Method for acquiring through hole loss of planar transformer

Abstract

The invention discloses a method for acquiring through hole loss of a planar transformer, which comprises the following steps of: establishing a mathematical model of through hole loss, determining current distribution parameters of a through hole array according to defined through hole radiuses and intervals, further calculating a magnetic field generated by through holes in a defined area by using a Biot-Savart law, further determining space current of the through holes, and determining the through hole loss of the planar transformer. And finally calculating to obtain the through hole loss.

Description

Technical Field

[0001] The present invention belongs to the technical field of planar transformer design, and more specifically, relates to a method for obtaining through-hole loss of a planar transformer. Background Art

[0002] High-efficiency and high-power density power supplies are one of the foundations for the continued development of the communications, automotive, aerospace and data processing industries. In the process of power supplies developing towards high efficiency, high frequency and high power density, the traditional magnetic component structure has more limitations in performance. For example, at frequencies above 100kHz, the winding loss caused by eddy current effects increases significantly. With the development of PCB technology and switching devices such as gallium nitride and silicon carbide, planar PCB magnetic components have been more widely studied due to their low height, better thermal properties, easy manufacturing and cost reduction, modularity, and predictable parasitic parameters.

[0003] As with traditional magnetic structures, the need for high-frequency operation also leads to increased winding losses in planar magnetic structures due to skin effect and proximity effect. In terms of winding losses, planar magnetic components are more suitable for high-frequency and high-power converters than old-fashioned wound magnetic components. However, planar magnetic component windings must comply with the limits of turn-to-turn and layer-to-layer spacing that can be manufactured, and the core window area is greatly reduced. Moreover, planar magnetic components cannot be directly replaced by Litz wire, and usually adopt the staggered winding method, which can be easily arranged in the core window through through-holes on the PCB winding.

[0004] A common method of reducing the size of power magnetic components is to operate at high frequencies. At a minimum typical PCB copper thickness of 0.5 oz / ft 2 The corresponding frequency of the single-layer skin depth at 25°C is 13.8MHz, which is 4.5MHz for the excitation winding 48AWG wire diameter. However, in high-current applications, multiple parallel windings must be used, which increases the interlayer loss of the planar magnetic winding and increases the number of necessary termination vias.

[0005] Therefore, for planar magnetic designs, especially those that carry high currents and use high layers, the losses of these terminal vias must be considered. In the calculation of through-hole losses, finite element simulation (FEM) technology is a traditional analysis method, especially through tools such as ANSYS to perform two-dimensional electromagnetic field simulation on through-holes. This method can accurately simulate the electromagnetic characteristics of through-holes and provide loss estimates under high-frequency signals. Although finite element simulation can provide high-precision data support for design, its modeling process is cumbersome and the calculation time is long. Especially in the face of large-scale PCB design, simulation efficiency often becomes a bottleneck. Therefore, it is necessary to optimize the design of through-hole loss model calculation method. Summary of the invention

[0006] The purpose of the present invention is to overcome the shortcomings of the prior art and provide a method for obtaining the through-hole loss of a planar transformer. By establishing a through-hole mathematical model, the efficiency of the existing through-hole loss calculation is improved, which is conducive to the rapid design iteration of the through-hole array.

[0007] To achieve the above-mentioned object of the invention, the present invention provides a method for obtaining through-hole loss of a planar transformer, characterized in that it comprises the following steps:

[0008] (1) Establish a mathematical model of through-hole array;

[0009] The mathematical model of the through-hole array is established by MATLAB simulation software, and the size of the through-hole array is defined as N×M, where N is the number of rows of the through-hole array, M is the number of columns of the through-hole array, N≥1, M≥1, and N and M cannot be 1 at the same time; the inner radius of each through-hole in the through-hole array is set to r inner , the outer radius is r outter , the through hole spacing is s;

[0010] (2) Define the magnetic field region generated by the through-hole array;

[0011] The center point of the through hole array is taken as the origin of the two-dimensional coordinate system. Each through hole generates 10(r outter +s)×10(r outter +s) size rectangular magnetic field region;

[0012] The magnetic field area generated by the through-hole array is divided into two areas with an interval of 0.01 (r outter +s) grid points, each grid point corresponds to a two-dimensional coordinate;

[0013] (3) Determine the current distribution parameter k of the through-hole array;

[0014] (4) Use the Biot-Savart law to calculate the external tangential magnetic field H of each micro-element segment on the outer surface of each through hole. m,j , where H m,j represents the external tangential magnetic field of the jth microelement segment of the outer surface of the mth through hole;

[0015] (5) Assuming that the current of each micro-element segment on the outer surface of each through hole is constant, the current of each micro-element segment is:

[0016]

[0017] Among them, I m,j represents the current of the jth microelement segment on the outer surface of the mth through hole;

[0018] (6) Calculate the through-hole array loss based on the through-hole spatial current distribution, including the total AC loss P loss_ac And the total DC loss Ploss_dc .

[0019] The object of the invention of the present invention is achieved in this way:

[0020] The present invention provides a method for obtaining the through-hole loss of a planar transformer. After establishing a mathematical model of the through-hole loss, the current distribution parameters of the through-hole array are determined according to the defined through-hole radius and spacing, and then the Biot-Savart law is used to calculate the magnetic field generated by the through-holes in the defined area, and the spatial current of the through-holes is further determined. Finally, the through-hole loss is calculated.

[0021] At the same time, the method for obtaining the through-hole loss of a planar transformer of the present invention also has the following beneficial effects:

[0022] (1) Compared with the finite element simulation model, the mathematical model of through-hole loss of the present invention has a simpler modeling process, higher efficiency, and can shorten the design cycle;

[0023] (2) By using mathematical models for loss prediction, we can reduce the reliance on high-precision simulation tools and lower the simulation cost. At the same time, the model can provide fast and reliable loss estimation, reducing the time and resources required for repeated design and testing, and helping to achieve a more cost-effective design. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 It is a schematic diagram of the through-holes for the winding termination of a planar transformer;

[0025] Figure 2 It is a flow chart of a method for obtaining through-hole loss of a planar transformer according to the present invention;

[0026] Figure 3 It is a schematic diagram of modeling a through-hole array of size 1×5;

[0027] Figure 4 It is the magnetic field intensity distribution diagram under three through-hole array arrangement modes;

[0028] Figure 5 It is the ANSYS Maxwell two-dimensional magnetic field intensity distribution diagram of three through-hole arrangements. DETAILED DESCRIPTION

[0029] The specific implementation of the present invention is described below in conjunction with the accompanying drawings so that those skilled in the art can better understand the present invention. It should be noted that in the following description, when the detailed description of known functions and designs may dilute the main content of the present invention, these descriptions will be omitted here.

[0030] Example

[0031] In this embodiment, the schematic diagram of the planar transformer winding terminal connection through hole is as follows: Figure 1 As shown in the figure, the winding part of the planar transformer consists of 3 layers of primary windings and 3 layers of secondary windings. The primary windings and the secondary windings are connected by two groups of 1x3 through-hole arrays. When the current in the winding passes through the through-hole, a certain through-hole loss will be generated. Therefore, how to accurately obtain the through-hole loss is a key issue in the optimization of the through-hole array layout design. To this end, we propose a method for obtaining the through-hole loss of the planar transformer, as shown in Figure 2 As shown, the specific steps include:

[0032] S1. Establishing mathematical model of through hole array;

[0033] The mathematical model of the through-hole array established by MATLAB simulation software is as follows: Figure 3 As shown, the size of the through hole array is defined as 1×5; the inner radius of each through hole in the through hole array is set to r inner =9mil, outer radius is r outter =10mil, the through hole spacing is s=10mil;

[0034] S2, defining the magnetic field region generated by the through-hole array;

[0035] like Figure 3 As shown, the center point of the through hole array is taken as the origin of the two-dimensional coordinate system, and each through hole generates 10 (r outter +s)×10(r outter +s) size rectangular magnetic field region;

[0036] The magnetic field area generated by the through-hole array is divided into two areas with an interval of 0.01 (r outter +s) grid points, each grid point corresponds to a two-dimensional coordinate;

[0037] S3, determining a current distribution parameter k of the through-hole array;

[0038] S3.1. The through holes at all vertex positions on the edge of the through hole array are regarded as outer through holes, and the through holes at all non-vertex positions on the edge of the through hole array are regarded as inner through holes;

[0039] In this embodiment, when N or M is less than 2, that is, the through hole array is a single row with multiple columns or a single column with multiple rows, the number of external through holes is 2, and the remaining through holes are all internal through holes, such as Figure 3As shown, when the through hole array is 1 row and 5 columns, the through holes at the two end points are outer through holes, and the three through holes in the middle are inner through holes; when N and M are both equal to 2, the number of outer through holes is 4, and the number of inner through holes is 0; when N or M is greater than 2, the number of outer through holes is 4, and the through holes at all non-vertex positions on the edge of the through hole array are inner through holes, that is, the remaining through holes in the rows and columns where the outer through holes are located are all inner through holes, such as: when the through hole array is 2 rows and 5 columns, the number of outer through holes is 4, and the number of inner through holes is 6; when the through hole array is 5 rows and 5 columns, the number of outer through holes is 4, and the number of inner through holes is 12;

[0040] S3.2, assuming that the total current I passing through the through-hole array is 1A, the current I A Evenly distributed to the outer vias, the current I B The current is evenly distributed to the inner vias, and the current of the remaining vias located in the central area of ​​the via array is 0;

[0041] In this embodiment, if Figure 3 As shown, when the through-hole array is 1 row and 5 columns, the current I A Evenly distributed to the two outer vias, the current I B Evenly distributed to the three inner through holes; when the through hole array is 5 rows and 5 columns, the current I A Evenly distributed to the 4 external vias, the current I B The current is evenly distributed to the 12 inner vias, and the current of the remaining 9 vias located in the central area of ​​the via array is 0;

[0042] S3.3. Define the current distribution parameter k and current I A ,I B The relationship is:

[0043]

[0044] S3.4, define the increment step size of the current distribution parameter k Δk=0.01, and the maximum value of k is 1;

[0045] S3.5, initialize k = 0, and then calculate the current I according to the relationship in step S3.3 A and I B ;

[0046] S3.6. Use the Biot-Savart law to calculate the magnetic field strength generated by each through hole at each grid point;

[0047] When a grid point is located inside any through hole, its magnetic field strength is recorded as 0; otherwise, the magnetic field strength generated by each through hole at each grid point is calculated according to the following formula;

[0048]

[0049] Among them, Hm,n represents the magnetic field intensity generated by the mth through hole at the nth grid point, I m is the current flowing through the mth through-hole, r n is the coordinate of the nth grid point, r m is the coordinate of the mth pass;

[0050] Traversing each through hole in the through hole array to obtain the magnetic field strength generated by each through hole at each grid point;

[0051] S3.7, increasing the current distribution parameter k with an increasing step size Δk until the k value reaches 1, and for different k values, calculating the magnetic field intensity generated by each through hole at each grid point under different k values ​​according to steps S3.5 and S3.6;

[0052] S3.8. Calculate the sum of the squares of the magnetic field strengths generated by each through hole at each grid point under different k values The k value corresponding to the minimum total sum is taken as the current distribution parameter of the through-hole array.

[0053] S4. Use the Biot-Savart law to calculate the external tangential magnetic field H of each micro-element segment on the outer surface of each through hole. m,j ;

[0054] S4.1. According to the current distribution parameter k of the through-hole array, first calculate the current I A ,I B , and then calculate the current of each through hole;

[0055] S4.2. Divide the perimeter of each through hole evenly into N p The center coordinates of the outer arc of each micro-element segment are marked as r m,j ,j=1,2,…,N p In this embodiment, if Figure 3 As shown, the perimeter of each through hole is evenly divided into 8 micro-element segments;

[0056] S4.3. Use the Biot-Savart law to calculate the external tangential magnetic field of each micro-element segment on the outer surface of each through hole:

[0057]

[0058] Among them, H m,j Represents the external tangential magnetic field of the jth infinitesimal segment on the outer surface of the mth through hole.

[0059] S5. Assuming that the current of each micro-element segment on the outer surface of each through hole is constant, the current of each micro-element segment is:

[0060]

[0061] Among them, Im,j represents the current of the jth microelement segment on the outer surface of the mth through hole;

[0062] S6. Calculate the through-hole array loss based on the through-hole spatial current distribution, including the total AC loss P loss_ac And the total DC loss P loss_dc ;

[0063] S6.1. Calculate the AC loss P of each microelement segment on the outer surface of each through hole loss，ac，m，j :

[0064]

[0065] Where R represents the resistance of each microelement segment on the outer surface of the through hole;

[0066] S6.2. Calculate the total AC loss P of the through-hole array loss_ac ;

[0067]

[0068] Among them, N q is the number of through holes;

[0069] S6.3. Calculate the DC loss P of each microelement segment on the outer surface of each through hole loss_dc,m,j :

[0070]

[0071] S6.4. Calculate the total DC loss P of the through-hole array loss_dc :

[0072]

[0073] Where I is the total current of the through-hole array.

[0074] Figure 4 It is the magnetic field intensity distribution diagram under three through-hole array arrangement modes;

[0075] In this embodiment, MATLAB is used to model three through-hole array arrangements of 1 row and 5 columns, 2 rows and 5 columns, and 5 rows and 5 columns to obtain the magnetic field intensity distribution diagram of the through-hole array, as shown in FIG. Figure 4 As shown, (a) is the magnetic field intensity distribution diagram of 1x5 through-hole array; (b) is the magnetic field intensity distribution diagram of 2x5 through-hole array; (c) is the magnetic field intensity distribution diagram of 5x5 through-hole array. Due to the influence of skin effect and proximity effect, it can be seen from the three magnetic field intensity distribution diagrams that the magnetic field intensity is mainly distributed at the edge of the through-hole array.

[0076] Figure 5 It is the ANSYS Maxwell two-dimensional magnetic field intensity distribution diagram of three through-hole arrangements.

[0077] In this embodiment, (a) is a magnetic field intensity distribution diagram of a 1x5 through-hole array; (b) is a magnetic field intensity distribution diagram of a 2x5 through-hole array; and (c) is a magnetic field intensity distribution diagram of a 5x5 through-hole array. Figure 5 It can be seen from the three magnetic field intensity distribution diagrams that the magnetic field is also mainly distributed at the edge of the through-hole array, while the magnetic field intensity inside the through-hole is basically 0. Figure 4 and Figure 5 By comparison, the mathematical model of the through-hole array is consistent with the complex finite element simulation results in describing the trend of the magnetic field distribution, proving that the mathematical model can be reliably used to predict and evaluate through-hole losses.

[0078] Definition of AC resistance coefficient F R The calculation formula is:

[0079]

[0080] In the present embodiment, the AC resistivity of the 1x5 through-hole array calculated in the ANSYS simulation is 1.35, while the AC resistivity in the MATLAB simulation is 1.33, with an error of 5.7%. The AC resistivity of the 2x5 through-hole array in the ANSYS simulation is 1.90, while the AC resistivity in the MATLAB simulation is 1.73, with an error of 8.9%. The AC resistivity of the 5x5 through-hole array in the ANSYS simulation is 3.20, while the AC resistivity in the MATLAB simulation is 3.38, with an error of 5.3%. Although the MATLAB mathematical modeling has a certain gap in accuracy with the ANSYS finite element simulation, the error is basically within 10%, which can meet the preliminary analysis of the magnetic field intensity distribution of the through-hole array. However, the ANSYS simulation needs to establish models of different through-hole arrays respectively, and the simulation time is basically more than 10s. At the same time, the results such as the AC resistivity need to be further calculated manually, and the operation process is relatively complicated. The MATLAB model can simulate multiple through-hole arrays at the same time as needed, and the simulation time is only about 0.02s. At the same time, it can directly calculate the AC resistivity of the through-holes and other results, which is convenient for comparative analysis of different through-hole array models. In general, the accuracy of MATLAB simulation is not as high as that of ANSYS finite element simulation, but because of its faster calculation speed, it can perform multiple design iterations in a short time, so it is more suitable for rapid evaluation and optimization of the combination of through-hole arrays in the early stage of design, and has high practicality and efficiency advantages.

[0081] Although the above describes the illustrative specific embodiments of the present invention to facilitate those skilled in the art to understand the present invention, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations using the concept of the present invention are protected.

Claims

1. A method for obtaining through-hole loss of a planar transformer, characterized in that: The following steps are involved: (1) Establish a mathematical model of through-hole array; The mathematical model of the through-hole array is established by MATLAB simulation software, and the size of the through-hole array is defined as N×M, where N is the number of rows of the through-hole array, M is the number of columns of the through-hole array, N≥1, M≥1, and N and M cannot be 1 at the same time; the inner radius of each through-hole in the through-hole array is set to r inner , the outer radius is r outter , the through hole spacing is s; (2) Define the magnetic field region generated by the through-hole array; The center point of the through hole array is taken as the origin of the two-dimensional coordinate system. Each through hole generates 10(r outter +s)×10(r outter +s) size rectangular magnetic field region; The magnetic field area generated by the through-hole array is divided into two areas with an interval of 0.01 (r outter +s) grid points, each grid point corresponds to a two-dimensional coordinate; (3) Determine the current distribution parameter k of the through-hole array; (4) Use the Biot-Savart law to calculate the external tangential magnetic field H of each micro-element segment on the outer surface of each through hole. m,j , where H m,j represents the external tangential magnetic field of the jth microelement segment of the outer surface of the mth through hole; (5) Assuming that the current of each micro-element segment on the outer surface of each through hole is constant, the current of each micro-element segment is: Among them, I m,j represents the current of the jth microelement segment on the outer surface of the mth through hole; (6) Calculate the through-hole array loss based on the through-hole spatial current distribution, including the total AC loss P loss_ac And the total DC loss P loss_dc .

2. The method for obtaining through-hole loss of a planar transformer according to claim 1, characterized in that: The method for determining the current distribution parameter k of the through-hole array is: (2.1) Assume that the size of the through hole array is N×M, where N is the number of rows of the through hole array, M is the number of columns of the through hole array, N≥1, M≥1, and N and M cannot be 1 at the same time; the through holes at all vertex positions on the edge of the through hole array are external through holes, and the through holes at all non-vertex positions on the edge of the through hole array are internal through holes; (2.2), let the total current passing through the through-hole array be I, the current I A Evenly distributed to the outer vias, the current I B The current is evenly distributed to the inner vias, and the current of the remaining vias located in the central area of ​​the via array is 0; (2.3), define the current distribution parameter k and the current I A ,I B The relationship is: (2.4), define the increment step size Δk of the current distribution parameter k, and the maximum value of k is 1; (2.5), initialize k = 0, and then calculate the current I according to the relationship in step (2.3) A and I B ; (2.6) Use the Biot-Savart law to calculate the magnetic field strength generated by each through hole at each grid point; When a grid point is located inside any through hole, its magnetic field strength is recorded as 0; otherwise, the magnetic field strength generated by each through hole at each grid point is calculated according to the following formula; Among them, H m,n represents the magnetic field intensity generated by the mth through hole at the nth grid point, I m is the current flowing through the mth through-hole, r n is the coordinate of the nth grid point, r m is the coordinate of the mth pass; Traversing each through hole in the through hole array to obtain the magnetic field strength generated by each through hole at each grid point; (2.7) Increase the current distribution parameter k with an increasing step size Δk until the k value reaches 1. For different k values, calculate the magnetic field intensity generated by each through hole at each grid point under different k values ​​according to steps (2.5) and (2.6); (2.8) Calculate the sum of the squares of the magnetic field strengths generated by each through hole at each grid point under different k values The k value corresponding to the minimum total sum is taken as the current distribution parameter of the through-hole array.

3. The method for obtaining through-hole loss of a planar transformer according to claim 1, characterized in that: The calculation method of the external tangential magnetic field of each micro-element segment on the outer surface of the through hole is: (3.1) According to the current distribution parameter k of the through-hole array, the current I is first calculated A ,I B , and then calculate the current of each through hole; (3.2) Divide the perimeter of each through hole evenly into N p The center coordinates of the outer arc of each micro-element segment are marked as r m,j ,j=1,2,…,N p ; (3.3) Use the Biot-Savart law to calculate the external tangential magnetic field of each micro-element segment on the outer surface of each through hole: Among them, H m,j Represents the external tangential magnetic field of the jth infinitesimal segment on the outer surface of the mth through hole.

4. The method for obtaining through-hole loss of a planar transformer according to claim 1, characterized in that: The calculation method of the through hole array loss is: (4.1) Calculate the AC loss P of each microelement segment on the outer surface of each through hole loss，ac，m，j : Where R represents the resistance of each microelement segment on the outer surface of the through hole; (4.2) Calculate the total AC loss P of the through-hole array loss_ac ; Among them, N q is the number of through holes; (4.3) Calculate the DC loss P of each microelement segment on the outer surface of each through hole loss_dc,m,j : (4.4), calculate the total DC loss P of the through-hole array loss_dc : Where I is the total current of the through-hole array.

Images