Method for Reconstructing Chip Radiation Inside System-in-Package Based on Magnitude of Near-Field Scanned Magnetic Field

Abstract

The invention discloses a method for reconstructing the radiation of a chip in a system-level package based on the near-field scanning magnetic field amplitude, which belongs to the field of data processing. The present invention first uses a near-field scanning test system to obtain the magnetic field amplitude on the near-field sampling plane of the chip. Because the medium with a high dielectric constant of the SIP substrate will significantly affect the distribution of the electromagnetic field around the chip, in order to more accurately describe the complex electromagnetic environment around the chip, a numerical calculation method is used to obtain the numerical Green's function on the SIP sampling plane. On this basis, the numerical Green's function matrix and the near-field magnetic field amplitude are used to establish the radiation magnetic field equation of the reconstruction model. In addition, the lack of phase information in the near-field electromagnetic field data will increase the risk of the optimization algorithm falling into a local optimal solution. Therefore, a method of performing local search in the solution space through a cooling process by a simulated annealing algorithm mixed with a differential evolution algorithm is used to improve the accuracy of the equation solution.

Description

Technical Field

[0001] The present invention belongs to the field of data processing, and in particular to a system-level package chip radiation reconstruction method based on near-field scanning magnetic field amplitude. Background Art

[0002] As system-in-package (SIP) integration and chip operating frequencies increase, managing electromagnetic interference (EMI) between multiple chips within the SIP becomes increasingly critical. Therefore, establishing a chip radiation model is crucial for SIP EMI prediction. When sufficient chip circuit information is available, the radiation model can be derived from simulation. However, in most practical situations, SIP component designers lack access to detailed chip information. Therefore, extracting an equivalent chip model based on electromagnetic field measurement techniques becomes particularly important in this context.

[0003] Existing research results have confirmed that the dipole model can effectively reconstruct the electromagnetic radiation of chips or electronic components. However, the size of the ceramic substrate in the SIP is generally small, sometimes even smaller than the wavelength of the electromagnetic wave, which may cause the electromagnetic field radiated by the chip to have edge effects on the small-sized substrate. At the same time, the substrate structure in the SIP is complex and contains multiple layers of dielectrics. Dielectrics with high dielectric constants store more electrical energy, which will reduce the intensity of the electromagnetic field in the air in the near-field region, thereby significantly affecting the distribution of the electromagnetic field around the chip. Existing research treats the metal plane on the substrate as an infinite metal plane, and uses the analytical form of the Green's function (AGF) to bridge the relationship between the dipole and the near-field electromagnetic field on the sampling plane, while ignoring the influence of the substrate dielectric. This is unreasonable.

[0004] On the other hand, current research relies on near-field scanning measurement techniques to establish accurate radiation source models. This involves obtaining electromagnetic field amplitude and phase information in the near-field plane, and then constructing a system of linear equations for inverse solution. However, compared to measuring magnetic field amplitude, phase measurement requires more complex measurement methods and calibration procedures, significantly increasing near-field scanning time. Therefore, establishing equivalent source models based on phase-free near-field scanning has become a hot topic of research. Among these, differential evolution (DE) optimization algorithms are widely used due to their simplicity, ease of implementation, and high adaptability. However, the lack of phase information in near-field electromagnetic field data increases the risk of differential evolution algorithms falling into local optimal solutions, making it difficult to obtain a highly accurate equivalent model. Summary of the Invention

[0005] In order to solve the problem that the lack of phase information in the near-field electromagnetic field data increases the risk of the differential evolution algorithm falling into a local optimal solution, the present invention proposes a system-level package chip radiation reconstruction method based on near-field scanning magnetic field amplitude.

[0006] The present invention first uses a near-field scanning test system to obtain the magnetic field amplitude on the chip's near-field sampling plane. Because the high dielectric constant of the SIP substrate significantly affects the distribution of the electromagnetic field around the chip, in order to more accurately describe the complex electromagnetic environment around the chip, a numerical calculation method is used to obtain the numerical Green's function on the SIP sampling plane. (NGF). On this basis, the radiation magnetic field equations of the reconstruction model are established using NGF and near-field magnetic field amplitudes. Furthermore, the lack of phase information in near-field electromagnetic field data increases the risk of the optimization algorithm falling into a local optimal solution. Therefore, a simulated annealing algorithm hybridized with a differential evolution algorithm is used to perform a local search in the solution space during a cooling process to improve the accuracy of the equation solution. Application examples demonstrate that the reconstruction method of the present invention can be used to reconstruct the radiation behavior of chips and quantitatively analyze the electromagnetic compatibility of SIPs.

[0007] Therefore, the technical solution of the present invention is a method for chip radiation reconstruction in a system-level package based on near-field scanning magnetic field amplitude, the method comprising:

[0008] Step 1: Equivalently consider the radiation of a chip as an array of N × N dipoles. The single dipole radiation source is located at r, and its electromagnetic field at r' in free space is calculated using the numerical Green's function. Combined dipole-dipole moment (D PZ ,D MX , D MY ) is solved, and the electromagnetic field generated by the array dipole at r' is calculated by the following formula;

[0009] ;

[0010] in, is the numerical Green's function matrix; 、 ,and They represent the magnitudes of the dipole moments of N × N dipoles in the corresponding directions; , and is the magnetic field amplitude in the direction corresponding to the M×M scanning field points;

[0011] Step 2: Establish numerical Green's function;

[0012] To obtain First, a complete finite element simulation model needs to be established. The unit dipole array plane is defined on the plane where the radiation chip is located. The unit dipole array plane size is 1-1.5 times the size of the radiation chip. The spacing of the unit dipole model in different polarization directions is defined, and the spacing size is uniform. The magnetic field amplitude of each component unit dipole at M×M field points on the measurement plane is obtained by simulation calculation. According to the following formula, the matrix of the numerical Green's function is obtained: ;

[0013] ;

[0014] Where, is the magnetic field radiated by the unit dipole at r' in free space, Represents the dipole moment of the unit dipole; the numerical Green's function of the unit magnetic dipole is obtained as shown in the following formula, that is, the radiation magnetic field of the unit dipole at r' in free space;

[0015] ;

[0016] In the formula 、 and Represents a unit magnetic dipole in the x direction The three column vectors of the x-component, y-component, and z-component of 、 and are the numerically calculated magnetic fields generated by a unit magnetic dipole in the x, y, and z directions on the measurement plane, respectively;

[0017] Similarly, the numerical Green's function of the unit dipole in the other two directions is calculated: ( 、 、 )and( 、 、 ); Finally, the equivalent dipole model can be reconstructed by combining the near-field measured electromagnetic field data with the reverse solution;

[0018] Step 3: Search for the optimal equivalent dipole combination array by minimizing the objective function;

[0019] The optimization algorithm implementation process includes: initializing the population The size and individual dimension D of the population. Each individual in the population represents an equivalent dipole combination. The entire parameter space of the equivalent dipole array constitutes the dimension D of the population individual. Each dimension represents the dipole moment and direction of the electromagnetic dipole. Each dipole combination is represented by a 6-dimensional vector. During initialization, the value of each parameter is randomly generated within its own search space. The dipole moments of all dipoles have consistent upper and lower bounds. The range of the search space needs to be precalculated.

[0020] ;

[0021] ;

[0022] in, 、 、 、 、 、 are the real and imaginary parts of the three components of the dipole moment in the Cartesian coordinate system, x, y, and z represent directions, represents the real part, represents the imaginary part, represents the electric dipole in the z direction, represents the magnetic dipole in the x-direction, represents the magnetic dipole in the y direction, is the value boundary;

[0023] The population evolves through iteration, and the ultimate goal is to find the most suitable individual in the population; the objective function is used to evaluate the quality of each individual, and the objective function is the difference between the field generated by the dipole and the scan field.

[0024] Furthermore, in step 3, the objective function for:

[0025] ;

[0026] Where m is the scanning field point, i is the magnetic field direction, Represents M×M scanning field points; is the magnetic field in direction i obtained by scanning at field point m, is the magnetic field in direction i generated by the superposition of N×N dipoles at point m, and its calculation formula is:

[0027] ;

[0028] In the formula 、 、 Respectively represent the superimposed magnetic field generated by the m-point N×N dipole in the x, y, and z directions, and the numerical Green's function obtained in step 2 is combined with the dipole moment parameter to be optimized ( 、 、 、 、 、 ) to calculate the component magnetic field amplitude , the objective function can be determined .

[0029] Furthermore, after the model optimization in step 3 is established, the following operations are performed:

[0030] After each step of differential optimization, the simulated annealing algorithm is used to randomly perturb the current solution, as shown in the following formula, gradually reducing the temperature; allowing the optimal solution or suboptimal solution to be accepted under a set probability, helping the algorithm to escape from the local optimum and search for the global optimum;

[0031] ;

[0032] in and denote the new solution and the current solution respectively, is the perturbation amplitude, which decreases with decreasing annealing temperature. is a random variable that follows a standard normal distribution.

[0033] This paper proposes a new chip radiation model reconstruction method. By measuring the chip's near-field magnetic field amplitude and combining it with numerical calculations, a high-precision magnetic field reconstruction model is established. The solution algorithm is optimized to enhance global optimization capabilities. Verification results demonstrate that this method offers significant advantages in reconstruction accuracy and stability, providing effective support for the electromagnetic compatibility design of SIPs. The main achievements are as follows:

[0034] (1) A chip radiation model reconstruction method based on numerical Green's function (NGF) and near-field magnetic field amplitude is proposed to achieve high-precision reconstruction of chip radiation behavior.

[0035] (2) A hybrid differential evolution (HDE) algorithm combining simulated annealing and differential evolution is proposed. Through local search during the cooling process, the solution accuracy is improved and the results are ensured to converge to the global optimal solution.

[0036] (3) Application examples show that this method is not only accurate but also effective in quantifying electromagnetic interference within SIP. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 It is the chip radiation equivalence theory.

[0038] Figure 2 Schematic diagram of magnetic field simulation.

[0039] Figure 3 Flowchart of the equivalent source reconstruction algorithm based on HDE.

[0040] Figure 4 An example of a near-field measurement plane and an equivalent model.

[0041] Figure 5 Comparison of magnetic fields of unit magnetic dipoles based on NGF and AGF.

[0042] Figure 6 Iterative curves of traditional DE and HDE.

[0043] Figure 7 Schematic diagram of magnetic field distribution on the scanning plane.

[0044] Figure 8 Schematic diagram of the electromagnetic interference analysis process within the SIP.

[0045] Figure 9 Comparison diagram of the interference magnetic field diagram in SIP.

[0046] Figure 10 is the internal electromagnetic resonance curve of the SIP based on the equivalent model. DETAILED DESCRIPTION

[0047] Reconstruct chip radiation model;

[0048] Due to the mirror effect of the metal ground plane (GND) on the substrate except for the pads, the radiation of a chip can be equivalent to an array of N × N dipole combinations, such as Figure 1 The electromagnetic field of a single dipole radiating source r at r' in free space can be expressed using the analytical Green's function (AGF) The solution is based on the dipole dipole moment, and the electromagnetic field generated by the array dipole at r' can be obtained simply by the superposition principle. Its expression is shown in the following formula, where M×M represents the number of field points on the scanning plane.

[0049] ;

[0050] in, is AGF, r and r' are the position parameters of the dipole source and the near-field scanning point respectively. AGF can be solved by relying on only these two parameters; 、 ,and They represent the magnitudes of the dipole moments of N × N dipoles in the corresponding directions; , and is the magnetic field amplitude in the direction corresponding to the M×M scanning field points; the dipole radiation model reconstructed after the magnetic field amplitude data is known can be determined by solving the above equation.

[0051] Establish an equivalent dipole model based on NGF;

[0052] The existence of the SIP substrate results in a complex electromagnetic environment around the reconstructed dipole radiation model, and it is impossible to use AGF to bridge the relationship between the dipole on the substrate plane and the magnetic field amplitude on the sampling plane, such as Figure 2 Therefore, in order to consider the influence of the dielectric storage electromagnetic field and the multi-layer metal plane of the substrate on the chip radiation electromagnetic field in the near field region, the present invention uses the full-wave numerical method to calculate the numerical Green's function (NGF) To obtain AGF; to obtain NGF First, a complete SIP finite element simulation model needs to be established. The unit dipole array plane is defined on the plane where the radiation chip is located. The unit dipole array plane size is 1-1.5 times the size of the radiation chip. The spacing of the unit dipole model in different polarization directions is defined, and the spacing size is uniform. The magnetic field amplitude of each component unit dipole at M×M field points on the measurement plane is obtained by simulation calculation. According to the following formula, the matrix of the numerical Green's function is obtained: ; N × N dipoles require N × N full-wave simulations.

[0053] ;

[0054] Where, is the magnetic field radiated by the unit dipole at r' in free space, Represents the dipole moment of the unit dipole, so the NGF of the component magnetic dipole is obtained as shown below, that is, the radiated magnetic field of the unit dipole at r' in free space;

[0055] ;

[0056] In the formula 、 and Represents a unit magnetic dipole M in the x direction x Numerical Green's function Three column vectors of the x-component, y-component, and z-component of ; 、 and are the numerically calculated magnetic fields generated by the unit magnetic dipole in the x, y and z directions on the measurement plane. Similarly, P is calculated z and M y of Finally, the equivalent dipole model can be reconstructed by combining the near-field measured electromagnetic field data with the inverse solution.

[0057] HDE algorithm optimizes the reconstruction model parameters;

[0058] In the inverse modeling process of the reconstructed source, the present invention proposes to use the hybrid differential evolution (HDE) algorithm to obtain the dipole array model parameters. Specifically, the optimization process searches for the optimal dipole combination by minimizing the objective function (i.e., the difference between the field generated by the dipole and the scanned field). The HDE algorithm first requires initializing the population size NP and the individual dimension D of the population. Each individual in the population represents an equivalent dipole combination, that is, each individual in the population is a candidate solution, such as Figure 3The entire parameter space of the equivalent dipole array constitutes the dimension D of the individual populations, where each dimension represents the dipole moment and direction of the electric / magnetic dipole. Therefore, each dipole combination can be represented by a 6-dimensional vector, as shown in the following equation.

[0059] ;

[0060] During initialization, the value of each parameter is randomly generated within its own search space, and all dipole moments have consistent upper and lower bounds, as shown in the following equation.

[0061] ;

[0062] For the search space, its range needs to be calculated in advance. This is because if the search space is limited, the algorithm may be limited to the local optimum even when the objective function value is small but not ideal. 、 、 、 、 、 are the real and imaginary parts of the three components of the dipole moment in the Cartesian coordinate system, represents the electric dipole in the z direction, represents the magnetic dipole in the x-direction, represents a magnetic dipole in the y-direction, M0 is the value boundary, and a population of NPs evolves iteratively, with the ultimate goal of finding the most suitable individual within the population. The objective function evaluates the quality of each individual and defines the goal to be optimized. In this study, the difference between the magnetic field amplitude generated by the dipole and the magnetic field amplitude from the near-field scan is defined as the objective function of the optimization algorithm, as shown in the following equation.

[0063] ;

[0064] Where m is the scanning field point, i is the magnetic field direction, Represents M×M scanning field points; is the magnetic field in direction i obtained by scanning at field point m, is the magnetic field in the direction i generated by the superposition of N×N dipoles at point m, and its calculation formula is shown below;

[0065] ;

[0066] In the formula 、 、 They represent the superimposed magnetic fields generated by the N×N dipole at point m in the x, y, and z directions respectively; Represents the numerical Green's function components of N×N electric / magnetic dipoles at point m, where the superscript is the field component and the subscript is the dipole component; the numerical Green's function is combined with the dipole moment parameter to be optimized 、 、 、 、 、 Combined, the component magnetic field amplitude is calculated , the objective function can be determined To address the problem of falling into local optima during chip radiation model reconstruction, the differential evolution algorithm, after population initialization, mutation, crossover, and selection, uses a simulated annealing algorithm to randomly perturb the current solution, as shown in the following equation, gradually lowering the temperature. This allows for the acceptance of optimal or suboptimal solutions with a certain probability, helping the algorithm escape local optima and search for a global optimum.

[0067] ;

[0068] where x new and x current represent the new solution and the current solution respectively, σ is the perturbation amplitude, which decreases with the decrease of annealing temperature; ε is a random variable that conforms to the standard normal distribution.

[0069] Model validation;

[0070] In order to verify the accuracy of the reconstruction method, HFSS full-wave simulation software was used to establish Figure 4 The simulation model example shown in Figure 1 is an example. In this model, the electromagnetic radiation of the chip is replaced by the radiation of a small-sized patch antenna. The patch antenna is 5mm×5mm in size and is located on a ceramic dielectric (dielectric constant 9.8). Lumped port excitation is used and the port power is set to 1W. Below the patch antenna is a 60mm×60mm metal ground plane. The near-field magnetic field data is collected on a 40mm×40mm plane 10mm away from the antenna. Table 1 shows the empirical standards for the near-field scan. The collected magnetic field results are shown in Figure 1. Figure 7 During data acquisition, the sampling step size in the x and y directions remained consistent at 2 mm. The dipole array area and the patch antenna were located at the same height plane, with an array size of 8 mm × 8 mm, and each dipole was separated by 2 mm in the x and y directions.

[0071] Table 1 Near-field scanning standards

[0072] Near-field scanning in conclusion Scanning plane size <![CDATA[S plane >(1~1.5)S chip ]]> Scan plane height <![CDATA[h plane <1-6min]]> Scan step <h2 style=";text-align:left;direction:ltr"><![CDATA[l <h2 style=";text-align:left;direction:ltr"> step <h2 style=";text-align:left;direction:ltr"> <1 / 2h<h2 style=";text-align:left;direction:ltr"> plane <h2 style=";text-align:left;direction:ltr"> ]]><h2 style=";text-align:left;direction:ltr">

[0073] In order to compare the differences between NGF and AGF, the unit magnetic dipole M of the above model in the scanning plane is also derived by analytical method. x The results are as follows Figure 5As shown in the figure, it can be seen that there are significant differences in the electric field distribution, which shows that using only AGF to model the radiation source within the packaging structure cannot accurately describe the electromagnetic field information of the radiation source.

[0074] In order to highlight the superiority of the HDE algorithm, the near-field magnetic field amplitude information of the radiation source obtained from the above experiment was used to establish the reconstruction source solution equations of the traditional DE algorithm and the HDE algorithm for optimization iteration. The objective function iteration curves of the two algorithms are shown in Figure 2. Figure 6 As shown. Figure 6 As can be seen in the figure, traditional DE algorithms often fall into local optimality, leading to multiple iteration stagnation and inefficient utilization of computing resources. In contrast, the HDE algorithm performs a local optimization process after each iteration, which helps overcome local optimality and enhances global search capabilities. Furthermore, it can be seen that the HDE algorithm helps reduce the value of the objective function, thereby more accurately obtaining parameters and achieving high-precision reconstruction models.

[0075] The dipole array model obtained by the algorithm is imported into HFSS software and simulated under the same electromagnetic environment to obtain the near-field magnetic field data on the same sampling plane. The results are compared with the simulation results of the patch antenna. Figure 6 As shown, the reconstructed model accurately reflects the distribution of electromagnetic radiation from the patch antenna on the medium. This invention also uses Feature Selective Validation (FSV) technology to evaluate the similarity of electromagnetic data. FSV describes the data range using natural language and is divided into six levels: excellent (0-0.1), very good (0.1-0.2), good (0.2-0.4), fair (0.4-0.8), poor (0.8-1.6), and very poor (>1.6). The FSV evaluation index for the electromagnetic field difference between the equivalent radiation source and the actual radiation source in this invention generally remains above the "good" level.

[0076] Model application;

[0077] In order to verify the effectiveness of the equivalent model in analyzing electromagnetic interference in SIP, the actual model and the equivalent model were used for application verification. First, the SIP simulation model schematic diagram was established, as shown in the figure below. Figure 8 As shown in the figure, the radiation source still uses the same patch antenna as before. Simulations were conducted to collect the amplitude of the near-field magnetic field generated by the patch antenna on the SIP ceramic substrate. Based on the equivalent method, a dipole equivalent source model was established. This equivalent model was then precisely positioned at the original location of the patch antenna to further quantify the electromagnetic interference generated within the SIP by the patch antenna model and the dipole equivalent model.

[0078] Figure 9A comparison of EMI analysis results within a SIP using the original radiating antenna model and the dipole equivalent model is presented. As can be seen from the figure, the interference magnetic field distributions generated by the two models are very similar. Furthermore, SIPs typically use a metal ground cover and ceramic substrate to form a shielded cavity to block the propagation of interfering electromagnetic waves, such as Figure 8 As shown in Figure 3, using the equivalent model to analyze the actual SIP structure can not only accurately predict the actual shielding cavity resonant frequency, but also quantify whether the interference electromagnetic field when the shielding cavity resonates exceeds the tolerable threshold of the sensitive device. Figure 10 The resonance curves of the same SIP using two radiation models are shown. The results show that the two models have good consistency in terms of resonant frequency and resonant field strength.

Claims

1. A method for chip radiation reconstruction in a system-level package based on near-field scanning magnetic field amplitude, characterized in that: The method includes: Step 1: Equivalently consider the radiation of a chip as an array of N × N dipoles. The single dipole radiation source is located at r, and its electromagnetic field at r' in free space is calculated using the numerical Green's function. Combined dipole-dipole moment (D PZ , D MX ,D MY ) is solved, and the electromagnetic field generated by the array dipole at r' is calculated by the following formula; ； in, is the numerical Green's function matrix; 、 ,and They represent the magnitudes of the dipole moments of N × N dipoles in the corresponding directions; , and is the magnetic field amplitude in the direction corresponding to the M×M scanning field points; Step 2: Establish numerical Green's function; To obtain First, a complete finite element simulation model needs to be established. The unit dipole array plane is defined on the plane where the radiation chip is located. The unit dipole array plane size is 1-1.5 times the size of the radiation chip. The spacing of the unit dipole model in different polarization directions is defined, and the spacing size is uniform. The magnetic field amplitude of each component unit dipole at M×M field points on the measurement plane is obtained by simulation calculation. According to the following formula, the matrix of the numerical Green's function is obtained: ; ； Where, is the magnetic field radiated by the unit dipole at r' in free space, Represents the dipole moment of the unit dipole; the numerical Green's function of the unit magnetic dipole is obtained as shown in the following formula, that is, the radiation magnetic field of the unit dipole at r' in free space; ； In the formula 、 and Represents a unit magnetic dipole in the x direction The three column vectors of the x-component, y-component, and z-component of 、 and are the numerically calculated magnetic fields generated by a unit magnetic dipole in the x, y, and z directions on the measurement plane, respectively; Similarly, the numerical Green's function of the unit dipole in the other two directions is calculated: ( 、 、 )and( 、 、 ); Finally, the equivalent dipole model can be reconstructed by combining the near-field measured electromagnetic field data with the reverse solution; Step 3: Search for the optimal equivalent dipole combination array by minimizing the objective function; The optimization algorithm implementation process includes: initializing the population The size and individual dimension D of the population. Each individual in the population represents an equivalent dipole combination. The entire parameter space of the equivalent dipole array constitutes the dimension D of the population individual. Each dimension represents the dipole moment and direction of the electromagnetic dipole. Each dipole combination is represented by a 6-dimensional vector. During initialization, the value of each parameter is randomly generated within its own search space. The dipole moments of all dipoles have consistent upper and lower bounds. The range of the search space needs to be precalculated. ； ； in, 、 、 、 、 、 are the real and imaginary parts of the three components of the dipole moment in the Cartesian coordinate system, x, y, and z represent directions, represents the real part, represents the imaginary part, represents the electric dipole in the z direction, represents the magnetic dipole in the x-direction, represents the magnetic dipole in the y direction, is the value boundary; The population evolves through iterations, with the ultimate goal of finding the most suitable individual in the population. The objective function is used to evaluate the quality of each individual, and the objective function is the difference between the field generated by the dipole and the scan field. After the model optimization in step 3 is established, the following operations are performed: After each step of differential optimization, the simulated annealing algorithm is used to randomly perturb the current solution, as shown in the following formula, gradually reducing the temperature; allowing the optimal solution or suboptimal solution to be accepted under a set probability, helping the algorithm to escape from the local optimum and search for the global optimum; ； in and denote the new solution and the current solution respectively, is the perturbation amplitude, which decreases with decreasing annealing temperature. is a random variable that follows a standard normal distribution.

2. A method for chip radiation reconstruction in a system-level package based on near-field scanning magnetic field amplitude according to claim 1, characterized in that: In step 3, the objective function for: ； Where m is the scanning field point, i is the magnetic field direction, Represents M×M scanning field points; is the magnetic field in direction i obtained by scanning at field point m, is the magnetic field in direction i generated by the superposition of N×N dipoles at point m.

3. The method for chip radiation reconstruction in a system-level package based on near-field scanning magnetic field amplitude according to claim 2, characterized in that: The calculation formula is: ； In the formula 、 、 Respectively represent the superimposed magnetic field generated by the m-point N×N dipole in the x, y, and z directions, and the numerical Green's function obtained in step 2 is combined with the dipole moment parameter to be optimized ( 、 、 、 、 、 ) to calculate the component magnetic field amplitude , the objective function can be determined .

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