Inductor miniaturization design method suitable for coupling inductor Buck converter

Abstract

The invention discloses an inductor miniaturization design method suitable for a coupling inductor Buck converter, which comprises the following steps of: finding out a coupling coefficient when a coupling inductor has a minimum effective current, and then designing geometric parameters of a miniaturized inductor to maximize magnetic flux density under the requirements of designing given maximum current density Jmax and maximum magnetic induction intensity Bmax. Meanwhile, the saturation risk of the magnetic core is effectively controlled, and the balance of miniaturization and performance improvement of the inductor is achieved. The method comprises the following steps: firstly, calculating an effective current value expression according to an inductance voltage and current differential relation, and calculating a coupling coefficient when the effective current is minimum; and then according to the equivalent magnetic circuit of the magnetic core, calculating a coupling coefficient relational expression to determine the relationship among the design parameter sectional area AS, the air gap size lgc and the number of turns N of the winding. And finally, through design requirements, reducing winding loss and determining the number of turns of the winding as small as possible so as to design values of other parameters.

Description

Technical Field

[0001] The present invention relates to a coupled inductor design optimization technology, and belongs to the field of power electronic magnetic component design and application. The present invention integrates multiple power electronic design principles, including core material selection, winding structure design, and inductor magnetic circuit modeling method, and particularly relates to an inductor miniaturization design method suitable for a coupled inductor Buck converter. Background Art

[0002] With the widespread application of modern electronic devices, the demand for miniaturization and high efficiency of equipment is increasing. In the field of power electronics, DC-DC converters, especially Buck (step-down) converters, play an important role in applications such as portable devices, industrial control systems, electric vehicles, communication equipment and smart homes. With the rapid development of artificial intelligence and cloud computing technologies, the energy consumption of data centers has gradually increased. In this context, the 48V architecture of server power supplies has attracted more and more attention due to its low loss characteristics. The typical 48V architecture includes a pre-regulator stage and a step-down stage, in which the step-down stage is responsible for converting the 48V input voltage into a stable 1V voltage. In this context, the traditional Buck converter requires a very small duty cycle, which is difficult to achieve in design. The 2N-order Buck converter can stably convert the 48V input voltage into a stable 1V voltage under a larger duty cycle, so it has been widely used.

[0003] However, in small-volume designs, traditional inductors often fail to meet the requirements of high power density and high efficiency, especially for 2N-order Buck converters, which contain 2N inductors. In order to improve energy conversion efficiency, reduce current ripple, and reduce volume, coupled inductor technology is used in many designs. Coupled inductor Buck converters have gradually attracted attention due to their compact structure and high efficiency. Coupled inductors can integrate multiple windings and realize multiple inductor functions through a single magnetic core, saving the volume of the magnetic core. Compared with discrete inductors, coupled inductors can significantly reduce the volume and weight of the converter without sacrificing performance, meeting the requirements of miniaturized design.

[0004] However, there are multiple technical challenges in achieving small size and high efficiency, including how to reasonably design the inductance value and coupling coefficient of the coupled inductor to optimize the effective current flowing through the inductor to reduce power loss, and how to calculate and design the magnetic core of the coupled inductor to obtain the optimal core size. Summary of the invention

[0005] The purpose of the present invention is to provide a method for miniaturizing the inductor design of a coupled inductor Buck converter to meet the high requirements of volume, efficiency and stability of today's multi-stage Buck converters. max and the maximum magnetic induction intensity Bmax Under this circumstance, the reasonable selection of magnetic materials, optimization of the core size and the number of winding turns effectively improve the conversion efficiency, reduce the component volume, and achieve higher power density. This innovative inductor design method will help promote the application of miniaturized power systems in various electronic products and provide support for technological progress in related fields.

[0006] The specific technical method of the present invention is as follows:

[0007] A method for miniaturizing an inductor suitable for a coupled inductor Buck converter is disclosed. The method couples two inductors on the basis of a 2N-order Buck converter, with a total of N pairs of coupled inductors. The self-inductance and mutual inductance of each pair of coupled inductors are the same, and there are a total of four working stages, that is, there are four sections of ripple. The current ripple amount at each stage of the coupled inductor is determined by solving the voltage balance equation at each stage of the coupled inductor. According to the relationship between the output voltage and the duty cycle of the 2N-order Buck converter, the four sections of current ripple are converted and weighted averaged to obtain the total inductor current ripple value. The ripple value is derived to determine the optimal coupling coefficient value to ensure that the total inductor current effective value is the lowest, so that the Buck circuit works in a state with low loss. Under the calculated coupling coefficient design requirements, according to the maximum current density J max and the maximum magnetic induction intensity B max According to the requirements, establish the number of turns N of the core winding and the cross-sectional area A of the side column S , window width and air gap size l gc Based on the mathematical model, a miniaturized planar coupled inductor core that meets the working conditions of the converter is designed.

[0008] Furthermore, the current ripple amount at each stage of the coupled inductor is determined by solving the voltage balance equation at each stage of the coupled inductor, which specifically includes the following steps: the coupled inductor buck converter has four working stages in one cycle, and the duration of each stage is represented by T 1 , T 2 , T 3 and T 4 To represent, a pair of coupled inductors is recorded as L 1 and L 2 , four-stage inductance L 1 The voltages on g -V C1 -V out , -V out , -V out , -V out , inductance L 2 The inductance of the four stages are -V out , -V out 、V C1 -V C2-V out , -V out , where V g Input voltage, V out Output voltage, V C1 and V C2 is the voltage across capacitors C1 and C2 in the circuit topology; the current in each stage is determined by the voltage across the inductor V L , the conduction time T and coupling coefficient M of each stage are determined; the inductance L is listed according to the voltage balance equation of the coupled inductor 1 and L 2 The voltage above v 1 and v 2 , about the current i flowing through the inductor 1 、i 2 The relationship between the differential component of time t, inductance L and mutual inductance M is formula (1) and formula (2). Substitute the voltage value across the inductor in each state in the four working states, and solve formula (1) and formula (2) to obtain the differential of the voltage V across the inductor with respect to the current of the two inductors with respect to time in the four states: The relationship between inductance L and mutual inductance M is obtained by integrating the current di in four states with respect to time. 1 The current ripple value I ripple1 , I ripple2 , I ripple3 and I ripple4 , expressed by formula (3)-formula (6);

[0009]

[0010]

[0011]

[0012]

[0013]

[0014]

[0015] Furthermore, according to the relationship between the output voltage and duty cycle of the 2N-order Buck converter, the four-segment current ripple is converted and weighted averaged to obtain the total inductor current ripple value, and the ripple value is derived to determine the optimal coupling coefficient value to ensure the minimum effective value of the total inductor current. The specific steps include: calculating the total current ripple, and derivation to calculate the coupling coefficient when the inductor current ripple is the minimum; due to the working state T 2 and T 4 The voltage across the inductor is the same, and the ripple change across the inductor is also the same, so Iripple2 =I ripple4 ; According to the 2N-order Buck converter output voltage V out Regarding the input voltage V in The relationship between the duty cycle d and the converter order N is Substitute into the current ripple expression of formula (3)-formula (6), and use the effective value formula Substitute the obtained four-segment inductor current ripple values ​​i in turn to solve the effective current values ​​of the four states, and calculate the total effective current value I by weighted average calculation of the four-segment current effective values. rms , the total ripple current is given by equation (7), which gives the inductor current and switching period T s 、Input voltage V in , duty cycle d, step-down converter order N, coupling coefficient K and self-inductance L, where the coupling coefficient By taking the derivative of the effective value and setting its derivative to zero, the coupling coefficient corresponding to the minimum effective value of the current is obtained. The coupling coefficient is given by formula (8). The coupling coefficient at the minimum effective value of the inductor current is only related to the value of the duty cycle d. The coupling coefficient K is selected according to the value of the duty cycle d of the Buck converter.

[0016]

[0017]

[0018] Furthermore, given the maximum current density J max and the maximum magnetic induction intensity B max Under the requirements, the core design of the miniaturized planar coupled inductor is realized by the following steps: According to the magnetic flux distribution, the middle column magnetic flux Designed for the magnetic flux of the two side columns The sum of the current density and the width of the middle column is determined to be twice the width of the side column, that is, the cross-sectional area of ​​the middle column is twice the cross-sectional area of ​​the side column; according to the maximum current density J max According to the requirements of the current density relationship I = J * h * W, where h is the selected PCB copper thickness, the window width W is calculated to ensure that the current density is less than the set maximum current density value; the magnetic resistance in the magnetic circuit It is related to the magnetic path length l, magnetic permeability μ and cross-sectional area A, where the side column air gap is l gs , the air gap in the middle column is l gc , let the cross-sectional area of ​​the side column be A, the cross-sectional area of ​​the middle column is twice the cross-sectional area of ​​the side column, so the cross-sectional area of ​​the middle column is 2A, the value of the magnetic permeability μ is a fixed value according to the selected core material, so the air gap magnetic resistance of the left and right side columns in the magnetic circuit of the E-type core is calculated and the middle column air gap reluctance Using Ampere's circuit theorem, according to the magnetomotive force N*I and magnetic flux in the magnetic circuit The relationship between the magnetic resistance R and the equivalent magnetic circuit equations is listed as formula (9), where R s is the side column air gap reluctance, R C is the air gap reluctance of the middle column; solve for the magnetic flux and The law of electromagnetic induction is a system of equations The values ​​of self-inductance L, mutual inductance M and coupling coefficient K are obtained. The values ​​of self-inductance, mutual inductance and coupling coefficient are given by formula (10), formula (11) and formula (12). According to formula (10), the inductance value, the number of winding turns N and the side column air gap l are obtained. gs 、Middle column air gap l gc and the cross-sectional area of ​​the side column A S The relationship between the coupling coefficient K and the side column air gap magnetic resistance R is obtained by formula (12). s and the middle column air gap magnetic resistance R C Substituting the air gap reluctance into the coupling coefficient, we can get that the coupling coefficient is only related to the side column air gap l gs The air gap between the center column and the gc The coupling coefficient K is obtained by taking the derivative when determining the effective value of the inductor current ripple, so the precise side column air gap is l. gs The air gap between the center column and the gc Numerical relationships;

[0019]

[0020]

[0021]

[0022]

[0023] Furthermore, according to the maximum current density J max and the maximum magnetic induction intensity B max According to the requirements, establish the number of turns N of the core winding and the cross-sectional area A of the side column S , window width and air gap size l gc The mathematical model used to design the optimal size of the coupled inductor includes the following steps: Inductance is the target quantity of the design, and N is assumed to be only one turn; The ratio of the side column air gap to the middle column air gap is determined according to formula (12), and the air gap, the number of winding turns N, and the side column cross-sectional area A are determined by formula (10). S The relationship between the two is that we only need to know the cross-sectional area A of the side column. S All unknown quantities can be determined by the value of The magnetic induction intensity B is taken into the maximum value B of the design limit max , the value of N, we get the value of the cross-sectional area of ​​the side column A SWhen determining the air gap length, the magnetic resistance of the magnetic core is taken into account. According to formula (10), the inductance value, the number of winding turns N, and the side column air gap l are obtained. gs 、Middle column air gap l gc and the cross-sectional area of ​​the side column A S The relationship between the side column air gap l is determined gs 、Middle column air gap l gc The value of .

[0024] The inductor miniaturization design method applicable to the coupled inductor Buck converter of the present invention has the following advantages:

[0025] (1) The inductor miniaturization design method of the coupled inductor Buck converter proposed in the present invention designs a coupling coefficient with the minimum effective value of the inductor current by combining the coupled inductor voltage balance equation with the working principle of the Buck circuit, thereby reducing the ripple and loss of the circuit.

[0026] (2) The inductor miniaturization design method of the coupled inductor Buck converter proposed in the present invention is to design a given maximum current density J max and the maximum magnetic induction intensity B max Under the requirements, under the design targets of inductance L and coupling coefficient K, the number of winding turns N and the side column air gap l are established through the E-type core equivalent magnetic circuit. gs 、Middle column air gap l gc and the cross-sectional area of ​​the side column A S The relationship between them is calculated and based on the definition of inductance, a minimum volume core is designed to fully utilize the core space and reasonably distribute the core magnetic flux distribution. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 A schematic diagram of a multi-inductor hybrid converter according to the present invention;

[0028] Figure 2 This is a graph showing the change of the effective value of the current with the coupling coefficient of the present invention;

[0029] Figure 3 The figure is a flow chart of the coupled inductor core design of the present invention;

[0030] Figure 4 This is a schematic diagram of the E-type magnetic core structure of the present invention;

[0031] Figure 5 It is the equivalent magnetic circuit diagram of the magnetic core of the present invention; DETAILED DESCRIPTION

[0032] In order to better understand the purpose, structure and function of the present invention, the following further describes in detail an inductor design method suitable for a small-volume coupled-inductor Buck converter of the present invention in conjunction with the accompanying drawings.

[0033] The inductor miniaturization design method for a coupled inductor Buck converter of the present invention is suitable for the output voltage and input voltage of a 2N-order Buck converter. The 48V voltage can be reduced to 1V under a larger duty cycle. Based on the 2N-order Buck converter, the two inductors L1 and L2 are coupled, and the coupling coefficient is M. There are a total of N pairs of coupled inductors, and each pair of coupled inductors is exactly the same. The voltage and current formulas (1) and (2) of the coupled inductors for the buck converter are listed as follows:

[0034]

[0035]

[0036] According to the conduction status of each stage of the Buck converter, the four-stage inductance L can be obtained. 1 The voltages on the inductor are Vg-VC1-Vout, -Vout, -Vout, and -Vout. 2 The inductances of the four stages are -Vout, -Vout, VC1-VC2-Vout, and -Vout. Substituting the voltage value of each state, we can get the relationship between the corresponding current di in the four states and the voltage V, inductance L and mutual inductance M. By integrating the di in the four states with respect to time, we can get the two inductances L in the four states. 1 , L 2 The respective current ripple values ​​I ripple1 , I ripple2 , I ripple3 and I ripple4 , as shown in formula (3)-formula (6). According to the output voltage of the 2N-order Buck converter The relationship is substituted into the current ripple expression of formula (3)-formula (6), and according to the effective value formula Solve the effective current values ​​of the four states in turn, and calculate the total effective current value I by weighted average of the effective current values ​​of the four segments. rms , the total ripple current is given by formula (7), it can be seen that the inductor effective current and the switching period T s 、Input voltage V in , duty cycle d, step-down converter order N, coupling coefficient K and self-inductance L, where the coupling coefficient By taking the derivative of the total effective current expression and setting the derivative to zero, the condition for the minimum effective current value can be found. Further solving the derivative equation, the coupling coefficient that minimizes the effective current value is obtained. The results show that the coupling coefficient is directly related to the value of the duty cycle d. Based on the range of duty cycle d in the Buck converter, the optimal coupling coefficient K can be determined, expressed as formula (8), so as to achieve the minimum effective value of the inductor current. This method provides a systematic way to optimize circuit design to minimize current ripple and thus improve circuit performance.

[0037]

[0038]

[0039]

[0040]

[0041]

[0042]

[0043] Coupled Inductor Core Design:

[0044] For the design of planar coupled inductor cores, EE type cores are selected. The selection of core materials needs to comprehensively consider factors such as operating frequency, loss, temperature rise, etc., and comprehensively consider the loss, price and applicable scope of the core materials. The selection of high magnetic permeability materials can generate a larger magnetic flux under a smaller magnetomotive force, effectively reduce magnetic resistance, and improve equipment efficiency. Then, the design parameters must be clarified to determine the designed inductance value and coupling coefficient. The method for determining the coupling coefficient is as described above, as well as the maximum current density and magnetic induction intensity.

[0045] The equivalent magnetic circuit of the coupled inductor is shown in Figure (4) of the attached figure. The magnetic flux of the middle column is the sum of the magnetic flux of the two side columns, so the width of the middle column can be designed to be twice the width of the side columns. Since this design needs to pass a large current, the window width must be determined first to ensure that the current density is less than the set value. 5oz copper foil is selected, and the window width W is calculated based on the current density relationship I = J*h*W, where h is the selected PCB copper thickness. Ensure that the current density is less than the set maximum current density value to determine the appropriate window width and reserve enough space for the current density.

[0046] In the magnetic circuit, the relationship between magnetomotive force, magnetic flux and magnetic resistance can be listed as formula (9), where R S is the total reluctance of the side column, which is the sum of the core reluctance and the air gap reluctance, R C is the sum of the magnetic resistance of the center column core and the air gap. It is related to the magnetic path length l, magnetic permeability μ and cross-sectional area A, where the side column air gap is l gs , the air gap in the middle column is l gc , calculate the air gap reluctance R of the left and right side columns in the E-type core magnetic circuit s and the middle column air gap magnetic resistance R C Since the magnetic resistance of the core is much smaller than the magnetic resistance of the air gap, the magnetic resistance of the core is temporarily ignored in the calculation of the coupling coefficient. Solving formula (9) can calculate the side column magnetic flux According to the law of electromagnetic induction Substituting the magnetic flux obtained above and comparing it with formula (1) and formula (2), the self-inductance, mutual inductance and coupling coefficient of the coupled inductor can be obtained, which are expressed as formula (10), formula (11) and formula (12). Based on the coupling coefficient k obtained above and formula (12), the relationship between the air gaps of the side column and the middle column can be obtained.

[0047]

[0048]

[0049]

[0050]

[0051] Since the inductance value is known, the inductance value, the number of winding turns N, and the side column air gap l can be obtained according to formula (10): gs 、Middle column air gap l gc and the cross-sectional area of ​​the side column A S According to formula (12), we can know that the side column air gap l gs 、Middle column air gap l gc According to the definition of inductance The magnetic induction intensity B is known, so as long as one of the parameters of the number of winding turns, the cross-sectional area of ​​the side column and the air gap is determined, the remaining parameters can be calculated. Generally speaking, the larger the air gap, the more winding turns are required, because the larger the air gap, the increased magnetic resistance makes it impossible for the same current to generate enough magnetic flux through the original number of turns, so it is necessary to provide a larger magnetomotive force by increasing the number of winding turns. The more winding turns there are, the larger the cross-sectional area required for the core to maintain the magnitude of the magnetic induction intensity under the same air gap conditions. However, the smaller the air gap, the more obvious the saturation effect of the core. Too small an air gap means that the distribution of the magnetic field will be more concentrated, especially in the core part. This easily causes the core to enter a saturated state, especially under high current. Once the core is saturated, the magnetic permeability drops sharply, and the magnetic flux will no longer increase linearly with the increase of current, thus affecting the stability of the inductance. Therefore, a reasonable balanced design is critical according to actual conditions.

[0052] Coupling coefficient design at minimum effective current:

[0053] Figure 1 The circuit topology of this design is shown below. The input voltage is 48V, the output voltage is 1V, the switching frequency is 200kHz, the switching duty cycle is 0.125, and there are three pairs of inductors, all with an inductance of 2uH. 1 and L 2 , L 3 and L 4 , L 5 and L 6 Coupling, assuming that the coupling coefficient is k. For the coupling inductor L 1 , L 2 For analysis, L 3 , L 4 and L 5 , L 6 The analysis is similar, so I won’t go into detail here. 1 , L 2 The voltage balance equations (1) and (2) of the coupled inductor are listed. The inductance L of the four stages is 1 The voltages on the inductor are Vg-VC1-Vout, -Vout, -Vout, and -Vout. 2 The inductance of the four stages are -Vout, -Vout, VC1-VC2-Vout, -Vout, where Vout = 1V, Vg = 48V, VC1-VC2 = 8V, L 1 =L 2 By combining the inductor voltage and current equations (1) and (2), and substituting the voltage value on the inductor in each stage, the inductor current differential di in each stage can be obtained. The inductor current ripple value I in each stage can be obtained by integrating the inductor current differential di with respect to time. ripple1 , I ripple2 , I ripple3 and I ripple4 , as shown in (3)-(6), the results show that the second ripple is equal to the fourth ripple.

[0054]

[0055]

[0056]

[0057]

[0058]

[0059]

[0060] According to the DC current of 33.33A, using the effective value formula Solve the effective current values ​​of the four states in turn, and calculate the total effective current value I by weighted average of the effective current values ​​of the four segments. rms The relationship between the coupling coefficient K and the effective value of the inductor current is shown in equation (7). This is a relationship between the coupling coefficient K and the effective value of the inductor current. Plotting the inductor current against the coupling coefficient, Figure 2 shows the effective current I rms Regarding the trend graph of the coupling coefficient K, it can be observed from the graph that when K = -0.24374, the total effective current I rms Minimum. By I rms After taking the derivative of k, let its derivative be 0. By finding the maximum value, we can also get the total effective current I when the coupling coefficient K = -0.24374. rms Minimum.

[0061]

[0062] Coupled Inductor Core Design:

[0063] For the design of the planar coupled inductor core, EE type core is selected, and the core material is high magnetic permeability DOMEC DMR95 material, which helps to improve the overall performance and energy efficiency of the system. The core schematic diagram is shown in Figure 4 As shown, the parameters are listed in the figure. The maximum current density is designed to be 30A / mm 2 ,The maximum value of magnetic induction intensity is 400mT. Under this condition, a miniaturized coupled inductor core is designed.

[0064] The equivalent magnetic circuit of the coupled inductor is as follows: Figure 5 As shown, the side column width is set to a, the middle column flux is equal to the sum of the side column flux, and in order to ensure that the magnetic induction intensity of the middle column does not exceed the maximum value, the middle column width is set to twice the side column width. Considering the thickness of the PCB board, the length e is set to 0.5mm. Because the design inductance value is 200nH, the inductor current DC is 33.3A, and the peak current is 44.3A. In order to ensure that the current density does not exceed 30A / mm 2 Therefore, we first determine the core window width. The core winding can adopt a PCB multi-layer parallel structure. This design adopts a double-layer parallel structure. The maximum current of one layer is 22.15A. A 5-ounce thick copper winding is selected, that is, 0.175mm thick. According to I=J*0.175*W, the window width W is calculated to be 4.22mm. Since the magnetic resistance of the air gap is several orders of magnitude larger than that of the core, the magnetic resistance of the core can be ignored. The magnetic resistance of the side column is provided by the side column air gap, and the magnetic resistance of the middle column is provided by the middle column. The magnetic resistance is calculated by the formula The coupling coefficient has been calculated to be -0.24374. According to the formula The side column air gap l can be calculated gs and the middle column air gap l gc The relationship lgs = 1.2071*lc, according to the formula Calculate the numerical relationship N between the number of winding turns, the cross-sectional area of ​​the side column and the air gap 2 *A S =0.2484*l gc Since the current passing through the copper sheet is very large, the coupling inductance loss is mainly due to the winding loss. Therefore, controlling the number of winding turns is very important for controlling the loss. First, assume that the winding N is 1 turn. According to the inductance definition equation The number of turns is 1, the magnetic induction intensity is 400mT, the current is 33.3A, and the cross-sectional area A is calculated. S Equal to 16.65mm 2 , take a equal to 2mm, b equal to 8.5mm. According to the relationship between air gap and cross-sectional area, the air gap size can be determined. Take the middle column air gap lgc = 0.07mm. Now consider the magnetic resistance of the magnetic circuit and bring the determined core size parameters into the magnetic resistance calculation, where R S is the total reluctance of the side column, which is the sum of the core reluctance and the air gap reluctance, R C It is the sum of the magnetic resistance of the center column core and the air gap. Then, using formula (9), the air gap of the side column is calculated to be lgs = 0.08 mm.

[0065] Substitute the above determined parameters into the magnetic circuit to verify the magnitude of the magnetic induction intensity, and use equation group (6) and After calculation, the inductance L 1 44.5V flows through the inductor L 2 When the maximum current value of 33.3V flows through, the magnetic induction intensity of the middle column is 0.312T, and the magnetic induction intensity of the side column is 0.394T, which meets the set maximum value. Finally, the length, width and height of the designed planar coupled inductor are 16.4mm*8.5mm*6mm, which significantly reduces the size of the device while maintaining good electromagnetic properties.

[0066] It is to be understood that the present invention is described by some embodiments, and it is known to those skilled in the art that various changes or equivalent substitutions may be made to these features and embodiments without departing from the spirit and scope of the present invention. In addition, under the teachings of the present invention, these features and embodiments may be modified to adapt to specific circumstances and materials without departing from the spirit and scope of the present invention. Therefore, the present invention is not limited by the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the scope of protection of the present invention.

Claims

1. A method for miniaturizing an inductor suitable for a coupled inductor Buck converter, characterized in that: The design method couples two inductors on the basis of a 2N-order Buck converter, with a total of N pairs of coupled inductors, the self-inductance and mutual inductance of each pair of coupled inductors are the same, and there are a total of four working stages, that is, there are four sections of ripple; the current ripple amount at each stage of the coupled inductor is determined by solving the voltage balance equation at each stage of the coupled inductor; according to the relationship between the output voltage and the duty cycle of the 2N-order Buck converter, the four sections of current ripple are converted and weighted averaged to obtain the total inductor current ripple value, and the ripple value is derived to determine the optimal coupling coefficient value to ensure that the total inductor current effective value is the lowest, so that the Buck circuit works in a state with low loss; under the calculated coupling coefficient design requirements, according to the maximum current density J max and the maximum magnetic induction intensity B max According to the requirements, establish the number of turns N of the core winding and the cross-sectional area A of the side column S , window width and air gap size l gc Based on the mathematical model, a miniaturized planar coupled inductor core that meets the working conditions of the converter is designed.

2. The inductor miniaturization design method for a coupled inductor Buck converter according to claim 1, characterized in that: The current ripple amount at each stage of the coupled inductor is determined by solving the voltage balance equation at each stage of the coupled inductor. The specific steps include: The coupled inductor buck converter has four working stages in one cycle. The duration of each stage is represented by T1, T2, T3 and T4 respectively. A pair of coupled inductors is recorded as L1 and L2. The voltage on the inductor L1 in the four stages is V g -V C1 -V out , -V out , -V out , -V out , the four stages of inductance on inductor L2 are -V out , -V out 、V C1 -V C2 -V out , -V out , where V g Input voltage, V out Output voltage, V C1 and V C2 is the voltage across capacitors C1 and C2 in the circuit topology; the current in each stage is determined by the voltage across the inductor V L , the conduction time T and coupling coefficient M of each stage are determined; according to the voltage balance equation of the coupled inductor, the voltages v1 and v2 on the inductors L1 and L2 are listed, and the differentials of the currents i1 and i2 flowing through the inductors with respect to time t, the inductance L and the mutual inductance M are expressed as formulas (1) and (2). In the four working states, the voltage values ​​across the inductors in each state are respectively substituted, and the differentials of the voltage V across the inductors with respect to the currents of the two inductors with respect to time are obtained by solving formulas (1) and (2). The relationship between inductance L and mutual inductance M is obtained by integrating the current di in four states with time to obtain the current ripple value I on the inductor L1 in four states ripple1 , I ripple2 , I ripple3 and I ripple4 , expressed by formula (3)-formula (6); 3. The inductor miniaturization design method for a coupled inductor Buck converter according to claim 2, characterized in that: According to the relationship between the output voltage and duty cycle of the 2N-order Buck converter, the four-segment current ripple is converted and weighted averaged to obtain the total inductor current ripple value. The ripple value is derived to determine the optimal coupling coefficient value to ensure the minimum effective value of the total inductor current. The specific steps include: by calculating the total current ripple, the coupling coefficient is derived to obtain the minimum inductor current ripple; since the voltage across the inductors in the working states T2 and T4 is the same, the ripple change across the inductors is also the same, so I ripple2 =I ripple4 ; According to the 2N-order Buck converter output voltage V out Regarding the input voltage V in The relationship between the duty cycle d and the converter order N is Substitute into the current ripple expression of formula (3)-formula (6), and use the effective value formula Substitute the obtained four-stage inductor current ripple values ​​i in turn, solve the effective current values ​​of the four states, and calculate the total effective current value I by weighted average of the four-stage current effective values. rms , the total ripple current is given by formula (7), which gives the inductor current and switching period T s 、Input voltage V in , duty cycle d, step-down converter order N, coupling coefficient K and self-inductance L, where the coupling coefficient By taking the derivative of the effective value and setting its derivative to zero, the coupling coefficient corresponding to the minimum effective value of the current is obtained. The coupling coefficient is given by formula (8). The coupling coefficient at the minimum effective value of the inductor current is only related to the value of the duty cycle d. The coupling coefficient K is selected according to the value of the duty cycle d of the Buck converter.

4. The inductor miniaturization design method for a coupled inductor Buck converter according to claim 3, characterized in that: At the given maximum current density J max and the maximum magnetic induction intensity B max Under the requirements, the core design of the miniaturized planar coupled inductor is realized by the following steps: According to the magnetic flux distribution, the middle column magnetic flux Designed for the magnetic flux of both sides The sum of the current density and the width of the middle column is determined to be twice the width of the side column, that is, the cross-sectional area of ​​the middle column is twice the cross-sectional area of ​​the side column; according to the maximum current density J max According to the requirements of the current density relationship I = J * h * W, where h is the selected PCB copper thickness, the window width W is calculated to ensure that the current density is less than the set maximum current density value; the magnetic resistance in the magnetic circuit It is related to the magnetic path length l, magnetic permeability μ and cross-sectional area A, where the side column air gap is l gs , the air gap in the middle column is l gc , let the cross-sectional area of ​​the side column be A, the cross-sectional area of ​​the middle column is twice the cross-sectional area of ​​the side column, so the cross-sectional area of ​​the middle column is 2A, the value of the magnetic permeability u is a fixed value according to the selected core material, so the air gap magnetic resistance R of the left and right side columns in the magnetic circuit of the E-type core is calculated s and the middle column air gap magnetic resistance R C ; Using Ampere's circuit theorem, according to the magnetomotive force N*I and magnetic flux in the magnetic circuit The relationship between the magnetic resistance R and the equivalent magnetic circuit equations is listed as formula (9), where R s is the side column air gap reluctance, R C is the air gap reluctance of the middle column; solve for the magnetic flux and The law of electromagnetic induction is a system of equations The values ​​of self-inductance L, mutual inductance M and coupling coefficient K are obtained. The values ​​of self-inductance, mutual inductance and coupling coefficient are given by formula (10), formula (11) and formula (12). According to formula (10), the value of L with respect to the magnetic resistance R of the side column air gap is obtained. s and the middle column air gap magnetic resistance R C Substituting the value of magnetic resistance into the relationship between the inductance and the number of winding turns N, the side column air gap l gs 、Middle column air gap l gc and the cross-sectional area of ​​the side column A s The relationship between the coupling coefficient K and the side column air gap magnetic resistance R is obtained by formula (12). s and the middle column air gap magnetic resistance R C Substituting the value of the air gap magnetic resistance into the coupling coefficient, we can get that the coupling coefficient is only related to the side column air gap l hs The air gap between the center column and the gc The coupling coefficient K has been derived by derivation, so the precise side column air gap is l gs The air gap between the center column and the gc Numerical relationships; 5. The inductor miniaturization design method for a coupled inductor Buck converter according to claim 4, characterized in that: According to the maximum current density J max and the maximum magnetic induction intensity B max According to the requirements, establish the number of turns N of the core winding and the cross-sectional area A of the side column S , window width and air gap size l gc The mathematical model used to design the optimal size of the coupled inductor includes the following steps: Inductance is the target quantity of the design, and N is assumed to be only one turn; The ratio of the side column air gap to the middle column air gap is determined according to formula (12), and the air gap, the number of winding turns N, and the side column cross-sectional area A are determined by formula (10). S The relationship between the two is that we only need to know the cross-sectional area A of the side column. S All unknown quantities can be determined by the value of The magnetic induction intensity B is taken into the maximum value B of the design limit max , the value of N, we get the value of the cross-sectional area of ​​the side column A S When determining the air gap length, the magnetic resistance of the magnetic core is taken into account. According to formula (10), the inductance value, the number of winding turns N, and the side column air gap l are obtained. gs 、Middle column air gap l gc and the cross-sectional area of ​​the side column A S The relationship between the side column air gap l is determined gs 、Middle column air gap l gc The value of .

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