Method for obtaining through-hole loss of planar transformer

Abstract

The application discloses a method for obtaining through-hole loss of a planar transformer. After a mathematical model of the through-hole loss is established, current distribution parameters of a through-hole array are determined according to defined through-hole radii and intervals, a magnetic field generated by the through-hole in a defined area is calculated by using Biot-Savart law, spatial current of the through-hole is further determined, and finally the through-hole loss is calculated.

Description

Technical Field

[0001] This invention belongs to the field of planar transformer design technology, and more specifically, relates to a method for obtaining the through-hole loss of a planar transformer. Background Technology

[0002] High-efficiency and high-power-density power supplies are fundamental to the continued development of the communications, automotive, aerospace, and data processing industries. As power supplies evolve towards higher efficiency, higher frequencies, and higher power densities, traditional magnetic component structures face increasing performance limitations. For example, at frequencies above 100kHz, winding losses increase significantly due to eddy current effects. However, with the development of PCB technology and switching devices such as gallium nitride and silicon carbide, planar PCB magnetic components are receiving more extensive research due to their low height, superior thermal characteristics, ease of manufacturing and cost reduction, modularity, and predictable parasitic parameters.

[0003] Similar to traditional magnetic structures, the demands of high-frequency operation, particularly for planar magnetic structures, lead to increased winding losses due to the skin and proximity effects. In terms of winding losses, planar magnetic elements are more suitable for high-frequency, high-power converters than older wire-wound magnetic elements. However, planar magnetic element windings must adhere to manufacturing limitations on turn-to-turn and layer-to-layer spacing, significantly reducing the core window area. Furthermore, planar magnetic elements cannot be directly replaced by Litz wire; instead, interleaved windings are typically used, which can be easily arranged within the core window on a PCB using vias.

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

[0005] Therefore, for planar magnetic designs, especially those carrying high currents and employing multiple layers, the losses of these terminated vias must be considered. Finite element method (FEM) simulation is a traditional analytical method for calculating via losses, particularly using tools like ANSYS to perform two-dimensional electromagnetic field simulations of vias. This method can accurately simulate the electromagnetic characteristics of vias and provide loss estimates under high-frequency signals. Although FEM provides high-precision data support for designs, its modeling process is cumbersome and computationally time-consuming. Especially in large-scale PCB designs, simulation efficiency often becomes a bottleneck. Therefore, it is necessary to optimize the via loss model calculation method. Summary of the Invention

[0006] The purpose of this 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 mathematical model of the through-hole, the efficiency of existing through-hole loss calculation is improved, which is conducive to the rapid design iteration of through-hole arrays.

[0007] To achieve the above-mentioned objective, the present invention provides a method for obtaining the through-hole loss of a planar transformer, characterized by comprising the following steps:

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

[0009] A mathematical model of the via array is established using MATLAB simulation software. The size of the via array is defined as N×M, where N is the number of rows and M is the number of columns, N≥1, M≥1, and N and M cannot both be 1. The inner radius of each via in the via array is set to r. inner The outer radius is r outter The spacing between the through holes is s;

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

[0011] With the center point of the via array as the origin of the two-dimensional coordinate system, each via generates 10(r) at its center position. outter +s)×10(r outter A rectangular magnetic field region of size +s);

[0012] The magnetic field region generated by the through-hole array is divided into intervals 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) Calculate the external tangential magnetic field H of each micro-segment on the outer surface of each through hole using Biot-Savart's law. m,j , where H m,j This represents the external tangential magnetic field of the j-th infinitesimal segment on the outer surface of the m-th through-hole;

[0015] (5) Assuming the current in each infinitesimal segment on the outer surface of each through hole is constant, then the current in each infinitesimal segment is:

[0016]

[0017] Among them, I m,j This represents the current in the j-th micro-element segment on the outer surface of the m-th through-hole;

[0018] (6) Calculate the via array loss based on the current distribution in the via space, including the total AC loss P. loss_ac and total DC loss Ploss_dc .

[0019] The objective of this invention is achieved as follows:

[0020] This invention discloses a method for obtaining the via loss of a planar transformer. After establishing a mathematical model of the via loss, the current distribution parameters of the via array are determined according to the defined via radius and spacing. Then, the magnetic field generated by the via within the defined region is calculated using Biot-Savart's law, and the spatial current of the via is further determined. Finally, the via loss is calculated.

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

[0022] (1) The mathematical model of the through hole loss of the present invention is simpler and more efficient than the finite element simulation model, and can shorten the design cycle.

[0023] (2) By using mathematical models for loss prediction, the reliance on high-precision simulation tools can be reduced, and the simulation cost can be lowered. 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 more cost-effective design. Attached Figure Description

[0024] Figure 1 This is a schematic diagram of the through holes at the winding ends of a planar transformer;

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

[0026] Figure 3 This is a schematic diagram of a 1×5 through-hole array model;

[0027] Figure 4 These are magnetic field intensity distribution diagrams for three different through-hole array arrangements;

[0028] Figure 5 This is a 2D magnetic field intensity distribution diagram of ANSYS Maxwell for three different through-hole arrangements. Detailed Implementation

[0029] The specific embodiments of the present invention will now be described with reference to the accompanying drawings to enable those skilled in the art to better understand the invention. It should be particularly noted that in the following description, detailed descriptions of known functions and designs that might obscure the main content of the invention will be omitted here.

[0030] Example

[0031] In this embodiment, the schematic diagram of the through hole at the winding end of the planar transformer is as follows: Figure 1 As shown, the planar transformer winding consists of three layers of primary windings and three layers of secondary windings. The primary windings and secondary windings are connected by two sets of 1x3 via arrays. When current flows through the vias, via losses are generated. Therefore, accurately obtaining these via losses is a key issue in optimizing the via array layout design. To address this, we propose a method for obtaining via losses in planar transformers, such as... Figure 2 As shown, the specific steps include:

[0032] S1. Establish a mathematical model for the through-hole array;

[0033] Mathematical models of through-hole arrays established using MATLAB simulation software, such as Figure 3 As shown, the size of the via array is defined as 1×5; the inner radius of each via in the via array is set to r. inner =9mil, outer radius is r outter =10mil, the through-hole spacing is s=10mil;

[0034] S2. Define the magnetic field region generated by the through-hole array;

[0035] like Figure 3 As shown, with the center point of the via array as the origin of the two-dimensional coordinate system, each via generates 10(r) at its center position. outter +s)×10(r outter A rectangular magnetic field region of size +s);

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

[0037] S3. Determine the current distribution parameter k of the via array;

[0038] S3.1. The through holes at all vertex positions on the edge of the through hole array are called external through holes, and the through holes at all non-vertex positions on the edge of the through hole array are called internal through holes.

[0039] In this embodiment, when N or M is less than 2, i.e., the via array is a single row with multiple columns or a single column with multiple rows, the number of external vias is 2, and the remaining vias are internal vias. Figure 3As shown, when the via array is 1 row and 5 columns, the vias at both ends are external vias, and the three throughs in the middle are internal vias. When N and M are both equal to 2, the number of external vias is 4, and the number of internal vias is 0. When N or M is greater than 2, the number of external vias is 4, and all vias at non-vertex positions on the edge of the via array are internal vias. That is, the remaining vias in the row and column where the external vias are located are internal vias. For example, when the via array is 2 rows and 5 columns, the number of external vias is 4, and the number of internal vias is 6; when the via array is 5 rows and 5 columns, the number of external vias is 4, and the number of internal vias is 12.

[0040] S3.2. Assume the total current I through the via array is 1A, and the current I... A The current I is evenly distributed to the external through-hole. B The current is evenly distributed to the inner through holes, and the current of the remaining through holes located in the central region of the through hole array is 0.

[0041] In this embodiment, as Figure 3 As shown, when the via array is 1 row and 5 columns, the current I... A The current I is evenly distributed to the two external through holes. B The current I is evenly distributed among the three internal vias; when the via array is 5 rows and 5 columns, the current I... A The current I is evenly distributed across the four external vias. B The current is evenly distributed to 12 internal vias, while the current in the remaining 9 vias located in the central region of the via array is 0.

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

[0043]

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

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

[0046] S3.6 Calculate the magnetic field strength generated by each through hole at each grid point using Biot-Savart's law;

[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 I represents the magnetic field strength generated by the m-th through-hole at the n-th grid point. m Let r be the current flowing through the m-th through hole. n Let r be the coordinates of the nth grid point. m Let m be the coordinates of the m-th element passed through.

[0050] By traversing each through hole in the through-hole array, the magnetic field strength generated by each through hole at each grid point is obtained;

[0051] S3.7. Increase the current distribution parameter k by incrementing the step size Δk until the value of k reaches 1. For different k values, calculate the magnetic field strength 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 squares of the magnitudes of the magnetic field strength generated by each through-hole at each grid point under different k values. The k value corresponding to the minimum sum is taken as the current distribution parameter of the via array.

[0053] S4. Calculate the external tangential magnetic field H of each micro-segment on the outer surface of each through-hole using Biot-Savart's law. m,j ;

[0054] S4.1. Based on the current distribution parameter k of the via array, first calculate the current I. A I B Then calculate the current in each through hole;

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

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

[0057]

[0058] Among them, H m,j This represents the external tangential magnetic field of the j-th infinitesimal segment on the outer surface of the m-th through-hole.

[0059] S5. Assuming the current in each infinitesimal segment on the outer surface of each through-hole is constant, then the current in each infinitesimal segment is:

[0060]

[0061] Among them, Im,j This represents the current in the j-th micro-element segment on the outer surface of the m-th through-hole;

[0062] S6. Calculate the via array loss based on the current distribution in the via space, including the total AC loss P. loss_ac and total DC loss P loss_dc ;

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

[0064]

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

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

[0067]

[0068] Where, N q Number of through holes;

[0069] S6.3 Calculate the DC loss P of each micro-element 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 via array. loss_dc :

[0072]

[0073] Where I represents the total current of the via array.

[0074] Figure 4 These are magnetic field intensity distribution diagrams for three different through-hole array arrangements;

[0075] In this embodiment, MATLAB is used to model three through-hole array arrangements: 1x5, 2x5, and 5x5, to obtain the magnetic field intensity distribution diagram of the through-hole array, as shown below. Figure 4 As shown, (a) is the magnetic field intensity distribution of a 1x5 through-hole array; (b) is the magnetic field intensity distribution of a 2x5 through-hole array; and (c) is the magnetic field intensity distribution of a 5x5 through-hole array. Due to the influence of the 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 This is a 2D magnetic field intensity distribution diagram of ANSYS Maxwell for three different through-hole arrangements.

[0077] In this embodiment, (a) is the magnetic field strength distribution diagram of a 1x5 through-hole array; (b) is the magnetic field strength distribution diagram of a 2x5 through-hole array; and (c) is the magnetic field strength distribution diagram of a 5x5 through-hole array. Figure 5 As can be seen from the three magnetic field strength distribution diagrams, the magnetic field is mainly distributed at the edges of the through-hole array, while the magnetic field strength inside the through-holes is essentially zero. Figure 4 and Figure 5 The comparison shows that the mathematical model of the through-hole array is consistent with the complex finite element simulation results in describing the trend of magnetic field distribution, proving that the mathematical model can be reliably used for the prediction and evaluation of through-hole loss.

[0078] Define AC resistivity F R The calculation formula is as follows:

[0079]

[0080] In this embodiment, the AC resistivity of the 1x5 via array calculated in ANSYS simulation is 1.35, while the AC resistivity in MATLAB simulation is 1.33, with an error of 5.7%. The AC resistivity of the 2x5 via array in ANSYS simulation is 1.90, while the AC resistivity in MATLAB simulation is 1.73, with an error of 8.9%. The AC resistivity of the 5x5 via array in ANSYS simulation is 3.20, while the AC resistivity in MATLAB simulation is 3.38, with an error of 5.3%. Although MATLAB mathematical modeling has a certain gap in accuracy compared to ANSYS finite element simulation, the error is generally within 10%, which is sufficient for the preliminary analysis of the magnetic field intensity distribution of the via array. However, ANSYS simulation requires building separate models for different via arrays, with simulation time generally exceeding 10 seconds. Furthermore, results such as the AC resistivity require further manual calculation, making the process more complex. MATLAB models can simulate multiple via arrays simultaneously as needed, with a simulation time of only about 0.02 seconds. They can also directly calculate results such as the AC resistance coefficient of the vias, facilitating comparative analysis of different via array models. In general, while MATLAB simulations are not as accurate as ANSYS finite element simulations, their faster calculation speed allows for multiple design iterations in a shorter time, making them more suitable for quickly evaluating and optimizing via array combinations in the early stages of design. This gives them a high degree of practicality and efficiency.

[0081] Although the illustrative specific embodiments of the present invention have been described above to enable those skilled in the art to understand the invention, it should be understood that the invention is not limited to the scope of the specific embodiments. For those skilled in the art, various changes are obvious as long as they are within the spirit and scope of the invention as defined and determined by the appended claims, and all inventions utilizing the concept of the present invention are protected.

Claims

1. A method for obtaining the through-hole loss of a planar transformer, characterized in that, Includes the following steps: (1) Establish a mathematical model for the through-hole array; A mathematical model of the via array was established using MATLAB simulation software, and the size of the via array was defined as follows: ,in, The number of rows in the through-hole array. The number of columns in the through-hole array. , ,and and Cannot all be 1; Set the inner radius of each through-hole in the through-hole array to 1. Outer radius is The through-hole spacing is ; (2) Define the magnetic field region generated by the through-hole array; Using the center point of the via array as the origin of the two-dimensional coordinate system, each via generates 10 ( ) at its center position. + )×10( + A rectangular magnetic field region of size 1.5; The magnetic field region generated by the through-hole array is divided into intervals of 0.01 ( + The grid points are arranged in a grid, with each grid point corresponding to a two-dimensional coordinate. (3) Determine the current distribution parameters of the via array. ; (4) Calculate the external tangential magnetic field of each micro-segment on the outer surface of each through hole using Biot-Savart's law. ,in, Indicates the first The first through-hole outer surface The external tangential magnetic field of the infinitesimal segment; (5) Assuming the current in each infinitesimal segment on the outer surface of each through hole is constant, then the current in each infinitesimal segment is: ； in, Indicates the first The first through-hole outer surface The current in the micro-element segment, Indicates the number of infinitesimal segments; (6) Calculate the via array loss based on the current distribution in the via space, including the total AC loss. and total DC loss .

2. The method for obtaining the through-hole loss of a planar transformer according to claim 1, characterized in that, Current distribution parameters of the via array The method for determining it is as follows: (2.1) Let the size of the through-hole array be... ,in, The number of rows in the through-hole array. The number of columns in the through-hole array. , ,and and They cannot all be 1 at the same time; the holes at all vertices of the edge of the through-hole array are called external through-holes, and the holes at all non-vertices of the edge of the through-hole array are called internal through-holes; (2.2) Let the total current through the via array be... Current The current is evenly distributed to the external through-hole. The current is evenly distributed to the inner through holes, and the current of the remaining through holes located in the central region of the through hole array is 0. (2.3) Define current distribution parameters With current , Relationship: ； (2.4) Define current distribution parameters incremental step size ,as well as The maximum value is 1; (2.5) Initialization Then calculate the current according to the relationship in step (2.3). and ; (2.6) Calculate the magnetic field strength generated by each through hole at each grid point using Biot-Savart's law; 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. ； in, Indicates the first The first through hole in the The magnetic field strength generated at each grid point For the first The current flowing through each through hole For the first The coordinates of each grid point For the first One passing coordinate; By traversing each through hole in the through-hole array, the magnetic field strength generated by each through hole at each grid point is obtained; (2.7) Using an increasing step size Increase current distribution parameters until When the value reaches 1, it applies to different... The values ​​are calculated according to steps (2.5) and (2.6). The magnetic field strength generated by each through hole at each grid point; (2.8) Calculate different The sum of squares of the magnitudes of the magnetic field strength generated by each through-hole at each grid point. The corresponding value when the sum is minimized The value is used as the current distribution parameter of the via array.

3. The method for obtaining the through-hole loss of a planar transformer according to claim 1, characterized in that, The method for calculating the external tangential magnetic field of each micro-element segment on the outer surface of the through hole is as follows: (3.1) Based on the current distribution parameters of the via array First calculate the current. , Then calculate the current in each through hole; (3.2) Divide the perimeter of each through hole evenly into Each infinitesimal element has a center coordinate of its outer circular arc, denoted as [element 1]. , ; (3.3) Calculate the external tangential magnetic field of each micro-segment on the outer surface of each through hole using Biot-Savart's law: ； in, Indicates the first The first through-hole outer surface The external tangential magnetic field of the micro-element segment.

4. The method for obtaining the through-hole loss of a planar transformer according to claim 1, characterized in that, The method for calculating the loss of the via array is as follows: (4.1) Calculate the AC loss of each micro-element segment on the outer surface of each through hole. : ； in, This represents the resistance of each micro-segment on the outer surface of the through hole; (4.2) Calculate the total AC loss of the through-hole array. ; ； in, Number of through holes; (4.3) Calculate the DC loss of each micro-element segment on the outer surface of each through hole. : ； (4.4) Calculate the total DC loss of the through-hole array. : ； in, This represents the total current of the via array.

Images