A machine learning-assisted on-chip transformer automatic synthesis method

Abstract

The present invention discloses a machine learning-assisted on-chip transformer automatic synthesis method. The method first sets the electrical parameter targets and process constraints of the on-chip transformer. An inverse artificial neural network is used to quickly predict a set of structural parameters as an initial solution. The structural parameters are then randomly sampled, with a portion of the sample space floating around the initial solution. Full-wave electromagnetic simulation is then performed to obtain samples. The sample full-wave simulation data is compressed, and a GPR proxy model is trained using prior knowledge of the on-chip transformer, thereby reducing the model's dimensionality and improving prediction accuracy. Global optimization is then performed, using the initial solution to constrain the optimization range. Multi-path optimization with different confidence lower bound constants is further employed to enhance the algorithm's convergence and exploratory capabilities. The present invention employs an algorithm that combines inverse networks with forward optimization, achieving lower computational costs and higher optimization speeds while ensuring accuracy. This advances the automation and intelligence of on-chip passive device design.

Description

Technical Field

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

[0002] On-chip passive transformers are crucial components in RF design, enabling impedance matching, signal coupling, power transmission, and DC isolation in RFICs. They play a crucial role in reducing component count and chip area. On-chip spiral transformers, consisting of two coupled spiral inductors, are typically defined by multiple geometric parameters. However, only a small fraction of the thousands of possible geometric parameter combinations can simultaneously meet both design specifications and design metrics. Therefore, deriving the transformer's geometric parameters from these metrics is fraught with difficulties. This process, the reverse of modeling, is known as the synthesis problem. The synthesis of on-chip spiral transformers has always been a major challenge in passive device design, and automated synthesis of on-chip transformers is crucial for automated RFIC design.

[0003] With the continuous development of machine learning technology, surrogate model-assisted methods appear to be the most suitable solution to address the above difficulties. The main idea is to replace expensive full-wave electromagnetic simulation models with fast surrogate models. These models allow the use of population-based metaheuristic algorithms to identify Pareto sets at a low computational cost. Achieving optimization goals under high-dimensional and small sample sizes is a complex and urgent problem. Finding fast and effective intelligent synthesis algorithms is crucial to the design and performance of transformers and even RFICs. Summary of the Invention

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

[0005] Technical solution: To achieve the above objectives, the present invention adopts a technical solution: a machine learning-assisted on-chip transformer automatic synthesis method, comprising the following steps:

[0006] Step 1: Set the on-chip transformer electrical performance parameter targets and transformer structural parameter constraints, and set related 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) surrogate model to learn the mapping between transformer structural parameters and performance parameters in the sample set, replacing traditional equivalent circuit models and costly full-wave electromagnetic simulations.

[0011] Step 6: Use a population-based metaheuristic 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 to learn the mapping relationship between performance parameters and structural parameters, and then a set of structural parameters is obtained as an initial solution based on the target prediction of the comprehensive performance parameters of the transformer. The inverse model introduces prior knowledge of the on-chip transformer to reduce the model dimension. For broadband optimization of inductance, all frequency points are replaced by more important frequency points within the 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 increasing the input parameter characteristics 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 the output structural parameters are line width, line spacing, inner diameter and number of turns of the primary and secondary coils.

[0016] Furthermore, in step 3, Latin Hypercube Sampling (LHS) is first used to randomly sample the transformer structural parameters, and then the transformer structural parameters are obtained within a space with a certain proportional value floating around the initial solution. Prior knowledge is then 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 increase 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 fitness function; for the case where the on-chip transformer synthesis problem has multiple highly sensitive input parameters, 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, avoiding 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 LCB standard for judging 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 only requires the transformer's electrical performance parameter targets and structural parameter constraints to achieve automatic integrated design of on-chip transformers, greatly improving the work efficiency of RF circuit designers;

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

[0027] (3) The present invention reduces computational cost and time by establishing a GPR proxy model instead of 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, which improves the prediction accuracy and speed of the model and saves time costs;

[0029] (5) The present invention uses randomly generated multiple 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 local optimality.

[0030] (6) The present invention adopts an algorithm that combines inverse network and forward optimization, which has lower computational 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 This is a schematic diagram of the reverse network one-to-many problem of the present invention;

[0033] Figure 3 This is a schematic diagram of the reverse modeling of the 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 graph for the optimization iteration of the embodiment of the present invention;

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

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

[0038] To make the objectives, technical solutions and advantages of the embodiments of the present invention more clear, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to 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 inverse artificial neural network involved in the embodiments of the present invention and the related improvement work involved in the present invention are explained.

[0040] On-chip transformer optimization problems involve numerous parameters and are highly sensitive. To save full-wave simulation time, a proxy model with a small sample size is required. The GPR proxy model has demonstrated excellent performance in machine learning-assisted circuit design. Furthermore, GPR outputs not only predict values ​​but also provide confidence intervals, representing a Gaussian-distributed probability function, which greatly facilitates the introduction of multi-path optimization techniques. Therefore, using an online updated Gaussian process regression model as a proxy model in machine learning-assisted on-chip transformer design offers significant advantages in both prediction accuracy and the number of optimization algorithm iterations.

[0041] Gaussian process regression predicts the value of an unknown point by learning the relationships between them. Therefore, a function that calculates the similarity between two points in the input space is crucial. This function is called a kernel function, also known as a covariance function. Many types of kernel functions can be used for GPR, including linear, polynomial, radial basis function (RBF), Maternal kernel, periodic, and rational quadratic functions. Each kernel function corresponds to different parameters to control the shape and scale, mapping the sample into a higher-dimensional space.

[0042] Because the parameters of the kernel function directly affect the complexity of the model, the performance of different kernel functions can vary significantly. However, there is currently no consensus on the selection of kernel functions; kernel functions must be selected based on the specific problem or application scenario. Some scholars have conducted research in this area, known as kernel engineering. Generally, this approach involves experimentation, and kernel functions can be combined with many optimization algorithms, often yielding unexpected performance results through permutations and combinations. Furthermore, kernel functions do not require knowledge of the feature space or the transformation function; their calculations are performed solely through dot products, making it possible to find data relationships in high-dimensional spaces with extremely low computational cost.

[0043] The most common kernel function in Gaussian processes 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 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 include 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 conducted below. The transformer structure adopts an interlaced quadrilateral, and the comprehensive target is the primary and secondary coil inductance L at 50GHz. 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 primary and secondary coils have the same number of turns.

[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 this invention all utilized a 40nm CMOS process. It is understood that the present invention's approach is not limited to a specific process and is applicable to a variety of processes. Considering chip design requirements, in addition to the structural constraints of each parameter, the input parameters must also meet the constraints listed in Table 1. The lower limit is closely tied to chip design rules, while the upper limit is as large as possible. Except for experienced engineers, most beginners and those with no transformer design experience have no way of knowing the approximate range of geometric parameters in advance, which is one of the primary design principles of this invention. Two metal layers are used: the main metal layer is located in the MTT2 layer, and the TM1 layer is used to lead out the inner ring ports.

[0059] The algorithm was run on a server with two AMD EPYC 7F52 processors and 512GB 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, meeting all performance requirements at the operating frequency. However, the RBF kernel performs poorly in terms of optimization. While ardmatern5 / 2, which uses fixed-length parameters for each predictor, and ardmatern3 / 2, as well as matern5 / 2, achieve similar results, matern3 / 2 clearly outperforms. Therefore, the on-chip transformer synthesis methods described below all use matern3 / 2 as the kernel function for the Gaussian regression process.

[0063] Multi-objective comprehensive problems are essentially inverse problems, where performance objectives are used to determine structural parameters. Traditional forward optimization often requires multiple iterations to converge, resulting in high computational costs. Furthermore, inverse modeling offers a promising alternative for solving the optimization tasks required for inverse problems. Unlike common optimization methods based on forward mapping, inverse models learn the relationship between performance parameters and structural parameters, rather than mapping structural parameters to performance parameters. They can directly predict the corresponding values ​​of structural parameters based on performance indicators, eliminating the need for any iterative algorithms based on forward models. Therefore, inverse modeling offers advantages in terms of computational time.

[0064] The present invention uses artificial neural networks (ANNs) to build an inverse model. ANNs are known for their predictive power; they can provide a highly accurate fit to new data after training. By incorporating prior knowledge into the ANN model, the accuracy and accuracy of large data samples can be improved.

[0065] While inverse models offer the advantage of rapid prediction rather than iterative optimization, they also present some challenging challenges. First, constructing inverse models for microwave design problems is quite complex. Depending on the desired objectives, especially when broadband problems are involved, the dimensionality of the input space can be very high. Therefore, training inverse models requires a large amount of full-wave simulation data as samples. Compared to forward surrogate model optimization with smaller sample sizes, the extensive "preparatory work" required is considerable. This makes single-shot prediction optimization less efficient, but if the inverse model is used multiple times, the training time can be spread over each use, which is a significant 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 corresponds to only one set of performance parameters, and there is only one solution. However, 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 2, this means that inverse models often encounter a one-to-many problem. It's generally impossible to train a model to fit multiple outputs to the same input, resulting in high training error and poor accuracy. Consequently, training models for many practical inverse problems is difficult.

[0067] In response to the above two problems and the actual transformer comprehensive application scenarios, the present invention proposes the following solutions. The first is to 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-resonance frequency and the mutual inductance resonance 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 can be selected at intervals when training the model, and sparse sampling is performed without affecting the overall trend. Of course, this method needs to be combined 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, thereby reducing the computational complexity of the model.

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

[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. 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. 1000 transformer samples are randomly generated. The structure is a single-ended interleaved quadrilateral with a target frequency of 45-55 GHz. The maximum and minimum values ​​of each input parameter in the 45-55 GHz operating frequency band are selected to reduce the dimension. 700 samples are used for training the model, 150 samples are used for validation, 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 i-th sample, is the predicted value of the i-th 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 multiple 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 were verified by full-wave simulation, and the performance parameters were obtained 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 within the broadband is 5.3%, all other objectives meet the requirements, and the deviation from the target value is relatively small. Notably, excluding the training time, the single prediction time of this inverse network is much shorter than the iterative optimization time of the forward model, which still holds important reference value for the automatic synthesis design of on-chip transformers.

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

[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, we seek to maximize the coupling coefficient k within the bandwidth, so the problem to be optimized becomes

[0087] max(k 24-32GHz )

[0088]

[0089] Among them, L p 、L s The inductance value of 24-32GHz obtained by full-wave simulation, Q pf , Q sf is the quality factor at 32GHz, 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, an embodiment of the present invention discloses a machine learning-assisted on-chip transformer automatic synthesis method, including 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, but generally include the primary and secondary coil inductance values ​​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 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 Numerical 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 needs 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 example, the classical Latin hypercube sampling method was used to randomly sample structural parameters. A portion of the sampled parameters were taken within a 30% range around the initial solution, with a total of 80 samples. Initial samples were collected through full-wave electromagnetic simulation. On the one hand, because full-wave simulation is very time-consuming, the number of samples in 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. Overly sparse sampling will result in very little information in certain areas, reducing the reliability of the proxy model.

[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 wideband on-chip transformer synthesis, due to the large number of frequency points, directly establishing a proxy model will cause the amount of data calculation to increase exponentially, significantly increasing the optimization time and even becoming 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 incorporated into the training of the proxy model, which results in a model with higher prediction accuracy and reduces the time required for proxy model training and prediction, while also improving efficiency and performance. For example, for a fully symmetrical interleaved winding structure transformer, this embodiment only models and predicts the inductance and quality factor of the primary coil, reducing the number of models by half; when optimizing a wide-band transformer, given the relatively smooth overall quality factor curve, 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 on-chip transformer synthesis problems with multiple highly sensitive input parameters, 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 (fluctuating by 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 sample is output to optimize a set of transformer structural parameters.

[0105] Specifically, the fitness function is modified using data pre-screening technology, allowing the optimization algorithm to add sample points in areas where the optimal solution may appear, avoiding falling into local optimality. At the same time, multiple LCB values ​​randomly generated within [-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 LCB criterion for judging 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: Full-wave simulation verification is performed on the structural parameters obtained in Step 6. If the design objectives are met, the optimal layout is output. If not, the simulation results are added to the sample set, and Steps 5 to 7 are repeated 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 target. When the optimization target includes maximization or minimization, the maximum or minimum value can be set to remain unchanged for a certain number of consecutive generations within the maximum number of iterations to fully optimize the transformer.

[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 figure shows the minimum coupling coefficient within the optimal sample bandwidth, meaning that all k within the bandwidth are greater than this value. Initially, the inverse network predicts the optimal sample as the initial solution, demonstrating the powerful predictive power of the artificial neural network. However, the optimal sample at this point is simply the sample closest to the optimization target within the sample set and does not necessarily fully meet the requirements. Therefore, after several rounds of optimization, the optimal sample changes, while the coupling coefficient decreases. This indicates that the optimization process has found a sample that generally meets the target, because in this case, there are other constraints when maximizing the coupling coefficient. After 16 rounds of exploration, the algorithm found a sample that meets all other requirements and has the largest coupling coefficient. Optimization continued, gradually increasing the coupling coefficient while satisfying the constraints until the 22nd round of optimization, when the algorithm converged. After 10 consecutive rounds of optimization, the optimal sample remained unchanged, concluding the optimization process and outputting the optimal solution.

[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 i-th sample, x ij The simulated value of the j-th frequency point of the i-th 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 in the figure, 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, and the broadband internal coupling coefficient k>0.832. It should be noted that the winding pattern of the primary and secondary coils in the symmetrically stacked 2:2 structure results in them being distributed on different metal layers, with varying metal thicknesses and distances from the substrate, resulting in varying losses. Consequently, their quality factors differ, but the overall trend remains the same.

[0118] The embodiments of the present invention further disclose 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 disclosed in the aforementioned embodiments. 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 when the program / instruction code is executed by the processor or controller, the steps of the method of the present invention are implemented. The program / instruction code can be executed entirely on the machine, partially on the machine, partially on the machine as a stand-alone software package and partially on a remote machine, or entirely on a remote machine or server.

[0119] Anything not described in detail in the present invention is well known to those skilled in the art.

[0120] In summary, the foregoing is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection 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 on-chip transformer electrical performance parameter targets and transformer structural parameter constraints, and set related process constraints; Step 2: Use an inverse artificial neural network to predict the transformer's electrical performance parameters and obtain a set of structural parameters as an initial solution. The 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 bandwidth optimization, all frequency points within the band are replaced by more important frequency points, or frequency points are selected at intervals during model training. For a completely symmetrical transformer structure, only the performance parameters of one coil, either primary or secondary, are selected for observation, and the input impedance is only focused on the portion within the operating 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. Step 3: Randomly sample the structural parameters to obtain a portion of the structural parameters, then sample the structural parameters around the initial solution to obtain another portion, 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 metaheuristic 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 the 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; and 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 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 the primary and secondary coils.

4. The machine learning-assisted on-chip transformer automatic synthesis method according to claim 1, characterized in that In step 3, first, Latin hypercube random sampling is used to obtain transformer structural parameters, and then random sampling is performed in a space with a certain proportional value floating around the initial solution to obtain transformer structural parameters, and then prior knowledge is added for pre-screening.

5. 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.

6. 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.

7. 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 about by using different lower confidence limits (LCB) constants is used to enhance the convergence and exploration of the algorithm.

8. 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 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. The LCB standard for judging the quality of new individuals is: ;in, is the structural parameter calculated by the GPR proxy model The corresponding function value is is the forecast standard deviation obtained by the GPR proxy model, It is the LCB value that measures the algorithm's exploration ability.

9. 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 8 are implemented.

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