Machine learning assisted on-chip transformer automatic synthesis method

Abstract

The invention discloses a machine learning-assisted on-chip transformer automatic synthesis method. The method comprises the following steps: firstly, setting an on-chip transformer electrical parameter target and a process constraint; quickly predicting by using a reverse artificial neural network to obtain a group of structure parameters as an initial solution; then structure parameters are sampled randomly, a part of sample space is obtained by floating around an initial solution, and full-wave electromagnetic simulation is carried out to obtain samples; sample full-wave simulation data is compressed, and then on-chip transformer priori knowledge is introduced to train a GPR proxy model, so that the dimension of the model is reduced, and the prediction accuracy is higher; and then global optimization is carried out, the optimization range is constrained through an initial solution, and the convergence and exploratory performance of the algorithm are enhanced through multi-path optimization brought by different lower confidence limit constants. According to the method, an algorithm combining a reverse network and forward optimization is adopted, so that the accuracy is ensured, the calculation cost is lower, the optimization speed is higher, and the automation and intelligence of the design of the on-chip passive device are promoted.

Description

Technical Field

[0001] The present invention belongs to the field of radio frequency passive devices, and in particular relates to an on-chip transformer automatic synthesis method assisted by machine learning. Background Art

[0002] On-chip passive transformers are important components in RF design. They can realize impedance matching, signal coupling, power transmission, DC isolation and other functions in RF integrated circuits. They play an important role in reducing the number of components and chip area. On-chip spiral transformers are composed of two spiral inductors coupled together. They are usually defined by multiple geometric parameters. Among the thousands of combinations of geometric parameters, only a few can meet the design specifications and design indicators at the same time. Therefore, it is difficult to deduce the geometric parameters of the transformer based on the indicators. This process, which is the opposite of modeling, is called a synthesis problem. The synthesis of on-chip spiral transformers has always been a major challenge in the design of passive devices. The realization of automatic synthesis of on-chip transformers is also the key to the automated design of RF integrated circuits.

[0003] With the continuous development of machine learning technology, the surrogate model-assisted method seems to be the most suitable solution to the above difficulties. The main idea is to replace the expensive full-wave electromagnetic simulation model with a fast surrogate model, which allows the use of a population-based meta-heuristic algorithm to identify Pareto sets at a lower computational cost. Achieving optimization goals under the premise of high dimensions and small samples is a complex and urgent problem to be solved. Finding fast and effective intelligent synthesis algorithms is crucial to the design and performance of transformers and even RF integrated circuits. Summary of the invention

[0004] Purpose of the invention: In view of the problems and shortcomings in the prior art, the present invention provides an on-chip transformer automatic synthesis method assisted by machine learning to reduce the computational cost of transformer synthesis and improve the optimization speed.

[0005] Technical solution: In order to achieve the above-mentioned purpose, the technical solution adopted by the present invention is: a machine learning-assisted on-chip transformer automatic synthesis method, comprising the following steps:

[0006] Step 1: Set the electrical performance parameter target of the on-chip transformer and the structural parameter constraints of the transformer, and set the relevant process constraints;

[0007] Step 2: Use an inverse artificial neural network (ANN) to predict the transformer point performance parameters and obtain a set of structural parameters as the initial solution;

[0008] Step 3: Randomly sample the structural parameters, then sample around the initial solution to obtain the structural parameters, and collect the initial samples through full-wave electromagnetic simulation;

[0009] Step 4: compress and transform the sample full-wave simulation data to reduce the sample dimension;

[0010] Step 5: Train a Gaussian Process Regression (GPR) proxy model to learn the mapping relationship between the transformer structural parameters and performance parameters in the sample set, replacing the traditional equivalent circuit model and costly full-wave electromagnetic simulation;

[0011] Step 6: Use a population-based meta-heuristic algorithm for global optimization, inverse the artificial neural network initial solution to constrain the optimization range, and optimize a set of transformer structural parameters;

[0012] Step 7: Full-wave simulation verification. Perform full-wave simulation verification on the structural parameters obtained in step 6. If the design goals are met, the optimal structural parameters and / or layout are output. If not, the simulation results are added to the sample set. Repeat steps 5 to 7 until the iteration stop condition is met.

[0013] Furthermore, in step 1, the transformer electrical performance parameters include a partial combination of primary and secondary coil inductance, quality factor, coupling coefficient, maximum available gain, insertion loss, operating frequency, minimum self-resonant frequency, input impedance and optimized bandwidth. The structural parameters include maximum line width, minimum line width, maximum line spacing, minimum line spacing, maximum inner diameter, minimum inner diameter, maximum number of coil turns, minimum number of coil turns and maximum area.

[0014] Furthermore, in step 2, an artificial neural network is used to establish an inverse model, learn the mapping relationship between performance parameters and structural parameters, and then predict a set of structural parameters as the initial solution based on the comprehensive performance parameter target of the transformer. The inverse model introduces the prior knowledge of the on-chip transformer to reduce the model dimension. For broadband optimization inductance, all frequency points are replaced by more important frequency points in the frequency band, or frequency points are selected at intervals during model training; for a completely symmetrical transformer structure, only the performance parameters of one primary or secondary coil are selected for observation, and the input impedance only focuses on the part within the working bandwidth; the minimum self-resonant frequency is determined by the positive or negative quality factor; the inverse model solves the one-to-many problem by adding input parameter features, and introduces auxiliary constraints in the input to limit the solution range of the output value.

[0015] Furthermore, in step 2, the inverse model input performance parameters include primary and secondary coil inductance, quality factor, coupling coefficient and maximum available gain and other performance parameters, and the output structural parameters are line width, line spacing, inner diameter and number of turns of primary and secondary coils.

[0016] Furthermore, in step 3, firstly, Latin Hypercube Sampling (LHS) is used to randomly sample the transformer structural parameters, and then the transformer structural parameters are obtained in a space with a certain floating ratio around the initial solution. Then, prior knowledge is added for pre-screening to remove some parameters that do not meet the transformer modeling requirements. At the same time, random sampling also allows the samples to cover the design space as much as possible.

[0017] Furthermore, in step 4, facing the problem of wide-band transformer design, due to the large number of frequency points, directly establishing a proxy model will cause the amount of data calculation to grow exponentially, greatly increasing the optimization time and even making it unacceptable. Therefore, discrete cosine transform is used for data compression to reduce the amount of proxy model calculation and ensure its accuracy.

[0018] Furthermore, in step 5, the learning effect and prediction accuracy of the GPR proxy model are improved by selecting the matern3 / 2 kernel function and the fitness function; for the on-chip transformer synthesis problem where there are multiple input parameters with high sensitivity, the single-objective GPR proxy model has higher accuracy and reduces the amount of calculation, so each performance parameter is modeled separately.

[0019] Furthermore, in step 6, a genetic algorithm is used for global optimization, and multi-path optimization brought about by using different lower confidence bound (LCB) constants is used to enhance the convergence and exploration of the algorithm.

[0020] Furthermore, in step 6, the fitness function is modified using data pre-screening technology, so that the optimization algorithm adds sample points in the area where the optimal solution may appear to avoid falling into the local optimum. At the same time, multiple randomly generated LCB values ​​are used for multi-path optimization to enhance the exploratory nature of the genetic algorithm without increasing the complexity of the algorithm. The standard for LCB to judge the quality of new individuals is:

[0021] y LCB =y(x)-ws(x)

[0022] Among them, y(x) is the function value corresponding to the structural parameter x calculated by the GPR proxy model, s(x) is the prediction standard deviation obtained by the GPR proxy model, and w is the LCB value that measures the algorithm's exploration ability.

[0023] The present invention also provides a computer program product, comprising a computer program / instruction, which, when executed by a processor, implements the steps of the machine learning-assisted on-chip transformer automatic synthesis method.

[0024] Beneficial effects: Compared with the prior art, the machine learning-assisted on-chip transformer automatic synthesis method provided by the present invention has the following advantages:

[0025] (1) The present invention can realize the automatic integrated design of on-chip transformers by only requiring the electrical performance parameter targets and structural parameter constraints of the transformers, which greatly improves the work efficiency of RF circuit designers;

[0026] (2) The present invention establishes a reverse artificial neural network, which can quickly predict a set of initial solutions, greatly improving the design efficiency and sample reuse rate, and saving computing resources;

[0027] (3) The present invention reduces the computational cost and time by establishing a GPR proxy model to replace the traditional equivalent circuit model and expensive full-wave electromagnetic simulation;

[0028] (4) The present invention combines prior knowledge and data compression to train the GPR model, thereby improving the prediction accuracy and speed of the model and saving time costs;

[0029] (5) The present invention uses a plurality of randomly generated LCB values ​​for multi-path optimization. Compared with the traditional method of fixing LCB values, the algorithm is re-randomly generated in each iteration, which greatly improves the exploratory nature of the algorithm and avoids falling into the local optimum.

[0030] (6) The present invention adopts an algorithm that combines inverse network and forward optimization, which has lower calculation cost and higher optimization speed while ensuring accuracy, and promotes the automation and intelligence of on-chip passive device design. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] Figure 1 is an overall flow chart of an embodiment of the present invention;

[0032] Figure 2 A schematic diagram of a one-to-many problem in a reverse network according to the present invention;

[0033] Figure 3 It is a schematic diagram of reverse modeling of artificial neural network of the present invention;

[0034] Figure 4 A diagram showing the training process of the neural network of the present invention;

[0035] Figure 5 The optimal sample coupling coefficient diagram for optimizing iterations of the embodiment of the present invention;

[0036] Figure 6 A diagram showing the coupling coefficient and prediction error of each round in an embodiment of the present invention;

[0037] Figure 7 Graph showing the primary and secondary coil inductance, quality factor and coupling coefficient of the optimal sample of the embodiment of the present invention. DETAILED DESCRIPTION

[0038] To make the purpose, technical solution and advantages of the embodiments of the present invention more clear, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the accompanying drawings in the embodiments of the present invention.

[0039] Before introducing the embodiments of the present invention in detail, the basic knowledge of the GPR proxy model and the reverse artificial neural network involved in the embodiments of the present invention and the related improvement work involved in the present invention are explained.

[0040] The on-chip transformer optimization problem has many parameters and high sensitivity. In order to save full-wave simulation time, a proxy model with a small sample size is needed. The GPR proxy model has a good performance in machine learning-assisted circuit design. At the same time, the output of GPR has a confidence interval in addition to the predicted value. It is a probability function of Gaussian distribution, which is very beneficial for the introduction of multi-path optimization technology. Therefore, the use of the online updated Gaussian process regression model as a proxy model in machine learning-assisted on-chip transformer design has a relatively stable advantage in both prediction accuracy and the number of optimization algorithm iterations.

[0041] Gaussian process regression predicts the value of unknown points by learning the relationship between points, so the function that calculates the similarity between two points in the input space is crucial, called the kernel function, also known as the covariance function. Many types of kernel functions can be used for GPR, the most common ones are linear, polynomial, radial basis function (RBF), Matern, periodic and rational quadratic functions, each kernel function corresponds to different parameters to control the shape and scale, mapping the sample to a higher dimensional space.

[0042] Since the parameters of the kernel function directly affect the complexity of the model, the effects of different kernel functions vary greatly. However, there is no unified conclusion on the selection of kernel functions. Kernel functions need to be selected according to different problems or different application scenarios. Some scholars have conducted research in this area, which is called kernel engineering. Generally speaking, they are tried, and kernel functions can be combined with many optimization algorithms, and permutations and combinations often show many unexpected performances. At the same time, the kernel function does not need to know the feature space and the transformation function, and is only calculated by dot product, making it possible to find data relationships in high-dimensional space with extremely low computational costs.

[0043] The most common kernel function in the Gaussian process is the RBF kernel, also known as the square exponential kernel or Gaussian kernel, which is defined as follows:

[0044]

[0045] Σ is the covariance of each feature in the observation. If Σ is a diagonal matrix, the formula can be simplified to:

[0046]

[0047] where σ j It is used to measure the importance of the j-th dimension feature of the definition space, and D is the total number of dimensions. j →∞, the jth dimension can be almost ignored. If Σ is isotropic, the isotropic square exponential kernel is:

[0048]

[0049] where σ 2 Called bandwidth, the kernel function has infinite spatial dimensions.

[0050] The Matern kernel function is another common GPR kernel that links the distance and similarity between training data. The specific form is as follows:

[0051]

[0052] where r = ||xx′||, v>0, K v is the modified Bessel function, Γ(ν) is the gamma function. When ν→∞, the Matern kernel function is close to the square exponential kernel. When , the formula can be simplified to:

[0053]

[0054] Compared with other kernel functions, it has an additional parameter smoothing factor, which is used to control the smoothness of the result function. Depending on the smoothing factor, commonly used ones are matern5 / 2 and matern3 / 2. When each predictor has a separate fixed-length parameter, there are kernels such as ardmatern5 / 2 and ardmatern3 / 2.

[0055] In order to select a suitable kernel function, a set of transformer comprehensive experiments are carried out below. The transformer structure adopts an interlaced quadrilateral, and the comprehensive target is the primary and secondary coil inductance L at the 50GHz frequency point. p =L s =0.15nH, coupling coefficient k = 0.7, self-resonant frequency f sr =80GHz, seek the maximum available gain G at the operating frequency max Maximize. Input parameters are line width W, line spacing S, outer diameter D out 、Number of turns of primary and secondary coils p 、N sSince the primary and secondary coils of the interlaced winding structure are completely symmetrical, this experiment can only focus on the inductance value L of the primary coil. p and quality factor Q p The same is true for the secondary coil. To ensure the n:n turns ratio, the same number of turns is selected for the primary and secondary coils.

[0056] Table 1

[0057] parameter Numerical lower bound Numerical upper bound Line width W(μm) 2.2 10 Line spacing S(μm) 1.5 5 <![CDATA[Outer diameter D out (μm)]]> 15 300 Number of turns N 1 3

[0058] The experiments in the present invention all adopt 40nm CMOS technology. It can be understood that the scheme of the present invention is not limited to a specific process and is applicable to different processes. Considering the chip design requirements, in addition to the structural constraints of each parameter, the input parameters should also meet the constraints in Table 1. The lower limit of the value is closely related to the chip design rules, and the upper limit of the value is as large as possible. Except for experienced engineers, most beginners and people who have no transformer-related design experience cannot know the approximate range of geometric parameters in advance, which is one of the original intentions of the present invention. Two layers of metal are used, the main metal is distributed in the MTT2 layer, and the TM1 layer is used to lead out the inner ring port.

[0059] The algorithm was run on a server with two AMD EPYC 7F52 processors and 512GB of memory without parallelization. In order to make the EMX simulation more accurate, the frequency sweep range was set to [0,f sr +10]GHz, with a step size of 100MHz.

[0060] Table 2

[0061] Kernel Function <![CDATA[G mau ]]> Q@50GHz L Error k Error RBF 0.855 6.9 3.8％ 2.9％ matern5 / 2 0.869 13.2 3.8％ 2.8％ matern3 / 2 0.878 13.2 4.5％ 1.1％ ardmatern5 / 2 0.868 8.9 3.8％ 2.7％ ardmatern3 / 2 0.868 9.1 4.2％ 3.3％

[0062] The experimental results are shown in Table 2. Various kernel functions can solve the on-chip transformer synthesis problem and meet the requirements of various indicators at the operating frequency. However, in comparison, the RBF kernel has the worst optimization effect. The results of ardmatern5 / 2, ardmatern3 / 2, and matern5 / 2, where each predictor has a separate fixed-length parameter, are similar, and matern3 / 2 shows a clear advantage. Therefore, the on-chip transformer synthesis methods described below all use matern3 / 2 as the kernel function of the Gaussian regression process.

[0063] For multi-objective comprehensive problems, which are essentially inverse problems, traditional forward optimization often requires multiple iterations to converge in order to solve structural parameters from performance objectives, and has high computational costs. In addition, the inverse model is another promising alternative for solving the optimization tasks required for inverse problems. Unlike common optimization methods based on forward mapping, the inverse model learns the relationship between performance parameters and structural parameters, rather than the mapping of structural parameters to performance parameters. It can directly predict the corresponding values ​​of structural parameters based on performance indicators, without the need for any iterative algorithms based on the forward model. Therefore, the inverse modeling method has advantages in terms of computational time.

[0064] The present invention uses artificial neural network ANN to establish the inverse model. Artificial neural networks are well known for their predictive ability. They can provide a highly close fit to new data after training. By introducing prior knowledge into the ANN model, the accuracy and requirements of large data samples can be improved.

[0065] Although the inverse model has the advantage of fast prediction rather than iterative optimization, there are also some very challenging problems. First, the construction of the inverse model of the microwave design problem is quite complicated. Depending on the desired goal, especially when it comes to broadband problems, the dimensionality of the input space is very high. Therefore, the training of the inverse model requires a large amount of full-wave simulation data as samples. Compared with the forward proxy model optimization under small samples, a lot of "preparation work" cannot be ignored. This is relatively inefficient for single prediction optimization, but if the inverse model is used multiple times, the training time is spread over each use, which is a great advantage.

[0066] Another problem that needs to be solved urgently is that the mapping relationship of the inverse model is often non-singular. For the forward model, a set of structural parameters only corresponds to a set of performance parameters, and there is only one solution, but for the inverse model, a set of performance parameters may be obtained from multiple sets of structural parameters, such as Figure 2 As shown in Figure 1, this means that inverse models often face a one-to-many problem. It is generally impossible to train a model to fit multiple output values ​​for the same input value at the same time, so the model training error will be high and the model accuracy will be poor. Therefore, in many practical inverse problems, it is difficult to train the model.

[0067] In view of the above two problems and the actual transformer comprehensive application scenarios, the present invention proposes the following solutions. First, introduce prior knowledge to reduce the model dimension. For a wide-band optimization problem, the traditional and classic method is to add the frequency feature dimension to the original input parameters, but this will increase the difficulty of training the inverse model. This paper adopts an inverse model combined with the prior knowledge of the on-chip transformer. The prior knowledge helps to avoid falling into the local minimum and improve the speed of finding the global minimum, while working well with less training data. It is known that the coil inductance is relatively stable when it is far away from the self-resonant frequency and the mutual inductance resonant frequency. For broadband optimization inductance, all frequency points can be replaced by several more important frequency points in the frequency band, such as the maximum value, minimum value, and the value at the center frequency of the bandwidth, or the frequency points are selected at intervals during the training model, and sparse sampling is performed without affecting the overall trend. Of course, this method needs to be coordinated with the modeling of the resonant frequency, and both are indispensable. In addition, for a completely symmetrical transformer structure, only the performance parameters of one primary or secondary coil are selected for observation, the input impedance only focuses on the part within the working bandwidth, and the minimum self-resonant frequency is determined by the positive or negative quality factor. In short, combining the characteristics of the transformer itself will neither excessively reduce the accuracy of the inverse model nor significantly reduce the dimension, so as to reduce the amount of calculation of the model.

[0068] The second is to solve the one-to-many problem by increasing the input parameter characteristics. In practical applications, a set of performance parameter optimization targets can correspond to a variety of structural parameters, but the performance parameters corresponding to these structural parameters must be different in the entire frequency range. Specific auxiliary constraints are introduced in the input to limit the solution range of the output value. Taking the on-chip transformer design as an example, at a certain operating frequency, there may be multiple groups of comprehensive results with the same primary and secondary coil inductance, quality factor and coupling coefficient. However, if the frequency feature dimension is increased at this time, the dimensional space will be appropriately increased to screen out some samples, or if the input impedance target requirement is added at this time, the one-to-many problem can be converted into a one-to-one problem and then solved.

[0069] Next, we will introduce the specific steps of using ANN to realize on-chip transformer synthesis through an example. The neural network used is a two-layer network with 10 hidden layers. The model diagram is as follows Figure 3 As shown. It is just the opposite of the forward model, the input is the primary and secondary coil inductance L p , L s , quality factor Q p , Q s , coupling coefficient k, maximum available gain G max The output is line width W, line spacing S, inner diameter D in , coil turns N p 、N s And other structural parameters.

[0070] The comprehensive target of the transformer is the primary and secondary coil inductance L in the 45-55GHz band. p =L s =0.15nH, the fluctuation within the bandwidth does not exceed 5%, the coupling coefficient k=0.7, the fluctuation within the bandwidth does not exceed 5%, the minimum self-resonant frequency f sr =80GHz, seek the maximum available gain G within the bandwidth max maximize.

[0071] Before prediction, the network must be trained first. 1000 transformer samples are randomly generated. The structure is a single-ended staggered interwinding quadrilateral. The target frequency is 45-55GHz. Each input parameter selects the maximum and minimum values ​​in the 45-55GHz working frequency band to reduce the dimension. 700 samples are used for training the model, 150 samples are used for verification, and 150 samples are used for testing. The ANN training process is shown in Figure 4 .

[0072] The prediction error of the model is measured using the mean square error, which is calculated as follows:

[0073]

[0074] Where n is the number of samples, y i is the simulated value of the ith sample, is the predicted value of the ith sample. The prediction error of the neural network is shown in Table 3, and the MSE is stable around 0.6.

[0075] Table 3

[0076] Observations MSE train 700 0.65 verify 150 0.39 test 150 0.59

[0077] After the neural network training is completed, prediction is performed according to the comprehensive target input: L p =[0.1545 0.1455],L s =[0.1545 0.1455],k=[0.721 0.679],G max =[0.89 0.86]. At this time, G is selected max The target value is an indicator that requires multiple iterations to achieve manually.

[0078] After many experiments, the average prediction time is 0.008 seconds, and the output solution is as follows:

[0079] Table 4

[0080] W(μm) S(μm) <![CDATA[D in (μm)]]> <![CDATA[N p / N s ]]> 2.83 1.85 15.87 2

[0081] The predicted structural parameters are verified by full-wave simulation, and the performance parameters are as follows:

[0082] Table 5

[0083]

[0084] It should be noted that the data listed in Table 5 are the minimum coupling coefficient and minimum G max , the inductance value with the largest deviation from the target value. Although the maximum deviation error of the inductance value in the broadband is 5.3%, other targets meet the requirements, and the difference between the inductance value and the target value is small. It is worth noting that the single prediction time of the inverse network is much shorter than the iterative optimization time of the forward model, excluding the training time, which is still of great reference significance for the automatic synthesis design of on-chip transformers.

[0085] Taking the wide-band maximization coupling coefficient as an example, a machine learning-assisted on-chip transformer automatic synthesis method disclosed in an embodiment of the present invention is described in detail below.

[0086] The comprehensive target is the primary and secondary coil inductance value L at 24-32GHz p =0.5nH, L s =0.5nH, the fluctuation within the bandwidth does not exceed 10%, the bandwidth upper limit f = 32GHz, the primary and secondary coil quality factor Q p >5,Q s >5, minimum self-resonant frequency f sr = 45GHz, and seek to maximize the coupling coefficient k within the bandwidth, so the problem that needs to be optimized becomes

[0087] max(k 24-32GHz )

[0088]

[0089] Among them, L p , L s The inductance value, Q, obtained from the full-wave simulation at 24-32 GHz pf , Q sf is the quality factor at 32 GHz, Q pfsr , Q sfsr is the quality factor at 45 GHz. If the quality factor at the minimum self-resonant frequency is greater than 0, it is considered to be non-resonant.

[0090] like Figure 1 As shown, a machine learning-assisted on-chip transformer automatic synthesis method disclosed in an embodiment of the present invention includes the following steps:

[0091] Step 1: Set the on-chip transformer electrical parameter targets and transformer structural parameter constraints, and set related process constraints.

[0092] In this embodiment, the relevant process constraints include the name of the process to be declared, the name of the metal layer used, the name of the constraint group, etc. The electrical parameter targets vary slightly depending on the optimization target. Generally speaking, they include the primary and secondary coil inductance L p , L s , quality factor Q p , Q s , coupling coefficient k, maximum available gain G max , insertion loss IL, operating frequency f, minimum self-resonant frequency f sr , input impedance Z in and optimized bandwidth BW. Structural parameters include maximum line width W max , minimum line width W min , maximum line spacing S max , minimum line spacing S min , maximum inner diameter D in,max , minimum inner diameter D in,min , maximum number of coil turns N max , minimum number of coil turns N min and the maximum area A max , and the user can also select the desired transformer structure. The geometric parameter constraints of the symmetrical stacked transformer are shown in Table 6.

[0093] Table 6

[0094] parameter Numerical lower bound Upper bound Line width W(μm) 2.2 10 Line spacing S(μm) 2 5 <![CDATA[Outer diameter D out (μm)]]> 15 300 Number of turns N 1 2

[0095] Step 2: Use the inverse artificial neural network to predict a set of structural parameters as the initial solution.

[0096] In this embodiment, an artificial neural network is used to learn the relationship between the performance parameters and structural parameters of the on-chip transformer. After the network training is completed, only a set of performance parameter targets need to be input to quickly solve a set of structural parameter solutions. Subsequent sampling and optimization ranges are related to the initial solution.

[0097] Step 3: Randomly sample the structural parameters to obtain a part of the structural parameters, then sample the structural parameters around the initial solution, and collect the initial samples through full-wave electromagnetic simulation.

[0098] In this embodiment, the classical sampling method Latin hypercube sampling is used to randomly sample the structural parameters, a portion of which is obtained within a 30% floating space around the initial solution, the number of samples is 80, and the initial samples are collected through full-wave electromagnetic simulation. On the one hand, since full-wave simulation is very time-consuming, the number of samples of the initial proxy model needs to be as small as possible, otherwise the algorithm efficiency will decrease. On the other hand, the design space needs to be covered as much as possible. Too sparse sampling will result in very little information in some areas, and the reliability of the proxy model is poor.

[0099] Step 4: Compress the sample full-wave simulation data to reduce the sample dimension and facilitate the training of the proxy model.

[0100] In this embodiment, for the on-chip transformer synthesis of a wide-bandwidth, due to the large number of frequency points, directly establishing a proxy model will cause the amount of data calculation to grow exponentially, greatly increasing the optimization time and even making it unacceptable. Therefore, discrete cosine transform is used for data compression to reduce the amount of proxy model calculation and ensure its accuracy.

[0101] Step 5: Train the GPR proxy model to learn the mapping relationship between the transformer structural parameters and performance parameters in the sample set, replacing the traditional equivalent circuit model and costly full-wave electromagnetic simulation.

[0102] In this embodiment, prior knowledge is combined when training the proxy model, which will make the model have higher prediction accuracy, and can also reduce the time of proxy model training and prediction, while improving efficiency and performance. For example, for a fully symmetrical interlaced winding structure transformer, this embodiment only models and predicts the inductance and quality factor of the primary coil, and the number of models is reduced by half; when optimizing the wide-band transformer, in view of the relatively smooth overall curve of the quality factor, modeling the bandwidth upper limit quality factor can also reduce the amount of model calculation. The GPR proxy model uses the matern3 / 2 kernel function. For the case where there are multiple input parameters with high sensitivity in the on-chip transformer synthesis problem, the single-target GPR proxy model has higher accuracy and reduces the amount of calculation, so each performance parameter is modeled separately.

[0103] Step 6: Use a population-based metaheuristic algorithm for global optimization, inverse the network initial solution to constrain the optimization range, and optimize a set of transformer structural parameters.

[0104] In this embodiment, a genetic algorithm is used for global optimization, the initial solution of the inverse network constrains the optimization range (with a fluctuation of 30% around the initial solution), and the fitness function is corrected using data pre-screening technology. The multi-path optimization brought about by different confidence lower limit constants enhances the convergence and exploratory nature of the algorithm. The results of the multi-path optimization are compared and the optimal samples are output to optimize a set of transformer structural parameters.

[0105] Specifically, the data pre-screening technology is used to modify the fitness function, so that the optimization algorithm can add sample points in the area where the optimal solution may appear to avoid falling into the local optimum. At the same time, multiple LCB values ​​randomly generated in [-2,2] are used for multi-path optimization to enhance the exploratory nature of the genetic algorithm without increasing the complexity of the algorithm. The standard for LCB to judge the quality of new individuals is:

[0106] y LCB =y(x)-ws(x)

[0107] Among them, y(x) is the function value corresponding to x calculated by the GPR proxy model, s(x) is the prediction standard deviation obtained by the GPR proxy model, and w is the LCB value that measures the algorithm's exploration ability.

[0108] Step 7: Full-wave simulation verification. Perform full-wave simulation verification on the structural parameters obtained in step 6. If the design goal is met, the optimal layout is output. If not, the simulation results are added to the sample set. Repeat steps 5 to 7 until the iteration stop condition is met. The optimization termination condition is set to optimize to the maximum number of iterations or each parameter reaches the expected optimization goal. When the optimization goal contains maximization or minimization, the maximum or minimum value can be set to remain unchanged for a number of consecutive generations and within the maximum number of iterations, so that the transformer is fully optimized.

[0109] The optimal sample of the optimization iteration described in the embodiment of the present invention is as follows: Figure 5 As shown, it is worth noting that Figure 5 The minimum coupling coefficient within the bandwidth of the optimal sample is shown in , that is, all k within the bandwidth are greater than this value. In the early stage of optimization, the initial solution predicted by the inverse network is the optimal sample, which also shows the powerful prediction ability of the artificial neural network. However, the optimal sample at this time is only the sample closest to the optimization target in the sample set, and it does not necessarily fully meet the conditions. Therefore, after several rounds of optimization, the optimal sample has changed and the coupling coefficient has decreased. This shows that in the optimization process, a sample that is generally more in line with the target has been found, because there are other constraints when maximizing the coupling coefficient in this case. After 16 rounds of exploration, the algorithm found a sample that meets all other requirements and has the largest coupling coefficient. The optimization continues. While satisfying the constraints, the coupling coefficient gradually increases until the 22nd round of optimization. The subsequent algorithm converges, and the optimal sample has not changed for 10 consecutive rounds. The entire optimization process ends and the optimal solution is output.

[0110] This embodiment uses the root mean square error to measure the prediction accuracy of the proxy model, and the calculation formula is:

[0111]

[0112] in is the output prediction matrix, n v is the number of samples used for validation, n i is the number of frequency points before the self-resonant frequency of the sample, is the predicted value of the jth frequency point of the ith sample, x ij The simulated value of the jth frequency point of the ith sample.

[0113] The minimum coupling coefficient within the bandwidth obtained in each round of optimization and its prediction error are as follows: Figure 6As shown, we can see that as the number of optimizations increases, the proxy model is updated online, the prediction accuracy of the model becomes higher and higher, and the prediction error within the entire bandwidth gradually decreases, which also shows the effectiveness of the GPR proxy model.

[0114] The final optimized transformer structural parameters are shown in Table 7.

[0115] Table 7

[0116] W(μm) S(μm) <![CDATA[D in (μm)]]> <![CDATA[N p ]]> <![CDATA[N s ]]> 2.45 2.52 54.99 2 2

[0117] The performance parameters of this symmetrical stacked 2:2 structure transformer are as follows Figure 7 In the 24-32GHz frequency band, the primary and secondary inductance values ​​are around 0.5nH, with a deviation of no more than 10%, which is relatively stable. The quality factors at 32GHz are Q p =7.87, Q s =12.02, broadband internal coupling coefficient k>0.832. It should be noted that the winding method of the primary and secondary coils of the symmetrical stacked 2:2 structure makes them distributed in different metal layers, with different metal thicknesses and distances from the substrate, and different losses, so their quality factors are different, but the overall trend is the same.

[0118] The embodiment of the present invention also discloses a computer program product, including a computer program / instruction, which implements the steps of the machine learning-assisted on-chip transformer automatic synthesis method disclosed in the above embodiment when the computer program / instruction is executed by the processor. The program / instruction code for implementing the method of the present invention can be written in any combination of one or more programming languages. These program / instruction codes can be provided to a processor or controller of a general-purpose computer, a special-purpose computer, or other programmable data processing device, so that the program / instruction code implements the steps of the method of the present invention when it is executed by the processor or controller. The program / instruction code can be executed entirely on the machine, partially on the machine, partially on the machine as an independent software package and partially on a remote machine, or entirely on a remote machine or server.

[0119] The matters not described in detail in the present invention are all known technologies to those skilled in the art.

[0120] In summary, the above is only a specific implementation of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art who is familiar with the technical field can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A machine learning-assisted on-chip transformer automatic synthesis method, characterized in that: The method comprises the following steps: Step 1: Set the electrical performance parameter target of the on-chip transformer and the transformer structure parameter constraints, and set the relevant process constraints; Step 2: Use the inverse artificial neural network to predict the transformer electrical performance parameters and obtain a set of structural parameters as the initial solution; Step 3: Randomly sample the structural parameters to obtain a part of the structural parameters, then sample around the initial solution to obtain a part of the structural parameters, and collect the initial samples through full-wave electromagnetic simulation; Step 4: compress and transform the sample full-wave simulation data to reduce the sample dimension; Step 5: Train the GPR proxy model to learn the mapping relationship between transformer structural parameters and performance parameters, replacing the traditional equivalent circuit model and full-wave electromagnetic simulation; Step 6: Use a population-based meta-heuristic algorithm for global optimization, inverse the artificial neural network initial solution to constrain the optimization range, and optimize a set of transformer structural parameters; Step 7: Full-wave simulation verification. Perform full-wave simulation verification on the structural parameters obtained in step 6. If the design goals are met, the optimal structural parameters and / or layout are output. If not, the simulation results are added to the sample set. Repeat steps 5 to 7 until the iteration stop condition is met.

2. The machine learning-assisted on-chip transformer automatic synthesis method according to claim 1, characterized in that: In step 1, the electrical performance parameters of the transformer include a partial combination of primary and secondary coil inductance, quality factor, coupling coefficient, maximum available gain, insertion loss, operating frequency, minimum self-resonant frequency, input impedance and optimized bandwidth; the structural parameters include maximum line width, minimum line width, maximum line spacing, minimum line spacing, maximum inner diameter, minimum inner diameter, maximum number of coil turns, minimum number of coil turns and maximum area.

3. The machine learning-assisted on-chip transformer automatic synthesis method according to claim 1, characterized in that: In the step 2, an artificial neural network is used to establish an inverse model to learn the mapping relationship between performance parameters and structural parameters. The inverse model introduces prior knowledge of the on-chip transformer to reduce the model dimension. For broadband optimization inductance, all frequency points are replaced by more important frequency points in the frequency band, or frequency points are selected at intervals when training the model. For a completely symmetrical transformer structure, only the performance parameters of one primary or secondary coil are selected for observation, and the input impedance only focuses on the part within the working bandwidth. The minimum self-resonant frequency is determined by the positive or negative quality factor. The inverse model solves the one-to-many problem by increasing the input parameter characteristics, and introduces auxiliary constraints in the input to limit the solution range of the output value.

4. The machine learning-assisted on-chip transformer automatic synthesis method according to claim 3, characterized in that: In step 2, the inverse model input performance parameters include primary and secondary coil inductance, quality factor, coupling coefficient and maximum available gain, and the output structural parameters are line width, line spacing, inner diameter and number of turns of primary and secondary coils.

5. The machine learning-assisted on-chip transformer automatic synthesis method according to claim 1, characterized in that: In step 3, firstly, Latin hypercube random sampling is used to obtain transformer structural parameters, and then random sampling is performed in a space with a certain proportion of floating values ​​around the initial solution to obtain transformer structural parameters, and then prior knowledge is added for pre-screening to clean out some parameters that do not meet the transformer modeling requirements.

6. The machine learning-assisted on-chip transformer automatic synthesis method according to claim 1, characterized in that: In step 4, discrete cosine transform is used to perform data compression.

7. The machine learning-assisted on-chip transformer automatic synthesis method according to claim 1, characterized in that: In step 5, the GPR proxy model selects the matern3 / 2 kernel function, and a single-objective GPR proxy model is modeled for each performance parameter.

8. The machine learning-assisted on-chip transformer automatic synthesis method according to claim 1, characterized in that: In step 6, a genetic algorithm is used for global optimization, and multi-path optimization brought by using different lower confidence limits (LCB) constants is used to enhance the convergence and exploration of the algorithm.

9. The machine learning-assisted on-chip transformer automatic synthesis method according to claim 1, characterized in that: In step 6, the fitness function is modified by using data pre-screening technology, so that the optimization algorithm increases sample points in the area where the optimal solution may appear to avoid falling into the local optimum; at the same time, multiple randomly generated LCB values ​​are used for multi-path optimization, and the standard of LCB for judging the quality of new individuals is: y LCB =y(x)-ws(x) Among them, y(x) is the function value corresponding to the structural parameter x calculated by the GPR proxy model, s(x) is the prediction standard deviation obtained by the GPR proxy model, and w is the LCB value that measures the algorithm's exploration ability.

10. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instructions are executed by a processor, the steps of the machine learning-assisted on-chip transformer automatic synthesis method according to any one of claims 1 to 9 are implemented.

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