A two-dimensional analytical calculation method and system for leakage inductance of a high-frequency transformer

Abstract

The application relates to a high-frequency transformer leakage inductance two-dimensional analytical calculation method and system, and belongs to the technical field of high-frequency transformers. The method comprises the following steps: according to the primary winding porosity and Maxwell equations, two differential equations corresponding to a first component of magnetic field intensity and electric field intensity are obtained, and first and second component relationship formulas are constructed by using the two differential equations; a first component mathematical model of magnetic field intensity is obtained according to the two component relationship formulas; according to the insulating layer thickness parameters, two differential equations corresponding to a second component of magnetic field intensity and electric field intensity are obtained, and third and fourth component relationship formulas are constructed by using the two differential equations, a second component expression of magnetic field is obtained by solving, and a second component mathematical model of magnetic field intensity is derived; the magnetic field energy of a single wire is calculated based on the two component mathematical models, the total magnetic energy of the primary winding is accumulated, a high-frequency transformer leakage inductance two-dimensional model is constructed from the total magnetic energy, and the leakage inductance two-dimensional analysis is completed. The application improves the calculation precision of the high-frequency transformer leakage inductance.

Description

Technical Field

[0001] This invention relates to the field of high-frequency transformer technology, and in particular to a two-dimensional analytical calculation method and system for the leakage inductance of high-frequency transformers. Background Technology

[0002] High-frequency transformers are core components of high-frequency power electronic circuits. Their leakage inductance parameters directly determine the switching power loss level and operational stability of power electronic devices, and have a crucial impact on the operating performance, safety, reliability, and energy efficiency of power electronic circuits. In the research and design of high-frequency transformers, to avoid or reduce the investment in expensive prototype design, the industry generally adopts a research and development model of simulation calculation followed by assembly and trial production. That is, before the transformer is assembled, its leakage inductance value is accurately calculated, providing preliminary theoretical support for transformer structure optimization and parameter design. Therefore, the accurate calculation technology of high-frequency transformer leakage inductance has become a core research direction in the field of high-frequency power electronic device design.

[0003] Currently, the mainstream calculation methods for leakage inductance in high-frequency transformers are mainly divided into two categories: finite element method (FEM) simulation and analytical calculation. While FEM simulation enables visual analysis of the transformer's electromagnetic field, it suffers from significant limitations in engineering applications. It demands extremely high precision in transformer structure modeling, parameter assignment, and component definition, and the modeling and simulation processes are time-consuming and inefficient. This makes it unsuitable for engineering scenarios involving batch optimization and iterative design of transformers, and it struggles to automate optimization processes, severely restricting its application in the efficient design of high-frequency transformers. In contrast, analytical calculation offers advantages such as ease of computation and high efficiency. It can also clearly characterize the generation mechanisms and correlations of transformer leakage inductance and winding losses, facilitating designers' understanding of core physical characteristics and laying a solid theoretical foundation for transformer structure optimization and performance upgrades.

[0004] Currently, analytical models used for calculating leakage inductance in high-frequency transformers mainly fall into two categories: one-dimensional analytical models and two-dimensional analytical models. Traditional one-dimensional analytical models are simple in structure and highly efficient in computation, but they have inherent technical limitations, failing to consider the impact of transformer winding edge effects on leakage inductance values. For high-frequency transformers with thick insulation layers, the edge effect is particularly pronounced, leading to significant deviations between the leakage inductance calculation results of the one-dimensional analytical model and the actual values. This results in computational accuracy that fails to meet high-precision design requirements, and the model's applicability and versatility are poor, making it unsuitable for calculating leakage inductance in complex high-frequency transformer structures. To overcome the shortcomings of one-dimensional analytical models in handling conditions with significant edge effects, the industry has gradually developed two-dimensional analytical calculation models. Among these, the two-dimensional analytical model based on the mirror method is currently the most widely used and representative technical solution. However, this method still faces many unavoidable technical problems in calculating leakage inductance in high-frequency transformers with complex winding structures, exhibiting significant deficiencies in both adaptability and computational accuracy. First, the image method assumes a uniform current distribution in the winding conductors, failing to accurately account for the skin effect and proximity squeezing effect of conductors under MHz-level high-frequency conditions. Furthermore, transformer leakage inductance exhibits non-linear decay characteristics with frequency at high frequencies, and a single frequency-varying correction factor cannot accurately fit this variation, leading to a significant increase in leakage inductance calculation errors under high-frequency conditions. Second, for complex transformer structures with interleaved windings, the number of image sequences required by the image method increases dramatically, significantly increasing the algorithm's computational load. This results in a cumbersome calculation process, long processing time, and low efficiency in engineering implementation. Finally, this method cannot directly quantify the leakage inductance of the transformer insulation layer; it can only indirectly estimate the insulation layer leakage inductance through the energy difference between the window and the conductor. For high-frequency transformers with a high insulation layer ratio, this indirect estimation method further amplifies the calculation error, severely impacting the overall accuracy of transformer leakage inductance calculation.

[0005] In summary, existing analytical calculation techniques for leakage inductance of high-frequency transformers suffer from insufficient accuracy and poor applicability in one-dimensional models. The mainstream two-dimensional model based on the mirror method generally suffers from technical bottlenecks such as large calculation errors, low computational efficiency, and limited adaptability in high-frequency operating conditions, complex winding structures, and transformer scenarios with high insulation ratios. These limitations make it difficult to meet the current needs for accurate calculation and optimized design of leakage inductance in high-frequency, miniaturized, and high-precision high-frequency transformers. Summary of the Invention

[0006] Therefore, the technical problem to be solved by the present invention is to overcome the problems of poor adaptability, low calculation accuracy, insufficient operation efficiency, and large deviation in the estimation of leakage inductance of high insulation ratio transformers in the prior art.

[0007] In a first aspect, to solve the above-mentioned technical problems, the present invention provides a two-dimensional analytical calculation method for the leakage inductance of a high-frequency transformer, comprising: S1. The high-frequency transformer includes a primary winding; obtain the original electric field strength expression and the original magnetic field strength expression of the primary winding; based on the porosity of the primary winding and Maxwell's equations, obtain the first differential equation and the second differential equation that satisfy the relationship between the first component of the magnetic field strength and the electric field strength. S2. Based on the original electric field strength expression, the first relational differential equation, and the curl expression of the first component of the magnetic field strength, obtain the first intensity component relationship between the first component of the magnetic field strength and the electric field strength component; based on the second relational differential equation and the curl expression of the electric field strength, obtain the second intensity component relationship between the first component of the magnetic field strength and the electric field strength component. S3. Based on the first intensity component relationship and the second intensity component relationship, obtain the expression for the first component of the magnetic field intensity; solve the expression for the first component of the magnetic field intensity to obtain the mathematical model of the first component of the magnetic field intensity in each layer of the primary winding; S4. Based on the Maxwell's equations and the insulation layer thickness parameter between the primary winding layers, the third and fourth differential equations relating the second component of the magnetic field strength to the electric field strength are obtained. S5. Based on the original electric field strength expression, the third relational differential equation, and the curl expression of the second component of the magnetic field strength, the relationship between the second component of the magnetic field strength and the third intensity component of the electric field strength is obtained; based on the fourth relational differential equation and the curl expression of the electric field strength, the relationship between the second component of the magnetic field strength and the fourth intensity component of the electric field strength is obtained. S6. Based on the third intensity component relationship and the fourth intensity component relationship, obtain the expression for the second component of the magnetic field intensity; solve the expression for the second component of the magnetic field intensity to obtain the mathematical model of the second component of the magnetic field intensity in each layer of the primary winding; S7. Based on the original magnetic field strength expression, the mathematical model of the first component of the magnetic field strength, and the mathematical model of the second component of the magnetic field strength, obtain the magnetic field strength in each conductor of the conductor matrix of the primary winding, and calculate the magnetic field energy in each conductor based on the magnetic field strength in each conductor; obtain the total magnetic field energy of the primary winding based on the magnetic field energy in each conductor. S8. Based on the total magnetic field energy, construct a two-dimensional model of the leakage inductance of the high-frequency transformer to complete the two-dimensional analysis of the leakage inductance of the high-frequency transformer.

[0008] In one embodiment of the present invention, step S8, in the process of constructing a two-dimensional model of the leakage inductance of the high-frequency transformer based on the total magnetic field energy, includes determining the correlation between the total magnetic field energy and the leakage inductance based on the arrangement structure of the windings of the high-frequency transformer; and constructing a two-dimensional model of the leakage inductance of the high-frequency transformer based on the correlation between the total magnetic field energy and the leakage inductance.

[0009] In one embodiment of the present invention, when the arrangement structure is such that the winding layers of the primary winding are closely arranged, the mathematical expression of the two-dimensional leakage inductance model is: ; , ; , ; , ; in, Indicates the leakage inductance value. Indicates magnetic permeability, This indicates the average turn length of the winding. Indicates the winding width. Indicates the number of turns per layer of the primary winding. Indicates the winding height. Indicates the number of layers in the primary winding. Indicates the diameter of the wire. Indicates the imaginary part. Indicates the angular frequency of the power supply. This indicates the conductivity of a round conductor winding. Indicates the porosity of the primary winding. This indicates the thickness parameter of the insulation layer between the primary winding layers. Represents a hyperbolic sine function. This represents the hyperbolic cosine function.

[0010] In one embodiment of the present invention, the high-frequency transformer further includes a secondary winding. When the arrangement structure is such that the winding layers of the primary winding and the winding layers of the secondary winding are alternately arranged, the mathematical expression of the two-dimensional leakage inductance model is: ; in, This represents the total leakage inductance value of the high-frequency transformer. This represents the effective value of the input current of the primary winding. Indicates the number of layers in the primary winding. Indicates the number of layers in the secondary winding. Indicates magnetic permeability, Indicates the average turn length of the winding. Indicates the winding height. Indicates the diameter of the wire. This indicates the magnetic field strength inside the conductor.

[0011] In one embodiment of the present invention, the mathematical model of the first component of the magnetic field strength in each layer of the primary winding is as follows: ; ; ; in, This represents the first component of the magnetic field strength within the p-th winding. This represents the coordinate position of the observation point inside the p-th winding on the x-axis. Indicates the winding layer number in the z-axis direction. Indicates the diameter of the wire. Indicates the number of turns per layer of the primary winding. This represents the effective value of the input current of the primary winding. Indicates the winding height. Indicates the imaginary part. Indicates the angular frequency of the power supply. Indicates magnetic permeability, This indicates the conductivity of a round conductor winding. Indicates the porosity of the primary winding. This represents the hyperbolic sine function.

[0012] In one embodiment of the present invention, the mathematical model of the second component of the magnetic field strength in each layer of the primary winding is as follows: ; ; ; in, This represents the second component of the magnetic field strength within the q-th winding layer. This represents the coordinate position of the observation point inside the q-th winding on the z-axis. Indicates the winding layer number in the x-axis direction. Indicates the diameter of the wire. Indicates the number of layers in the primary winding. This represents the effective value of the input current of the primary winding. Indicates the winding width. Indicates the imaginary part. Indicates the angular frequency of the power supply. Indicates magnetic permeability, Indicates the conductivity of a round conductor winding. This indicates the thickness parameter of the insulation layer between the primary winding layers. This represents the hyperbolic sine function.

[0013] In one embodiment of the present invention, the expression for the magnetic field strength in each conductor of the primary winding conductor matrix is ​​as follows: ; , ; , ; in, This represents the magnetic field strength vector inside the (p,q)th conductor in the conductor matrix. This represents the coordinate position of the (p,q)th conductor along the x-axis. Indicates the winding layer number in the z-axis direction. Indicates the diameter of the wire. This represents the coordinate position of the (p,q)th conductor along the z-axis. Indicates the winding layer number in the x-axis direction. Indicates the number of turns per layer of the primary winding. This represents the effective value of the input current of the primary winding. Indicates the winding height. Indicates the number of layers in the primary winding. Indicates the winding width. Indicates the imaginary part. Indicates the angular frequency of the power supply. Indicates magnetic permeability, This indicates the conductivity of a round conductor winding. Indicates the porosity of the primary winding. This indicates the thickness parameter of the insulation layer between the primary winding layers. Represents the unit vector along the x-axis. This represents the unit vector along the z-axis. This represents the hyperbolic sine function.

[0014] In one embodiment of the present invention, the expression for the total magnetic field energy of the primary winding is: ; , ; , ; , ; , ; in, This represents the total magnetic field energy of the primary winding. This represents the magnetic field energy within the (p,q)th conductor. Indicates magnetic permeability, Indicates the average turn length of the winding. Indicates the winding width. Indicates the number of turns per layer of the primary winding. Indicates the winding height. Indicates the number of layers in the primary winding. Indicates the diameter of the wire. This represents the effective value of the input current of the primary winding. Indicates the imaginary part. Indicates the angular frequency of the power supply. This indicates the conductivity of a round conductor winding. Indicates the porosity of the primary winding. This indicates the thickness parameter of the insulation layer between the primary winding layers. Represents a hyperbolic sine function. This represents the hyperbolic cosine function.

[0015] In one embodiment of the present invention, the expression for the first component of the magnetic field strength is: ; The expression for the second component of the magnetic field strength is: ; in, Represents the first component of the magnetic field strength. This represents the second component of the magnetic field strength. Indicates the imaginary part. Indicates the angular frequency of the power supply. Indicates magnetic permeability, This indicates the conductivity of a round conductor winding. Indicates the porosity of the primary winding. This indicates the thickness parameter of the insulation layer between the primary winding layers.

[0016] Secondly, to solve the above-mentioned technical problems, the present invention provides a two-dimensional analytical calculation system for the leakage inductance of a high-frequency transformer, used to implement the above-mentioned two-dimensional analytical calculation method for the leakage inductance of a high-frequency transformer, comprising: The first module for constructing relational differential equations is used to obtain the original electric field strength expression and the original magnetic field strength expression of the primary winding; based on the porosity of the primary winding and Maxwell's equations, the first relational differential equation and the second relational differential equation satisfied by the first component of the magnetic field strength and the electric field strength are obtained; wherein, the high-frequency transformer includes the primary winding; The first intensity component relationship construction module is used to obtain the first intensity component relationship between the first component of the magnetic field intensity and the electric field intensity component based on the original electric field intensity expression, the first relationship differential equation, and the curl expression of the first component of the magnetic field intensity; and to obtain the second intensity component relationship between the first component of the magnetic field intensity and the electric field intensity component based on the second relationship differential equation and the curl expression of the electric field intensity. The first component mathematical model construction module is used to obtain the expression for the first component of magnetic field strength based on the first intensity component relationship and the second intensity component relationship; and to solve the expression for the first component of magnetic field strength to obtain the mathematical model for the first component of magnetic field strength in each layer of winding in the primary winding. The second module for constructing relational differential equations is used to obtain the third and fourth relational differential equations satisfied by the second component of the magnetic field strength and the electric field strength based on the Maxwell equations and the insulation layer thickness parameter between the primary winding layers. The second intensity component relationship construction module is used to obtain the third intensity component relationship between the second component of the magnetic field intensity and the electric field intensity component based on the original electric field intensity expression, the third relationship differential equation, and the curl expression of the second component of the magnetic field intensity; and to obtain the fourth intensity component relationship between the second component of the magnetic field intensity and the electric field intensity component based on the fourth relationship differential equation and the curl expression of the electric field intensity. The second component mathematical model construction module is used to obtain the expression for the second component of magnetic field strength based on the third intensity component relationship and the fourth intensity component relationship; and to solve the expression for the second component of magnetic field strength to obtain the mathematical model for the second component of magnetic field strength in each layer of winding in the primary winding. The total magnetic field energy calculation module is used to obtain the magnetic field strength in each conductor of the conductor matrix of the primary winding according to the original magnetic field strength expression, the mathematical model of the first component of the magnetic field strength, and the mathematical model of the second component of the magnetic field strength, and to calculate the magnetic field energy in each conductor according to the magnetic field strength in each conductor; and to obtain the total magnetic field energy of the primary winding according to the magnetic field energy in each conductor. The analysis module is used to construct a two-dimensional model of the leakage inductance of the high-frequency transformer based on the total magnetic field energy, and to complete the two-dimensional analysis of the leakage inductance of the high-frequency transformer.

[0017] Compared with the prior art, the above-described technical solution of the present invention has the following advantages: (1) The two-dimensional analytical calculation method and system for leakage inductance of high-frequency transformer described in this invention get rid of the technical defects of traditional one-dimensional leakage inductance calculation model, which can only perform axial calculation and cannot consider the winding edge effect. It adopts the two-dimensional analytical modeling idea, and constructs the first component mathematical model of magnetic field intensity of the corresponding winding body and the second component mathematical model of magnetic field intensity of the corresponding interlayer insulation layer respectively, which fully covers the magnetic field distribution characteristics of the primary winding of high-frequency transformer. By splitting the solution logic of the magnetic field differential equation of the winding body and the insulation layer, the magnetic field distortion characteristics of the winding edge region are described, which effectively solves the problems of the one-sided magnetic field calculation and poor working condition adaptability of traditional one-dimensional model, and makes the magnetic field solution model highly consistent with the actual electromagnetic distribution state of the transformer.

[0018] (2) By establishing a two-dimensional magnetic field intensity distribution mathematical model and using the Maxwell equations in the frequency domain to solve the problem, this invention can fully characterize the leakage inductance frequency characteristics caused by the skin effect and proximity effect, thus improving the leakage inductance calculation accuracy under high-frequency operating conditions. At the same time, the model of this invention can directly solve the leakage inductance of the insulation layer, and can still maintain high calculation accuracy for transformer structures with a high insulation layer ratio and complex winding arrangement (such as interleaved windings). Attached Figure Description

[0019] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0020] Figure 1 This is a flowchart of a two-dimensional analytical calculation method for the leakage inductance of a high-frequency transformer in a preferred embodiment of the present invention; Figure 2 This is a schematic diagram of a high-frequency transformer with a half-circular conductor winding and the coordinate system used in a preferred embodiment of the present invention. Figure 3 This is a schematic diagram of the dimensions of the primary winding and the first integration path used in a preferred embodiment of the present invention; Figure 4 This is a schematic diagram of the dimensions of the primary winding and the second integration path used in a preferred embodiment of the present invention; Figure 5 This is a schematic diagram of the longitudinal integration path used for the staggered windings in a preferred embodiment of the present invention; Figure 6 This is a schematic diagram of the use of a transverse integral path for staggered windings in a preferred embodiment of the present invention. Detailed Implementation

[0021] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0022] Example 1: Reference Figure 1 As shown, this invention provides a two-dimensional analytical calculation method for the leakage inductance of a high-frequency transformer, including but not limited to the following steps: S1. The high-frequency transformer includes a primary winding; obtain the original electric field strength expression and the original magnetic field strength expression of the primary winding; based on the porosity of the primary winding and Maxwell's equations, obtain the first differential equation and the second differential equation that satisfy the relationship between the first component of the magnetic field strength and the electric field strength. S2. Based on the original electric field strength expression, the first relational differential equation, and the curl expression of the first component of the magnetic field strength, the first intensity component relationship between the first component of the magnetic field strength and the electric field strength is obtained; based on the second relational differential equation and the curl expression of the electric field strength, the second intensity component relationship between the first component of the magnetic field strength and the electric field strength is obtained. S3. Based on the relationship between the first intensity component and the second intensity component, the expression for the first component of the magnetic field intensity is obtained; the expression for the first component of the magnetic field intensity is solved to obtain the mathematical model of the first component of the magnetic field intensity in each layer of the primary winding. S4. Based on Maxwell's equations and the insulation layer thickness parameter between the primary winding layers, the third and fourth differential equations of the relationship between the second component of the magnetic field strength and the electric field strength are obtained. S5. Based on the original electric field strength expression, the third relational differential equation, and the curl expression of the second component of the magnetic field strength, the relationship between the second component of the magnetic field strength and the third intensity component of the electric field strength is obtained; based on the fourth relational differential equation and the curl expression of the electric field strength, the relationship between the second component of the magnetic field strength and the fourth intensity component of the electric field strength is obtained. S6. Based on the relationship between the third and fourth intensity components, the expression for the second component of the magnetic field intensity is obtained; the expression for the second component of the magnetic field intensity is solved to obtain the mathematical model of the second component of the magnetic field intensity in each layer of the primary winding. S7. Based on the original magnetic field strength expression, the mathematical model of the first component of magnetic field strength, and the mathematical model of the second component of magnetic field strength, obtain the magnetic field strength in each conductor of the primary winding's conductor matrix, and calculate the magnetic field energy in each conductor based on the magnetic field strength in each conductor; and obtain the total magnetic field energy of the primary winding based on the magnetic field energy in each conductor. S8. Based on the total magnetic field energy, construct a two-dimensional model of the leakage inductance of the high-frequency transformer and complete the two-dimensional analysis of the leakage inductance of the high-frequency transformer.

[0023] The present invention discloses a two-dimensional analytical calculation method for leakage inductance of high-frequency transformers, which overcomes the technical shortcomings of traditional one-dimensional leakage inductance calculation models that can only perform axial calculations and cannot consider winding edge effects. By adopting a two-dimensional analytical modeling approach, mathematical models of the first component of the magnetic field strength of the corresponding winding body and the second component of the magnetic field strength of the corresponding interlayer insulation layer are constructed respectively, which fully covers the magnetic field distribution characteristics of the primary winding of the high-frequency transformer. By decomposing the solution logic of the magnetic field differential equations of the winding body and the insulation layer, the magnetic field distortion characteristics of the winding edge region are described, which effectively solves the problems of the one-sided magnetic field calculation and poor adaptability to operating conditions of traditional one-dimensional models, and makes the magnetic field solution model highly consistent with the actual electromagnetic distribution state of the transformer. Meanwhile, this invention employs Maxwell's equations to construct a differential equation solution system throughout the process. By combining core structural parameters such as winding porosity and insulation layer thickness, multiple sets of coupled differential relationships are established. This fully considers the changes in leakage inductance frequency characteristics caused by the skin effect and proximity effect under high-frequency operating conditions. Unlike the shortcomings of the traditional two-dimensional model of the image method, which simplifies electromagnetic constraints and ignores the influence of high-frequency electromagnetic coupling, this method derives the coupling relationship between electric field and magnetic field strength step by step, restoring the dynamic law of leakage inductance changing with frequency. This significantly improves the problem of large calculation errors and distorted results in high-frequency scenarios of the traditional model, and significantly improves the calculation accuracy of high-frequency leakage inductance. Furthermore, this invention decomposes the magnetic field strength into a first component of the winding body and a second component of the insulation layer. By solving for the magnetic field distribution within the winding and between the insulation layers using two independent and coupled differential equation systems, the leakage inductance parameters of the insulation layer can be directly calculated. This overcomes the technical limitation of traditional analytical models that cannot calculate the leakage inductance of the insulation layer independently. Even for high-frequency transformers with complex structures such as high insulation layer ratios and interleaved windings, the magnetic field energy can still be accurately solved layer by layer and region, maintaining a stable and high accuracy in leakage inductance calculation, effectively broadening the applicability of the method. This method effectively reduces the difficulty of solving higher-order electromagnetic equations, and the model has strong portability and computability, facilitating programmed simulation and batch engineering calculations. It can efficiently adapt to the engineering needs of industrial high-frequency transformer optimization design and performance verification. Simultaneously, this invention constructs a leakage inductance model by combining the calculation of the magnetic field energy of a single conductor with the superposition of the total magnetic field energy across the entire domain. The calculation is based on the electromagnetic energy physics of the leakage inductance, overcoming the drawbacks of traditional calculation methods that rely on empirical formulas and simplified approximations, and avoiding human calculation errors caused by empirical parameters. This further ensures the authenticity and reliability of the leakage inductance calculation results under complex structures and high-frequency operating conditions.

[0024] Specifically, in this embodiment of the invention, a coordinate system is constructed for the windings in the high-frequency transformer. The origin of the coordinate system is located at the rightmost point of the lowest winding in the winding region (i.e., the right end point of the lowest winding), and the x-axis extends to the right and the z-axis extends upward. That is, the x-axis and z-axis are not limited to one winding layer.

[0025] Specifically, in step S1, the original electric field strength expression and the original magnetic field strength expression of the primary winding are obtained. Specifically, if the current of the primary winding of the high-frequency transformer is set to be inward along the y-axis, then the original electric field strength can be expressed as: (1) Reference Figure 2 As shown, in this embodiment of the invention, the magnetic field strength includes two components: the x-axis and the z-axis. Therefore, the original expression for the magnetic field strength is: (2) in, Indicates electric field strength. This represents the component of the electric field intensity along the y-axis. Indicates magnetic field strength; This represents the component of the magnetic field strength along the x-axis, i.e., the second component of the magnetic field strength. This represents the component of the magnetic field strength along the z-axis, i.e., the first component of the magnetic field strength. Represents the unit vector along the x-axis. This represents the unit vector along the y-axis. This represents the unit vector along the z-axis.

[0026] Furthermore, referring to Figure 3 The integration path shown yields the first component of the magnetic field strength based on Maxwell's equations and the porosity of the primary winding. With electric field strength The differential equations satisfy the given conditions. These differential equations include the first relational differential equation and the second relational differential equation.

[0027] Furthermore, the specific expressions for the first and second relational differential equations are as follows: (3) (4) in, Represents the Hamiltonian operator. This indicates the conductivity of a round conductor winding. It represents the porosity of the primary winding, which is related to the gap between turns in each layer of winding; Indicates the imaginary part. Indicates the angular frequency of the power supply. It represents the magnetic permeability.

[0028] Specifically, in step S2, for Expanding, we obtain the curl expression for the first component of the magnetic field strength as follows: (5) in, This represents the rate of change of the field quantity along the x-axis in space. This represents the rate of change of the field quantity along the y-axis in space. This represents the rate of change of the field quantity along the z-axis in space.

[0029] Furthermore, based on the original electric field strength expression (1), the first relational differential equation (3), and the curl expression (5) of the first component of the magnetic field strength, we obtain... And the relationship between the first component of the magnetic field strength and the first intensity component of the electric field strength is obtained: (6)

[0030] Furthermore, on Expanding this, we obtain the expression for the curl of the electric field intensity: (7)

[0031] Furthermore, based on the second relational differential equation (4) and the electric field curl expression (7), we obtain And the relationship between the first component of the magnetic field strength and the second component of the electric field strength is obtained: (8)

[0032] Specifically, in step S3, the first intensity component relationship (6) is substituted into the second intensity component relationship (8) to obtain the expression for the first component of the magnetic field intensity: (9)

[0033] Furthermore, by using boundary conditions to solve the expression for the first component of the magnetic field strength (9), the mathematical model of the first component of the magnetic field strength in each layer (e.g., the p-th layer) of the primary winding is obtained, and the specific expression is as follows: (10) ; ; in, This represents the first component of the magnetic field strength within the p-th winding. This represents the coordinate position of the observation point inside the p-th winding on the x-axis. Indicates the winding layer number in the z-axis direction; , Indicates the diameter of the wire; Indicates the number of turns per layer of the primary winding. This represents the effective value of the input current of the primary winding. Indicates the winding height. Indicates the imaginary part. Indicates the angular frequency of the power supply. Indicates magnetic permeability, This indicates the conductivity of a round conductor winding. Indicates the porosity of the primary winding. This represents the hyperbolic sine function.

[0034] In this embodiment of the invention, the first component mathematical model (10) of the magnetic field strength represents the magnetic field strength in the p-th layer winding, and the coordinate 0 point of x is located at the leftmost side of the p-th layer winding.

[0035] Specifically, in step S4, refer to Figure 4 The integration path shown (i.e., the integration path along the x-axis) yields, based on Maxwell's equations and the insulation layer thickness parameter between the primary winding layers, the third and fourth differential equations relating the second component of the magnetic field strength to the electric field strength. The specific expressions are as follows: (11) (12) in, This parameter represents the thickness of the insulation layer between the primary winding layers and is related to the thickness of the insulation layer between the primary winding layers.

[0036] Specifically, in step S5, for Expanding the expression, we obtain the curl expression for the second component of the magnetic field strength: (13)

[0037] Furthermore, based on the original electric field strength expression (1), the third relational differential equation (11), and the curl expression (13) of the second component of the magnetic field strength, we can obtain... And the relationship between the second component of the magnetic field strength and the third component of the electric field strength is obtained: (14)

[0038] Furthermore, based on the fourth relational differential equation (12) and the electric field curl expression (7), we obtain And the relationship between the second component of the magnetic field strength and the fourth component of the electric field strength is obtained: (15)

[0039] Specifically, in step S6, the third intensity component relationship (14) is substituted into the fourth intensity component relationship (15) to obtain the expression for the second component of the magnetic field intensity: (16)

[0040] Furthermore, by solving the expression (16) for the second component of the magnetic field strength using boundary conditions, we obtain the mathematical model of the second component of the magnetic field strength in each layer (e.g., the qth layer) of the primary winding transversely: (17) ; ; in, This represents the second component of the magnetic field strength within the q-th winding layer. This represents the coordinate position of the observation point inside the q-th winding on the z-axis. Indicates the winding layer number in the x-axis direction; , Indicates the diameter of the wire. Indicates the number of layers in the primary winding. Indicates the winding width. Indicates the imaginary part. Indicates the angular frequency of the power supply. Indicates magnetic permeability, Indicates the conductivity of a round conductor winding. This indicates the thickness parameter of the insulation layer between the primary winding layers. This represents the hyperbolic sine function.

[0041] In this embodiment of the invention, the mathematical model (17) of the second component of the magnetic field strength is the magnetic field strength in the q-th layer of winding from top to bottom in the transverse direction, and the coordinate 0 point of z is located at the bottom of the q-th layer of winding.

[0042] Specifically, in step S7, the total magnetic field strength in each conductor of the primary winding conductor matrix is ​​calculated. The specific steps are as follows: S710, the first component mathematical model of magnetic field strength (10) gives the magnetic field strength in the p-th winding in the longitudinal direction (i.e., the z-axis direction), while the second component mathematical model of magnetic field strength (17) gives the magnetic field strength in the q-th winding in the transverse direction (i.e., the x-axis direction). Substituting formulas (10) and (17) into the original magnetic field strength expression (2), the magnetic field strength in the (p,q)-th conductor in the conductor matrix can be obtained.

[0043] Furthermore, the expression for the magnetic field strength within each (e.g., the (p,q)th) conductor in the primary winding's conductor matrix is: (18) in, Let represent the magnetic field intensity vector inside the (p,q)th conductor in the conductor matrix; here, This represents the coordinate position of the (p,q)th conductor along the x-axis. This represents the coordinate position of the (p,q)th conductor along the z-axis.

[0044] S720. Calculate the magnetic field energy in each conductor based on the magnetic field strength within each conductor. The expression for calculating the magnetic field energy in the (p,q)th conductor is as follows: (19)

[0045] S730, computing with layer The total magnetic field energy of the primary winding of the turns is calculated using the following expression: (20) , ; , ; in, This represents the total magnetic field energy of the primary winding. This represents the magnetic field energy within the (p,q)th conductor. Indicates magnetic permeability, Indicates the average turn length of the winding. Indicates the winding width. Indicates the number of turns in the primary winding. Indicates the winding height. Indicates the number of layers in the primary winding. Indicates the diameter of the wire. Represents a hyperbolic sine function. This represents the hyperbolic cosine function.

[0046] Specifically, in step S8, the process of constructing a two-dimensional model of the leakage inductance of the high-frequency transformer based on the total magnetic field energy includes determining the correlation between the total magnetic field energy and the leakage inductance based on the winding arrangement of the high-frequency transformer; and constructing a two-dimensional model of the leakage inductance of the high-frequency transformer based on the correlation between the total magnetic field energy and the leakage inductance. The high-frequency transformer also includes a secondary winding. The winding arrangement of the high-frequency transformer includes a tightly packed primary winding and an alternating arrangement of the primary and secondary windings, as shown below. Figure 2 and Figure 5 As shown. It should be noted that, in Figures 2 to 6 In red, the primary winding is represented; in blue, the secondary winding is represented.

[0047] Specifically, because of the total magnetic field energy The solution process involved two analyses, one using the longitudinal winding and the other the transverse winding. This means that the current was used twice in the process of differentiating the total magnetic field energy. Therefore, the leakage inductance of the primary winding will satisfy the following equation: .(twenty one)

[0048] Furthermore, when the primary winding layers are closely arranged, the mathematical expression of the two-dimensional leakage inductance model obtained by solving formula (21) is: ;(twenty two) in, This represents the leakage inductance value.

[0049] Furthermore, the two-dimensional leakage inductance model (22) is the formula for calculating the two-dimensional leakage inductance of the primary winding. To calculate the leakage inductance of the secondary winding, it is only necessary to... , , Simply replace 't' with the parameters of the secondary winding.

[0050] Furthermore, for the case where the winding layers of the primary winding and the secondary winding are arranged alternately, Figure 5 The windings, which feature an alternating arrangement of longitudinal integration paths, are shown. Figure 5 It can be seen that p in the mathematical model (10) of the first component of the magnetic field strength will always be equal to 1. Figure 6 For windings with staggered transverse integration paths, by Figure 6 It is clear that this situation will be without Components, i.e. Therefore, for interleaved windings, H will have no x-component, only a z-component, and p=1. Thus, p=1 and Substituting into formula (18), the magnetic field strength of the staggered windings can be solved. Under this arrangement, the total magnetic field energy of the primary winding satisfies the following relationship: ;(twenty three) The relationship satisfied by the total magnetic field energy of the secondary winding is: .(twenty four)

[0051] Therefore, the total magnetic field energy of the primary and secondary windings satisfies the following relationship: (25)

[0052] Furthermore, when the winding layers of the primary winding and the secondary winding are arranged alternately, the mathematical expression of the two-dimensional leakage inductance model is obtained according to formula (25): (26) in, This represents the total leakage inductance value of the high-frequency transformer. This represents the magnetic field strength inside the conductor. In this formula, Satisfies formula (18), and p=1 and .

[0053] The analytical calculation method for two-dimensional leakage inductance proposed in this invention is applicable not only to closely spaced winding structures but also to complex, staggered winding structures. Furthermore, this invention does not rely on introducing a frequency-varying factor; instead, it employs rigorous theoretical modeling to fully consider the frequency variations in leakage inductance caused by the skin effect and proximity effect, thus increasing its calculation accuracy at high frequencies. In addition, the method described in this invention is also applicable to transformers with a high insulation layer ratio. When calculating the leakage inductance of transformers with a high insulation layer ratio, the calculation method proposed in this invention still maintains high calculation accuracy.

[0054] Furthermore, to describe the method of the embodiments of the present invention in detail, the following exemplary steps are given: Step 1: Set the operating frequency Vacuum permeability Conductivity of wires and the porosity of the primary winding Substitution In the middle, calculate ; operating frequency Vacuum permeability Conductivity of wires and the porosity of the secondary winding Substitution In the middle, calculate .

[0055] Step 2: Combine the wire diameter t with the value obtained in Step 1. and Substitute them into the following formulas respectively: ; ; ; ; It can be obtained , , , .

[0056] Step 3: Adjust the vacuum permeability Average turns of winding Number of turns per layer of the primary winding Number of layers in the primary winding Total winding width and the results obtained in steps 1 and 2 , , , , , Substituting these values ​​into formula (22), the leakage inductance of the primary winding can be calculated.

[0057] Step 4: Adjust the vacuum permeability Average turns of winding The number of layers in the secondary winding, the number of turns per layer in the secondary winding, the total width of the winding, and the values ​​obtained in steps 1 and 2. , , , , , Substituting these values ​​into formula (22), the leakage inductance of the secondary winding can be calculated.

[0058] Step 5: The total leakage inductance of the winding is the sum of the leakage inductance value calculated in Step 3 and the leakage inductance value calculated in Step 4.

[0059] This invention proposes a two-dimensional analytical calculation method for leakage inductance based on Maxwell's equations. Existing one-dimensional analytical calculation models cannot account for winding edge effects, while traditional two-dimensional analytical models based on the image method also have shortcomings. This invention overcomes the deficiencies of both types of models simultaneously. This invention establishes a two-dimensional mathematical model of magnetic field intensity distribution and uses Maxwell's equations in the frequency domain for solution. This model can fully characterize the frequency characteristics of leakage inductance caused by the skin effect and proximity effect, significantly improving the calculation accuracy of leakage inductance under high-frequency operating conditions. Furthermore, this invention's model can directly solve for leakage inductance in the insulation layer, maintaining high calculation accuracy even for transformer structures with high insulation layer ratios and complex winding arrangements (such as interleaved windings).

[0060] Example 2:

[0061] Based on the same inventive concept, this embodiment provides a two-dimensional analytical calculation system for the leakage inductance of a high-frequency transformer. The principle of solving the problem is similar to the two-dimensional analytical calculation method for the leakage inductance of a high-frequency transformer provided in Embodiment 1, and the repeated parts will not be described again.

[0062] This embodiment provides a two-dimensional analytical calculation system for the leakage inductance of a high-frequency transformer, used to implement the two-dimensional analytical calculation method for the leakage inductance of a high-frequency transformer described in Embodiment 1, including: The first module for constructing relational differential equations is used to obtain the original electric field strength expression and the original magnetic field strength expression of the primary winding; based on the porosity of the primary winding and Maxwell's equations, the first relational differential equation and the second relational differential equation satisfied by the first component of the magnetic field strength and the electric field strength are obtained; wherein, the high-frequency transformer includes the primary winding; The first construction module for the intensity component relationship is used to obtain the first intensity component relationship between the first component of the magnetic field intensity and the electric field intensity based on the original electric field intensity expression, the first relationship differential equation, and the curl expression of the first component of the magnetic field intensity; and to obtain the second intensity component relationship between the first component of the magnetic field intensity and the electric field intensity based on the second relationship differential equation and the curl expression of the electric field intensity. The first component mathematical model construction module is used to obtain the expression for the first component of magnetic field strength based on the first intensity component relationship and the second intensity component relationship; and to solve the expression for the first component of magnetic field strength to obtain the mathematical model for the first component of magnetic field strength in each layer of winding in the primary winding. The second module for constructing relational differential equations is used to obtain the third and fourth relational differential equations satisfied by the second component of the magnetic field strength and the electric field strength based on Maxwell's equations and the insulation layer thickness parameter between the primary winding layers. The second module for constructing the intensity component relationship is used to obtain the third intensity component relationship between the second component of the magnetic field intensity and the electric field intensity component based on the original electric field intensity expression, the third relationship differential equation, and the curl expression of the second component of the magnetic field intensity; and to obtain the fourth intensity component relationship between the second component of the magnetic field intensity and the electric field intensity component based on the fourth relationship differential equation and the curl expression of the electric field intensity. The second component mathematical model construction module is used to obtain the expression for the second component of the magnetic field strength based on the relationship between the third and fourth intensity components; and to solve the expression for the second component of the magnetic field strength to obtain the mathematical model of the second component of the magnetic field strength in each layer of the primary winding. The total magnetic field energy calculation module is used to obtain the magnetic field intensity in each conductor of the primary winding's conductor matrix based on the original magnetic field intensity expression, the mathematical model of the first component of the magnetic field intensity, and the mathematical model of the second component of the magnetic field intensity, and to calculate the magnetic field energy in each conductor based on the magnetic field intensity in each conductor; and to obtain the total magnetic field energy of the primary winding based on the magnetic field energy in each conductor. The analysis module is used to construct a two-dimensional model of the leakage inductance of the high-frequency transformer based on the total magnetic field energy, and to complete the two-dimensional analysis of the leakage inductance of the high-frequency transformer.

[0063] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0064] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0065] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0066] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0067] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A two-dimensional analytical calculation method for the leakage inductance of a high-frequency transformer, characterized in that, include: S1. The high-frequency transformer includes a primary winding; obtain the original electric field strength expression and the original magnetic field strength expression of the primary winding; Based on the porosity of the primary winding and Maxwell's equations, the first and second differential equations relating the first component of the magnetic field strength to the electric field strength are obtained. S2. Based on the original electric field strength expression, the first relational differential equation, and the curl expression of the first component of the magnetic field strength, obtain the first intensity component relationship between the first component of the magnetic field strength and the electric field strength component; based on the second relational differential equation and the curl expression of the electric field strength, obtain the second intensity component relationship between the first component of the magnetic field strength and the electric field strength component. S3. Based on the first intensity component relationship and the second intensity component relationship, obtain the expression for the first component of the magnetic field intensity; solve the expression for the first component of the magnetic field intensity to obtain the mathematical model of the first component of the magnetic field intensity in each layer of the primary winding; S4. Based on the Maxwell's equations and the insulation layer thickness parameter between the primary winding layers, the third and fourth differential equations relating the second component of the magnetic field strength to the electric field strength are obtained. S5. Based on the original electric field strength expression, the third relational differential equation, and the curl expression of the second component of the magnetic field strength, the relationship between the second component of the magnetic field strength and the third intensity component of the electric field strength is obtained; based on the fourth relational differential equation and the curl expression of the electric field strength, the relationship between the second component of the magnetic field strength and the fourth intensity component of the electric field strength is obtained. S6. Based on the third intensity component relationship and the fourth intensity component relationship, obtain the expression for the second component of the magnetic field intensity; solve the expression for the second component of the magnetic field intensity to obtain the mathematical model of the second component of the magnetic field intensity in each layer of the primary winding; S7. Based on the original magnetic field strength expression, the mathematical model of the first component of the magnetic field strength, and the mathematical model of the second component of the magnetic field strength, obtain the magnetic field strength in each conductor of the conductor matrix of the primary winding, and calculate the magnetic field energy in each conductor based on the magnetic field strength in each conductor. The total magnetic field energy of the primary winding is obtained based on the magnetic field energy in each conductor. S8. Based on the total magnetic field energy, construct a two-dimensional model of the leakage inductance of the high-frequency transformer to complete the two-dimensional analysis of the leakage inductance of the high-frequency transformer.

2. The two-dimensional analytical calculation method for leakage inductance of a high-frequency transformer according to claim 1, characterized in that, In step S8, the process of constructing a two-dimensional model of the leakage inductance of the high-frequency transformer based on the total magnetic field energy includes determining the correlation between the total magnetic field energy and the leakage inductance based on the arrangement structure of the windings of the high-frequency transformer; and constructing a two-dimensional model of the leakage inductance of the high-frequency transformer based on the correlation between the total magnetic field energy and the leakage inductance.

3. The two-dimensional analytical calculation method for leakage inductance of a high-frequency transformer according to claim 2, characterized in that, When the arrangement structure is such that the winding layers of the primary winding are closely arranged, the mathematical expression of the two-dimensional leakage inductance model is: ； ， ； ， ； ， ； in, Indicates the leakage inductance value. Indicates magnetic permeability, This indicates the average turn length of the winding. Indicates the winding width. This indicates the number of turns per layer of the primary winding. Indicates the winding height. Indicates the number of layers in the primary winding. Indicates the diameter of the wire. Indicates the imaginary part unit. Indicates the angular frequency of the power supply. This indicates the conductivity of a round conductor winding. This indicates the porosity of the primary winding. This indicates the thickness parameter of the insulation layer between the primary winding layers. Represents the hyperbolic sine function. This represents the hyperbolic cosine function.

4. The two-dimensional analytical calculation method for leakage inductance of a high-frequency transformer according to claim 2, characterized in that, The high-frequency transformer also includes a secondary winding. When the arrangement structure is such that the winding layers of the primary winding and the winding layers of the secondary winding are alternately arranged, the mathematical expression of the two-dimensional leakage inductance model is: ； in, This represents the total leakage inductance value of the high-frequency transformer. This represents the effective value of the input current of the primary winding. Indicates the number of layers in the primary winding. Indicates the number of layers in the secondary winding. Indicates magnetic permeability, This indicates the average turn length of the winding. Indicates the winding height. Indicates the diameter of the wire. This indicates the magnetic field strength inside the conductor.

5. The two-dimensional analytical calculation method for leakage inductance of a high-frequency transformer according to claim 1, characterized in that, The mathematical model for the first component of the magnetic field strength in each layer of the primary winding is as follows: ； ； ； in, This represents the first component of the magnetic field strength within the p-th winding. This represents the coordinate position of the observation point inside the p-th winding on the x-axis. Indicates the winding layer number in the z-axis direction. Indicates the diameter of the wire. This indicates the number of turns per layer of the primary winding. This represents the effective value of the input current of the primary winding. Indicates the winding height. Indicates the imaginary part unit. Indicates the angular frequency of the power supply. Indicates magnetic permeability, This indicates the conductivity of a round conductor winding. This indicates the porosity of the primary winding. This represents the hyperbolic sine function.

6. The two-dimensional analytical calculation method for leakage inductance of a high-frequency transformer according to claim 1, characterized in that, The mathematical model for the second component of the magnetic field strength in each layer of the primary winding is as follows: ； ； ； in, This represents the second component of the magnetic field strength within the q-th winding layer. This represents the coordinate position of the observation point inside the q-th winding on the z-axis. Indicates the winding layer number in the x-axis direction. Indicates the diameter of the wire. Indicates the number of layers in the primary winding. This represents the effective value of the input current of the primary winding. Indicates the winding width. Indicates the imaginary part unit. Indicates the angular frequency of the power supply. Indicates magnetic permeability, Indicates the conductivity of a round conductor winding. This indicates the thickness parameter of the insulation layer between the primary winding layers. This represents the hyperbolic sine function.

7. The two-dimensional analytical calculation method for leakage inductance of a high-frequency transformer according to claim 1, characterized in that, The expression for the magnetic field strength in each conductor of the primary winding conductor matrix is ​​as follows: ； ， ； ， ； in, This represents the magnetic field strength vector inside the (p,q)th conductor in the conductor matrix. This represents the coordinate position of the (p,q)th conductor along the x-axis. Indicates the winding layer number in the z-axis direction. Indicates the diameter of the wire. This represents the coordinate position of the (p,q)th conductor along the z-axis. Indicates the winding layer number in the x-axis direction. This indicates the number of turns per layer of the primary winding. This represents the effective value of the input current of the primary winding. Indicates the winding height. Indicates the number of layers in the primary winding. Indicates the winding width. Indicates the imaginary part unit. Indicates the angular frequency of the power supply. Indicates magnetic permeability, This indicates the conductivity of a round conductor winding. This indicates the porosity of the primary winding. This indicates the thickness parameter of the insulation layer between the primary winding layers. Represents the unit vector along the x-axis. This represents the unit vector along the z-axis. This represents the hyperbolic sine function.

8. The two-dimensional analytical calculation method for leakage inductance of a high-frequency transformer according to claim 1, characterized in that, The expression for the total magnetic field energy of the primary winding is: ； ， ； ， ； ， ； ， ； in, This represents the total magnetic field energy of the primary winding. This represents the magnetic field energy within the (p,q)th conductor. Indicates magnetic permeability, This indicates the average turn length of the winding. Indicates the winding width. This indicates the number of turns per layer of the primary winding. Indicates the winding height. Indicates the number of layers in the primary winding. Indicates the diameter of the wire. This represents the effective value of the input current of the primary winding. Indicates the imaginary part unit. Indicates the angular frequency of the power supply. This indicates the conductivity of a round conductor winding. This indicates the porosity of the primary winding. This indicates the thickness parameter of the insulation layer between the primary winding layers. Represents the hyperbolic sine function. This represents the hyperbolic cosine function.

9. The two-dimensional analytical calculation method for leakage inductance of a high-frequency transformer according to claim 1, characterized in that, The expression for the first component of the magnetic field strength is: ； The expression for the second component of the magnetic field strength is: ； in, Represents the first component of the magnetic field strength. This represents the second component of the magnetic field strength. Indicates the imaginary part unit. Indicates the angular frequency of the power supply. Indicates magnetic permeability, This indicates the conductivity of a round conductor winding. This indicates the porosity of the primary winding. This indicates the thickness parameter of the insulation layer between the primary winding layers.

10. A two-dimensional analytical calculation system for the leakage inductance of a high-frequency transformer, used to implement the two-dimensional analytical calculation method for the leakage inductance of a high-frequency transformer as described in any one of claims 1 to 9, characterized in that, include: The first module for constructing relational differential equations is used to obtain the original electric field strength expression and the original magnetic field strength expression of the primary winding; Based on the porosity of the primary winding and Maxwell's equations, the first and second differential equations relating the first component of the magnetic field strength to the electric field strength are obtained; wherein, the high-frequency transformer includes the primary winding; The first intensity component relationship construction module is used to obtain the first intensity component relationship between the first component of the magnetic field intensity and the electric field intensity component based on the original electric field intensity expression, the first relationship differential equation, and the curl expression of the first component of the magnetic field intensity; and to obtain the second intensity component relationship between the first component of the magnetic field intensity and the electric field intensity component based on the second relationship differential equation and the curl expression of the electric field intensity. The first component mathematical model construction module is used to obtain the expression for the first component of magnetic field strength based on the first intensity component relationship and the second intensity component relationship; and to solve the expression for the first component of magnetic field strength to obtain the mathematical model for the first component of magnetic field strength in each layer of winding in the primary winding. The second module for constructing relational differential equations is used to obtain the third and fourth relational differential equations satisfied by the second component of the magnetic field strength and the electric field strength based on the Maxwell equations and the insulation layer thickness parameter between the primary winding layers. The second intensity component relationship construction module is used to obtain the third intensity component relationship between the second component of the magnetic field intensity and the electric field intensity component based on the original electric field intensity expression, the third relationship differential equation, and the curl expression of the second component of the magnetic field intensity; and to obtain the fourth intensity component relationship between the second component of the magnetic field intensity and the electric field intensity component based on the fourth relationship differential equation and the curl expression of the electric field intensity. The second component mathematical model construction module is used to obtain the expression for the second component of magnetic field strength based on the third intensity component relationship and the fourth intensity component relationship; and to solve the expression for the second component of magnetic field strength to obtain the mathematical model for the second component of magnetic field strength in each layer of winding in the primary winding. The total magnetic field energy calculation module is used to obtain the magnetic field strength in each conductor of the conductor matrix of the primary winding according to the original magnetic field strength expression, the mathematical model of the first component of the magnetic field strength, and the mathematical model of the second component of the magnetic field strength, and to calculate the magnetic field energy in each conductor according to the magnetic field strength in each conductor; and to obtain the total magnetic field energy of the primary winding according to the magnetic field energy in each conductor. The analysis module is used to construct a two-dimensional model of the leakage inductance of the high-frequency transformer based on the total magnetic field energy, and to complete the two-dimensional analysis of the leakage inductance of the high-frequency transformer.

Images