\&Right\; Arrow;}{x}}^{*})\\ K({\stackrel{\&Right\; Arrow;}{x}}^{*},x)& k({\stackrel{\&Right\; Arrow;}{x}}^{*},{\stackrel{\&Right\; Arrow;}{x}}^{*})\end{array}\right]),$ Let the prior distribution of yield observation Y be Gaussian distribution: Y～N(0,K(X,X)), K(X,X) is a symmetric positive definite covariance matrix, matrix element is the correlation between the design variables of the individuals to be predicted in the population, and y ^* is the predicted value of yield at each individual observation point in the population is the design variable of the individual to be predicted in the population.

Preferably, in the above analog integrated circuit optimization method, the acquisition of the training point set of the current population includes:

Determine which generation population the current population is;

When the population is the first-generation population, Monte Carlo analysis is performed on all individual observation points of the first-generation population, and all individual observation points in the first-generation population are training Point set, using the training point set of the first generation population as the training point set (Y, X) of the current population;

When the population is the Z generation population, all individual observation points of the Z-1 generation population are used as the training point set (Y, X) of the current population.

An analog integrated circuit optimization system comprising:

The collection module is used to obtain the initial circuit netlist and transistor statistical model input by the user;

An analysis module, configured to analyze the initial circuit netlist and transistor statistical model to obtain design variables, optimization objectives and constraints;

A population generation module, configured to randomly generate an initial population according to the range of the design variables;

The first evolution module is used to change the design variable, and generate a circuit netlist corresponding to each individual in the initial population according to the modified design variable, and the circuit netlist represents a new generation population;

The simulation module is used to simulate the new-generation population by using a circuit-level simulation program to obtain the circuit performance index of each individual in the new-generation population. The SPICE model and Gaussian process regression are used to simulate the new-generation population by using a SPICE model and Gaussian process regression. The population is subjected to Monte Carlo analysis and estimation to obtain an estimated yield value, and the estimated yield value includes the to-be-predicted value of the yield rate at each individual observation point in the population;

The second evolution module is used to evolve the new-generation population to obtain the next-generation population by using an evolutionary algorithm according to the circuit performance index and the estimated value of yield;

The decision verification module is used to judge whether the evolution is over according to the preset maximum evolution algebra, if yes, generate the Pareto optimal solution set corresponding to the current population, make a decision and verify it according to the Pareto optimal solution set, if not, change the design variables, according to the modified design variables to generate a circuit netlist corresponding to each individual in the initial population, the circuit netlist represents a new generation population until the Pareto optimal solution set corresponding to the current population is generated, and according to the Pareto The best solution set is used for decision-making and verification.

Preferably, in the above-mentioned simulation integrated circuit optimization system, the simulation module includes:

A yield calculation unit is used to obtain the training point set (Y, X) of the current population, Y is the observed value of the yield of each individual observation point in the population, and X is each individual observation point in the population;

According to the training point set (Y, X), the posterior distribution of the value to be predicted y ^* of yield calculated by formula 1 is: $\left\{\begin{array}{c}{\mathrm{the\; y}}^{*}|x,Y,{\stackrel{\&Right\; Arrow;}{x}}^{*}~N({\stackrel{\&Right\; Arrow;}{\mathrm{the\; y}}}^{*},{\mathrm{\σ}}_{\mathrm{the\; y}*}^2)\\ {\stackrel{\‾}{\mathrm{the\; y}}}^{*}=K({\stackrel{\&Right\; Arrow;}{x}}^{*},x)K{(x,x)}^{-1}Y\\ {\∂}_f^2=k({\stackrel{\&Right\; Arrow;}{x}}^{*},{\stackrel{\&Right\; Arrow;}{x}}^{*})-K({\stackrel{\&Right\; Arrow;}{x}}^{*},x)K{(x,x)}^{-1}K(x,{\stackrel{\&Right\; Arrow;}{x}}^{*})\end{array}\right.,$ Get the average value of the predicted value of the yield of each individual in the current population and its variance Judging the variance Whether it is within the allowable error range, if not, select a new individual x ^* in the current population, and perform Monte Carlo analysis to obtain the yield observation value y of the selected new individual x ^* , put (x ^* , y ) into the training point set (Y, X), and re-predict until the variance of the average value of the expected value of the yield of each individual All are within the allowable error range, y ^* is the expected value of yield;

Wherein, the formula one is: $\left[\begin{array}{c}Y\\ {\mathrm{the\; y}}^{*}\end{array}\right]~N(0,\left[\begin{array}{cc}K(x,x)& K(x,{\stackrel{\&Right\; Arrow;}{x}}^{*})\\ K({\stackrel{\&Right\; Arrow;}{x}}^{*},x)& k({\stackrel{\&Right\; Arrow;}{x}}^{*},{\stackrel{\&Right\; Arrow;}{x}}^{*})\end{array}\right]),$ Let the prior distribution of yield observation value Y be Gaussian distribution: Y～N(0,K(X,X)), K(X,X) is a symmetric positive definite covariance matrix, is the design variable of the individual to be predicted in the population, matrix element is the correlation between the design variables of the individuals to be predicted in the population, and y ^* is the value to be predicted of the yield rate at each individual observation point in the population.

Preferably, in the above-mentioned analog integrated circuit optimization system, the simulation module further includes:

The training point set selection module is used to judge which generation population the current population is; when the population is the first generation population, Monte Carlo analysis is performed on all individuals of the first generation population, and the first generation All individuals in the population are the training point set of the first generation population, and the training point set of the first generation population is used as the training point set (Y, X) of the current population; when the population is the Z generation population , taking all the individuals of the Z-1 generation population as the training point set (Y, X) of the current population.

It can be seen from the above scheme that the analog integrated circuit optimization method provided by the embodiment of the present invention uses a circuit-level simulation program (Simulation program with integrated circuit emphasis, SPICE) to simulate the new generation population to obtain the circuit performance of each individual in the new generation population At the same time as the indicators, the SPICE model and Gaussian process regression are used to perform Monte Carlo analysis and estimation on the new generation of populations using SPICE simulators to obtain yield estimates; so that the circuit performance indicators and yields are used as constraints during the population evolution process. Participating in the evolutionary algorithm, thereby solving the problem of low yield in the prior art when the final decision is made.

Description of drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention. Those skilled in the art can also obtain other drawings based on these drawings without creative work.

FIG. 1 is a flow chart of an analog integrated circuit optimization method disclosed in an embodiment of the present invention;

FIG. 2 is a schematic structural diagram of an analog integrated circuit optimization system disclosed in an embodiment of the present invention.

detailed description

The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some of the embodiments of the present invention, not all of them. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without creative efforts fall within the protection scope of the present invention.

In the traditional rapid design and optimization methods of analog integrated circuits, it is still difficult to use the yield rate as an optimization constraint or optimization goal in the optimization process. The main reason is that the accurate estimation of the circuit yield rate is obtained by Monte Carlo analysis of the SPICE model (mainly the BSIM model of CMOS transistors) provided by the chip foundry with process statistics information. Monte Carlo analysis itself requires a large number of samples, while evolutionary algorithms need to perform Monte Carlo analysis on each individual in each generation of the population, which greatly increases the computational cost of experimental measurements, making it almost impossible to add yield indicators to the simplified algorithm accomplish. Therefore, Monte Carlo analysis can only be performed to verify the yield after obtaining the Pareto optimal solution set.

In view of this, the embodiment of the present application discloses an analog integrated circuit optimization method that takes both yield and performance into consideration, see Figure 1, including:

Step S101: Obtain an initial circuit netlist and transistor statistical model;

Step S102: analyzing the initial circuit netlist and transistor statistical model to obtain design variables, optimization objectives and constraints;

Step S103: Randomly generate an initial population according to the range of the design variable;

Step S104: changing the design variable, and generating a circuit netlist corresponding to each individual in the initial population according to the modified design variable, the circuit netlist represents a new generation population, which is recorded as the first generation population;

Step 105: Simulate the new-generation population by using a circuit-level simulation program (Simulation program with integrated circuit emphasis, SPICE), to obtain the circuit performance indicators of each individual in the new-generation population, such as area, power consumption and other indicators, and the SPICE model is used And Gaussian process regression using SPICE simulator to perform Monte Carlo analysis and estimation on the new generation population to obtain the yield estimate;

Step S106: Evolutionary algorithm is used to evolve the new-generation population according to the circuit performance index and the estimated value of yield rate to obtain the next-generation population, which is recorded as the second-generation population, where the generation number of the population is increased by 1 for each evolution;

Step S107: judge whether the evolution of the next-generation population is over according to the preset maximum evolutionary number, if yes, execute step S108, otherwise execute step S104;

Step S108: Generate a Pareto optimal solution set corresponding to the current population, make a decision and verify it based on the Pareto optimal solution set.

In the process of optimizing the circuit in the above-mentioned method disclosed in the above-mentioned embodiments of the present application, in addition to considering the traditional optimization objectives, the yield rate is also taken as one of the optimization objectives, so the yield rate on the Pareto optimal solution set can also be Meet preset requirements. At the same time, the combination of Monte Carlo and Gaussian Process Regression (GPR) is used in the optimization process to speed up the evaluation of yield.

It can be understood that, in the method disclosed in the above-mentioned embodiments of the present application, in step S105, "using the SPICE model and Gaussian process regression to use the SPICE simulator to perform Monte Carlo analysis and estimation on the new generation population to obtain the estimated yield" specifically Can include:

Obtain the training point set (Y, X) of the current population, Y is the observed value of the yield of each individual observation point in the population, X is each individual observation point in the population;

According to the training point set (Y, X), the posterior distribution of the expected value y ^* of the yield rate of each individual in the population is calculated by formula (1) as $\left\{\begin{array}{c}{\mathrm{the\; y}}^{*}|x,Y,{\stackrel{\&Right\; Arrow;}{x}}^{*}~N({\stackrel{\&Right\; Arrow;}{\mathrm{the\; y}}}^{*},{\mathrm{\σ}}_{\mathrm{the\; y}*}^2)\\ {\stackrel{\‾}{\mathrm{the\; y}}}^{*}=K({\stackrel{\&Right\; Arrow;}{x}}^{*},x)K{(x,x)}^{-1}Y\\ {\mathrm{\σ}}_f^2=k({\stackrel{\&Right\; Arrow;}{x}}^{*},{\stackrel{\&Right\; Arrow;}{x}}^{*})-K({\stackrel{\&Right\; Arrow;}{x}}^{*},x)K{(x,x)}^{-1}K(x,{\stackrel{\&Right\; Arrow;}{x}}^{*})\end{array}\right.,$ Get the average value of the predicted value of the yield of each individual in the current population and its variance Judging the variance Is it within the allowable error range? If yes, use the predicted value y ^* of the yield rate as the estimated value of the yield rate. If not, select a new individual x ^* in the current population and perform Monte Carlo analysis to obtain The yield observation value y of the selected new individual x ^* , add (x ^* , y) to the training point set (Y, X), and re-predict until the average value of the yield to be predicted for each individual Variance are all within the allowable error range, y ^* is the predicted value of yield, is the design variable of the individual to be predicted in the population;

Wherein, described formula (1) is: $\left[\begin{array}{c}Y\\ {\mathrm{the\; y}}^{*}\end{array}\right]~N(0,\left[\begin{array}{cc}K(x,x)& K(x,{\stackrel{\&Right\; Arrow;}{x}}^{*})\\ K({\stackrel{\&Right\; Arrow;}{x}}^{*},x)& k({\stackrel{\&Right\; Arrow;}{x}}^{*},{\stackrel{\&Right\; Arrow;}{x}}^{*})\end{array}\right]),$ Let the prior distribution of the yield observation value Y be a Gaussian distribution: Y～N(0,K(X,X)), K(X,X) is a symmetric positive definite covariance matrix, and the matrix elements is the correlation between the design variables of the individuals to be predicted in the population, and y ^* is the value to be predicted of the yield rate at each individual observation point in the population.

The reasoning process of using Monte Carlo in combination with GPR to estimate the yield in the above embodiment can be described as follows:

$\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; f</span>}<span\; class="notranslate">\; (</span>\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

in, is the design variable, y is the observed value of the yield rate, and the prior distribution of the observed value of the yield rate is Gaussian distribution: Y～N(0, K(X, X))(3)

Where Y=(y ₁ ,y ₂ ,…y _n ) ^T is multiple individual observation points in the population The observed value of the yield rate, the joint prior distribution of the observed value Y of the yield rate and the expected value y* of the yield rate is:

$\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; Y</span>}\\ {\mathrm{<span\; class="notranslate">\; the\; y</span>}}_{<span\; class="notranslate">\; *</span>}\end{array}\right]<span\; class="notranslate">\; ~</span>\mathrm{<span\; class="notranslate">\; N</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 0</span>}<span\; class="notranslate">\; ,</span>\left[\begin{array}{cc}\mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; ,</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; )</span>\\ \mathrm{<span\; class="notranslate">\; K</span>}<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; x</span>}<span\; class="notranslate">\; )</span>& \mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; ,</span>{\stackrel{<span\; class="notranslate">\; \&Right\; Arrow;</span>}{\mathrm{<span\; class="notranslate">\; x</span>}}}_{<span\; class="notranslate">\; *</span>}<span\; class="notranslate">\; )</span>\end{array}\right]<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

Among them, K(X, X) is a symmetric positive definite covariance matrix, is the design variable of the individual to be predicted in the population, matrix element It is the correlation between the design variables of different individuals to be predicted in the population. The posterior distribution of the measured value y* of the yield obtained from (4) is: $\left\{\begin{array}{c}{\mathrm{the\; y}}^{*}|x,Y,{\stackrel{\&Right\; Arrow;}{x}}^{*}~N({\stackrel{\&Right\; Arrow;}{\mathrm{the\; y}}}^{*},{\mathrm{\&sigma;}}_{\mathrm{the\; y}*}^2)\\ {\stackrel{\&OverBar;}{\mathrm{the\; y}}}^{*}=K({\stackrel{\&Right\; Arrow;}{x}}^{*},x)K{(x,x)}^{-1}Y\\ {\mathrm{\&sigma;}}_f^2=k({\stackrel{\&Right\; Arrow;}{x}}^{*},{\stackrel{\&Right\; Arrow;}{x}}^{*})-K({\stackrel{\&Right\; Arrow;}{x}}^{*},x)K{(x,x)}^{-1}K(x,{\stackrel{\&Right\; Arrow;}{x}}^{*})\end{array}\right.,$ in for The average of the individual predicted yields, is the square of its variance.

Referring to the analog integrated circuit optimization method disclosed in the above-mentioned embodiments of the present application, the number of individuals in each generation is a fixed value during the population evolution process, and since new individuals are constantly added to the training point set (Y, X), the evolutionary algebra is getting higher and higher. Larger, the fewer new training points need to be added, so the fewer individuals need to perform Monte Carlo analysis, and the more accurate the predicted yield value is, this process makes it almost unnecessary to add new training points after evolution to a certain generation , that is, there is no need for Monte Carlo analysis, which will speed up the evolutionary algorithm.

It can be understood that, for the above method, the present application also discloses an analog integrated circuit optimization system, and the two can be used for reference. Referring to Fig. 2, the analog integrated circuit optimization system disclosed in the embodiment of the present application includes:

The collection module 10 is used to obtain the initial circuit netlist and transistor statistical model input by the user;

The analysis module 20 is used to analyze and obtain design variables, optimization objectives and constraints according to the initial circuit netlist and transistor statistical model;

A population generation module 30, configured to randomly generate an initial population according to the scope of the design variables;

The first evolution module 40 is configured to change the design variable, and generate a circuit netlist corresponding to each individual in the initial population according to the modified design variable, and the circuit netlist represents a new generation population;

The simulation module 50 is used to simulate the new-generation population by using a circuit-level simulation program to obtain the circuit performance index of each individual in the new-generation population, and the SPICE model and Gaussian process regression are used to simulate the new generation population using a SPICE simulator. Performing Monte Carlo analysis and estimation on the first-generation population to obtain an estimated yield value, the estimated yield rate includes the expected value of the yield rate at each individual observation point in the population;

The second evolution module 60 is used to evolve the new-generation population by using an evolutionary algorithm according to the circuit performance index and the estimated yield value to obtain the next-generation population;

The verification decision module 70 is used to judge whether the evolution is over according to the preset maximum evolution algebra, if yes, generate the Pareto optimal solution set corresponding to the current population, make a decision and verify it according to the Pareto optimal solution set, if not, change the Design variables, generate a circuit netlist corresponding to each individual in the initial population according to the modified design variables, the circuit netlist represents a new generation of population, until the Pareto optimal solution set corresponding to the current population is generated, and according to The Pareto optimal solution set is used for decision-making and verification.

Corresponding to the above method, the simulation module 50 includes:

Yield calculation unit 51, the yield calculation unit 51 is used to obtain the training point set (Y, X) of the current population, Y is the observed value of the yield of each individual observation point in the population, and X is the observation value of each individual observation point in the population. individual observation points;

According to the training point set (Y, X), the posterior distribution of the value to be predicted y ^* of yield calculated by formula 1 is: $\left\{\begin{array}{c}{\mathrm{the\; y}}^{*}|x,Y,{\stackrel{\&Right\; Arrow;}{x}}^{*}~N({\stackrel{\&Right\; Arrow;}{\mathrm{the\; y}}}^{*},{\mathrm{\&sigma;}}_{\mathrm{the\; y}*}^2)\\ {\stackrel{\&OverBar;}{\mathrm{the\; y}}}^{*}=K({\stackrel{\&Right\; Arrow;}{x}}^{*},x)K{(x,x)}^{-1}Y\\ {\mathrm{\&sigma;}}_f^2=k({\stackrel{\&Right\; Arrow;}{x}}^{*},{\stackrel{\&Right\; Arrow;}{x}}^{*})-K({\stackrel{\&Right\; Arrow;}{x}}^{*},x)K{(x,x)}^{-1}K(x,{\stackrel{\&Right\; Arrow;}{x}}^{*})\end{array}\right.,$ Get the average value of the predicted value of the yield of each individual in the current population and its variance Judging the variance Is it within the allowable error range? If yes, use the predicted value y ^* of the yield rate as the estimated value of the yield rate. If not, select a new individual x ^* in the current population and perform Monte Carlo analysis to obtain The yield observation value y of the selected new individual x ^* , add (x ^* , y) to the training point set (Y, X), and re-predict until the average value of the yield to be predicted for each individual Variance All are within the allowable error range, y ^* is the expected value of yield;

Wherein, the formula one is: $\left[\begin{array}{c}Y\\ {\mathrm{the\; y}}^{*}\end{array}\right]~N(0,\left[\begin{array}{cc}K(x,x)& K(x,{\stackrel{\&Right\; Arrow;}{x}}^{*})\\ K({\stackrel{\&Right\; Arrow;}{x}}^{*},x)& k({\stackrel{\&Right\; Arrow;}{x}}^{*},{\stackrel{\&Right\; Arrow;}{x}}^{*})\end{array}\right]),$ Let the prior distribution of yield observation value Y be Gaussian distribution: Y～N(0,K(X,X)), K(X,X) is a symmetric positive definite covariance matrix, is the design variable of the individual to be predicted in the population, matrix element is the correlation between the design variables of the individuals to be predicted in the population, and y ^* is the value to be predicted of the yield rate at each individual observation point in the population.

Corresponding to the above method, the simulation module 50 may also include:

Training point set selection module 52, the training point set selection module 52 is used to judge which generation population the current population is; when the population is the first generation population, perform Monte Carlo on all individuals of the first generation population Caro analysis, all individuals in the first-generation population are the training point sets of the first-generation population, and the training point sets of the first-generation population are used as the training point sets (Y, X) of the current population; when When the population is the Z generation population, all the individuals of the Z-1 generation population are used as the training point set (Y, X) of the current population.

Each embodiment in this specification is described in a progressive manner, each embodiment focuses on the difference from other embodiments, and the same and similar parts of each embodiment can be referred to each other.

The above description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention will not be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (6)

1. A method for optimizing an analog integrated circuit, comprising: Obtain initial circuit netlist and transistor statistical model; Analyzing the initial circuit netlist and transistor statistical model to obtain design variables, optimization objectives and constraints; Randomly generating an initial population according to the range of the design variables; changing the design variable, and generating a circuit netlist corresponding to each individual in the initial population according to the modified design variable, the circuit netlist representing a new generation population; By using a circuit-level simulation program to simulate the new-generation population, the circuit performance indicators of each individual in the new-generation population are obtained, and the SPICE model and Gaussian process regression are used to perform Monte Carlo analysis and estimation on the new-generation population using a SPICE simulator. Obtaining an estimated value of yield, the estimated value of yield includes the value to be predicted of yield at each individual observation point in the population; Evolving the new-generation population by using an evolutionary algorithm according to the circuit performance index and the estimated yield value to obtain the next-generation population; Determine whether the evolution is over according to the preset maximum evolution algebra, if yes, generate the Pareto optimal solution set corresponding to the current population, make a decision and verify it according to the Pareto optimal solution set, if not, change the design variable, and then change it according to the changed The design variable generates the first circuit netlist corresponding to each individual in the initial population, and the first circuit netlist represents the new generation population until the Pareto optimal solution set corresponding to the current population is generated, and according to the Pareto optimal solution set The solution set is decided and verified. 2. The analog integrated circuit optimization method according to claim 1, wherein said adopting SPICE model and Gaussian process regression utilizes SPICE simulator to carry out Monte Carlo analysis and estimation of new generation population to obtain yield estimate, comprising: Obtain the training point set (Y, X) of the current population, Y is the observed value of the yield of each individual observation point in the population, X is each individual observation point in the population; According to the training point set (Y, X), the posterior distribution of the to-be-predicted value y* of the yield of each individual observation point in the group is calculated by formula (1) as $\left\{\begin{array}{c}\mathrm{the\; y}*|x,Y,\stackrel{\&Right\; Arrow;}{x}*~N(\stackrel{\&Right\; Arrow;}{\mathrm{the\; y}}*,{\mathrm{\&sigma;}}_{\mathrm{the\; y}*}^2)\\ \stackrel{\&OverBar;}{\mathrm{the\; y}}*=K(\stackrel{\&Right\; Arrow;}{x}*,x)K{(x,x)}^{-1}Y\\ {\mathrm{\&sigma;}}_f^2=k(\stackrel{\&Right\; Arrow;}{x}*,\stackrel{\&Right\; Arrow;}{x}*)-K(\stackrel{\&Right\; Arrow;}{x}*,x)K{(x,x)}^{-1}K(x,\stackrel{\&Right\; Arrow;}{x}*)\end{array}\right.,$ Then determine the average value of the expected value of the yield of each individual observation point in the current population and its variance Judging the variance Whether it is within the allowable error range, if not, select a new individual x* in the current population, and perform Monte Carlo analysis to obtain the yield observation value y of the selected new individual x*, put (x*, y ) into the training point set (Y, X), and re-predict until the variance of the average value of the yield to be predicted for each individual observation point All are within the allowable error range, and y* is the predicted value of yield; Wherein, described formula (1) is: $\left[\begin{array}{c}Y\\ \mathrm{the\; y}*\end{array}\right]~N(0,\left[\begin{array}{cc}K(x,x)& K(x,\stackrel{\&Right\; Arrow;}{x}*)\\ K(\stackrel{\&Right\; Arrow;}{x}*,x)& k(\stackrel{\&Right\; Arrow;}{x}*,\stackrel{\&Right\; Arrow;}{x}*)\end{array}\right]),$ Let the prior distribution of yield observation Y be Gaussian distribution: Y～N(0,K(X,X)), K(X,X) is a symmetric positive definite covariance matrix, matrix element is the correlation between the design variables of the individuals to be predicted in the population, and y* is the predicted value of the yield rate at each individual observation point in the population is the design variable of the individual to be predicted in the population. 3. The method for optimizing an analog integrated circuit according to claim 2, wherein said obtaining the training point set of the current population comprises: Determine which generation population the current population is; When the population is the first-generation population, Monte Carlo analysis is performed on all individual observation points of the first-generation population, and all individual observation points in the first-generation population are training Point set, using the training point set of the first generation population as the training point set (Y, X) of the current population; When the population is the Z generation population, all individual observation points of the Z-1 generation population are used as the training point set (Y, X) of the current population. 4. An analog integrated circuit optimization system, characterized in that, comprising: The collection module is used to obtain the initial circuit netlist and transistor statistical model input by the user; An analysis module, configured to analyze the initial circuit netlist and transistor statistical model to obtain design variables, optimization objectives and constraints; A population generation module, configured to randomly generate an initial population according to the range of the design variables; The first evolution module is used to change the design variable, and generate a circuit netlist corresponding to each individual in the initial population according to the modified design variable, and the circuit netlist represents a new generation population; The simulation module is used to simulate the new-generation population by using a circuit-level simulation program to obtain the circuit performance index of each individual in the new-generation population. The SPICE model and Gaussian process regression are used to simulate the new-generation population by using a SPICE model and Gaussian process regression. The population is subjected to Monte Carlo analysis and estimation to obtain an estimated yield value, and the estimated yield value includes the expected value of the yield rate at each individual observation point in the population; The second evolution module is used to evolve the new-generation population to obtain the next-generation population by using an evolutionary algorithm according to the circuit performance index and the estimated value of yield; The decision verification module is used to judge whether the evolution is over according to the preset maximum evolution algebra, if yes, generate the Pareto optimal solution set corresponding to the current population, make a decision and verify it according to the Pareto optimal solution set, if not, change the design variables, according to the modified design variables to generate a circuit netlist corresponding to each individual in the initial population, the circuit netlist represents a new generation population until the Pareto optimal solution set corresponding to the current population is generated, and according to the Pareto The best solution set is used for decision-making and verification. 5. The analog integrated circuit optimization system according to claim 4, wherein the simulation module includes: A yield calculation unit is used to obtain the training point set (Y, X) of the current population, Y is the observed value of the yield of each individual observation point in the population, and X is each individual observation point in the population; According to the training point set (Y, X), the posterior distribution of the yield to be predicted value y* calculated by formula 1 is: $\left\{\begin{array}{c}\mathrm{the\; y}*|x,Y,\stackrel{\&Right\; Arrow;}{x}*~N(\stackrel{\&Right\; Arrow;}{\mathrm{the\; y}}*,{\mathrm{\&sigma;}}_{\mathrm{the\; y}*}^2)\\ \stackrel{\&OverBar;}{\mathrm{the\; y}}*=K(\stackrel{\&Right\; Arrow;}{x}*,x)K{(x,x)}^{-1}Y\\ {\mathrm{\&sigma;}}_f^2=k(\stackrel{\&Right\; Arrow;}{x}*,\stackrel{\&Right\; Arrow;}{x}*)-K(\stackrel{\&Right\; Arrow;}{x}*,x)K{(x,x)}^{-1}K(x,\stackrel{\&Right\; Arrow;}{x}*)\end{array}\right.,$ Get the average value of the predicted value of the yield of each individual in the current population and its variance Judging the variance Whether it is within the allowable error range, if not, select a new individual x* in the current population, and perform Monte Carlo analysis to obtain the yield observation value y of the selected new individual x*, put (x*, y ) into the training point set (Y, X), and re-predict until the variance of the average value of the expected value of the yield of each individual All are within the allowable error range, and y* is the predicted value of yield; Wherein, the formula one is: $\left[\begin{array}{c}Y\\ \mathrm{the\; y}*\end{array}\right]~N(0,\left[\begin{array}{cc}K(x,x)& K(x,\stackrel{\&Right\; Arrow;}{x}*)\\ K(\stackrel{\&Right\; Arrow;}{x}*,x)& k(\stackrel{\&Right\; Arrow;}{x}*,\stackrel{\&Right\; Arrow;}{x}*)\end{array}\right]),$ Let the prior distribution of yield observation value Y be Gaussian distribution: Y～N(0,K(X,X)), K(X,X) is a symmetric positive definite covariance matrix, is the design variable of the individual to be predicted in the population, matrix element is the correlation between the design variables of the individuals to be predicted in the population, and y* is the value to be predicted of the yield rate at each individual observation point in the population. 6. The analog integrated circuit optimization system according to claim 5, wherein the simulation module further comprises: The training point set selection module is used to judge which generation population the current population is; when the population is the first generation population, Monte Carlo analysis is performed on all individuals of the first generation population, and the first generation All individuals in the population are the training point set of the first generation population, and the training point set of the first generation population is used as the training point set (Y, X) of the current population; when the population is the Z generation population , taking all the individuals of the Z-1 generation population as the training point set (Y, X) of the current population.