Differential mode EMI filter inductance broadband behavior prediction method

Abstract

The invention discloses a differential mode EMI filter inductor broadband behavior prediction method. The method comprises the steps of establishing an equivalent high-frequency circuit model according to an actual geometric structure of a differential mode EMI filter inductor of a target magnetic powder core; the inductance value and the capacitance value in the equivalent high-frequency circuit model are divided into an internal area, an external area and parallel areas of the front face and the back face according to the actual geometric structure of the target magnetic powder core differential mode EMI filter inductor, and the inductance values and the capacitance values in the equivalent high-frequency circuit model in the different areas are calculated; substituting the inductance value and the capacitance value into an equivalent high-frequency circuit model, calculating the impedance of the circuit at each frequency point by using a circuit analysis method, and forming an impedance curve of the target magnetic powder core differential mode EMI filter inductor; the impedance curve is used for representing the broadband behavior of the target magnetic powder core differential mode EMI filter inductor; according to the method, the limitation of a traditional method is broken through, inductor high-frequency modeling is not limited to nanocrystalline and MnZn magnetic core materials, the inductor high-frequency modeling can be effectively applied to magnetic powder core materials, the method is particularly suitable for a differential-mode EMI filter inductor, calculation resources are remarkably saved, the design efficiency is improved, the development cost is reduced, and the high-frequency performance and the filtering effect of the inductor are effectively improved.

Description

Technical Field

[0001] The present invention relates to the technical field of high-pressure valve cold sensor systems, and in particular to a method for predicting broadband behavior of a differential-mode EMI filter inductor. Background Art

[0002] With the rapid development of the global economy and the rise of emerging industries, the demand for electricity continues to increase. To meet this challenge, ultra-high voltage direct current (UHVDC) technology has become a key solution for achieving long-distance, efficient, and low-loss power transmission. This technology not only meets the strategic goals of optimizing the national energy structure and green development, but also greatly improves the stability and reliability of the power grid. As the core equipment in the ultra-high voltage direct current transmission system, the stability of the converter valve directly affects the safe operation of the power system. Under high power and long-term operation conditions, the converter valve will generate a lot of heat, which may cause the equipment to overheat and affect its normal operation, and even cause system failure in extreme cases. Therefore, the reliability of the valve cooling system is particularly important, and its sensors need to monitor key data such as circulating water temperature and flow in real time and feed it back to the control system. However, the concentrated power electronic equipment in the converter station will generate strong electromagnetic interference during operation, especially high-frequency switching current. These interference signals may cause differential mode interference through the current loop, thereby affecting the stability of the control system. In addition, as the sensor design tends to be miniaturized, the sensitivity of its internal circuit to differential mode interference has also increased. In order to suppress differential mode interference, differential mode inductors are usually required in filters, but the presence of parasitic capacitance may cause impedance shift caused by high-frequency signals, thus affecting the filtering effect. Therefore, accurate modeling of differential mode inductors is particularly important for optimizing filter performance, meeting electromagnetic compatibility standards, and ensuring that the weight and volume of the equipment are not increased.

[0003] As an important magnetic material, magnetic powder core is widely used in the field of power electronics, especially in differential mode inductors. Magnetic powder core is made of metal powder (such as iron, nickel, silicon alloy), wrapped with a layer of insulating material on the outside, and has the advantages of high saturation flux density, soft saturation characteristics and high Curie temperature. These characteristics make magnetic powder core have significant advantages in high-frequency applications such as differential mode inductors, flyback transformers and electromagnetic interference (EMI) filters. The performance of differential mode inductors in high-frequency environments is closely related to their magnetic properties. Therefore, accurately modeling the high-frequency behavior of magnetic powder cores is of great significance for the design and optimization of differential mode inductors.

[0004] In recent years, many studies have focused on high-frequency modeling of inductors, which can be divided into two categories: behavioral modeling and physical modeling. In order to more accurately calculate the capacitance in the inductor, the currently proposed models usually need to consider assumptions that are closer to the actual distribution of electric field lines. These assumptions can be used as a basis for calculating the turn-to-turn capacitance (C tt ) and the capacitance between the turns and the core (Ctc ) is the basis of the inductor. In addition, in order to optimize the structure and performance of the inductor, high-frequency physical parameters are often combined with the actual geometry of the inductor for modeling. This approach can better reflect the electromagnetic behavior of the inductor under high-frequency working conditions and provide more accurate guidance for the design of the inductor, thereby improving its efficiency and stability. However, these models are only applicable to inductors with high permeability (μ) or high dielectric constant (ε) cores, such as MnZn and nanocrystalline cores, which can be regarded as perfect electric conductors (PEC). In contrast, inductors with low μ or low ε cores such as magnetic powder cores cannot use the PEC assumption because the core material has a low μ and the insulating layer or distributed air gap between the powders significantly reduces the overall ε of the core. Therefore, the existing high-frequency analytical models are not applicable in the application of magnetic powder core inductors and have large errors compared with the actual measurement results. Summary of the invention

[0005] The present invention provides a method for predicting the broadband behavior of a differential-mode EMI filter inductor, so as to overcome the technical problem that, in the process of using the existing high-frequency analytical model to perform high-frequency modeling on low magnetic permeability and low dielectric constant materials such as magnetic powder cores, the electromagnetic behavior of the magnetic powder core inductor cannot be accurately predicted, and the differential-mode EMI inductor using the magnetic powder core cannot be optimized.

[0006] In order to achieve the above object, the technical solution of the present invention is:

[0007] A method for predicting broadband behavior of differential mode EMI filter inductors, characterized by comprising:

[0008] S1: Establish an equivalent high-frequency circuit model based on the actual geometric structure of the differential-mode EMI filter inductor of the target magnetic powder core;

[0009] S2: Divide the target magnetic powder core differential mode EMI filter inductor into an inner region, an outer region, and parallel regions on the front and back sides according to its actual geometric structure; and calculate the inductance and capacitance values ​​corresponding to each region in the equivalent high-frequency circuit model after partitioning;

[0010] S3: Substitute the inductance value and the capacitance value into the equivalent high-frequency circuit model, use the circuit analysis method to calculate the impedance of the circuit at each frequency point, and form an impedance curve of the target magnetic powder core differential mode EMI filter inductor; the impedance curve is used to characterize the broadband behavior of the target magnetic powder core differential mode EMI filter inductor.

[0011] Furthermore, the equivalent high-frequency circuit model includes N series-connected turn units L NN , inter-turn capacitance C tt , turns to the core capacitance C tc and static core capacitance C cs ;

[0012] The turn unit includes a turn of coil connected in series with the self-inductance L s and resistor R s , where the resistance represents the eddy current loss and hysteresis loss in the magnetic core; each of the inter-turn capacitances C tt In parallel with the corresponding turn unit, each turn to the core capacitor C tc One end corresponds to the self-inductance L s connected, and the other end is connected to the corresponding static core capacitor C cs One end of the static core capacitor C cs The other end is connected to the last turn to the core capacitor C tc The other end is connected.

[0013] Furthermore, the specific steps for solving the inductance include:

[0014] The impedance of a single-turn inductor is solved according to Ampere's loop law, as shown in formula (1):

[0015]

[0016] Where Z is the impedance of a single-turn inductor, μ 0 is the vacuum permeability, μ′ r Represents the real part of the complex permeability, μ″ r represents the imaginary part of the complex permeability, h c Indicates the thickness of the core, R o is the outer diameter of the core, R in is the inner diameter of the core;

[0017] In an inductor, the impedance of a single turn of coil is represented by L ii , L s Represents the self-inductance of a single-turn coil, R s represents the eddy current loss and hysteresis loss of a single-turn coil. The mutual inductance and leakage inductance between turns i and j are M respectively. ij and L σij , the leakage inductance is the inductance of the winding unit. The relationship between mutual inductance and leakage inductance is shown in formula (2).

[0018] L ii =M ij +L σij (2)

[0019] The leakage inductance between turn i and turn , is modeled, and the leakage inductance value is divided into three regions: the inner region, the outer region and the parallel region. The leakage inductance of the parallel region is divided into the front and back sides. The leakage inductance expression after partitioning is shown in formula (3):

[0020] L σij =Lσin +L σo +L σl +L σl′w (3)

[0021] Among them, L σin Represents the internal area leakage inductance, L σo Represents the external area leakage inductance, L σl Indicates the positive leakage inductance of the parallel region; L σl′w It represents the back leakage inductance of the parallel region;

[0022] Assuming that the winding lengths inside and outside the magnetic core are infinite, the magnetic scalar potential method is used to solve the leakage inductance of the inner region and the leakage inductance of the outer region, as shown in formulas (4) and (5),

[0023]

[0024] in, is a constant, σ c is the conductivity of the conductor, μ c J is the magnetic permeability of the conductor, the conductor is the winding; 0 and J 1 are the first-kind complex-valued Bessel functions of order zero and order one, respectively; h w Indicates the thickness of the core and winding, r in represents the inner diameter r of the core containing the winding cin Indicates the inner diameter of the core, d c represents the conductor radius, w i Indicates the thickness of the wire insulation layer;

[0025] In the parallel region, the image method is used to solve the magnetic field generated by the conductor, and the magnetic field is divided into two parts: the magnetic field generated by the original current and the magnetic field generated by the image current. The relationship between the original current and the image current is shown in formula (6):

[0026]

[0027] Among them, I 2 Represents the mirror current, I 1 represents the original current;

[0028] Obtain the component of the magnetic field perpendicular to the core surface and obtain the relationship between the magnetic field in this direction, as shown in formula (7):

[0029]

[0030] Where x represents the distance between two turns of the coil, H 1 represents the magnetic field component generated by the original current, H 1y It represents the component of the magnetic field generated by the original current that is perpendicular to the surface of the magnetic core, H 2vIt represents the component of the magnetic field generated by the image current that is perpendicular to the surface of the magnetic core, H 2 represents the magnetic field component generated by the image current, β is the angle between the line connecting the current-carrying conductor and its image and the line connecting the center line of the image and the magnetic field evaluation point. The calculation formula is shown in formula (8):

[0031] tanβ=x / 2 / w s (8)

[0032] Among them, w s Indicates the distance from the turn to the core;

[0033] The total magnetic field perpendicular to the core surface is H y =H 1y +H 2y , so the magnetic field perpendicular to the core surface is as shown in formula (9),

[0034]

[0035] The leakage magnetic flux on the front side of the parallel region between two adjacent units in the parallel region is calculated by the magnetic field in the parallel region, as shown in formula (10):

[0036]

[0037] Among them, φ σl Represents the leakage flux on the front side of the parallel region, R co Represents the outer radius of the magnetic powder core, R cin represents the inner radius of the magnetic powder core, and z represents the thickness of the magnetic core;

[0038] The leakage inductance on the front side of the parallel region is calculated using the leakage flux on the front side of the parallel region and the original current, as shown in formula (11):

[0039]

[0040] Among them, L wl Indicates the inductance value in the parallel region;

[0041] Considering the actual geometric characteristics of the winding in the common-mode EMI filter inductor, the actual winding length of the winding is calculated, as shown in formula (12):

[0042]

[0043] Among them, R in Indicates the inner diameter of the core; l' w Indicates the actual winding length of the winding;

[0044] The leakage flux on the back side of the parallel region is calculated based on the actual winding length of the winding, as shown in formula (13):

[0045]

[0046] Among them, φ σl′w represents the leakage flux on the back side of the parallel region;

[0047] The leakage inductance on the back of the parallel region is calculated based on the leakage magnetic flux and the original current on the back of the parallel region, as shown in formula (14):

[0048]

[0049] Among them, L σl′w Represents the leakage inductance on the back side of the parallel region.

[0050] Furthermore, the specific steps for solving the inter-turn capacitance include:

[0051] The inter-turn capacitance is divided into the inner region, the outer region, and the parallel regions of the front and back sides for solution. The inter-turn capacitance after partitioning is shown in formula (15):

[0052] C tt =C ttin +C tto +C ttl +C ttl′w (15)

[0053] Among them, C ttin represents the inter-turn capacitance of the inner region, C tto represents the inter-turn capacitance of the external region, C ttl represents the inter-turn capacitance on the front side of the parallel region, C ttl′w represents the inter-turn capacitance on the back side of the parallel region;

[0054] The specific analytical formulas for the inter-turn capacitance of the three regions are shown in formulas (16), (17) and (18), respectively.

[0055]

[0056] Among them, ε i Represents the dielectric constant of the medium, ε a represents the dielectric constant of air, δ o Indicates the distance between turns on the outside of the winding, w i Indicates the dielectric thickness, δ in Indicates the distance between turns inside the winding; h w Indicates the thickness of the core and winding; d c Represents the conductor radius; R o is the outer diameter of the core; R in is the inner diameter of the core; r represents a variable, δ l Represents the distance between turns in the parallel region.

[0057] Furthermore, the specific steps for solving the turn-to-core capacitance include:

[0058] Considering the actual winding length of the winding and the geometric characteristics of the common-mode EMI filter inductor, the equivalent distance from the turn to the core is calculated, as shown in formula (19):

[0059]

[0060] Among them, w s Indicates the distance from the equivalent turn to the core, w c Indicates the maximum distance between a single-turn coil and the magnetic core, w e Indicates the minimum distance between a single-turn coil and the magnetic core;

[0061] The turn-to-core capacitance is divided into the inner region, the outer region and the parallel region for solution. The partitioned turn-to-core capacitance is shown in formula (20):

[0062] C tc =C tcin +C tco +C tcl +C tcl′w (20)

[0063] Among them, C tcin represents the turns-to-core capacitance of the inner region, C tco represents the turns-to-core capacitance of the external region, C tcl represents the parallel front turn to core capacitance, C tcl′w It represents the capacitance of the turns parallel to the back surface to the core;

[0064] Determine the length of the electric field lines in the winding insulation layer, as shown in formula (21),

[0065] x tc，wi =w i (twenty one)

[0066] Among them, x tc，wi represents the length of the electric field lines in the winding insulation layer, w i Indicates the thickness of the medium;

[0067] Considering the boundary conditions at the interface between the air and the core insulation layer, the length of the electric field lines in the air and the core insulation layer is obtained, and the deflection angle of the electric field lines in the air is calculated, as shown in formula (22):

[0068]

[0069] α represents the deflection angle between the two media of air and the core insulation layer;

[0070] The length of the electric field line in the air is calculated based on the equivalent distance from the turn to the core, the length of the electric field line and the deflection angle of the electric field line as shown in formula (23):

[0071]

[0072] Among them, w s Indicates the distance from the equivalent turn to the core;

[0073] The length of the electric field line in the core insulation layer is shown in formula (24),

[0074] x tc,ci =w ci / cosα ci (twenty four)

[0075] Among them, x tc,ci represents the length of the electric field lines in the core insulation layer, w ci represents the core thickness, α ci represents the deflection angle of the electric field line in the magnetic core, as shown in formula (25),

[0076]

[0077] Among them, ε ci represents the core dielectric constant, ε a represents the dielectric constant of air;

[0078] According to the length of the electric field lines in the air and the core insulation layer, the analytical formulas for the turn-to-core capacitance in the inner region, the outer region, and the parallel region are constructed, as shown in formulas (26)-(29):

[0079]

[0080] Among them, w ci Indicates the core insulation thickness, w sin Indicates the distance from the inner area to the core, w so Indicates the distance from the outer region to the core, w sl Indicates the distance from the turn to the core in the front area of ​​the parallel region; l' w Indicates the actual winding length of the winding.

[0081] Furthermore, the specific steps for solving the static core capacitance include:

[0082] The static core capacitance is divided into the inner region, the outer region and the parallel region for solution. In the three regions, the inner and outer static core capacitances have the same form, and the expression of the static core capacitance is obtained, as shown in formula (30):

[0083] C cs =C csin +Ccso +C cslw +C csl′w (30)

[0084] Considering the material of the magnetic powder core and the dielectric boundary conditions, the length of the electric field line in the magnetic core is calculated. The deflection angle of the electric field line in the magnetic core is shown in formula (31):

[0085]

[0086] According to formula (31), the length of the electric field line in the magnetic core is obtained, as shown in formula (32),

[0087] x cs =R t / cosα c +l arc (32)

[0088] Among them, l arc Represents the arc length of the electric field line inside the magnetic core, R t is half the thickness of the core, and has different values ​​in different regions. For the inner and outer regions, R t The expression of is shown in formula (33),

[0089] R t =(R o -R in ) / 4 (33)

[0090] In the parallel region, R t The expression of is shown in formula (34),

[0091] R t =h w / 2 (34)

[0092] Among them, h w Indicates the thickness of the core and winding;

[0093] According to the length of the electric field line in the core, the analytical formula of the static core capacitance in different regions is constructed, as shown in formula (35):

[0094]

[0095] Among them, C csin and C cso represents the internal and external static core capacitance, C cslw represents the static core capacitance on the front side of the parallel region;

[0096] The expression for the static core capacitance on the back side of the parallel region is shown in formula (36),

[0097]

[0098] Beneficial effects: The present invention provides a method for predicting broadband behavior of differential mode EMI filter inductors, which has the following advantages:

[0099] 1. The prediction method of the present invention breaks through the limitations of traditional methods, so that high-frequency modeling of inductors is not limited to nanocrystalline and MnZn magnetic core materials, but can also be effectively applied to magnetic powder core materials, especially for differential mode EMI filter inductors;

[0100] 2. The parameter analytical calculation method used in the equivalent high-frequency circuit model of the present invention avoids the resource consumption of a large number of simulation solutions required in traditional modeling methods, significantly saves computing resources, and improves design efficiency;

[0101] 3. By considering the real geometric structure and electric field behavior of the inductor, the inductor is divided into three regions for calculation. Different calculation methods are used in each region to simplify the calculation of leakage inductance and capacitance, reduce the calculation workload, and provide more accurate analytical formulas for key parameters such as leakage inductance and parasitic capacitance, which provides a reliable basis for the design and optimization of differential mode EMI filter inductors and can effectively improve the high-frequency performance and filtering effect of the inductor;

[0102] 4. The high-frequency circuit model and analytical method provided by the present invention enable designers to quickly obtain the performance data of the inductor, avoiding a large amount of experimental and simulation work, thereby greatly improving the design efficiency and reducing the development cost;

[0103] 5. The method of the present invention not only has high accuracy and adaptability, but also avoids complex simulation calculations, saves time and economic costs, and therefore has significant application value in the design of differential mode EMI filter inductors. BRIEF DESCRIPTION OF THE DRAWINGS

[0104] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0105] Figure 1 A method flow chart of a method for predicting broadband behavior of a differential mode EMI filter inductor provided by the present invention;

[0106] Figure 2 This is the geometric structure diagram of the magnetic powder core differential mode EMI filter inductor;

[0107] Figure 3 This is the cross-sectional structure diagram of the magnetic powder core differential mode EMI filter inductor;

[0108] Figure 4 This is a high-frequency circuit diagram of the magnetic powder core differential mode EMI filter inductor proposed by the present invention;

[0109] Figure 5 A geometrical schematic diagram of the internal and external area leakage inductance calculation formula proposed by the present invention;

[0110] Figure 6 A geometrical schematic diagram of the parallel region leakage inductance calculation formula proposed by the present invention;

[0111] Figure 7 A geometrical schematic diagram of the classification of inductor regions when calculating parameters of the present invention;

[0112] Figure 8 The electric field coupling between different materials;

[0113] Fig. 9 This is a geometrical diagram of the calculation formula for the inter-turn capacitance proposed in the present invention;

[0114] Fig.10 This is a geometrical schematic diagram of the calculation formula for the capacitance between turns and the magnetic core proposed in the present invention;

[0115] Fig.11 A schematic diagram of the parallel region geometry proposed by the present invention;

[0116] Fig.12 This is a geometrical schematic diagram of the calculation formula for the static capacitance of the magnetic core proposed in the present invention. DETAILED DESCRIPTION

[0117] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0118] This embodiment provides a method for predicting broadband behavior of differential mode EMI filter inductors. Figure 1 As shown, including:

[0119] S1: Establish an equivalent high-frequency circuit model based on the actual geometric structure of the differential-mode EMI filter inductor of the target magnetic powder core;

[0120] S2: Divide the target magnetic powder core differential mode EMI filter inductor into an inner region, an outer region, and parallel regions on the front and back sides according to its actual geometric structure; and calculate the inductance and capacitance values ​​corresponding to each region in the equivalent high-frequency circuit model after partitioning;

[0121] S3: Substitute the inductance value and the capacitance value into the equivalent high-frequency circuit model, use the circuit analysis method to calculate the impedance of the circuit at each frequency point, and form an impedance curve of the target magnetic powder core differential mode EMI filter inductor; the impedance curve is used to characterize the broadband behavior of the target magnetic powder core differential mode EMI filter inductor.

[0122] Specifically, the geometric structure diagram of the application object of the high-frequency broadband behavior prediction method of the magnetic powder core differential mode EMI filter inductor proposed in the present invention is as follows: Figure 2 As shown in the figure, the magnetic powder core differential mode EMI filter inductor consists of a magnetic core and a tightly wound winding. In the figure, R o is the outer diameter of the core, R co is the outer diameter of the powder core differential mode EMI filter inductor, R in is the inner diameter of the core, R cin h is the inner diameter of the powder core differential mode EMI filter inductor, c Indicates the thickness of the core, h w represents the thickness of the core and winding, ρ and Represents two parameters of the angular coordinate system, z represents the thickness of the magnetic core; Figure 3 The cross-sectional structure of the magnetic powder core differential mode EMI filter inductor is shown in the figure. c is the maximum distance between a single turn coil and the magnetic core in the winding, w e is the minimum distance between a single-turn coil and the magnetic core, w plis the thickness of the magnetic core insulation; first, an equivalent high-frequency circuit model is established according to the geometric structure, so that designers can quickly obtain the performance data of the inductor, avoiding a lot of experiments and simulation work, thereby greatly improving design efficiency and reducing development costs; secondly, according to the actual geometric structure of the target magnetic powder core differential mode EMI filter inductor, it is divided into an internal area, an external area, and parallel areas on the front and back sides; and the inductance and capacitance values ​​corresponding to each area in the partitioned equivalent high-frequency circuit model are calculated, avoiding the resource consumption of a large amount of simulation solution in the traditional modeling method, significantly saving computing resources, and improving design efficiency. By considering the real geometric structure and electric field behavior of the inductor, the inductor is divided into three areas for calculation, each of which has a capacitance of 0.133 W. Different calculation methods are used in different regions to simplify the calculation of leakage inductance and capacitance, reduce the calculation workload, and provide more accurate analytical formulas for key parameters such as leakage inductance and parasitic capacitance, provide a reliable basis for the design and optimization of differential mode EMI filter inductors, and effectively improve the high-frequency performance and filtering effect of the inductor; finally, the inductance value and capacitance value are substituted into the equivalent high-frequency circuit model, and the impedance of the circuit at each frequency point is calculated using a circuit analysis method, and an impedance curve of the target magnetic powder core differential mode EMI filter inductor is formed; the impedance curve is used to characterize the broadband behavior of the target magnetic powder core differential mode EMI filter inductor, which can effectively predict the broadband behavior of the magnetic powder core differential mode EMI filter inductor, breaking through the limitations of traditional methods.

[0123] In a specific embodiment, the scheme for establishing an equivalent high-frequency circuit model according to the actual geometric structure of the differential-mode EMI filter inductor of the target magnetic powder core is:

[0124] like Figure 4 This is the equivalent high-frequency circuit model of the magnetic powder core differential mode EMI filter inductor proposed by the present invention. In this circuit, the physical parameters from the actual energy equivalent and the connection relationship between them are clearly displayed. Each turn is regarded as a unit. The equivalent high-frequency circuit model includes N series-connected turn units L NN , inter-turn capacitance C tt , turns to the core capacitance C tc and static core capacitance C cs ;

[0125] The winding unit includes a series-connected coil with a self-inductance L s and resistor R s , where the resistance represents the eddy current loss and hysteresis loss in the magnetic core; each of the inter-turn capacitances C tt In parallel with the corresponding turn unit, each turn to the core capacitor C tc One end corresponds to the self-inductance L s connected, and the other end is connected to the corresponding static core capacitor C csOne end of the static core capacitor C cs The other end is connected to the last turn to the core capacitor C tc The other end is connected.

[0126] In this embodiment, in order to simplify the calculation, according to the geometric structure of the inductor, the capacitance of the wound part is decomposed into the turn-to-core capacitance (C tc ) and static core capacitance (C cs ), based on these unit structures, C tc One terminal is connected to the left side of the unit and the other terminal is connected to C cs , similarly, C cs And in the last unit with C tc For the convenience of description, without affecting the calculation accuracy, we assume that the C corresponding to the remaining turns is cs Also connected to the last turn C tc The reason for this treatment is that no matter what winding method is used, it is difficult to accurately quantify the proportion of electric field lines that terminate on the turn surface in the low potential area. At the same time, the electric field lines will preferentially terminate on the conductor with the lowest potential; for some turns close to the last turn, its C tc and C cs should be neglected because the electric field lines generated by these turns can flow directly to the low potential area without passing through the core; moreover, in this case the winding does not cover the entire core, the spacing between the first and last turns is large, and the last turn does not have an adjacent turn to form C tt Therefore, artificially change the C of the first turn tt Defined as half of the original turn, the other half is considered as the C of the last turn tt ; Finally, an equivalent high-frequency circuit model is formed based on the above content.

[0127] In a specific embodiment, the specific solution for calculating the inductance value is:

[0128] Relative permeability is one of the most important parameters for evaluating the magnetic properties of an inductor. In a wide frequency range, especially in the high frequency region, it is a common and effective method to use complex permeability to model the inductor impedance. This model includes the core loss and ignores the winding loss. The impedance of a single-turn inductor is solved according to Ampere's loop law, as shown in formula (37):

[0129]

[0130] Where Z is the impedance of a single-turn inductor, μ 0 is the vacuum magnetic permeability, μ′ r Represents the real part of the complex permeability, μ″ r represents the imaginary part of the complex permeability, h cIndicates the thickness of the core, R o is the outer diameter of the core, R in is the inner diameter of the core;

[0131] In an inductor, the impedance of a single turn of coil is represented by L ii , L s Represents the self-inductance of a single-turn coil, R s represents the eddy current loss and hysteresis loss of a single-turn coil. The mutual inductance and leakage inductance between turns i and j are M respectively. ij and L σij , the leakage inductance is the inductance of the turn unit. The relationship between mutual inductance and leakage inductance is shown in formula (38):

[0132] L ii =M ij +L σij (38)

[0133] Model the leakage inductance between turn i and turn ,. In the actual winding process, there will be a "winding advance" phenomenon in the winding, and the winding length in the parallel area needs to be corrected, such as Figure 7 As shown, the leakage inductance value is divided into three regions: internal region, external region and parallel region. The parallel region leakage inductance is divided into front and back regions to improve the accuracy of the leakage inductance model. The leakage inductance expression after partitioning is shown in formula (39).

[0134] L σij =L σin +L σo +L σl +L σl′w (39)

[0135] Among them, L σin Represents the internal area leakage inductance, L σo Represents the external area leakage inductance, L σl Indicates the positive leakage inductance of the parallel region; L σl′w It represents the back leakage inductance of the parallel region;

[0136] like Figure 5 As shown, assuming that the winding length inside and outside the magnetic core is infinite, the magnetic scalar potential method is used to solve the internal area leakage inductance and the external area leakage inductance. Considering the skin effect of the conductor, the internal area leakage inductance and the external area leakage inductance are shown in formulas (40) and (41).

[0137]

[0138]

[0139] in, is a constant, σ c is the conductivity of the conductor, μ cJ is the magnetic permeability of the conductor, the conductor is the winding; 0 and J 1 are the first-kind complex-valued Bessel functions of order zero and order one, respectively; h w Indicates the thickness of the core and winding, r in represents the inner diameter of the core containing the winding, r cin Indicates the inner diameter of the core, d c represents the conductor radius, w i Indicates the thickness of the wire insulation layer;

[0140] like Figure 6 As shown, in the parallel region, the image method is used to solve the magnetic field generated by the conductor, and the magnetic field is divided into two parts: the magnetic field generated by the original current and the magnetic field generated by the image current. The relationship between the original current and the image current is shown in formula (42).

[0141]

[0142] Among them, I 2 Represents the mirror current, I 1 represents the original current;

[0143] Obtain the component of the magnetic field perpendicular to the core surface. Only this component passes through the integration surface and is orthogonal to the integration surface. The relationship between the magnetic field in this direction is obtained, as shown in formula (43):

[0144]

[0145] Where x represents the distance between two turns of the coil, H 1 represents the magnetic field component generated by the original current, H 1y It represents the component of the magnetic field generated by the original current that is perpendicular to the surface of the magnetic core, H 2y It represents the component of the image current generated in the direction perpendicular to the core surface, H 2 represents the magnetic field component generated by the image current, β is the angle between the line connecting the current-carrying conductor and its image and the line connecting the center line of the image and the magnetic field evaluation point. The calculation formula is shown in formula (44):

[0146] tanβ=x / 2 / w s (44)

[0147] Among them, w s Indicates the distance from the turn to the core;

[0148] The total magnetic field perpendicular to the core surface is H y =H 1y +H 2y , so the magnetic field perpendicular to the core surface is as shown in formula (45),

[0149]

[0150] The leakage magnetic flux on the front side of the parallel region between two adjacent units in the parallel region is calculated by the magnetic field in the parallel region, as shown in formula (46):

[0151]

[0152] Among them, φ σl Represents the leakage flux on the front side of the parallel region, R co Represents the outer radius of the magnetic powder core, R cin represents the inner radius of the magnetic powder core, and z represents the thickness of the magnetic core;

[0153] The leakage inductance on the front side of the parallel region is calculated using the leakage flux on the front side of the parallel region and the original current, as shown in formula (47):

[0154]

[0155] Among them, L wl Indicates the inductance value in the parallel region;

[0156] During the winding process, the winding length in the parallel region is not equal to half of the difference between the inner and outer diameters of the inductor. In order to improve the accuracy, the actual geometric characteristics of the winding in the common mode EMI filter inductor are considered, such as Fig.11 As shown in the formula (49), the actual winding length of the winding is calculated.

[0157]

[0158] Among them, R in Indicates the inner diameter of the core; l' w Indicates the actual winding length of the winding;

[0159] The leakage flux on the back side of the parallel region is calculated based on the actual winding length of the winding, as shown in formula (50):

[0160]

[0161] Among them, φ σl′w represents the leakage flux on the back side of the parallel region;

[0162] The leakage inductance on the back of the parallel region is calculated based on the leakage magnetic flux and the original current on the back of the parallel region, as shown in formula (51):

[0163]

[0164] Among them, L σl′w Represents the leakage inductance on the back side of the parallel region.

[0165] Usually, L σij The order of magnitude of Lij It is several orders of magnitude smaller and can often be ignored in inductor models with high dielectric constant (ε) or high permeability (μ). However, due to the lower ε and lower μ of the magnetic powder core, the leakage inductance L σij The impact on the impedance curve cannot be ignored. Therefore, in the magnetic powder core, leakage inductance modeling is essential, which helps to improve the accuracy of the impedance model. At the same time, the side area is further divided into two parts to improve the accuracy of the leakage inductance model. In addition, the winding insulation and the length change caused by the winding bending are also considered to obtain the accurate winding length, and then obtain the accurate leakage inductance value.

[0166] In a specific embodiment, the specific solution for the inter-turn capacitance is:

[0167] The inter-turn capacitance is divided into the inner region, the outer region, and the parallel regions of the front and back sides for solution. The inter-turn capacitance after partitioning is shown in formula (52):

[0168] C tt =C ttin +C tto +C ttl +C ttl′w (52)

[0169] Among them, C ttin represents the inter-turn capacitance of the inner region, C tto represents the inter-turn capacitance of the external region, C ttl represents the inter-turn capacitance on the front side of the parallel region, C ttl′w represents the inter-turn capacitance on the back side of the parallel region;

[0170] like Figure 8 As shown in the figure, in the case of MnZn or nanocrystalline cores, the core can be approximately regarded as a conductor, and the energy is mainly concentrated between turns and between turns and the core. In contrast, in the case of magnetic powder cores, the core cannot be approximately regarded as a conductor, resulting in most of the energy being concentrated between turns. Therefore, C in the case of magnetic powder cores is tt Need to be enhanced, through comparative analysis, it can be seen that C in the case of magnetic powder core tt It is about twice that of MnZn or nanocrystalline cores;

[0171] like Figure 9-11 As shown in the figure, d c represents the conductor radius, w i Represents the thickness of the wire insulation layer, w pl Represents the thickness of the core insulation layer, l w represents the winding length on the front side, and l′w represents the winding length on the back side;

[0172] Therefore, the specific analytical formulas for the inter-turn capacitance of the three regions are shown in formulas (53), (54) and (55), respectively.

[0173]

[0174] Among them, ε i Represents the dielectric constant of the medium, ε a represents the dielectric constant of air, δ o Indicates the distance between turns on the outside of the winding, w i Indicates the dielectric thickness, δ in Indicates the distance between turns inside the winding; h w Indicates the thickness of the core and winding; d c Represents the conductor radius; R o is the outer diameter of the core; R in is the inner diameter of the core; r is a variable, δ l Represents the distance between turns in the parallel region.

[0175] In a specific embodiment, the specific solution for the turn-to-core capacitance is:

[0176] Considering the actual winding length of the winding and the geometric characteristics of the common-mode EMI filter inductor, the equivalent distance from the turn to the core is calculated, as shown in formula (56):

[0177]

[0178] Among them, w s Indicates the distance from the equivalent turn to the core, w c Indicates the maximum distance between a single-turn coil and the magnetic core, w e Indicates the minimum distance between a single-turn coil and the magnetic core;

[0179] The turn-to-core capacitance is divided into the inner region, the outer region and the parallel region for solution. The turn-to-core capacitance after differentiation is shown in formula (57):

[0180] C tc =C tcin +C tco +C tcl +C tcl′w (57)

[0181] Among them, C tcin represents the turns-to-core capacitance of the inner region, C tco represents the turns-to-core capacitance of the external region, C tcl represents the parallel front turn to core capacitance, C tcl′w It represents the capacitance of the turns parallel to the back surface to the core;

[0182] Since the magnetic powder core cannot be replaced by the assumption of a perfect conductor (PEC), in fact, the electric field lines between the turns and the core and in the inner region of the core are continuous, so from an energy point of view, these capacitors should be considered as a whole. However, for the convenience of representation, we geometrically split it into C tc With C cs Two parts, such as Fig.10 As shown, here we first calculate C tc , we need to first determine the length of the electric field lines in the winding insulation layer, as shown in formula (58),

[0183] x tc，wi =w i (58)

[0184] Among them, x tc，wi represents the length of the electric field lines in the winding insulation layer, w i Indicates the thickness of the medium;

[0185] Considering the boundary conditions at the interface between the two media, the length of the electric field lines in the air and the core insulation layer is further obtained. First, considering that the free charge surface density at the interface between different media is zero, the deflection angle of the electric field lines in the air is calculated, as shown in formula (59):

[0186]

[0187] Among them, α represents the deflection angle between the two media of air and the magnetic core insulation layer;

[0188] The length of the electric field line in the air is calculated based on the equivalent distance from the turn to the magnetic core, the length of the electric field line and the deflection angle of the electric field line as shown in formula (60):

[0189]

[0190] Among them, w s Indicates the distance from the equivalent turn to the core;

[0191] The length of the electric field line in the core insulation layer is shown in formula (61),

[0192] x tc,ci =w ci / cosα ci (61)

[0193] Among them, x tc,ci represents the length of the electric field lines in the core insulation layer, w ci represents the core thickness, α ci represents the deflection angle of the electric field line in the magnetic core, as shown in formula (62),

[0194]

[0195] Among them, ε ci represents the core dielectric constant, ε a represents the dielectric constant of air;

[0196] The analytical formulas for the turn-to-core capacitance of the inner region, outer region, and parallel region are constructed based on the lengths of the electric field lines in the air and the core insulation layer, as shown in formulas (63)-(66):

[0197]

[0198] Among them, w ci Indicates the core insulation thickness, w sin Indicates the distance from the inner area to the core, w so Indicates the distance from the outer region to the core, w sl Indicates the distance from the turn to the core in the front area of ​​the parallel region; l' w Indicates the actual winding length of the winding.

[0199] In a specific embodiment, the specific solution for the static core capacitance is:

[0200] The static core capacitance is divided into the inner region, the outer region and the parallel region for solution. In the three regions, the inner and outer static core capacitances have the same form, and the expression of the static core capacitance is obtained, as shown in formula (67):

[0201] C cs =C csin +C cso +C cslw +C csl′w (67)

[0202] Since the magnetic powder core is regarded as a medium, the electric field lines will also diverge or refract at the boundary of the medium. When the electric field lines gradually approach the axis of the core cross section, they will end at the lowest potential area, and this section of the electric field lines is recorded as x cs , x cs The dielectric boundary conditions also need to be met. Therefore, the material of the magnetic powder core and the dielectric boundary conditions are considered to calculate the length of the electric field line in the magnetic core. The deflection angle of the electric field line in the magnetic core is shown in formula (69):

[0203]

[0204] like Fig.12 As shown, the current flows in from the high potential and flows out from the low potential. According to formula (69), the length of the electric field line in the magnetic core is obtained, as shown in formula (70),

[0205] x cs =R t / cosα c +larc (70)

[0206] Among them, l arc Represents the arc length of the electric field line inside the magnetic core, R t is half the thickness of the core, and has different values ​​in different regions. For the inner and outer regions, R t The expression of is shown in formula (71),

[0207] R t =(R o -R in ) / 4 (71)

[0208] In the parallel region, R t The expression of is shown in formula (72),

[0209] R t =h w / 2 (72)

[0210] Among them, h w Indicates the thickness of the core and winding;

[0211] According to the length of the electric field line in the core, the analytical formula of the static core capacitance in different regions is constructed, as shown in formula (73):

[0212]

[0213] Among them, C csin and C cso represents the internal and external static core capacitance, C cslw represents the static core capacitance on the front side of the parallel region;

[0214] The expression for the static core capacitance on the back side of the parallel region is shown in formula (74),

[0215]

[0216] Among them, C csl′w Represents the static core capacitance on the back side of the parallel region.

[0217] The parameter analysis and calculation method adopted in the circuit model of the present invention avoids the resource consumption of a large amount of simulation solutions required in traditional modeling methods, significantly saves computing resources, and improves design efficiency.

[0218] By considering the actual geometric structure and electric field behavior of the inductor, the present invention provides more accurate analytical formulas for key parameters such as leakage inductance and parasitic capacitance, providing a reliable basis for the design and optimization of differential mode EMI filter inductors, and can effectively improve the high-frequency performance and filtering effect of the inductor.

[0219] In a specific embodiment, the inductance value and the capacitance value are substituted into the equivalent high-frequency circuit model, and the impedance of the circuit at each frequency point is calculated using a circuit analysis method, and an impedance curve of the target magnetic powder core differential mode EMI filter inductor is formed; the impedance curve is used to characterize the broadband behavior of the target magnetic powder core differential mode EMI filter inductor:

[0220] Substitute the calculated parameters into the equivalent high-frequency circuit model, and then use the circuit analysis method to calculate the impedance of the circuit at each frequency point, and finally obtain the impedance curve of the target magnetic powder core differential mode EMI filter inductor under wide frequency. The impedance curve is the wide-frequency behavior of the target magnetic powder core differential mode EMI filter inductor.

[0221] The method of the present invention not only has high accuracy and adaptability, but also avoids complex simulation calculations, saves time and economic costs, and therefore has significant application value in the design of differential mode EMI filter inductors.

[0222] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for predicting broadband behavior of differential mode EMI filter inductors, characterized in that: include: S1: Establish an equivalent high-frequency circuit model based on the actual geometric structure of the differential-mode EMI filter inductor of the target magnetic powder core; S2: Divide the target magnetic powder core differential mode EMI filter inductor into an inner region, an outer region, and parallel regions on the front and back sides according to its actual geometric structure; and calculate the inductance and capacitance values ​​corresponding to each region in the equivalent high-frequency circuit model after partitioning; S3: Substitute the inductance value and the capacitance value into the equivalent high-frequency circuit model, use the circuit analysis method to calculate the impedance of the circuit at each frequency point, and form an impedance curve of the target magnetic powder core differential mode EMI filter inductor; the impedance curve is used to characterize the broadband behavior of the target magnetic powder core differential mode EMI filter inductor.

2. A method for predicting broadband behavior of differential mode EMI filter inductors according to claim 1, characterized in that: The equivalent high-frequency circuit model includes N series-connected turn units L NN , inter-turn capacitance C tt , turns to core capacitance C tc and static core capacitance C cs ; The turn unit includes a turn of coil in series with the self-inductance L s and resistor R s , where the resistance represents the eddy current loss and hysteresis loss in the magnetic core; each of the inter-turn capacitances C tt In parallel with the corresponding turn unit, each turn to the core capacitor C tc One end corresponds to the self-inductance L s connected, and the other end is connected to the corresponding static core capacitor C cs One end of the static core capacitor C cs The other end is connected to the last turn to the core capacitor C tc The other end is connected.

3. A method for predicting broadband behavior of differential mode EMI filter inductors according to claim 2, characterized in that: The specific steps for solving the inductance value include: The impedance of a single-turn inductor is solved according to Ampere's loop law, as shown in formula (1): Where Z is the impedance of a single-turn inductor, μ0 is the magnetic permeability of vacuum, and μ′ is r Represents the real part of the complex permeability, μ″ r represents the imaginary part of the complex permeability, h c Indicates the thickness of the core, R o is the outer diameter of the core, R in is the inner diameter of the core; In an inductor, the impedance of a single turn of coil is represented by L ii , L s Represents the self-inductance of a single-turn coil, R s represents the eddy current loss and hysteresis loss of a single-turn coil. The mutual inductance and leakage inductance between turns i and j are M respectively. ij and L σij , the leakage inductance is the inductance of the turn unit. The relationship between mutual inductance and leakage inductance is shown in formula (2). L ii =M ij +L σij (2) The leakage inductance between turn i and turn j is modeled, and the leakage inductance value is divided into three regions: the inner region, the outer region, and the parallel region. The leakage inductance of the parallel region is divided into the front and back sides. The leakage inductance expression after partitioning is shown in formula (3): L σij =L σin +L σo +L σl +L σl′w (3) Among them, L σin Represents the internal area leakage inductance, L σo Represents the external area leakage inductance, L σl Indicates the positive leakage inductance of the parallel region; L σl′w It represents the back leakage inductance of the parallel region; Assuming that the winding lengths inside and outside the magnetic core are infinite, the magnetic scalar potential method is used to solve the leakage inductance of the inner region and the leakage inductance of the outer region, as shown in formulas (4) and (5), in, is a constant, σ c is the conductivity of the conductor, μ c is the magnetic permeability of the conductor, the conductor is the winding; J0 and J1 are the first-order complex-valued Bessel functions of the zeroth and first order, respectively; h w Indicates the thickness of the core and winding, r in represents the inner diameter of the core containing the winding, r cin Indicates the inner diameter of the core, d c represents the conductor radius, w i Indicates the thickness of the wire insulation layer; In the parallel region, the image method is used to solve the magnetic field generated by the conductor, and the magnetic field is divided into two parts: the magnetic field generated by the original current and the magnetic field generated by the image current. The relationship between the original current and the image current is shown in formula (6): Among them, I2 represents the mirror current, and I1 represents the original current; Obtain the component of the magnetic field perpendicular to the core surface and obtain the relationship between the magnetic field in this direction, as shown in formula (7): Where x represents the distance between the two turns of the coil, H1 represents the magnetic field component generated by the original current, and H 1y It represents the component of the magnetic field generated by the original current that is perpendicular to the surface of the magnetic core, H 2y represents the component of the magnetic field generated by the image current perpendicular to the core surface, H2 represents the magnetic field component generated by the image current, β is the angle between the line connecting the current-carrying conductor and its image and the line connecting the center line of the image and the magnetic field evaluation point. The calculation formula is shown in formula (8): tanβ=x / 2 / w s (8) Among them, w s Indicates the distance from the turn to the core; The total magnetic field perpendicular to the core surface is H y =H 1y +H 2y , so the magnetic field perpendicular to the core surface is as shown in formula (9), The leakage magnetic flux on the front side of the parallel region between two adjacent units in the parallel region is calculated by the magnetic field in the parallel region, as shown in formula (10): Among them, φ σl Represents the leakage flux on the front side of the parallel region, R co Represents the outer radius of the magnetic powder core, R cin represents the inner radius of the magnetic powder core, and z represents the thickness of the magnetic core; The leakage inductance on the front side of the parallel region is calculated using the leakage flux on the front side of the parallel region and the original current, as shown in formula (11): Among them, L wl Indicates the inductance value in the parallel region; Considering the actual geometric characteristics of the winding in the common-mode EMI filter inductor, the actual winding length of the winding is calculated, as shown in formula (12): Among them, R in Indicates the inner diameter of the core; l' w Indicates the actual winding length of the winding; The leakage flux on the back side of the parallel region is calculated based on the actual winding length of the winding, as shown in formula (13): Among them, φ σl′w represents the leakage flux on the back side of the parallel region; The leakage inductance on the back of the parallel region is calculated based on the leakage magnetic flux and the original current on the back of the parallel region, as shown in formula (14): Among them, L σl′w Represents the leakage inductance on the back side of the parallel region.

4. The method for predicting broadband behavior of differential mode EMI filter inductors according to claim 3, characterized in that: The specific steps for solving the inter-turn capacitance include: The inter-turn capacitance is divided into the inner region, the outer region, and the parallel regions of the front and back sides for solution. The inter-turn capacitance after partitioning is shown in formula (15): C tt =C ttin +C tto +C ttl +C ttl′w (15) Among them, C ttin represents the inter-turn capacitance of the inner region, C tto represents the inter-turn capacitance of the external region, C ttl represents the inter-turn capacitance on the front side of the parallel region, C ttl′w represents the inter-turn capacitance on the back side of the parallel region; The specific analytical formulas for the inter-turn capacitance of the three regions are shown in formulas (16), (17) and (18), respectively. Among them, ε i Represents the dielectric constant of the medium, ε a represents the dielectric constant of air, δ o Indicates the distance between turns on the outside of the winding, w i Indicates the dielectric thickness, δ in Indicates the distance between turns inside the winding; h w Indicates the thickness of the core and winding; d c Represents the conductor radius; R o is the outer diameter of the core; R in is the inner diameter of the core; r is a variable, δ l Represents the distance between turns in the parallel region.

5. A method for predicting broadband behavior of differential mode EMI filter inductors according to claim 4, characterized in that: The specific steps to solve the turn-to-core capacitance include: Considering the actual winding length of the winding and the geometric characteristics of the common-mode EMI filter inductor, the equivalent distance from the turn to the core is calculated, as shown in formula (19): Among them, w s Indicates the distance from the equivalent turn to the core, w c Indicates the maximum distance between a single-turn coil and the magnetic core, w e Indicates the minimum distance between a single-turn coil and the magnetic core; The turn-to-core capacitance is divided into the inner region, the outer region and the parallel region for solution. The partitioned turn-to-core capacitance is shown in formula (20): C tc =C tcin +C tco +C tcl +C tcl′w (20) Among them, C tcin represents the turns-to-core capacitance of the inner region, C tco represents the turns-to-core capacitance of the external region, C tcl represents the parallel front turn to core capacitance, C tcl′w It represents the capacitance of the turns parallel to the back surface to the core; Determine the length of the electric field lines in the winding insulation layer, as shown in formula (21), x tc,wi =w i (21) Among them, x tc,wi represents the length of the electric field lines in the winding insulation layer, w i Indicates the thickness of the medium; Considering the boundary conditions at the interface between the air and the core insulation layer, the length of the electric field lines in the air and the core insulation layer is obtained, and the deflection angle of the electric field lines in the air is calculated, as shown in formula (22): α represents the deflection angle between the two media of air and the core insulation layer; The length of the electric field line in the air is solved according to the equivalent distance from the turn to the core, the length of the electric field line and the deflection angle of the electric field line, as shown in formula (23): Among them, w s Indicates the distance from the equivalent turn to the core; The length of the electric field line in the core insulation layer is shown in formula (24), x tc,ci =w ci / cosα ci (24) Among them, x tc,ci represents the length of the electric field lines in the core insulation layer, w ci represents the core thickness, α ci represents the deflection angle of the electric field line in the magnetic core, as shown in formula (25), Among them, ε ci represents the core dielectric constant, ε a represents the dielectric constant of air; According to the length of the electric field lines in the air and the core insulation layer, the analytical formulas for the turn-to-core capacitance in the inner region, the outer region, and the parallel region are constructed, as shown in formulas (26)-(29): Among them, w ci Indicates the core insulation thickness, w sin Indicates the distance from the inner area to the core, w so Indicates the distance from the outer region to the core, w sl Indicates the distance from the turn to the core in the front area of ​​the parallel region; l' w Indicates the actual winding length of the winding.

6. A method for predicting broadband behavior of differential mode EMI filter inductors according to claim 5, characterized in that: The specific steps to solve the static core capacitance include: The static core capacitance is divided into the inner region, the outer region and the parallel region for solution. In the three regions, the inner and outer static core capacitances have the same form, and the expression of the static core capacitance is obtained, as shown in formula (30): C cs =C csin +C cso +C cslw +C csl′w (30) Considering the material of the magnetic powder core and the dielectric boundary conditions, the length of the electric field line in the magnetic core is calculated. The deflection angle of the electric field line in the magnetic core is shown in formula (31): ε c Represents the dielectric constant of the magnetic core; According to formula (31), the length of the electric field line in the magnetic core is obtained, as shown in formula (32), x cs =R t / cosα c +l arc (32) Among them, l arc Represents the arc length of the electric field line inside the magnetic core, R t is half the thickness of the core, and has different values ​​in different regions. For the inner and outer regions, R t The expression of is shown in formula (33), R t =(R o -R in ) / 4 (33) In the parallel region, R t The expression of is shown in formula (34), R t =h w / 2 (34) Among them, h w Indicates the thickness of the core and winding; According to the length of the electric field line in the core, the analytical formula of the static core capacitance in different regions is constructed, as shown in formula (35): Among them, C csin and C cso represents the internal and external static core capacitance, C cslw represents the static core capacitance on the front side of the parallel region; The expression for the static core capacitance on the back side of the parallel region is shown in formula (36),

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