A method for extracting small signal model parameters of GaN HEMT based on improved spider optimization algorithm

Abstract

The application discloses a GaN HEMT small signal model parameter extraction method based on an improved spider wasp optimization algorithm, which comprises the following steps: obtaining two groups of S parameters of a GaN HEMT device under cold pinch-off bias and working bias; determining the initial values of the intrinsic parameters and the parasitic parameters in the model by using the two groups of S parameters; constructing an optimized parameter vector, and performing physical boundary constraint on each optimized parameter in the optimized parameter vector; adopting the improved spider wasp optimization algorithm, taking the minimum fitting error of the model simulation S parameters and the measured S parameters as the target, and iteratively optimizing the optimized parameter vector until the preset termination condition is met; and after the termination condition is met, selecting the individual with the minimum objective function from the current iteration population as the final parameter of the GaN HEMT small signal model. The application can improve the stability, convergence and fitting precision of parameter identification, and provides a reliable parameter basis for establishing an accurate GaN HEMT small signal model and further using the GaN HEMT small signal model for radio frequency circuit simulation and design.

Description

Technical Field

[0001] This invention relates to the field of radio frequency / microwave semiconductor device modeling and parameter identification technology, and in particular to a method for parameter extraction and global optimization calibration of small-signal models of gallium nitride high electron mobility transistors (GaN HEMTs). Background Technology

[0002] With the development of RF systems such as 5G / 6G communications, radar, and high-efficiency power amplifiers, gallium nitride high electron mobility transistors (GaN HEMTs) are widely used in microwave / millimeter-wave power devices and RF front-ends due to their advantages such as high breakdown voltage, high electron mobility, and high power density. To support circuit-level simulation and design optimization, it is typically necessary to establish a small-signal equivalent circuit model of the GaN HEMT in engineering, and extract and calibrate the model parameters using S-parameter measurement data under given bias conditions.

[0003] Existing small-signal modeling generally adopts a structure of "external parasitic network + internal intrinsic network": the external network is used to describe the parasitic resistance / inductance / capacitance effects caused by leads, electrodes, and packaging; the internal network is used to describe the intrinsic admittance and capacitance characteristics formed by device channel and gate control effects, such as transconductance, output conductance, and gate-source / gate-drain / drain-source capacitance. During modeling, the measured S-parameters are usually converted into equivalent Z / Y parameters. After de-embedding or separating external parasitic effects, an equivalent circuit driven by the parameter set is established. The error between the "model-calculated S-parameters" and the "measured S-parameters" is used as the objective function, and numerical optimization techniques are employed to search for parameters that minimize the error, thereby obtaining small-signal model parameters that can be used for circuit simulation in ADS and other applications.

[0004] Due to the large number of equivalent circuit parameters, significant variable coupling, and nonlinear characteristics of the objective function, existing technologies commonly use swarm intelligence or evolutionary optimization methods such as genetic algorithms, particle swarm optimization, differential evolution, and imperial competition algorithms for global optimization. Some studies have also introduced novel metaheuristic algorithms (such as the Spider-Bee Optimization Algorithm SWO) to improve optimization capabilities in complex search spaces.

[0005] Although existing hybrid / phased parameter extraction processes are available in engineering, they still have the following problems and drawbacks in practical applications:

[0006] Easily trapped in local optima and lacking convergence stability: Significant coupling exists between external parasitic parameters and internal intrinsic parameters in the small-signal equivalent circuit. This coupling, especially under different frequency bands or biases, affects the objective function to varying degrees, leading to a complex, multi-peaked, and non-convex error function. Traditional optimization algorithms, or those directly employing the original SWO's random initialization and single search strategy, are prone to early "pseudo-convergence," oscillating or stagnating in local regions, resulting in unstable fitting accuracy and significant differences in repeated experimental results.

[0007] Sensitive to initial values / population distribution, with poor parameter repeatability: Existing swarm intelligence algorithms typically initialize the population randomly. For high-dimensional, strongly coupled parameter extraction problems, different random initial distributions can significantly alter the search path, causing the obtained parameter solutions to fluctuate greatly between runs, affecting the model's reproducibility and engineering reliability. Furthermore, some parameters may drift due to "weak constraints by the error function," resulting in a model that fits well in some frequency bands but lacks generalization ability in other frequency bands or under other biases.

[0008] The dynamic balance between global exploration and local development is difficult to achieve, resulting in low iterative efficiency. Parameter extraction often requires simultaneous consideration of amplitude and phase fitting, and measurement noise and de-embedding errors introduce non-ideal perturbations, leading to numerous "approximately equivalent solutions" in the search space. Insufficient algorithm exploration can lead to premature convergence; insufficient development makes it difficult to refine to high-precision solutions. Existing methods often employ fixed or empirical step size / update intensity control, which cannot adaptively adjust at different stages, resulting in excessive iterations and high function evaluation costs. Summary of the Invention

[0009] In view of this, the purpose of this invention is to provide a parameter extraction method for GaN HEMT small-signal models based on an improved spider-bee optimization algorithm. This invention addresses the "high-dimensional, strongly coupled, multi-peak / multi-solution" characteristics of GaN HEMT small-signal equivalent circuit parameters by proposing a hybrid parameter extraction method combining "analytical initial values ​​+ improved spider-bee global optimization calibration". Compared to methods relying solely on direct extraction, this invention significantly reduces S-parameter fitting errors and improves parameter extraction stability. Compared to common swarm intelligence algorithms (such as particle swarm optimization, gray wolf, and standard spider-bee algorithms), this invention effectively alleviates initial value sensitivity, premature convergence, and late-stage scale mismatch problems through space-filling initialization, niche multi-population preservation, and success history-driven step-size adaptation.

[0010] The objective of this invention is achieved through the following technical solution:

[0011] This invention provides a method for extracting parameters of a GaN HEMT small-signal model based on an improved spider bee optimization algorithm, comprising the following steps:

[0012] S1: Obtain two sets of S-parameters of the GaN HEMT device at a preset frequency point under cold pinch-off bias and operating bias.

[0013] S2: Using the S-parameters under cold pinch-off bias, extract the initial values ​​of parasitic parameters, and construct a parasitic network using the initial values ​​of parasitic parameters; using the parasitic network, perform parasitic de-embedding on the S-parameters under working bias to obtain the initial values ​​of intrinsic parameters of the intrinsic network, thereby constructing a GaN HEMT small-signal model.

[0014] S3: Constructing the parameter vector to be optimized for the GaN HEMT small-signal model Physical boundary constraints are applied to each parameter in the parameter vector to be optimized based on the initial values ​​of the parasitic parameters and the initial values ​​of the intrinsic parameters. The parameter vector to be optimized includes one or more combinations of parasitic parameters and / or intrinsic parameters. This indicates the total number of parameters to be optimized;

[0015] S4: An improved spider-bee optimization algorithm is adopted, with the goal of minimizing the fitting error between the model simulation S-parameters and the measured S-parameters. The parameter vector to be optimized is iteratively optimized until the preset termination condition is met.

[0016] S5: After the termination condition is met, select the individual with the smallest objective function from the current iteration population as the parameter of the final GaN HEMT small signal model.

[0017] Furthermore, step S4 specifically includes the following steps:

[0018] S41: Generate an initial population using the LHS method, and map the individuals in the initial population to the physical boundaries of the corresponding parameters in step S3;

[0019] S42: Perform distance clustering on the current population to generate... The system is divided into several subgroups, and the individual with the smallest objective function in each subgroup is selected as the local elite of the subgroup.

[0020] S43: Based on the distance between local elites, determine whether there are two subgroups in the same attraction domain, and perform a merging operation or a reseeding operation on the weaker subgroups in the two subgroups that belong to the same attraction domain to obtain the updated current population. Here, the weaker subgroups are the subgroups whose objective function values ​​are larger for the local elites of the two subgroups.

[0021] S44: Based on the current step size strength, perform position updates and boundary processing on each individual in the updated current population to obtain the next generation population;

[0022] S45: Employs a successful history-driven adaptive step size adjustment method to generate the next generation's corresponding step size strength;

[0023] S46: Take the next generation as the current generation and repeat steps S42-S45 until the iteration termination condition is met.

[0024] Furthermore, step S41 specifically includes the following steps:

[0025] S411: In normalized space The LHS method is used to generate the sample matrix. N represents the initial population size;

[0026] S412: Will The initial individuals are obtained by mapping to the physical boundary. For linear scale parameters in the parameter vector to be optimized, the initial iteration value of the parameter is obtained by linear mapping based on the physical boundary of the parameter and the element value of the parameter in the sample matrix. For multi-order-of-magnitude parameters in the parameter vector to be optimized, the initial iteration value of the parameter is obtained by logarithmic field mapping based on the physical boundary of the parameter and the element value of the parameter in the sample matrix. This process generates the initial population.

[0027] Furthermore, the linear mapping can be expressed by the formula:

[0028] ,

[0029] in, and They represent the first and second elements in the parameter vector to be optimized, respectively. The physical lower bound of each parameter. Indicates the first Among the individual parameters to be optimized, the first one is... The initial values ​​for each parameter during iteration.

[0030] Furthermore, the logarithmic field mapping is expressed by the formula:

[0031] ,

[0032] in, and They represent the first and second elements in the parameter vector to be optimized. The physical lower bound of each parameter. Indicates the first Among the individual parameters to be optimized, the first one is... The initial values ​​for each parameter during iteration.

[0033] Furthermore, the merging operation in step S43 refers to merging all individuals in the weak subgroups of the two subgroups into the non-weak subgroups of the two subgroups to generate a new subgroup, wherein the local elites of the new subgroup are the local elites of the non-weak subgroups.

[0034] The reseeding operation in step S43 refers to using the LHS method to regenerate new individuals for the weak subpopulation. The new individuals satisfy the physical boundary constraints in S2, thereby obtaining a new subpopulation, and recalculating the local elites of the new subpopulation.

[0035] The current population is updated by using new subpopulations obtained through merging or reseeding.

[0036] Furthermore, step S44 specifically includes the following steps:

[0037] For each individual in the updated current population, execute S441-S442:

[0038] S441: Generate a direction term corresponding to the individual based on the local elites of the subgroup to which the individual belongs, the current global best individual, and random individuals in the current population;

[0039] S442: Obtain the current generation step length strength, and use the current generation step length strength and the direction term corresponding to the individual to generate the next generation individual corresponding to the individual;

[0040] S443: Perform boundary processing on each parameter in the generated next generation of individuals to obtain the next generation population.

[0041] Furthermore, step S45 specifically includes:

[0042] S451: Represent the current as the [number]. The next generation is referred to as the generation number. +1 generation, for the first For each individual in generation +1, determine whether the objective function value of that individual is less than the value of the corresponding individual in generation +1. If the objective function value of an individual is less than a certain value, it indicates that the individual has been successfully updated, and the [number]th [unit] [is set] [to be] [the next] [unit]. step length strength Joined the successful step size set middle;

[0043] S452: Obtain the... Daibuchang Center and according to and Generate the first +1 generation step center ;

[0044] S453: From The sampling of the center distribution sampling +1 generation step strength .

[0045] Furthermore, step size center Expressed as a formula:

[0046]

[0047] in, For learning rate, To prevent extremely small positive numbers with a denominator of zero.

[0048] Furthermore, the objective function is the mean square error, maximum absolute error, and weighted relative error of the simulated S-parameters and measured S-parameters at all frequency points.

[0049] The beneficial effects of this invention are:

[0050] 1) This invention uses LHS space-filling initialization instead of traditional random initialization, which makes the initial population more evenly distributed and has higher coverage in the parameter space. It can explore potential feasible solution regions more fully under the same population size, significantly reduce the fluctuation of fitting results caused by random initial value bias, reduce the probability of "early search blind zone" and "getting stuck in local basin in the first generation", thereby improving the repeatability and stability of parameter extraction.

[0051] 2) This invention introduces niche clustering and a subgroup elitism mechanism to perform parallel search across multiple subgroups of the population, and maintains diversity through contiguous basin discrimination and reseeding / merging strategies. This mechanism effectively avoids the problem of traditional swarm intelligence algorithms rapidly collapsing to the vicinity of a single elitist during iteration and losing their exploration ability. Under multi-peak error function conditions, it can still maintain parallel search for different "attraction domains," thereby increasing the probability of finding a better global solution and reducing the loss of fitting accuracy caused by getting trapped in local optima.

[0052] 3) This invention utilizes a success history-driven adaptive step size adjustment mechanism to adjust the step size center and search intensity online based on the update behavior of "error reduction". This allows the algorithm to maintain a sufficient exploration span in the early stages and automatically shrink to enter a fine search in the later stages, overcoming problems such as later-stage oscillations, convergence stagnation, or excessive conservatism caused by fixed step sizes or empirical parameter tuning. Under the same function evaluation budget, a lower fitting error can be obtained and the convergence speed can be improved; under the same error target, the number of iterations and computational overhead can be reduced.

[0053] Other advantages, objectives, and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination, or may be learned from practice of the invention. The objectives and other advantages of the invention can be realized and obtained through the following description. Attached Figure Description

[0054] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will now be described in further detail with reference to the accompanying drawings, wherein:

[0055] Figure 1 This is a schematic flowchart of a GaN HEMT small-signal model parameter extraction method based on an improved spider bee optimization algorithm;

[0056] Figure 2 This is a schematic flowchart for parameter extraction;

[0057] Figure 3 This is a flowchart of the improved spider bee optimization algorithm;

[0058] Figure 4 This is the small-signal equivalent circuit diagram of a GaN HEMT;

[0059] Figure 5 This is a comparison chart of algorithm iteration changes;

[0060] Figure 6 This is a comparison chart of measured and simulated S-parameter Smith charts. Detailed Implementation

[0061] The preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be understood that the preferred embodiments are for illustrative purposes only and are not intended to limit the scope of protection of the present invention.

[0062] Combination Figure 1 Value to Figure 4 The method for extracting parameters of GaN HEMT small-signal model based on the improved spider bee optimization algorithm includes the following steps:

[0063] S1: Obtain two sets of S-parameters of the GaN HEMT device at a preset frequency point under cold pinch-off bias and operating bias.

[0064] S2: Using the S-parameters under cold pinch-off bias, extract the initial values ​​of parasitic parameters, and construct a parasitic network using the initial values ​​of parasitic parameters; using the parasitic network, perform parasitic de-embedding on the S-parameters under working bias to obtain the initial values ​​of intrinsic parameters of the intrinsic network, thereby constructing a GaN HEMT small-signal model.

[0065] S3: Constructing the parameter vector to be optimized for the GaN HEMT small-signal model Physical boundary constraints are applied to each parameter in the parameter vector to be optimized, wherein the parameter vector to be optimized includes one or more combinations of parasitic parameters and / or intrinsic parameters. This represents the total number of parameters to be optimized. The upper and lower bounds of the physical boundary of each parameter can be determined based on the initial values ​​of each parameter calculated in S2, or based on empirical values.

[0066] S4: An improved spider-bee optimization algorithm is adopted, with the goal of minimizing the fitting error between the model simulation S-parameters and the measured S-parameters. The parameter vector to be optimized is iteratively optimized until the preset termination condition is met.

[0067] S5: After the termination condition is met, select the individual with the smallest objective function from the current iteration population as the parameter of the final GaN HEMT small signal model.

[0068] Figure 4 This is a diagram of the small-signal equivalent circuit model (i.e., small-signal model) of a GaN HEMT. (See diagram below.) Figure 4 As shown, the model has an external parasitic network and an internal intrinsic network within the red dashed box (i.e., Figure 4 It consists of two parts: "Intrinsic FET".

[0069] Parasitic networks include gate parasites, drain parasites, and source parasites.

[0070] Gate parasites include pad capacitances Cpg1 and Cpg2 (i.e., parallel capacitance between the gate pad and ground), parasitic inductances Lg1 and Lg2 (i.e., series inductance of the gate lead / interconnect), parasitic resistance Rg (i.e., gate series resistance), and feedback conductance Ggsf (i.e., gate-source feedback conductance, characterizing high-frequency leakage effect).

[0071] Drain parasitics include pad capacitances Cpd1 and Cpd2 (i.e., parallel capacitance between the drain pad and ground), parasitic inductances Ld1 and Ld2 (series inductance of drain leads / interconnects), and parasitic resistance Rd (i.e., drain series resistance).

[0072] Source parasitism includes parasitic inductance Ls (i.e., source series inductance) and parasitic resistance Rs (i.e., source series resistance).

[0073] The aforementioned inductance, capacitance, resistance, and conductance together constitute the parasitic parameters.

[0074] The intrinsic network includes gate-source (GS) branches, gate-drain (GD) branches, and drain-source (DS) branches.

[0075] The parameters of the gate-source branch include the gate-source capacitance Cgs (the intrinsic capacitance between the gate and source) and the gate-source resistance Rgs (the gate-source channel resistance); the parameters of the gate-drain branch include the gate-drain capacitance Cgd (the Miller capacitance between the gate and drain), the gate-drain resistance Rgd (the gate-drain leakage resistance), and the gate-drain feedback conductance Ggdf (the gate-drain high-frequency feedback conductance); the parameters of the drain-source branch include the drain-source capacitance Cds (the intrinsic capacitance between the drain and source) and the drain-source conductance Gds (the drain-source output conductance, characterizing the channel length modulation effect). These parameters in the intrinsic network are called intrinsic parameters.

[0076] In Figure 4 In the middle, the controlled current source That is, the intrinsic drain-source current, which is controlled by the gate-source voltage Vgs, and its expression is:

[0077] ,

[0078] in, Indicates the gate-source voltage. The transconductance represents the ability of the gate-source voltage to control the drain-source current. This represents the carrier transport delay time, reflecting the phase delay at high frequencies.

[0079] This equivalent circuit model achieves accurate characterization of the device's high-frequency electrical characteristics through a hierarchical structure that separates parasitic and intrinsic features.

[0080] Combination Figure 2 In S1 and S2, based on multiple preset frequency points, two sets of S-parameters can be obtained: the S-parameters of the GaN HEMT under cold pinch-off bias and the S-parameters under operating bias.

[0081] Let the frequency sampling point be Let M represent the number of frequency sampling points. Then the measured complex S-parameter matrix can be expressed as:

[0082]

[0083] Represents the m-th frequency point The measured S-parameter matrix below, ), , , These represent the corresponding input reflection coefficient, reverse transmission coefficient, forward transmission coefficient, and output reflection coefficient, respectively.

[0084] To facilitate parasitic / intrinsic separation and linearization extraction, the two sets of S-parameters are frequency-unified and outliers are removed. The S-parameters are then transformed to the admittance domain (and / or equivalently to the impedance domain) using the following formula for subsequent extraction:

[0085]

[0086]

[0087] It is the admittance matrix. It is an impedance matrix. It is the system characteristic impedance. Represents the identity matrix. express The S-parameter matrix at frequency.

[0088] For the S-parameters under cold pinch-off bias, parasitic parameters in the parasitic network of the GaN HEMT small-signal model can be extracted by frequency band. For example, in the low-frequency band, the initial values ​​of pad capacitances Cpg1, Cpg2, Cpd1, and Cpd2 in the parasitic network can be extracted using the linear relationship between the imaginary part of the Y-parameters (obtained by transforming the S-parameters to the admittance domain) and the angular frequency. In the mid-to-high frequency state, after removing the pad capacitances, the initial values ​​of parasitic resistance and parasitic inductance in the parasitic network, i.e., the initial values ​​of Rg, Rd, Rs, Lg1, Lg2, Ld1, Ld2, and Ls, can be extracted using the near-linear characteristics of the real / imaginary part of the Z-parameters (obtained by transforming the S-parameters to the impedance domain) with frequency. The extracted initial values ​​of parasitic parameters can be used to construct the parasitic network.

[0089] Then, based on the parasitic network determined above, parasitic de-embedding is performed on the S-parameters under the operating bias to obtain the intrinsic two-port response. Subsequently, the intrinsic part is decomposed according to the admittance branch to obtain the intrinsic capacitance, intrinsic resistance, output conductance, transconductance, and delay time constant (e.g., Cgs, Cgd, Cds, Rgs, Rgd, Gds, Gm, Ggsf, Ggdf). Analytical / linearized initial values ​​for parameters such as parasitic parameters and intrinsic parameters are obtained. Based on these initial values, a small-signal initial model for GaN HEMT can be established.

[0090] In order to formalize the parameter extraction problem into an optimization problem with boundary constraints, this invention obtains the parameter vector, parameter dimension, and upper and lower bound constraints to be optimized based on the selected small-signal equivalent circuit topology (parasitic network + intrinsic network) and the reasonable physical / empirical range of the device.

[0091] Among them, for the parameter vector to be optimized For each dimension, set upper and lower bounds:

[0092] ,in, yes The lower and upper bounds of the d-th parameter in the equation are denoted as . and , .in It should include at least a portion of the parasitic parameters and intrinsic parameters (such as...) wait).

[0093] To quantify the consistency between the model and the actual measurements and use it as a driving force for optimization, based on the results obtained in step 1... The parameter vector to be optimized obtained in step 3 and the equivalent circuit simulation results The objective function can be obtained. .

[0094] Where, for any candidate parameter The equivalent circuit calculation yielded the following:

[0095]

[0096] in, Indicates the use of candidate parameters At the m-th frequency point The S-parameter matrix of the model simulation is as follows; , , , These represent the simulated values ​​of the corresponding input reflection coefficient, reverse transmission coefficient, forward transmission coefficient, and output reflection coefficient, respectively.

[0097] In S4, the objective function can be the mean square error, maximum absolute error, or weighted relative error between the simulated and measured S-parameters at all frequency points. For example, the objective function in the form of weighted relative error can be expressed as:

[0098]

[0099] in, This is the weight (default value is 1). To prevent extremely small positive numbers with a denominator of zero.

[0100] The optimization objective of parameter optimization is: .

[0101] This invention employs an improved spider-bee optimization algorithm (ISWO), combined with Figure 3 The algorithm specifically includes the following steps:

[0102] S41: The LHS method is used to generate an initial population, and the individuals in the initial population are mapped to the physical boundary of the corresponding parameter in step S3. This step can obtain an initial population that satisfies the boundary constraints and has better spatial coverage.

[0103] S42: Perform distance clustering on the current population to generate... Each subgroup (i.e., niche) is selected, and the individual with the smallest objective function in each subgroup is selected as the local elite of the subgroup.

[0104] S43: Based on the distance between local elites, determine whether there are two subgroups in the same attraction domain, and merge or reseed the weaker subgroups in the two subgroups that belong to the same attraction domain to obtain the updated current population. Here, the weaker subgroups refer to the subgroups corresponding to the objective function values ​​(also known as fitness) of the local elites of the two subgroups. Through steps S42 and S43, population diversity can be maintained in the multimodal / multi-solution parameter space, and premature convergence can be avoided by preventing all individuals from collapsing to a single elite.

[0105] S44: Based on the current step size strength, perform position updates and boundary processing on each individual in the updated current population to obtain the next generation population;

[0106] S45: Adopting a successful history-driven adaptive step size adjustment method to generate the next generation's corresponding step size strength, this step can achieve stable fine-tuning in the later stage while ensuring global exploration;

[0107] S46: Take the next generation as the current generation and repeat steps S42-S45 until the iteration termination condition is met.

[0108] It should be noted that the improved spider-bee optimization algorithm requires initialization of other parameters at the beginning, such as setting the iteration count counter. and initialize =0; Initialize step size center Successful step size set and the =0th generation initial step strength wait.

[0109] Specifically, step S41 may include the following steps:

[0110] S411: In normalized space The Latin hypercube sampling (LHS) method is used to generate the sample matrix. N represents the initial population size;

[0111] S412: Will The initial individuals are obtained by mapping to the physical boundary, which in turn generates the initial population.

[0112] For the linear scaling parameter in the parameter vector to be optimized, the initial value for iteration is obtained by linear mapping based on the physical boundary corresponding to the parameter and the element value of the parameter in the sample matrix. The linear mapping is expressed by the formula:

[0113] ,

[0114] in, and They represent the first and second elements in the parameter vector to be optimized. The physical lower bound of each parameter. Indicates the first individual In the parameter vector to be optimized, the first The initial values ​​for each parameter during iteration.

[0115] For parameters spanning orders of magnitude in the parameter vector to be optimized, the initial values ​​for iteration are obtained by using a logarithmic field mapping method, based on the physical boundary of the parameter and its corresponding element value in the sample matrix. The logarithmic field mapping is expressed by the formula:

[0116] .

[0117] Generating the initial population using the LHS space-filling method can reduce uneven coverage and sensitivity to initial values ​​caused by random initialization, and improve the efficiency of early global exploration.

[0118] In some embodiments, S42 and S43 may specifically include:

[0119] First, for the current population (which can be denoted as the th), Normalize the individuals (i.e., each parameter in an individual) in the population, that is:

[0120] ,

[0121] in, Indicates the first The first generation of the population The d-th parameter in each individual express The result after normalization =[ ];

[0122] Next, distance clustering is used to divide the current population into... Subgroup And select local elites within each subgroup:

[0123] .

[0124] In the above formula Indicates the first in the current population Individual, Represents the k-th subgroup The local elites are also called "subgroup elites".

[0125] Then, perform "same basin discrimination / merging or reseeding" on the elites of the subgroup: set a threshold. (Can shrink with iteration), if

[0126]

[0127] Then it is believed that the first Subgroups located within the same attraction domain (i.e., the same basin) are merged or reseeded (i.e., replaced with all or some individuals by new LHS samples) for weaker subgroups to avoid wasting resources on redundant searches. Here, a weaker subgroup is defined as the subgroup with the larger objective function value corresponding to the local elites of the two subgroups. For example, given two subgroups A and B, the elites of these two subgroups are denoted as follows: and The normalized individuals corresponding to these two subgroups of elites (denoted as...) and If the distance between subgroups A and B is less than a threshold, it indicates that subgroups A and B are located in the same attraction domain. Assuming that the objective function value corresponding to the elite of subgroup A is greater than the objective function value corresponding to the elite of subgroup B, then subgroup A is designated as a weak subgroup, and subgroup B as a non-weak subgroup.

[0128] Specifically, the merging operation (also known as "niche management merging") refers to merging all individuals in the weak subgroup of two subgroups into the non-weak subgroup of the two subgroups to generate a new subgroup, wherein the local elites of the new subgroup are the local elites of the non-weak subgroup.

[0129] The reseeding operation (i.e., "local reseeding") refers to using the LHS method to regenerate new individuals for the weak subpopulation (generating multiple individuals to replace all or some of the individuals in the weak subpopulation). The new individuals also satisfy the physical boundary constraints in S2, thus obtaining a new subpopulation, and recalculating the local elites of this new subpopulation. It should be noted that after reseeding to obtain a new subpopulation, the elites of this subpopulation are no longer subject to the same basin discrimination in step S43 with the elites of other subpopulations, and directly proceed to the subsequent steps for processing.

[0130] The current population is updated by using new subpopulations obtained through merging or reseeding.

[0131] It should be noted that the above merging or reseeding operations refer to subgroups located in the same attraction domain. If a subgroup is not located in the same attraction domain as any other subgroup, the subgroup is retained unchanged in this iteration.

[0132] Once you have obtained the elites of each subgroup, you can use those elites to guide subsequent updates.

[0133] Specifically, in step S44, for the updated current population (the... Each individual in the population , Execute S441-S442 to obtain the next generation of individuals for each individual. :

[0134] S441: Based on the local elites of the subgroup to which the individual belongs, the current global best individual, and random individuals in the current population, generate a direction term corresponding to the individual. The current global optimal individual is the elite in the subgroup of the current generation whose objective function is minimized.

[0135] S442: Get the current generation (number) (Alternative) step size strength (That is, all individuals in the same generation use the same step size strength), using the current generation step size strength and the direction term corresponding to that individual. Generate the next generation of individuals corresponding to that individual. ,Right now:

[0136] ,

[0137] S443: Perform boundary processing on each parameter in the generated next-generation individuals (i.e., obtain...) Figure 3 The "candidate solutions" in the boundary conditions are used to obtain the next generation population. The boundary treatment can be expressed as:

[0138] .

[0139] To address the scale mismatch issue caused by fixed step sizes, resulting in insufficient early exploration or inadequate later refinement or oscillations, the step size strength needs to be adaptively adjusted for each generation. This invention employs a success history-driven adaptive step size adjustment method to generate the step size strength corresponding to the next generation. Specifically, it includes the following steps:

[0140] S451: Represent the current as the [number]. The next generation is referred to as the generation number. +1 generation, for the first For each individual in generation +1, determine the individual's... objective function value (Right now Figure 3 Is the candidate fitness (in the model) less than the first fitness corresponding to that individual? Individual objective function value If less than (i.e. If the individual is successfully updated (i.e., there is improvement), then the first individual will be updated. step length strength Joined the successful step size set (The initial value of this set is empty); otherwise, it means that the update was unsuccessful (i.e., there is no improvement), so the update is rejected and the original individuals are retained (i.e., the original solution is retained);

[0141] For example, suppose the first There are 4 individuals in the current generation: individual 1, individual 2, individual 3, and individual 4. The step strength of the current generation is... =0.1. After updating these four individuals, the objective function values ​​for individuals 1 and 3 decrease, while those for individuals 2 and 4 increase. This indicates that the updates for individuals 1 and 3 were successful, while the updates for individuals 2 and 4 were unsuccessful. ={0.1,0.1} contains only two step strength values.

[0142] S452: Obtain the... Daibuchang Center and according to and Generate the first +1 generation step center This can be expressed as a formula:

[0143]

[0144] in, For learning rate, To prevent extremely small positive numbers with a denominator of zero.

[0145] S453: From Centered on (i.e., with) Sampling the first sample from a distribution with a mean (e.g., a normal or heavy-tailed distribution). +1 generation step strength .

[0146] By using adaptive step size intensity, the exploration scale can be automatically increased when "larger step sizes are more likely to succeed" and automatically contracted to fine-tuning when "only small step sizes can continuously improve".

[0147] To output a set of model parameters that meets accuracy requirements and is reproducible, the final optimal parameters are obtained based on the maximum number of iterations / maximum number of function evaluations and the convergence of the objective function. The small-signal model is then output. The specific details of this step are as follows:

[0148] The iteration terminates when any one of the following conditions is met: the number of iterations reaches the maximum number of iterations. ;or ; or continuous The improvement margin is less than the threshold. .

[0149] Output after termination

[0150]

[0151] And Write the equivalent circuit model for circuit simulation verification and subsequent design.

[0152] The process and advantages of the present invention will be illustrated below through specific embodiments.

[0153] In this embodiment, the broadband measured S-parameters of a certain GaN HEMT device are used as modeling data, and the system characteristic impedance is taken as Z0=50 Ω.

[0154] Cold pinch-off bias: VDS=0 V, VGS=-5 V; Measurement frequency range: 0.1–8 GHz.

[0155] Operating bias: VDS=10 V, VGS=-3 V; Measurement frequency range: 0.1–8 GHz.

[0156] like Figure 4 As shown, a small-signal equivalent circuit model of a GaN HEMT is established. This equivalent circuit consists of parasitic and intrinsic components:

[0157] The parasitic components include pad capacitors Cpg1, Cpg2, Cpd1, Cpd2, gate / drain / source parasitic inductances Lg1, Lg2, Ld1, Ld2, Ls, and parasitic resistances Rg, Rd, Rs;

[0158] The intrinsic components include intrinsic capacitances Cgs, Cgd, and Cds; intrinsic resistances Rgs and Rgd; output conductance Gds; transconductance Gm; and gate-dependent leakage / feedback conductances Ggsf and Ggdf, as well as the delay time constant τ.

[0159] The mixed parameter extraction process is as follows:

[0160] Step 1: S-parameter preprocessing and transformation

[0161] To facilitate parasitic / intrinsic separation and linearization extraction, the two sets of S-parameters are frequency-unified and outliers are removed. The S-parameters are then transformed to the admittance domain (or equivalently to the impedance domain) using the following formula for subsequent extraction:

[0162] Step 2: Cold pinch-off extraction of parasitic parameters and construction of parasitic network, as well as working bias parasitic de-embedding and extraction of initial values ​​of intrinsic parameters.

[0163] Under cold-pinch conditions, the parasitic network initial values ​​are obtained by first extracting the pad capacitance in the low-frequency band and then extracting the parasitic resistance and parasitic inductance in the mid-to-high frequency band, and then solidifying them for subsequent de-embedding.

[0164] In this embodiment, the parasitic parameter extraction results are as follows:

[0165] Cpg1=4.75 fF, Cpg2=4.75 fF, Cpd1=4.75 fF, Cpd2=4.75 fF;

[0166] Lg1=35.28 pH, Lg2=28.70 pH, Ld1=30.28 pH, Ld2=31.79 pH, Ls=5.26 pH;

[0167] Rg = 1.86 Ω, Rd = 1.73 Ω, Rs = 1.38 Ω. It should be noted that the parasitic resistances Rg / Rd / Rs mentioned above are derived from the parasitic extraction results of this embodiment.

[0168] Based on the identified parasitic network, the working bias S-parameters are de-embedded to obtain the intrinsic two-port response. Subsequently, the intrinsic part is decomposed according to the admittance branch to obtain analytical / linearized initial values ​​of parameters such as Cgs, Cgd, Cds, Rgs, Rgd, Gds, Gm, Ggsf, Ggdf, and τ (used to establish the initial model).

[0169] Next, perform ISWO optimization calibration, which is step 3: construct the set of optimization variables, boundary conditions, and objective function.

[0170] In this embodiment, starting with the initial values ​​of the parasitic parameters and intrinsic parameters obtained in step 2, the parasitic network parameters are fixed, and only the intrinsic parameter set is adjusted. Perform global optimization calibration (e.g.) Figure 2 As shown, ISWO optimization is performed only on the intrinsic parameter set.

[0171] The objective function uses a comprehensive index of the S-parameter fitting error under the working bias: for any scattering parameter components ( Its relative error is defined as

[0172] ,

[0173] The average value of the four component errors is used as the comprehensive evaluation index (i.e., the objective function):

[0174] ,

[0175] in For frequency points, These are measured values. These are values ​​obtained from calculations / simulations of the equivalent circuit.

[0176] Step 4: LHS space filling initialization

[0177] To mitigate the uneven coverage caused by random initialization, this invention employs Latin hypercube sampling (LHS) in the normalized space. Endogenous generation Each sample is mapped to the physical upper and lower bounds of the parameters to form an initial population. For parameters spanning orders of magnitude (such as partial capacitance / inductance / conductance), it is preferable to perform the mapping in the logarithmic domain followed by the inverse transformation to avoid sample "squeezing" at the linear scale.

[0178] Step 5: Niche clustering and multi-population collaborative search (maintaining diversity and suppressing precocious maturation)

[0179] In each iteration, the population is clustered by niche clustering and divided into... Subgroup And maintain local elites within each subgroup. Subgroups are updated according to their respective... To guide independent evolution and prevent the entire population from collapsing into a single global elite, an elite distance criterion is introduced to prevent multiple subgroups from falling into the same attraction domain and wasting resources: when the distance between elites from two subgroups in the normalized space is less than a threshold... When determined to be within the same basin, the weaker subgroups are merged or partially reseeded; among them It can be gradually reduced with iteration, achieving "strong maintenance of multiple peaks in the early stage and focused refinement in the later stage".

[0180] Step 6: Successful history-driven adaptive step size adjustment

[0181] Only updates that bring real improvements (meeting the criteria) are counted. The corresponding step size intensity set And update the step size center parameter accordingly. For example, an update form similar to Lehmer mean can be used:

[0182]

[0183] in The learning rate. Then, using... The next generation step size is sampled in the distribution centered on the spider bee to adjust the perturbation amplitude of the update operator. This allows the algorithm to automatically increase the step size in the early stage to enhance exploration and automatically shrink the step size in the later stage to enter a stable refinement, thereby improving convergence stability and accuracy.

[0184] Step 7: Termination and Output

[0185] When the maximum number of iterations or the objective function is reached The iteration stops when the value is less than a preset threshold. The optimal set of intrinsic parameters is output and together with the parasitic parameters obtained in step 2, they form the final small signal model.

[0186] In this embodiment, the intrinsic parameters obtained after ISWO optimization calibration are as follows:

[0187] Cgs = 79.98 fF, Cgd = 83.61 fF, Cds = 25.11 fF; Rgs = 3.56 Ω, Rgd = 0.79 Ω; Gds = 0.089 mS, Gm = 10.12 mS; Ggsf = 1.26 mS, Ggdf = 12.5 μS; delay time constant τ = 16.36 ps. The relative errors of this embodiment on the four S-parameter components are as follows:

[0188] S11: 0.17%, S12: 0.13%, S21: 0.14%, S22: 0.20%, average error: 0.16%.

[0189] In comparison, the average error is 3.68% when using the direct extraction method; and the average errors are 0.93% / 0.86% / 0.66% when using GWO / PSO / SWO, respectively.

[0190] Figure 5 This is a comparison chart of the iterative changes of various algorithms (GWO / PSO / SWO / ISWO); Figure 6 This is a comparison chart of the measured and simulated S-parameters using the Smith chart. (See attached image.) Figure 5 As shown, ISWO can quickly reduce the target error and enter the stable convergence region earlier in the initial iteration; as Figure 6As shown, the simulated trajectories corresponding to each comparison algorithm can reproduce the main trends of the measured S-parameters to a certain extent; however, in local regions of the complex plane, especially at trajectory bends, changes in the radius of curvature, and densely distributed curve areas in the mid-to-high frequency band, the differences between different algorithms are more obvious. The Smith circle trajectory proposed in this invention has a higher degree of overlap with the measured curve (i.e., "Measure"), with smaller local deviations, especially in details such as trajectory bends and dense distribution areas in the mid-to-high frequency band, and the trajectory changes are more continuous, indicating that it has better phase consistency and impedance mapping accuracy in the complex plane. Combined with the error statistics, it can be seen that the method of this invention achieves low errors in all four S-parameter components, indicating that it can not only improve the fitting accuracy of individual components, but also improve the overall consistency and stability of the model over a wide frequency range.

[0191] In summary, without altering the existing publicly available small-signal modeling framework (equivalent circuit topology, S-parameter error objective function construction, and conventional phased / hybrid parameter extraction process), this invention achieves higher parameter extraction stability and repeatability (reducing result fluctuations caused by random initialization) simply by improving key aspects of the parameter extraction optimizer; stronger global optimization capability and resistance to premature convergence (maintaining diversity across multiple subgroups); and higher convergence efficiency and final fitting accuracy (achieving a balance between exploration and refinement through successful history adaptive step size). This makes the resulting GaN HEMT small-signal model more suitable for circuit-level simulation and engineering design optimization. Furthermore, this invention addresses the problems of initial value sensitivity, susceptibility to local optima, and insufficient fine-search capability in the GaN HEMT small-signal model parameter extraction process, improving the stability, convergence, and fitting accuracy of parameter identification. This provides a reliable parameter foundation for establishing accurate GaN HEMT small-signal models and further application in RF circuit simulation and design.

[0192] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A method for extracting parameters of a GaN HEMT small-signal model based on an improved spider-bee optimization algorithm, characterized in that, Includes the following steps: S1: Obtain two sets of S-parameters of the GaN HEMT device at a preset frequency point under cold pinch-off bias and operating bias. S2: Using the S-parameters under cold pinch-off bias, extract the initial values ​​of parasitic parameters, and construct a parasitic network using the initial values ​​of parasitic parameters; Using the parasitic network, parasitic de-embedding is performed on the S-parameters under the working bias to obtain the initial values ​​of the intrinsic parameters of the intrinsic network, thereby constructing a GaN HEMT small-signal model. S3: Constructing the parameter vector to be optimized for the GaN HEMT small-signal model Physical boundary constraints are applied to each parameter in the parameter vector to be optimized, wherein the parameter vector to be optimized includes one or more combinations of parasitic parameters and / or intrinsic parameters. This indicates the total number of parameters to be optimized; S4: An improved spider-bee optimization algorithm is adopted, with the goal of minimizing the fitting error between the model simulation S-parameters and the measured S-parameters. The parameter vector to be optimized is iteratively optimized until the preset termination condition is met. S5: After the termination condition is met, select the individual with the smallest objective function from the current iteration population as the parameter of the final GaNHEMT small signal model.

2. The method according to claim 1, characterized in that, Step S4 specifically includes the following steps: S41: Generate an initial population using the LHS method, and map the individuals in the initial population to the physical boundaries of the corresponding parameters in step S3; S42: Perform distance clustering on the current population to generate... The system is divided into several subgroups, and the individual with the smallest objective function in each subgroup is selected as the local elite of the subgroup. S43: Based on the distance between local elites, determine whether there are two subgroups in the same attraction domain, and perform a merging operation or a reseeding operation on the weaker subgroups in the two subgroups that belong to the same attraction domain to obtain the updated current population. Here, the weaker subgroups are the subgroups whose objective function values ​​are larger for the local elites of the two subgroups. S44: Based on the current step size strength, perform position updates and boundary processing on each individual in the updated current population to obtain the next generation population; S45: Employs a successful history-driven adaptive step size adjustment method to generate the next generation's corresponding step size strength; S46: Take the next generation as the current generation and repeat steps S42-S45 until the iteration termination condition is met.

3. The method according to claim 2, characterized in that, Step S41 specifically includes the following steps: S411: In normalized space The LHS method is used to generate the sample matrix. N represents the initial population size; S412: Will The initial individuals are obtained by mapping to the physical boundary. For linear scale parameters in the parameter vector to be optimized, the initial iteration value of the parameter is obtained by linear mapping based on the physical boundary of the parameter and the element value of the parameter in the sample matrix. For multi-order-of-magnitude parameters in the parameter vector to be optimized, the initial iteration value of the parameter is obtained by logarithmic field mapping based on the physical boundary of the parameter and the element value of the parameter in the sample matrix. This process generates the initial population.

4. The method according to claim 3, characterized in that, The linear mapping is expressed by the formula: ， in, and They represent the first and second elements in the parameter vector to be optimized. The physical lower bound of each parameter. Indicates the first Among the individual parameters to be optimized, the first one is... The initial values ​​for each parameter during iteration.

5. The method according to claim 3, characterized in that, The logarithmic field mapping is expressed by the formula: ， in, and They represent the first and second elements in the parameter vector to be optimized. The physical lower bound of each parameter. Indicates the first Among the individual parameters to be optimized, the first one is... The initial values ​​for each parameter during iteration.

6. The method according to claim 2, characterized in that, The merging operation in step S43 refers to merging all individuals in the weak subgroup of the two subgroups into the non-weak subgroup of the two subgroups to generate a new subgroup, wherein the local elites of the new subgroup are the local elites of the non-weak subgroup. The reseeding operation in step S43 refers to using the LHS method to regenerate new individuals for the weak subpopulation. The new individuals satisfy the physical boundary constraints in S2, thereby obtaining a new subpopulation, and recalculating the local elites of the new subpopulation. The current population is updated by using new subpopulations obtained through merging or reseeding.

7. The method according to claim 2, characterized in that, Step S44 specifically includes the following steps: For each individual in the updated current population, execute S441-S442: S441: Generate a direction term corresponding to the individual based on the local elites of the subgroup to which the individual belongs, the current global best individual, and random individuals in the current population; S442: Obtain the current generation step length strength, and use the current generation step length strength and the direction term corresponding to the individual to generate the next generation individual corresponding to the individual; S443: Perform boundary processing on each parameter in the generated next generation of individuals to obtain the next generation population.

8. The method according to claim 2, characterized in that, Step S45 specifically includes: S451: Represent the current as the [number]. The next generation is called the generation number. +1 generation, for the first For each individual in generation +1, determine whether the objective function value of that individual is less than the value of the corresponding individual in generation +1. If the objective function value of an individual is less than a certain value, it indicates that the individual has been successfully updated, and the [number]th [unit] [is set] [to be] [the next] [unit]. step length strength Joined the successful step size set middle; S452: Obtain the... Daibuchang Center and according to and Generate the first +1 generation step center ; S453: From The sampling of the center distribution sampling +1 generation step strength .

9. The method according to claim 6, characterized in that, Step Center Expressed as a formula: in, For learning rate, To prevent extremely small positive numbers with a denominator of zero.

10. The method according to claim 1, characterized in that, The objective function is the mean square error, maximum absolute error, and weighted relative error of the simulated S-parameters and measured S-parameters at all frequency points.

Images