Method for establishing multi-dimensional piecewise linear transistor behavior model based on PSO optimization

Abstract

This invention discloses a method for establishing a multidimensional piecewise linear transistor behavior model based on PSO optimization. This method utilizes the CSWPL function to describe the relationship between the incident and reflected waves at the ports of GaN power transistors. Based on the CSWPL function, the dimensions are expanded through self-nesting to establish a corresponding behavior model. Then, the PSO algorithm is used to optimize the partition thresholds in the multidimensional piecewise linear behavior model, further improving the model's accuracy. Based on the PSO algorithm and CSWPL function, this invention develops a model for predicting the behavior of GaN HEMT devices under large signal and different input power conditions, achieving high accuracy. Experiments demonstrate that the behavior model established in this invention fits the measured data very well.

Description

Technical Field

[0001] This invention belongs to the field of semiconductor device technology and relates to the modeling of semiconductor devices in electronic design automation (EDA), specifically to a method for establishing a multidimensional piecewise linear transistor behavior model based on PSO optimization. Background Technology

[0002] In recent years, with the continuous advancement of microelectronics technology, related fields such as semiconductor modeling have also flourished. As a crucial component of communication systems, the field of large-signal modeling for radio frequency power transistors has also made significant progress. Existing radio frequency power transistor models mainly fall into four categories: physical models, empirical models, lookup table models, and behavioral models. Physical models are guided by semiconductor physics and can directly guide semiconductor device fabrication, but they also have the highest computational load and complexity. Empirical models are equivalent circuit models of transistors constructed based on expressions related to the physical laws governing the circuit. They are constrained by the expressions of equivalent circuits and nonlinear elements, and cannot well fit complex electrical characteristics using empirical formulas, thus limiting model accuracy. Lookup table models are directly constructed based on measured transistor data. Lookup table models have very high accuracy at measurement points, but the data required for modeling is extremely cumbersome. Behavioral models represent the behavior of the system by describing its input states and corresponding output states.

[0003] While current new semiconductor devices, such as GaN devices, have excellent performance, their complex electrical characteristics mean that using physical and empirical models can reduce circuit design efficiency and fail to fully utilize the device's performance. Behavioral models, on the other hand, are black-box-like mathematical models that do not require consideration of complex electrical characteristics and physical processes, giving them a natural advantage.

[0004] Traditional behavioral models include Cardiff models, X-parameter models, Volterra series models, etc., all of which can support the modeling of nonlinear characteristics of various RF / MW devices and easily establish nonlinear functions for transistors, avoiding the tedious process of establishing empirical formulas in empirical modeling. Piecewise linear functions, such as the piecewise linear (CWPL) function, are frequently used in RF device modeling because they can accurately fit the nonlinear characteristics of strongly nonlinear systems. Typical CWPL models include power amplifier models and transistor models. Power amplifier models generally need to consider digital predistortion (DPD) technology, while power transistor models need to fully fit the input-output behavior of transistor ports and do not need to consider DPD-related modeling. Since partitioning and thresholding of CWPL function models are often prioritized, threshold optimization can be performed using the Synchronous Random Perturbation (SPSA) algorithm compared to traditional models such as Cardiff and X-parameter models. However, the SPSA algorithm escapes local optima through random perturbation, and its essence is still a gradient descent algorithm. When it encounters a non-differentiable point, the gradient changes drastically, resulting in weak stability and nonlinear optimization ability. At the same time, CWPL only fits in one dimension, so there is room for further improvement. In addition, the SPSA algorithm cannot make full use of parameter information and requires a lot of random attempts. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention proposes a method for establishing a multidimensional piecewise linear transistor behavior model based on PSO optimization. This method proposes a multidimensional piecewise linear transistor behavior model that represents complex wave variables as a structure with separated magnitude and phase. Furthermore, it extends the dimension based on the CWPL function, which can improve the accuracy and precision of the model. The PSO algorithm is further used for optimization, making the input / output behavior characteristics of the model more accurate, which can be used to accurately predict the nonlinear behavior of GaNHEMT devices.

[0006] The method for establishing a multidimensional piecewise linear transistor behavior model based on PSO optimization includes the following steps:

[0007] Step 1: Data Extraction

[0008] Keeping the frequency constant, measure the wave variables A of incident and scattered waves at each port of the GaN power transistor under different input powers. p B p , where p = 1, 2, represents the port number of the power transistor.

[0009] Step 2: Model Building

[0010] Using the CSWPL function to describe the behavioral model of GaN power transistors:

[0011]

[0012] Where m is the harmonic order, A 11 A 21 B represents the fundamental wave of the incident wave at port 1 and port 2, respectively. 21 This represents the fundamental wave of the scattered wave at port two. L represents the maximum Fourier order, and K and J represent A... 11 and A 21 The number of partitions, β k and β j A represents 11 and A 21 The partition threshold is determined. The measured data extracted in step 1 is used to train the behavior model, resulting in model coefficients c.

[0013] Step 3: Model Optimization

[0014] The normalized mean square error (NMSE) of the measured data in step 1 and the output data of the model in step 2 is used as the fitness evaluation function of the model. The partition threshold of the behavior model of the GaN power transistor trained in step 2 is optimized using the PSO algorithm, and the optimal threshold coefficient B is output. k .

[0015] Step 4: Model Update

[0016] Use the optimal threshold coefficient B obtained in step 3. k The behavior model in step 2 is updated to obtain the final multidimensional piecewise linear transistor behavior model.

[0017] The present invention has the following beneficial effects:

[0018] The CSWPL function is used to describe the input state and corresponding output state of a power transistor, and a corresponding behavioral model is established. Based on the CSWPL function, the incident wave A at port two is further modified. 21 The partitioning operation significantly improves the model's accuracy and precision. Furthermore, the PSO algorithm is used to perform a global optimum search on a manually set partition threshold, further enhancing the accuracy of the behavioral model. Experimental results demonstrate that the behavioral model output values ​​established by this method have a good fit with the measured data, and the convergence time required during the optimization process is also significantly reduced. Attached Figure Description

[0019] Figure 1 This is a schematic diagram of wave variable extraction for power transistors.

[0020] Figure 2 In this example, the input conditions are 2GHz and the input power is 20dBm. 21 Scatter plot;

[0021] Figure 3 In this example, the input conditions are 2GHz and the input power is 25dBm. 21 Scatter plot;

[0022] Figure 4 This is a comparison of the convergence speeds of the SPSA and PSO algorithms when the input conditions are 2GHz and the input power is 20dBm in the example.

[0023] Figure 5 This is a comparison chart of NMSE performance at different thresholds when the input conditions are 2GHz and the input power is 25dBm, as shown in the example. Detailed Implementation

[0024] This embodiment uses a 10W GaN power transistor manufactured by Wolfspeed as an example to illustrate, with reference to the accompanying drawings, the method for establishing a multidimensional piecewise linear transistor behavior model based on PSO optimization and its advantages.

[0025] The method for establishing a multidimensional piecewise linear transistor behavior model based on PSO optimization includes the following steps:

[0026] Step 1: Data Extraction

[0027] like Figure 1 As shown, with the frequency maintained at 2GHz, the voltage V, current I, and reference impedance Z0 at each port of the GaN power transistor under different input powers are measured. The wave variables A and B of the incident and scattered waves at the corresponding ports are calculated.

[0028]

[0029]

[0030] The variables in wave variables A and B are all complex numbers, representing complex vector descriptions of the signal in the frequency domain.

[0031] Step 2: Model Building

[0032] The behavior model of GaN power transistors is described using the CSWPL function. CSWPL borrows from the topological structure of the Cardiff model, representing complex wave variables as structures with separated magnitude and phase. Furthermore, it expands the dimensionality of the CSWPL function through self-nesting—not only for the incident wave A at port one... 11 Partitioning is performed, and the incident wave A at port two is also affected. 21 Partitioning was performed, which greatly improved the model's accuracy and precision.

[0033]

[0034] Where m is the harmonic order, A 11 A 21 B represents the fundamental wave of the incident wave at port 1 and port 2, respectively. 21 The fundamental wave of the scattered wave at port 2 is represented by p = 1 and 2, which represent the port numbers of the power transistor. L represents the maximum Fourier order, and K and J represent A... 11 and A 21 The number of partitions, β k and β j A represents 11 and A 21 The partition threshold is determined. One-tenth of the measured data extracted in step 1 is used for training the behavior model to obtain the model coefficients c.

[0035] Step 3: Model Optimization

[0036] In the multidimensional piecewise linear behavior model established in step 2, A 11 A 21 The partitioning thresholds are all chosen manually based on experience without optimization. Finding the optimal partitioning threshold through optimization algorithms could further improve the model's accuracy. Since the CSWPL model expands upon CWPL in terms of dimensions, the optimization of the two dimensions is mutually exclusive; achieving optimality in one dimension may result in poor performance in the other. Therefore, the SPSA algorithm, suitable for single-objective optimization, may not be significantly effective in optimizing the CSWPL function model. Particle swarm optimization (PSO) is a swarm metaheuristic algorithm that effectively searches for the global optimum, avoiding local optima. Its key is to simulate a swarm of massless particles searching for the optimal solution. Individuals in the swarm continuously update their positions through an iterative process, gradually approaching the optimal solution. Traditional PSO optimization for multi-objective problems often adds a non-dominated solution set and then selects one from the non-dominated set as the final solution based on actual needs. This application optimizes the partitioning threshold of the GaN power transistor behavior model trained in step 2 using the PSO algorithm. It uses the normalized mean square error (NMSE) of the measured data from step 1 and the model output data from step 2 as the fitness evaluation function, outputting the optimal threshold coefficient B. k :

[0037] s3.1 Generate a particle swarm of size N and initialize the random positions B of the particles. k,0 and initial velocity v i B k,0 It is a matrix of size 2*K.

[0038] s3.2 Substitute the current position of the particle into the CSWPL model and calculate the NMSE of each particle as its fitness.

[0039] s3.3. Based on the fitness of each particle, the position corresponding to the lowest fitness of the current particle in the CSWPL model is taken as the best position pbest', and compared with the best position pbest it has passed through. If it is better, it is updated to the best position pbest found by the current individual.

[0040] s3.4. Based on the fitness of each particle, compare the position gbest' corresponding to the lowest fitness of all particles in the CSWPL model with the best position gbest that the population passes through. If it is better, then take it as the best position gbest found by the current population.

[0041] s3.5. Change the position and velocity of the particles to adjust their behavior:

[0042] v i+1 =ω*v i +c1*rand()*(pbest i -B k,i )+c2*rand()*(gbest-B k )

[0043] B k,i+1 =B k,i +v i+1

[0044] Among them, v i Let represent the velocity of the i-th iteration, ω be the inertia coefficient representing the ability to remember previous behaviors and routes, c1 be the self-awareness coefficient, and c2 be the social awareness coefficient. This is the threshold coefficient matrix for the i-th iteration. `rand()` is used to generate random numbers between 0 and 1. `pbest` i It is the best position for a single particle to be found so far, and gbest means the best position for the current population to be found.

[0045] s3.6 Repeat s3.2 to 3.5 until 200 iterations, then output the optimal threshold coefficient B. k And NMSE.

[0046] In this application, since the coefficients in the PSO algorithm are a two-dimensional matrix, the complexity of optimization can be reduced while achieving better optimization results.

[0047] Step 4: Model Update

[0048] Use the optimal threshold coefficient B obtained in step 3. kThe behavior model in step 2 is updated to obtain the final multidimensional piecewise linear transistor behavior model.

[0049] To demonstrate the beneficial effects of this method, the measured data from step 1 are compared with the output values ​​of the CSWPL model before optimization in step 2, the output values ​​of the CSWPL model optimized using the SPAS algorithm, and the output values ​​of the CSWPL model optimized by this method. Figure 2 , Figure 3 For a transistor operating at a frequency of 2 GHz, at input power of 20 dBm and 25 dBm, B 21 The scatter plot shows that the output value of the model optimized by this method is closest to the measured data.

[0050] Figure 4 The graph shows a comparison of the convergence speeds of the CSWPL model optimization using the SPSA and PSO algorithms when the input power is 20dBm. It can be seen that the convergence time required by the PSO algorithm is much shorter than that of the SPSA algorithm. Figure 5 The image shows a comparison of NMSE performance under different partition thresholds when the input power is 25dBm. The results demonstrate that the proposed optimized model can accurately predict transistor characteristics. Compared to current mainstream optimized CWPL function models, the improved model still provides high prediction accuracy, effectively reflecting the output characteristics of the device under test. Furthermore, comparing the outputs of the models before and after optimization verifies the effectiveness of the proposed device optimization behavior modeling technique.

[0051] The above description is only a preferred embodiment of the present invention. It should be noted that those skilled in the art can make several improvements and modifications without departing from the concept of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for establishing a multidimensional piecewise linear transistor behavior model based on PSO optimization, characterized in that: Specifically, the following steps are included: Step 1: Data Extraction Keeping the frequency constant, measure the wave variables A of incident and scattered waves at each port of the GaN power transistor under different input powers. p B p Where p = 1, 2, represents the port number of the power transistor; Step 2: Model Building Using the CSWPL function to describe the behavioral model of GaN power transistors: Where m is the harmonic order, A 11 A 21 B represents the fundamental wave of the incident wave at port 1 and port 2, respectively. 21 This represents the fundamental wave of the scattered wave at port two; L represents the maximum Fourier order, and K and J represent A... 11 and A 21 The number of partitions, β k and β j A represents 11 and A 21 The partition threshold is determined; the measured data extracted in step 1 is used to train the behavior model to obtain the model coefficients c. Step 3: Model Optimization The normalized mean square error of the measured data in step 1 and the output data of the model in step 2 is used as the fitness evaluation function of the model. The PSO algorithm is used to optimize the partition threshold of the behavior model of the GaN power transistor after training in step 2, and the optimal threshold coefficient B is output. k ; Step 4: Model Update Use the optimal threshold coefficient B obtained in step 3. k The behavior model in step 2 is updated to obtain the final multidimensional piecewise linear transistor behavior model.

2. The method for establishing a multidimensional piecewise linear transistor behavior model based on PSO optimization as described in claim 1, characterized in that: In step 1, maintaining a frequency of 2 GHz, measure the voltage V, current I, and reference impedance Z0 at each port of the GaN power transistor under different input powers, and calculate the wave variables A and B of the incident and scattered waves at the corresponding ports: The variables in wave variables A and B are all complex numbers, representing complex vector descriptions of the signal in the frequency domain.

3. The method for establishing a multidimensional piecewise linear transistor behavior model based on PSO optimization as described in claim 1, characterized in that: The specific process of optimizing the partition threshold using the PSO algorithm in step 3 is as follows: s3.1 Generate a particle swarm with a population size of N, set the maximum number of iterations T, and initialize the random positions B of the particles. k,0 and initial velocity v i B k,0 It is a matrix of size 2*K; s3.2 Substitute the current position of the particle into the CSWPL model and calculate the NMSE of each particle as its fitness; s3.

3. Based on the fitness of each particle, take the position corresponding to the lowest fitness of the current particle in the CSWPL model as the best position pbest', and compare it with the best position pbest that it has passed through. If it is better, then update it to the best position pbest found by the current individual. s3.

4. Based on the fitness of each particle, compare the position gbest' corresponding to the lowest fitness of all particles in the CSWPL model with the best position gbest that the population passes through. If it is better, then take it as the best position gbest discovered by the current population. s3.

5. Change the position and velocity of the particles to adjust their behavior: in i+1 =ω*v i +c1*rand()*(pbest i -B k,i )+c2*rand()*(gbest-B k ) B k,i+1 =B k,i +v i+1 Among them, v i Let represent the velocity of the i-th iteration, ω be the inertia coefficient representing the ability to remember previous behaviors and routes, c1 be the self-awareness coefficient, and c2 be the social awareness coefficient. This is the threshold coefficient matrix for the i-th iteration. `rand()` is used to generate random numbers between 0 and 1. `pbest` i This is the best position for the discovery of a single particle so far; gbest indicates the best position for the current population. s3.6 Repeat s3.2 to 3.5 until the maximum number of iterations is reached, then output the optimal threshold coefficient B. k And NMSE.

4. The method for establishing a multidimensional piecewise linear transistor behavior model based on PSO optimization as described in claim 3, characterized in that: Set the maximum number of iterations T = 200.

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