Dual-e type variable inductance design method based on coupling index

Abstract

The application discloses a double-E type variable inductance design method based on a coupling index, which comprises the following steps: 1) performing magnetic coupling analysis on the coupling problem of the main winding and the control winding of the double-E type variable inductance, and defining a coupling index reflecting the coupling degree of the double-E type variable inductance according to the analysis result; 2) designing the main winding turns according to the maximum alternating current magnetic flux density and the maximum inductance value of the double-E type variable inductance and in combination with the coupling index; 3) establishing an improved Brauer magnetization curve model, improving the accuracy of the knee point of the Brauer magnetization curve model by adopting a segmented function, determining the relationship between the minimum equivalent permeability and the maximum magnetic field strength, and designing the control winding turns in combination with the minimum inductance value; and 4) evaluating the coupling degree of the design result according to the coupling index, ensuring that the coupling degree is within an acceptable range, and completing the double-E type variable inductance design. The application solves the problem that the existing design method does not consider the winding coupling problem of the variable inductance in actual application.

Description

Technical Field

[0001] This invention relates to the technical field of variable inductor parameter design, and in particular to a dual-E type variable inductor design method based on coupling index. Background Technology

[0002] Variable inductors, with their continuously adjustable and controllable inductance, have attracted numerous researchers to conduct in-depth studies and are widely used in fields such as LED power supplies and resonant converters. Depending on their structure, variable inductors can be classified into double-E type, triple-E type, quadruple-U type, and voltage-controlled type, among others. The double-E type variable inductor, due to its simple structure, small size, and constant saturation level, has greater application advantages compared to other variable inductors.

[0003] Although the double-E variable inductor employs a symmetrical control winding structure, theoretically canceling the induced voltage generated by the main winding on the control winding, the nonlinear characteristics of the core magnetization curve and the asymmetry in the number of turns in the control winding due to manufacturing issues mean that an induced voltage still exists in the control winding, indicating coupling between the main winding and the control winding. Severe coupling can cause oscillations in the variable inductor control current, potentially leading to negative feedback failure; it can also increase the equivalent AC resistance of the main winding, causing a decrease in system efficiency; and it can distort the AC current flowing through the main winding, resulting in decreased reliability. Currently, the design methods for double-E variable inductors do not consider coupling issues; therefore, reducing the coupling degree of double-E variable inductors is a major problem that needs to be solved. Summary of the Invention

[0004] The purpose of this invention is to overcome the shortcomings and deficiencies of existing double-E type variable inductor design methods. It proposes a double-E type variable inductor design method based on coupling indices, addressing the problem that existing methods do not consider the winding coupling issues present in practical applications of variable inductors. This method, based on magnetic coupling analysis, defines a coupling index to effectively reflect the degree of coupling of the variable inductor and proposes an improved Brauer magnetization curve model. Combining the coupling index with the determination of the number of turns in the main winding and the control winding, a novel double-E type variable inductor design method is provided, ensuring that the degree of coupling of the variable inductor remains within an acceptable range.

[0005] To achieve the above objectives, the technical solution provided by this invention is: a design method for a double-E type variable inductor based on coupling indices, comprising the following steps:

[0006] 1) Perform magnetic coupling analysis on the coupling problem between the main winding and control winding of the double-E type variable inductor, and define a coupling index that reflects the degree of coupling of the double-E type variable inductor based on the analysis results;

[0007] 2) Based on the maximum AC magnetic flux density and maximum inductance of the double-E type variable inductor, the number of turns of the main winding is designed in conjunction with the coupling index;

[0008] 3) Establish an improved Brauer magnetization curve model, use piecewise functions to improve the accuracy of the Brauer magnetization curve model near the knee point, determine the relationship between the minimum equivalent permeability and the maximum magnetic field strength, and design the number of turns of the control winding in combination with the minimum inductance.

[0009] 4) Based on the coupling index, evaluate the degree of coupling of the design results to ensure that it is within an acceptable range and complete the design of the double-E type variable inductor.

[0010] Furthermore, in step 1), a magnetic coupling analysis is performed on the double-E type variable inductor and coupling indices are defined, including the following steps:

[0011] 1.1) Establish a double-E type variable inductor magnetic coupling model. The alternating current in the main winding generates an alternating magnetic flux in the magnetic core, and induces electromotive forces in opposite directions on the control windings on both sides:

[0012]

[0013] In the formula, e i It is the induced electromotive force generated by the control winding on one side, N DCi It is the actual number of turns of the control winding on one side, φ i It is the AC magnetic flux acting on a certain side of the control winding, t is time, i=1 indicates that it acts on the left control winding, i=2 indicates that it acts on the right control winding;

[0014] Due to the nonlinear characteristics of the core magnetization curve and the asymmetry in the number of turns of the control winding caused by manufacturing issues, an induced electromotive force exists in the control winding, thus resulting in a coupling current. Combining the magnetic circuit law and fundamental wave analysis, this induced electromotive force satisfies:

[0015]

[0016] In the formula, e1 is the induced electromotive force generated by the left control winding, e2 is the induced electromotive force generated by the right control winding, and N DC1 N is the actual number of turns in the control winding on the left. DC2 It is the actual number of turns of the control winding on the right, I r ω is the amplitude of the alternating current, μ is the angular frequency of the alternating current, and μ is the angular frequency of the alternating current. AC A is the equivalent permeability of the core column. e It is the equivalent area of ​​the magnetic core, l e It is the equivalent magnetic circuit length of the magnetic core;

[0017] 1.2) Based on the magnetic coupling analysis results of the double-E type variable inductor, the coupling index is defined as follows:

[0018]

[0019] In the formula, N DC It controls the number of turns in the winding, N AC It is the number of turns in the main winding, f s The operating frequency is the coupling index; the coupling index reflects the degree of coupling of the double-E type variable inductor. The smaller the coupling index, the lower the degree of coupling. Therefore, the coupling index can be used to evaluate the degree of coupling of the variable inductor.

[0020] Furthermore, in step 2), the number of turns of the main winding is designed, including the following steps:

[0021] 2.1) Select a suitable magnetic core model and confirm its basic parameters;

[0022] 2.2) To achieve the maximum inductance of the variable inductor, the number of turns in the main winding must satisfy the following:

[0023]

[0024] In the formula, L max R is the maximum inductance of the variable inductor. m It is a magnetic core reluctance;

[0025] 2.3) To prevent saturation of the variable inductor, an upper limit value B for the AC magnetic flux density is set. M The number of turns in the main winding must meet the following requirements:

[0026]

[0027] 2.4) Based on the coupling index, the number of turns in the main winding should be as small as possible. Therefore, the number of turns in the main winding is determined as follows:

[0028]

[0029] Furthermore, in step 3), the number of turns of the control winding is designed, including the following steps:

[0030] 3.1) When the inductance of the variable inductor drops to its minimum value, the equivalent permeability of the magnetic core is at its minimum. Based on the minimum and maximum inductance values ​​of the variable inductor, determine the required minimum equivalent permeability μ. min for:

[0031]

[0032] In the formula, μ i R is the initial permeability of the magnetic core, μ0 is the permeability of free space, and R is the initial permeability of the magnetic core. o It is the reluctance of the outer magnetic arm of the magnetic core, L min It is the minimum inductance value of the variable inductor, R. g It is the air gap reluctance of the magnetic core, R c It is the reluctance of the core column;

[0033] 3.2) The Brauer magnetization curve model is improved by using a piecewise function to enhance the accuracy near the knee point, thus obtaining the relationship between DC magnetic field strength and DC magnetic flux density:

[0034]

[0035] In the formula, B is the DC magnetic flux density, H(B) is the DC magnetic field strength H as a function of B, and c1, c2, and c3 are all Brauer magnetization curve model coefficients.

[0036] 3.3) Differentiating the improved Brauer magnetization curve model yields the relationship between equivalent permeability and DC magnetic flux density:

[0037]

[0038] In the formula, μ is the equivalent permeability;

[0039] Therefore, according to the minimum equivalent permeability μ min The maximum DC magnetic flux density B can be determined. max ;

[0040] 3.4) Combining the improved Brauer magnetization curve model, based on the maximum DC magnetic flux density B max Able to determine the maximum magnetic field strength H max Based on Maxwell's equations, the number of turns in the control winding is determined as follows:

[0041]

[0042] In the formula, l o It is the length of the magnetic circuit of the outer magnetic arm of the magnetic core, I DC It is a DC control current.

[0043] Furthermore, in step 4), the degree of coupling of the design results is evaluated, including the following steps:

[0044] Calculate the coupling index of the current design result. If the coupling index is less than 1000, the coupling degree of the design result is considered to be within an acceptable range, and the variable inductor design is completed. If the coupling index is greater than or equal to 1000, the coupling degree of the design result is considered to be within an unacceptable range, and return to step 2) to reselect a suitable magnetic core until the coupling degree of the design result is within an acceptable range, and the variable inductor design is completed.

[0045] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0046] 1. This invention provides the first quantitative analysis of the magnetic coupling mechanism of a variable inductor, overcoming the shortcomings of traditional qualitative analysis of the magnetic coupling of variable inductors.

[0047] 2. This invention proposes for the first time a coupling index that reflects the degree of coupling of a variable inductor. Based on the coupling index, the negative impact of the coupling of the double-E type variable inductor can be effectively reduced.

[0048] 3. Based on the coupling index, this invention considers the degree of coupling in the design process of variable inductor parameters, thus improving the shortcomings of the existing double-E type variable inductor parameter design method that ignores the coupling problem.

[0049] 4. This invention proposes for the first time an improved Brauer magnetization curve model, which uses a piecewise function to improve the accuracy of the magnetization curve model near the knee point. The number of control winding turns calculated based on this model is more accurate.

[0050] 5. This invention has wide applicability in the design of double-E type variable inductor parameters. The design process is intuitive and simple, and it has broad application prospects. Attached Figure Description

[0051] Figure 1 This is a flowchart illustrating the method of the present invention.

[0052] Figure 2 This is a schematic diagram of the magnetic coupling mechanism of a double-E type variable inductor.

[0053] Figure 3 This is a schematic diagram of the structural parameters of a double-E type variable inductor.

[0054] Figure 4 This is a schematic diagram of the equivalent magnetic circuit of a double-E type variable inductor.

[0055] Figure 5 A schematic diagram illustrating the error in the Brauer magnetization curve model. Detailed Implementation

[0056] The present invention will be further described in detail below with reference to the embodiments and accompanying drawings, but the embodiments of the present invention are not limited thereto.

[0057] The design specifications of the dual-E type variable inductor are shown in Table 1:

[0058] Table 1

[0059] parameter numerical values <![CDATA[Minimum sensing value L min > 8.4μH <![CDATA[Maximum sensing value L max > 28.9μH <![CDATA[Control current I DC > 0～1.8A <![CDATA[AC current amplitude I r > 2.8A <![CDATA[Operating frequency f s > 300kHz

[0060] like Figure 1 As shown in the figure, this embodiment discloses a design method for a dual-E type variable inductor based on coupling index, including the following steps:

[0061] 1) Perform magnetic coupling analysis on the coupling problem between the main winding and control winding of the double-E type variable inductor. Based on the analysis results, define a coupling index reflecting the degree of coupling of the double-E type variable inductor. The magnetic coupling analysis and definition of the coupling index for the double-E type variable inductor include the following steps:

[0062] 1.1) Establish a double-E type variable inductor magnetic coupling model, such as... Figure 2 As shown, the magnetic coupling mechanism of a variable inductor is analyzed. The alternating current i in the main winding... r An alternating magnetic flux φ is generated in the magnetic core. AC According to the law of magnetic circuits, φ AC The flux is divided into φ1 and φ2, flowing through the two magnetic arms respectively. According to the law of electromagnetic induction, the alternating magnetic flux generates induced electromotive forces in opposite directions on the two magnetic arms:

[0063]

[0064] In the formula, e i It is the induced electromotive force generated by the control winding on one side, N DCi It is the actual number of turns of the control winding on one side, φ i It is the AC magnetic flux acting on a certain side of the control winding, t is time, i=1 indicates that it acts on the left control winding, and i=2 indicates that it acts on the right control winding.

[0065] Due to the nonlinear characteristics of the core magnetization curve and the asymmetry in the number of turns of the control winding caused by manufacturing processes, an induced electromotive force |e1-e2| exists in the control winding, resulting in a coupling current |i1-i2|. From mathematical inequalities, we know that:

[0066] |e1-e2|≤|e1|+|e2|=e1+e2

[0067] In the formula, e1 is the induced electromotive force generated by the left control winding, and e2 is the induced electromotive force generated by the right control winding.

[0068] The sum of the induced electromotive forces of the two control windings is expressed as:

[0069]

[0070] In the formula, μ AC It is the equivalent permeability of the core pillar, N. DC1 N is the actual number of turns in the control winding on the left. DC2 H is the actual number of turns of the control winding on the right side. AC It is the strength of the alternating magnetic field generated by the alternating current, A e It is the equivalent area of ​​the magnetic core.

[0071] Combining the magnetic circuit law and the fundamental wave analysis method, we can obtain:

[0072]

[0073] In the formula, I r ω is the amplitude of the alternating current, ω is the angular frequency of the alternating current, and l e It is the equivalent magnetic circuit length of the magnetic core.

[0074] 1.2) Based on the magnetic coupling analysis results of the double-E type variable inductor, the coupling index is defined as follows:

[0075]

[0076] In the formula, N DC It controls the number of turns in the winding, N AC It is the number of turns in the main winding, f s It refers to the operating frequency, measured in kHz, and the equivalent area of ​​the magnetic core, A. e The unit is mm. 2 The equivalent magnetic circuit length l of the magnetic core e The unit is mm.

[0077] The coupling index reflects the degree of coupling in a double-E type variable inductor; the smaller the coupling index, the lower the coupling degree. Therefore, the coupling degree of a variable inductor can be evaluated based on the coupling index. The coupling index shows that the coupling degree of a variable inductor is affected by the number of turns in the main winding, the number of turns in the control winding, the AC current amplitude, the operating frequency, and the core size.

[0078] 2) Based on the maximum AC flux density and maximum inductance of the double-E type variable inductor, and in conjunction with the coupling index, design the number of turns N of the main winding. AC This includes the following steps:

[0079] 2.1) In this embodiment, DMR95-EE33 is initially selected as the variable inductor core, and the relevant structural parameters are as follows: Figure 3 As shown.

[0080] 2.2) As Figure 4 As shown, determining the minimum number of turns in the main winding based on the maximum inductance value requires calculating the variable inductor reluctance R. m :

[0081]

[0082] In the formula, R g It is the air gap reluctance, R c It is the reluctance of the core column, R o It is the magnetic reluctance of the outer magnetic arm of the magnetic core, l g It is the air gap length, which is taken as 0.4 mm in this embodiment, μ0 is the vacuum permeability, and l c It is the length of the magnetic circuit in the core, μ i It is the initial permeability of the magnetic core, A cIt is the area of ​​the cylinder in the magnetic core, l o A is the length of the magnetic circuit of the outer magnetic arm of the magnetic core. o It is the area of ​​the outer magnetic arm of the magnetic core.

[0083] To achieve the maximum inductance of the variable inductor, the number of turns in the main winding must meet the following requirements:

[0084]

[0085] In the formula, L max It is the maximum inductance value of the variable inductor;

[0086] 2.3) To prevent saturation of the variable inductor, an upper limit value B for the AC magnetic flux density is set. M Generally, the value is taken as 0.1T to 0.2T. In this embodiment, 0.1T is used. The number of turns in the main winding must meet the following requirements:

[0087]

[0088] 2.4) Based on the coupling index, the number of turns in the main winding should be as small as possible; therefore, the number of turns in the main winding is determined as follows:

[0089]

[0090] 3) Establish an improved Brauer magnetization curve model, use piecewise functions to improve the accuracy of the Brauer magnetization curve model near the knee point, determine the relationship between the minimum equivalent permeability and the maximum magnetic field strength, and design the number of turns N of the control winding in combination with the minimum inductance value. DC This includes the following steps:

[0091] 3.1) When a control current is applied to the control winding, the equivalent permeability of the outer ring of the magnetic core decreases, and the inductance decreases. The minimum inductance is expressed as:

[0092]

[0093] In the formula, μ min It is the minimum equivalent permeability of the outer ring of the magnetic core corresponding to the minimum inductance value.

[0094] Based on the minimum and maximum inductance values ​​of the variable inductor, the required minimum equivalent permeability is determined as follows:

[0095]

[0096] 3.2) As Figure 5 As shown, an improved Brauer magnetization curve model is established, and a piecewise function is used to improve the accuracy of the magnetization curve model near the knee point, thus obtaining the relationship between DC magnetic field strength and DC magnetic flux density:

[0097]

[0098] In the formula, B is the DC magnetic flux density, H(B) is the DC magnetic field strength H as a function of B, and c1, c2, and c3 are Brauer magnetization curve model coefficients, which are taken as 0.059, 34.345, and 156.739 respectively in this embodiment.

[0099] 3.3) Differentiating the improved Brauer magnetization curve model yields the relationship between equivalent permeability and DC magnetic flux density:

[0100]

[0101] In the formula, μ is the equivalent permeability;

[0102] Therefore, according to the minimum equivalent permeability μ min The maximum DC magnetic flux density B can be determined. max .

[0103] 3.4) Combining the magnetization curve model, based on the maximum DC magnetic flux density B max The maximum magnetic field strength H can be determined. max Based on Maxwell's equations, the number of turns in the control winding is determined as follows:

[0104]

[0105] 4) Based on the coupling index, evaluate the degree of coupling of the design results to ensure it is within an acceptable range, and complete the double-E type variable inductor design; the evaluation of the degree of coupling of the design results includes the following steps:

[0106] Calculate the coupling index of the current design results:

[0107]

[0108] If the coupling index of the current design result is less than 1000, the coupling degree of the design result is considered to be within an acceptable range, and the variable inductor design is completed. If the coupling index is greater than or equal to 1000, the coupling degree of the design result is considered to be within an unacceptable range, and the process returns to step 2), a suitable magnetic core is selected again, until the coupling degree of the design result is within an acceptable range, and the variable inductor design is completed.

[0109] By using the above steps, the parameters of the double-E type variable inductor were determined, and the parameter design for effectively reducing the coupling degree of the variable inductor based on the coupling index was completed.

[0110] In summary, after adopting the above solutions, the present invention is more reasonable and feasible in practical applications, can effectively reduce the coupling degree of the double E-type variable inductor, has a simple design, broad application prospects, and is worth promoting.

[0111] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A design method for a double-E type variable inductor based on coupling indices, characterized in that, Includes the following steps: 1) Perform magnetic coupling analysis on the coupling problem between the main winding and control winding of the double-E type variable inductor. Based on the analysis results, define a coupling index reflecting the degree of coupling of the double-E type variable inductor, including the following steps: 1.1) Establish a double-E type variable inductor magnetic coupling model. The alternating current in the main winding generates an alternating magnetic flux in the magnetic core, and induces electromotive forces in opposite directions on the control windings on both sides: ； In the formula, e i It is the induced electromotive force generated by the control winding on one side. It is the actual number of turns of the control winding on one side, ϕ i It is the AC magnetic flux acting on a certain side of the control winding, t is time, i=1 indicates that it acts on the left control winding, and i=2 indicates that it acts on the right control winding; Due to the nonlinear characteristics of the core magnetization curve and the asymmetry in the number of turns of the control winding caused by manufacturing issues, an induced electromotive force exists in the control winding, thus resulting in a coupling current. Combining the magnetic circuit law and fundamental wave analysis, this induced electromotive force satisfies: ； In the formula, e1 is the induced electromotive force generated by the left control winding, e2 is the induced electromotive force generated by the right control winding, and N DC1 N is the actual number of turns in the control winding on the left. DC2 It is the actual number of turns of the control winding on the right, I r ω is the amplitude of the alternating current, μ is the angular frequency of the alternating current, and μ is the angular frequency of the alternating current. AC A is the equivalent permeability of the core column. e It is the equivalent area of ​​the magnetic core, l e It is the equivalent magnetic circuit length of the magnetic core; 1.2) Based on the magnetic coupling analysis results of the double-E type variable inductor, the coupling index is defined as follows: ； In the formula, N DC It controls the number of turns in the winding, N AC It is the number of turns in the main winding, f s It is the operating frequency; the coupling index can reflect the degree of coupling of the double-E type variable inductor. The smaller the coupling index, the lower the degree of coupling. Therefore, the coupling index can be used to evaluate the degree of coupling of the variable inductor. 2) Based on the maximum AC magnetic flux density and maximum inductance of the double-E type variable inductor, and in combination with the coupling index, design the number of turns of the main winding; 3) Establish an improved Brauer magnetization curve model, use piecewise functions to improve the accuracy of the Brauer magnetization curve model near the knee point, determine the relationship between the minimum equivalent permeability and the maximum magnetic field strength, and design the number of turns of the control winding in combination with the minimum inductance. 4) Based on the coupling index, evaluate the degree of coupling of the design results to ensure that it is within an acceptable range and complete the design of the double-E type variable inductor.

2. The design method for a dual-E type variable inductor based on coupling index according to claim 1, characterized in that, In step 2), the number of turns of the main winding is designed. Includes the following steps: 2.1) Select a suitable magnetic core model and confirm its basic parameters; 2.2) To achieve the maximum inductance of the variable inductor, the number of turns in the main winding must satisfy the following: ； In the formula, L max R is the maximum inductance of the variable inductor. m It is a magnetic core reluctance; 2.3) To prevent saturation of the variable inductor, an upper limit value B for the AC magnetic flux density is set. M The number of turns in the main winding must meet the following requirements: ； 2.4) Based on the coupling index, the number of turns in the main winding should be as small as possible. Therefore, the number of turns in the main winding is determined as follows: 。 3. The design method for a dual-E type variable inductor based on coupling index according to claim 2, characterized in that, In step 3), the number of turns of the control winding is designed, including the following steps: 3.1) When the inductance of the variable inductor drops to its minimum value, the equivalent permeability of the magnetic core is at its minimum. Based on the minimum and maximum inductance values ​​of the variable inductor, determine the required minimum equivalent permeability μ. min for: ； In the formula, μ i R is the initial permeability of the magnetic core, μ0 is the permeability of free space, and R is the initial permeability of the magnetic core. o It is the reluctance of the outer magnetic arm of the magnetic core, L min It is the minimum inductance value of the variable inductor, R. g It is the air gap reluctance of the magnetic core, R c It is the reluctance of the core column; 3.2) The Brauer magnetization curve model is improved by using a piecewise function to enhance the accuracy near the knee point, thus obtaining the relationship between DC magnetic field strength and DC magnetic flux density: ； In the formula, B is the DC magnetic flux density, H(B) is the DC magnetic field strength H as a function of B, and c1, c2, and c3 are all Brauer magnetization curve model coefficients. 3.3) Differentiating the improved Brauer magnetization curve model yields the relationship between equivalent permeability and DC magnetic flux density: ； In the formula, μ is the equivalent permeability; Therefore, according to the minimum equivalent permeability μ min The maximum DC magnetic flux density B can be determined. max ; 3.4) Combining the improved Brauer magnetization curve model, based on the maximum DC magnetic flux density B max Able to determine the maximum magnetic field strength H max Based on Maxwell's equations, the number of turns in the control winding is determined as follows: ； In the formula, l o It is the length of the magnetic circuit of the outer magnetic arm of the magnetic core, I DC It is a DC control current.

4. The design method for a dual-E type variable inductor based on coupling index according to claim 3, characterized in that, In step 4), the degree of coupling of the design results is evaluated, including the following steps: Calculate the coupling index of the current design result. If the coupling index is less than 1000, the coupling degree of the design result is considered to be within an acceptable range, and the variable inductor design is completed. If the coupling index is greater than or equal to 1000, the coupling degree of the design result is considered to be within an unacceptable range, and return to step 2) to reselect a suitable magnetic core until the coupling degree of the design result is within an acceptable range, and the variable inductor design is completed.

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