Method for calculating magnetic conductivity of ferrite core with circular cross section in annular inductor

Abstract

The invention relates to the technical field of magnetic conductivity calculation, and discloses a magnetic conductivity calculation method for a ferrite core with a circular cross section in an annular inductor. When the magnetic field intensity is calculated, high-frequency analysis is carried out based on a Maxwell equation set, a virtual quantity Bessel equation is deduced and obtained based on the characteristic that the magnetic field in a ferrite magnetic core with a circular cross section in the annular inductor is uniform and based on a cylindrical coordinate system, and a magnetic field intensity calculation model is solved and obtained. The limitation that a traditional measuring method needs to depend on a measuring device is broken through. When the electric field intensity is calculated, an electric field intensity calculation model is obtained based on the relationship between the electric field intensity and the magnetic field intensity in the Maxwell equation set. And calculating the complex power of the annular inductor based on the calculated magnetic field intensity and electric field intensity, and obtaining a magnetic conductivity prediction model in combination with the equivalent circuit model. The method is based on calculation of a theoretical model, is not limited by a specific frequency band and a measuring instrument, is also applicable in a high-frequency range, and is more accurate in magnetic conductivity prediction.

Description

Technical Field

[0001] The present invention relates to the technical field of magnetic permeability calculation, and particularly to a method for calculating the magnetic permeability of a ferrite core with a circular cross-section in a toroidal inductor. Background Art

[0002] In switched-mode power converters, ferrite cores are widely used in high-frequency transformers and inductors. To miniaturize these devices, it is necessary to reduce the volume of the core. To enable these miniaturized cores with reduced volume to have the same power handling capacity as before, the operating frequency of these devices inevitably needs to be increased; however, increasing the operating frequency will result in higher core losses, and core losses will directly affect the efficiency and performance of magnetic devices. Therefore, for circuit designers, accurately determining core losses is very important.

[0003] In the evaluation of core losses, the theoretical analysis method is more effective and important. To conduct a theoretical evaluation of core losses, researchers need to obtain the value of the magnetic permeability of the ferrite core in advance. The value of the magnetic permeability is a key input parameter for theoretical evaluation and optimized design of ferrite devices. What is usually provided in the manufacturer's data sheet is the initial magnetic permeability, while the actual true magnetic permeability value will change with different operating frequencies and core sizes. Therefore, it is particularly important to determine the value of the true magnetic permeability for specific magnetic devices.

[0004] Currently, there are several magnetic permeability measurement devices on the market, such as impedance analysis method, transmission line method, resonant cavity method, vibrating sample magnetometer, superconducting quantum interference device, magneto-optical effect method, and nuclear magnetic resonance method. These several measurement methods all have high limitations, all rely on expensive measuring instruments, and have high-frequency uncertainty, only applicable to a certain frequency band, with certain limitations.

[0005] The existing magnetic permeability calculation methods that do not require the aid of a measuring instrument are for calculating a toroidal ferrite core with a square cross-section. Since there are corners in the toroidal core with a square cross-section, magnetic field concentration or non-uniformity may occur at the corners. Therefore, when facing a toroidal ferrite core with a circular cross-section where the magnetic field distribution is uniform, the calculation method established based on the non-uniform magnetic field characteristics of the core with a square cross-section cannot be directly applied to calculate the magnetic permeability of the core with a circular cross-section. In scenarios such as rotating equipment like generators, where this kind of core needs to rotate or requires an omnidirectional magnetic field, a core with a circular cross-section must be used. Therefore, a calculation method that can more accurately calculate the magnetic permeability of a core with a circular cross-section is needed. Summary of the Invention

[0006] Therefore, the technical problem to be solved by the present invention is to overcome the problem that the prior art cannot calculate the magnetic permeability of a core with a circular cross-section.

[0007] To solve the above technical problems, the present invention provides a method for calculating the permeability of a circular cross-section ferrite core in a toroidal inductor, including:

[0008] Performing high-frequency analysis on the circular cross-section ferrite core to obtain the corresponding Maxwell's equations;

[0009] Based on the cylindrical coordinate system and Maxwell's equations, obtaining the initial expression of the magnetic field strength with respect to the radius, and performing curl calculation to obtain the corresponding curl expression;

[0010] Performing curl calculation on the curl expression again to obtain the second curl expression, and combining with Maxwell's equations to obtain the second curl complex expression;

[0011] Based on Maxwell's equations and the second curl complex expression, constructing magnetic field parameters; based on the second curl complex expression and the magnetic field parameters, constructing and solving the imaginary argument Bessel equation of the magnetic field strength to obtain the exact solution as the magnetic field strength calculation model;

[0012] Based on Maxwell's equations, obtaining the correlation relationship between the electric field strength and the magnetic field strength; based on the correlation relationship and the magnetic field strength calculation model, obtaining the electric field strength calculation model;

[0013] Inputting the specification parameters of the circular cross-section ferrite core and the effective value of the supply current of the toroidal inductor into the magnetic field strength calculation model and the electric field strength calculation model to obtain the magnetic field strength and the electric field strength at the radius r on the circular cross-section ferrite core;

[0014] Integrating the magnetic field strength and the electric field strength at each radius position on the circular cross-section ferrite core to calculate and obtain the complex power of the toroidal inductor;

[0015] Based on the specification parameters of the circular cross-section ferrite core, the effective value of the supply current of the toroidal inductor, and the complex power, calculating and obtaining the true permeability of the toroidal inductor.

[0016] Preferably, performing high-frequency analysis on the circular cross-section ferrite core to obtain the Maxwell's equations of the magnetoquasistatic system, including:

[0017] Ampere's circuital law:

[0018] Faraday's law of electromagnetic induction:

[0019] Gauss's law of magnetism:

[0020] Gauss's law of electricity:

[0021] Among them, H represents the magnetic field strength, E represents the electric field strength, B represents the magnetic induction intensity, D represents the electric displacement vector, J c represents the current density, j represents the imaginary unit, ω represents the angular frequency, ρ v represents the charge density.

[0022] Preferably, based on the cylindrical coordinate system and Maxwell's equations, an initial expression of the magnetic field strength with respect to the radius is obtained, and the curl calculation is performed to obtain the corresponding curl expression, including:

[0023] Based on the cylindrical coordinate system and Maxwell's equations, the initial expression of the magnetic field strength H with respect to the radius r is obtained, expressed as:

[0024] H = H(r)e z ;

[0025] Based on the initial expression, the curl calculation is performed to obtain the corresponding curl expression, expressed as:

[0026]

[0027] Among them, H(r) represents the magnetic field strength at the radius r on the circular cross-section ferrite core, e z represents the unit vector in the z-axis direction, e θ represents the unit vector in the θ-axis direction.

[0028] Preferably, the curl of the curl expression is calculated again to obtain the second curl expression, and combined with the electromagnetic induction theorem in Maxwell's equations, the second curl complex expression is obtained, including:

[0029] The curl of the curl expression is calculated again to obtain the second curl expression, expressed as:

[0030]

[0031] Based on the second curl expression and Maxwell's equations, the second curl complex expression is obtained, expressed as:

[0032]

[0033] Among them, μ represents the initial permeability, σ represents the conductivity, and ε represents the permittivity.

[0034] Preferably, based on Maxwell's equations and the second curl complex expression, the magnetic field parameters are constructed; based on the second curl complex expression and the magnetic field parameters, the imaginary argument Bessel equation of the magnetic field strength is constructed, including:

[0035] Based on Maxwell's equations and the second curl complex expression, the magnetic field parameter k is constructed, expressed as:

[0036]

[0037] Based on the quadratic curl complex expression and magnetic field parameters, a Bessel equation of imaginary argument for the magnetic field intensity is constructed, expressed as:

[0038]

[0039] Preferably, solve the Bessel equation of imaginary argument to obtain an exact solution as the magnetic field intensity calculation model, including:

[0040] Obtain the general solution of the Bessel equation of imaginary argument containing undetermined coefficients c1 and c2, expressed as:

[0041] H(r) = c1I0(kr) + c2K0(kr);

[0042] I0(kr) is the zero-order Bessel function of the first kind of imaginary argument, and its expression is:

[0043]

[0044] K0(kr) is the zero-order Bessel function of the second kind of imaginary argument, and its expression is:

[0045]

[0046] When the radius r of the circular cross-section ferrite core is 0, K0(0) = ∞, c2 = 0, and the general solution of the Bessel equation of imaginary argument is simplified to:

[0047] H(r) = c1I0(kr);

[0048] When the radius r of the circular cross-section ferrite core is r = R,

[0049] Substitute the boundary condition of r = R into H(r) = c1I0(kr) to obtain the undetermined coefficient

[0050] Based on the undetermined coefficients c1 and c2, obtain the exact solution of the Bessel equation of imaginary argument, expressed as:

[0051]

[0052] The magnetic field intensity calculation model is expressed as:

[0053] Among them, Γ represents the gamma function, and R1 and R2 respectively represent the outer radius and inner radius of the circular cross-section ferrite core.

[0054] Preferably, the specification parameters of the circular cross-section ferrite core include: the average circumferential perimeter of the circular cross-section ferrite core, the number of turns of the core winding, the area of the circular cross-section, the outer radius and the inner radius.

[0055] Preferably, based on Maxwell's equations, the correlation relation between the electric field strength and the magnetic field strength is obtained; based on the correlation relation and the magnetic field strength calculation model, the electric field strength calculation model is obtained, including:

[0056] Based on Maxwell's equations, the correlation relation between the electric field strength and the magnetic field strength is obtained, expressed as:

[0057]

[0058] Based on the correlation relation and the magnetic field strength calculation model, the electric field strength calculation model is obtained, expressed as:

[0059]

[0060] where I1(kr) represents the first kind of Bessel function of the first order with imaginary argument.

[0061] Preferably, by integrating the magnetic field strength and the electric field strength at each radius position on the circular cross-section ferrite core, the complex power of the toroidal inductor is calculated, expressed as:

[0062] S = ∫∫∫σ|E| 2 dV + jω(∫∫∫μ|H| 2 dV - ∫∫∫ε|E| 2 dV).

[0063] Preferably, the acquisition of the permeability prediction model includes:

[0064] The toroidal inductor is equivalent to an equivalent circuit in which a resistor and an inductor are connected in series. Based on the equivalent resistance and the equivalent inductance in the equivalent circuit, the equivalent permeability calculation model is obtained, expressed as: μ c = μ′ - jμ″;

[0065] Based on the relationship between the equivalent inductance L and the real part μ′ of the permeability, the real part expression is obtained, expressed as:

[0066]

[0067] Based on the relationship between the equivalent resistance R and the imaginary part μ″ of the permeability, the imaginary part expression is obtained, expressed as:

[0068]

[0069] The power of the toroidal inductor satisfies: S = I 2 (R + jωL);

[0070] Based on the conditions satisfied by the real part expression, the imaginary part expression and the power of the toroidal inductor, the real part Re(S) and the imaginary part Im(S) of the complex power are obtained, expressed as: Re(S)=I 2 R, Im(S)=I 2 ωL;

[0071] Substitute the real part and the imaginary part of the complex power into the equivalent permeability calculation model to obtain the permeability prediction model, expressed as:

[0072] where μ c represents the permeability, S represents the complex power of the toroidal inductor to be measured, Im(S) and Re(S) respectively represent the imaginary part and the real part of the complex power, and j represents the imaginary unit; l, N and A respectively represent the average circumferential perimeter, the number of turns and the cross-sectional area of the circular cross-section ferrite core, and ω and I respectively represent the supply frequency and the effective value of the supply current.

[0073] The above technical solution of the present invention has the following beneficial effects compared with the prior art:

[0074] In the method for calculating the permeability of the circular cross-section ferrite core in the toroidal inductor of the present invention, the characteristic that the magnetic field distribution in the circular cross-section ferrite core is uniform is considered during the calculation process, so that the constructed magnetic field strength calculation model and the electric field strength calculation model are more applicable to the circular cross-section ferrite core, and thus the calculated permeability is more accurate. When calculating the magnetic field strength in the present invention, high-frequency analysis is carried out based on Maxwell's equations, and based on the characteristic that the magnetic field in the circular cross-section ferrite core of the toroidal inductor is uniform, and based on the cylindrical coordinate system, the Bessel equation of imaginary argument is derived and solved to obtain the magnetic field strength calculation model, breaking through the limitation that the traditional measurement method needs to rely on the measurement device. When calculating the electric field strength, the electric field strength calculation model is obtained based on the relationship between the electric field strength and the magnetic field strength in Maxwell's equations. In the present invention, by substituting the specification parameters of the magnetic core into the calculation model, the magnetic field strength and the electric field strength can be calculated. Based on the calculated magnetic field strength and electric field strength, the complex power of the toroidal inductor is calculated, and then combined with the equivalent circuit model, the permeability prediction model is obtained. The calculation based on the theoretical model in the present invention is not limited by a specific frequency band and a measuring instrument, and is also applicable in the high-frequency range; and based on the characteristic that the magnetic field in the circular cross-section ferrite core is uniform, the magnetic field strength and the electric field strength are calculated, so that the permeability prediction model is completely applicable to the circular cross-section ferrite core, and the predicted permeability is more accurate. Furthermore, based on the accurate permeability of the circular cross-section ferrite core, the core loss is evaluated to improve the working efficiency and performance of the magnetic device. Description of the Drawings

[0075] In order to make the content of the present invention easier to be clearly understood, the following further details the present invention according to specific embodiments of the present invention in conjunction with the accompanying drawings, where:

[0076] Figure 1 It is a step flowchart of a method for calculating the permeability of a circular cross-section ferrite core in the toroidal inductor provided by the present invention;

[0077] Figure 2 (a) of is a schematic diagram of a toroidal inductor; Figure 2 (b) of is an equivalent circuit diagram of the toroidal inductor. Specific Embodiments

[0078] The following further illustrates the present invention in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present invention and be able to implement it, but the embodiments cited do not limit the present invention.

[0079] Refer to Figure 1 As shown, the step flowchart of the method for calculating the permeability of a circular cross-section ferrite core in the toroidal inductor provided by the present invention, the specific steps include:

[0080] S101: Perform high-frequency analysis on the circular cross-section ferrite core to obtain the Maxwell equations of the magnetic quasi-static system, including:

[0081] Ampere's circuital law:

[0082] Faraday's law of electromagnetic induction:

[0083] Gauss's law of magnetism:

[0084] Gauss's law of electricity:

[0085] where H represents the magnetic field strength, E represents the electric field strength, B represents the magnetic induction intensity, D represents the electric displacement vector, J c represents the current density, j represents the imaginary unit, ω represents the angular frequency, ρ v represents the charge density.

[0086] S102: Based on the cylindrical coordinate system and the Maxwell equations, obtain the initial expression of the magnetic field strength with respect to the radius, and perform curl calculation to obtain the corresponding curl expression, including:

[0087] S102-1: Based on the cylindrical coordinate system and the Maxwell equations, obtain the initial expression of the magnetic field strength H with respect to the radius r, expressed as: H = H(r)e z ;

[0088] S102-2: Calculate the curl based on the initial expression to obtain the corresponding curl expression, expressed as:

[0089] where H(r) represents the magnetic field strength at radius r on the circular cross-section ferrite core, and e z represents the unit vector in the z-axis direction, and e θ represents the unit vector in the θ-axis direction.

[0090] S103: Calculate the curl of the curl expression again to obtain the second curl expression, and combine with Maxwell's equations to obtain the second curl complex expression, including:

[0091] S103-1: Calculate the curl of the curl expression again to obtain the second curl expression, expressed as:

[0092]

[0093] S103-2: Based on the second curl expression and Maxwell's equations, obtain the second curl complex expression, expressed as:

[0094]

[0095] where μ represents the initial permeability, σ represents the conductivity, and ε represents the permittivity.

[0096] S104: Construct magnetic field parameters based on Maxwell's equations and the second curl complex expression; construct and solve the imaginary Bessel equation of the magnetic field strength based on the second curl complex expression and the magnetic field parameters to obtain the exact solution as the magnetic field strength calculation model;

[0097] S105: Obtain the correlation relationship between the electric field strength and the magnetic field strength based on Maxwell's equations; obtain the electric field strength calculation model based on the correlation relationship and the magnetic field strength calculation model;

[0098] S106: Input the specification parameters of the circular cross-section ferrite core and the effective value of the supply current of the toroidal inductor into the magnetic field strength calculation model and the electric field strength calculation model to obtain the magnetic field strength and the electric field strength at radius r on the circular cross-section ferrite core;

[0099] S107: Integrate the magnetic field strength and the electric field strength at each radius position on the circular cross-section ferrite core to calculate and obtain the complex power of the toroidal inductor, expressed as:

[0100] S = ∫∫∫σ|E| 2 dV + jω(∫∫∫μ|H| 2 dV - ∫∫∫ε|E| 2 dV);

[0101] S108: Calculate and obtain the true permeability of the toroidal inductor based on the specification parameters of the ferrite core with a circular cross-section, the effective value of the supply current of the toroidal inductor, and the complex power.

[0102] Specifically, in step S104, obtaining the magnetic field strength calculation model includes:

[0103] S104-1: Based on Maxwell's equations and the quadratic curl complex expression, construct the magnetic field parameter k, expressed as:

[0104] S104-2: Based on the quadratic curl complex expression and the magnetic field parameter, construct the imaginary argument Bessel equation of the magnetic field strength, expressed as:

[0105] S104-3: Obtain the general solution of the imaginary argument Bessel equation containing the undetermined coefficients c1 and c2, expressed as:

[0106] H(r) = c1I0(kr) + c2K0(kr);

[0107] I0(kr) is the zero-order first-kind Bessel function of the imaginary argument, and the expression is:

[0108]

[0109] K0(kr) is the zero-order second-kind Bessel function of the imaginary argument, and the expression is:

[0110]

[0111] S104-4: When the radius r of the ferrite core with a circular cross-section is 0, K0(0) = ∞, c2 = 0, and the general solution of the imaginary argument Bessel equation is simplified to: H(r) = c1I0(kr);

[0112] S104-5: When the radius r of the ferrite core with a circular cross-section is r = R,

[0113] S104-6: Substitute the boundary condition of r = R into H(r) = c1I0(kr) to obtain the undetermined coefficient

[0114] S104-7: Based on the undetermined coefficients c1 and c2, obtain the exact solution of the imaginary argument Bessel equation, expressed as:

[0115] Therefore, the magnetic field strength calculation model is expressed as:

[0116] Wherein, Γ represents the gamma function, and R1 and R2 respectively represent the outer peripheral radius and the inner peripheral radius of the ferrite core with a circular cross-section.

[0117] The specification parameters of the ferrite core with a circular cross-section include: the average circumferential perimeter of the ferrite core with a circular cross-section, the number of turns of the core winding, the area of the circular cross-section, the outer peripheral radius, and the inner peripheral radius.

[0118] Specifically, in S105, the obtaining of the electric field strength calculation model includes:

[0119] S105-1: Based on Maxwell's equations, obtain the correlation relation between the electric field strength and the magnetic field strength, expressed as:

[0120] S105-2: Based on the correlation relation and the magnetic field strength calculation model, obtain the electric field strength calculation model, expressed as:

[0121] Wherein, I1(kr) represents the first-order Bessel function of the first kind with imaginary argument.

[0122] In the method for calculating the magnetic permeability of the ferrite core with a circular cross-section in the toroidal inductor of the present invention, the characteristic of uniform magnetic field distribution in the ferrite core with a circular cross-section is considered during the calculation process, so that the constructed magnetic field strength calculation model and electric field strength calculation model are more applicable to the ferrite core with a circular cross-section, and thus the calculated magnetic permeability is more accurate. When calculating the magnetic field strength in the present invention, high-frequency analysis is carried out based on Maxwell's equations. Based on the characteristic of uniform magnetic field in the ferrite core with a circular cross-section in the toroidal inductor, the Bessel equation with imaginary argument is derived and solved in the cylindrical coordinate system to obtain the magnetic field strength calculation model, breaking through the limitation that the traditional measurement method needs to rely on a measurement device. When calculating the electric field strength, the electric field strength calculation model is obtained based on the relationship between the electric field strength and the magnetic field strength in Maxwell's equations.

[0123] Specifically, in step S108, calculating and obtaining the true magnetic permeability of the toroidal inductor includes:

[0124] S108-1: Equivalent the toroidal inductor to an equivalent circuit in which a resistor and an inductor are connected in series. Based on the equivalent resistance and equivalent inductance in the equivalent circuit, obtain the equivalent magnetic permeability calculation model, expressed as: μ c = μ′ - jμ″;

[0125] S108-2: Based on the relationship between the equivalent inductance L and the real part μ′ of the magnetic permeability, obtain the real part expression, expressed as:

[0126] S108-3: Based on the relationship between the equivalent resistance R and the imaginary part μ” of the magnetic permeability, obtain the expression of the imaginary part, expressed as:

[0127] S108-4: The power of the toroidal inductor satisfies: S = I 2 (R + jωL);

[0128] Based on the real part expression, the imaginary part expression and the condition satisfied by the power of the toroidal inductor, obtain the real part Re(S) and the imaginary part Im(S) of the complex power, expressed as: Re(S) = I 2 R, Im(S) = I 2 ωL;

[0129] S108-5: Substitute the real part and the imaginary part of the complex power into the equivalent magnetic permeability calculation model to obtain the magnetic permeability prediction model, expressed as:

[0130] S108-6: Substitute the specification parameters of the circular cross-section ferrite core, the effective value of the supply current of the toroidal inductor and the complex power into the magnetic permeability prediction model to obtain the true magnetic permeability of the toroidal inductor;

[0131] where, μ c represents the magnetic permeability, S represents the complex power of the toroidal inductor to be measured, Im(S) and Re(S) respectively represent the imaginary part and the real part of the complex power, and j represents the imaginary unit; l, N and A respectively represent the average circumferential perimeter, the number of turns and the cross-sectional area of the circular cross-section ferrite core, and ω and I respectively represent the supply frequency and the effective value of the supply current.

[0132] In the present invention, by substituting the specification parameters of the magnetic core into the calculation model, the magnetic field strength and the electric field strength can be calculated. Based on the calculated magnetic field strength and electric field strength, the complex power of the toroidal inductor is calculated, and then combined with the equivalent circuit model, the magnetic permeability prediction model is obtained. The calculation of the present invention based on the theoretical model is not limited by a specific frequency band and a measuring instrument, and is also applicable in the high-frequency range; and based on the characteristic that the magnetic field of the circular cross-section ferrite core is uniform, the magnetic field strength and the electric field strength are calculated, so that the magnetic permeability prediction model is completely applicable to the circular cross-section ferrite core, and the predicted magnetic permeability is more accurate.

[0133] Based on the above embodiments, in the embodiments of the present invention, using the method for calculating the magnetic permeability of the circular cross-section ferrite core in the toroidal inductor provided by the present invention, calculate the magnetic permeability of the toroidal ferrite core, specifically including:

[0134] S201: Use Maxwell's equations to calculate the magnetic field strength distribution and the electric field strength distribution inside the toroidal ferrite core;

[0135] The Maxwell's equations for the magnetoquasistatic system are expressed as:

[0136] Assume that the magnetic field intensity has a uniform distribution on the surface of the toroidal ferrite core. The cylindrical coordinate system is adopted for analysis. The unit vectors in the three directions of the cylindrical coordinate system are e r 、e θ 、e z .

[0137] Assume that the magnetic field intensity is only a function of the radius r and is independent of θ. Therefore, the magnetic field intensity is expressed as: H = H(r)e z ;

[0138] Therefore,

[0139]

[0140] Take the curl of the formula in the Maxwell's equations for the magnetoquasistatic system and combine it with to obtain:

[0141] where μ is the initial permeability and σ is the conductivity.

[0142] Let Calculate the Bessel equation of the imaginary argument with respect to H, which is expressed as:

[0143]

[0144] Its general solution is: H(r) = c1I0(kr) + c2K0(kr);

[0145] where,

[0146] When the radius r of the circular cross-section ferrite core is r = 0 and K0(0) = ∞, it can be inferred that c2 = 0.

[0147] In the region of the core r < R, the magnetomotive force is affected not only by the exciting current but also by the eddy current and displacement current. However, at the outer peripheral interface of the core where r = R, the magnetic field intensity is determined only by the exciting current.

[0148] Assume that the magnetic field on the outer peripheral interface of the core is uniform, and it will satisfy the following relationship:

[0149] where R1 and R2 are the outer and inner peripheral radii of the core respectively; is the average radius of the magnetic core; N is the number of turns of the winding of the toroidal inductor, and I is the effective value of the supply current.

[0150] The coefficient c1, expressed as:

[0151] Therefore, the exact solution of the imaginary argument Bessel equation, that is, the magnetic field strength expression, is:

[0152]

[0153] where H(R) is the magnetic field strength on the outer peripheral surface of the magnetic core; R1 and R2 are the outer peripheral radius and the inner peripheral radius of the magnetic core respectively; N is the number of turns of the winding of the toroidal inductor, I is the effective value of the supply current, and R is the radius of the cross-section of the magnetic core. I0(kr) and I0(kR) are the zero-order Bessel functions of the first kind with imaginary argument.

[0154] Combining the two expressions of the magnetic induction intensity, and J c = σE, D = εE, the following expression can be derived:

[0155]

[0156] Further calculation gives the expression for the electric field strength distribution in the magnetic core, expressed as:

[0157]

[0158] where σ is the conductivity and ε is the permittivity. I1(kr) is the first-order Bessel function of the first kind with imaginary argument.

[0159] S202: Calculate the complex power of the toroidal inductor;

[0160] The calculation expression for the complex power of the toroidal inductor is:

[0161] S = ∫∫∫σ|E| 2 dV + jω(∫∫∫μ|H| 2 dV - ∫∫∫ε|E| 2 dV);

[0162] where μ is the initial magnetic permeability coefficient, ε is the permittivity, and σ is the conductivity.

[0163] Substitute the magnetic field strength expression and the electric field strength expression into the above calculation expression for the complex power of the toroidal inductor to calculate the complex power of the toroidal inductor.

[0164] S203: Calculate the true magnetic permeability coefficient;

[0165] As shown in (a) of Figure 2 is a schematic diagram of the toroidal inductor; Refer to Figure 2As shown in (b), it is the equivalent circuit diagram of the toroidal inductor; the toroidal inductor can be equivalent to an equivalent circuit with a resistor and an inductor in series according to the circuit concept; the real part μ′ and the imaginary part μ″ of the true permeability μ = μ′ - jμ″ can be calculated based on the equivalent resistance and inductance in series, and the calculation method and model are as follows: c The real part μ′ and the imaginary part μ″ of μ = μ′ - jμ″ can be calculated and obtained based on the equivalent resistance and inductance in series, and the calculation method and model are as follows:

[0166] There is the following relationship between the equivalent resistance in series in the equivalent circuit and the imaginary part of the permeability:

[0167] There is the following relationship between the inductance in series in the equivalent circuit and the real part of the permeability:

[0168] Where N is the number of turns, l is the circumference of the average circumference of the magnetic core, A is the cross-sectional area, and ω is the supply frequency.

[0169] And the complex power relationship formula for supplying the toroidal inductor is: S = I 2 (R + jωL);

[0170] Therefore: Re(S) = I 2 R, Im(S) = I 2 ωL;

[0171] Substitute the relationship between the equivalent resistance and inductance in series in the equivalent circuit and the imaginary part and real part of the permeability into the complex power relationship formula of the toroidal inductor, and obtain the prediction model of the real part and imaginary part of the permeability, which is expressed as:

[0172] Furthermore, obtain the prediction model of the permeability, which is expressed as:

[0173]

[0174] Where S is the total complex power of the inductor, N is the number of turns, l is the circumference of the average circumference of the magnetic core, A is the cross-sectional area, and ω is the supply frequency.

[0175] Substitute the complex power of the toroidal inductor calculated in step S202 into the prediction model of the permeability to obtain the true permeability of the toroidal ferrite core in the toroidal inductor.

[0176] An embodiment of the present invention proposes an accurate complex permeability prediction method for an annular ferrite magnetic core with a circular cross-section. Based on a complete theoretical analysis and derivation, it has a high theoretical support. In addition, the prediction method gives a specific mathematical model. The measurer only needs to input the geometric dimensions of the magnetic core into the mathematical model to calculate the complex permeability. Compared with traditional expensive measuring equipment, the most prominent feature of this method is its simplicity, convenience, accuracy, and it can give the variation of the complex permeability with frequency and is still applicable in the high-frequency range, which will contribute to the optimized design of inductors and has good application prospects in the production of annular inductors in the fields of electronic information and electronic circuits.

[0177] The permeability calculation method of the ferrite magnetic core with a circular cross-section in the annular inductor of the present invention takes into account the characteristic of uniform magnetic field distribution in the ferrite magnetic core with a circular cross-section during the calculation process, making the constructed magnetic field strength calculation model and electric field strength calculation model more applicable to the ferrite magnetic core with a circular cross-section, and thus the calculated permeability is more accurate. When calculating the magnetic field strength in the present invention, high-frequency analysis is carried out based on Maxwell's equations. Based on the characteristic of uniform magnetic field in the ferrite magnetic core with a circular cross-section in the annular inductor and based on the cylindrical coordinate system, the Bessel equation of imaginary argument is derived and solved to obtain the magnetic field strength calculation model, breaking through the limitation that the traditional measurement method needs to rely on measuring devices. When calculating the electric field strength, the electric field strength calculation model is obtained based on the relationship between the electric field strength and the magnetic field strength in Maxwell's equations. By substituting the specification parameters of the magnetic core into the calculation model in the present invention, the magnetic field strength and the electric field strength can be calculated. Based on the calculated magnetic field strength and electric field strength, the complex power of the annular inductor is calculated, and then combined with the equivalent circuit model, the permeability prediction model is obtained. The calculation based on the theoretical model in the present invention is not limited by a specific frequency band and measuring instrument and is also applicable in the high-frequency range. And based on the characteristic of uniform magnetic field in the ferrite magnetic core with a circular cross-section, the magnetic field strength and the electric field strength are calculated, making the permeability prediction model fully applicable to the ferrite magnetic core with a circular cross-section and predicting the permeability more accurately.

[0178] Those skilled in the art should understand that the embodiments of the present application can be provided as a method, a system, or a computer program product. Therefore, the present application can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0179] This application is described with reference to the flowcharts and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and combinations of flows and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to the processors of general-purpose computers, special-purpose computers, embedded processors, or other programmable data processing devices to generate a machine, such that the instructions executed by the processors of the computer or other programmable data processing devices produce means for implementing the functions specified in the Figure 1 one or more flows and / or blocks Figure 1 one or more blocks.

[0180] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory produce a manufactured article including instruction means that implement the functions specified in the Figure 1 one or more flows and / or blocks Figure 1 one or more blocks.

[0181] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operating steps are executed on the computer or other programmable device to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable device provide steps for implementing the functions specified in the Figure 1 one or more flows and / or blocks Figure 1 one or more blocks.

[0182] Obviously, the above embodiments are merely examples for clear illustration and are not limitations on the implementation manners. For those of ordinary skill in the art, other different forms of changes or variations can be made based on the above description. It is not necessary and impossible to enumerate all implementation manners here. And the obvious changes or variations derived therefrom are still within the protection scope of the present invention.

Claims

1. A method for calculating the magnetic permeability of a circular cross-section ferrite core in a toroidal inductor, characterized in that: include: Perform high-frequency analysis on a circular cross-section ferrite core to obtain the corresponding Maxwell equations; Based on the cylindrical coordinate system and Maxwell's equations, the initial expression of the magnetic field intensity with respect to the radius is obtained, and the curl is calculated to obtain the corresponding curl expression; The curl expression is calculated again to obtain the quadratic curl expression, and combined with Maxwell's equations to obtain the quadratic curl complex expression; Based on Maxwell's equations and the complex expression of quadratic curl, the magnetic field parameters are constructed; Based on the complex expression of quadratic curl and magnetic field parameters, the imaginary Bessel equation of magnetic field intensity is constructed and solved to obtain the exact solution as the calculation model of magnetic field intensity. Based on the Maxwell equations, a correlation formula between electric field strength and magnetic field strength is obtained; based on the correlation formula and the magnetic field strength calculation model, an electric field strength calculation model is obtained; Input the specification parameters of the circular cross-section ferrite core and the effective value of the supply current of the toroidal inductor into the magnetic field strength calculation model and the electric field strength calculation model to obtain the magnetic field strength and electric field strength at the radius r on the circular cross-section ferrite core; Integrate the magnetic field intensity and electric field intensity at each radial position on the circular cross-section ferrite core to calculate the complex power of the toroidal inductor; Based on the specifications of the circular cross-section ferrite core, the effective value of the supply current of the toroidal inductor and the complex power, the real magnetic permeability of the toroidal inductor is calculated.

2. The method for calculating the magnetic permeability of a circular cross-section ferrite core in a toroidal inductor according to claim 1, characterized in that: Perform high-frequency analysis on a ferrite core with a circular cross section to obtain Maxwell's equations for a magneto-quasistatic system, including: Ampere's circuit law: Faraday's law of electromagnetic induction: Gauss's law for magnetic field: Gauss's law for electric field: Among them, H represents the magnetic field intensity, E represents the electric field intensity, B represents the magnetic induction intensity, D represents the electric displacement vector, and J c represents the current density, j represents the imaginary unit, ω represents the angular frequency, ρ v represents the charge density.

3. The method for calculating the magnetic permeability of a circular cross-section ferrite core in a toroidal inductor according to claim 2, characterized in that: Based on the cylindrical coordinate system and Maxwell's equations, the initial expression of the magnetic field intensity with respect to the radius is obtained, and the curl calculation is performed to obtain the corresponding curl expression, including: Based on the cylindrical coordinate system and Maxwell's equations, the initial expression of the magnetic field intensity H with respect to the radius r is obtained as follows: H=H(r)e z ; Based on the initial expression, the curl is calculated and the corresponding curl expression is obtained, which is expressed as: Where H(r) is the magnetic field strength at radius r on a circular cross-section ferrite core, e z represents the unit vector in the z-axis direction, e θ represents the unit vector in the direction of the θ axis.

4. The method for calculating the magnetic permeability of a circular cross-section ferrite core in a toroidal inductor according to claim 3, characterized in that: The curl expression is calculated again to obtain the quadratic curl expression. Combined with the electromagnetic induction theorem in Maxwell's equations, the quadratic curl complex expression is obtained, including: The curl expression is calculated again to obtain the quadratic curl expression, which is expressed as: Based on the quadratic curl expression and Maxwell's equations, the quadratic curl complex expression is obtained, which is expressed as: Wherein, μ represents the initial magnetic permeability and σ represents the electrical conductivity.

5. The method for calculating the magnetic permeability of a circular cross-section ferrite core in a toroidal inductor according to claim 4, characterized in that: Based on Maxwell's equations and the complex expression of quadratic curl, the magnetic field parameters are constructed; Based on the complex expression of quadratic curl and magnetic field parameters, the imaginary Bessel equation of magnetic field intensity is constructed, including: Based on Maxwell's equations and the complex expression of quadratic curl, the magnetic field parameter k is constructed and expressed as: Based on the complex expression of quadratic curl and magnetic field parameters, the imaginary Bessel equation of magnetic field intensity is constructed and expressed as:

6. The method for calculating the magnetic permeability of a circular cross-section ferrite core in a toroidal inductor according to claim 5, characterized in that: Solve the Bessel equation of imaginary quantity and obtain the exact solution as the magnetic field strength calculation model, including: Get the general solution of the imaginary Bessel equation including the unknown coefficients c1 and c2, expressed as: H(r)=c1I0(kr)+c2K0(kr); I0(kr) is the zero-order first-kind imaginary Bessel function, expressed as: K0(kr) is the zero-order second-order imaginary Bessel function, expressed as: When the radius r of the circular cross-section ferrite core is 0, K0(0) = ∞, c2 = 0, and the general solution of the imaginary Bessel equation is simplified to: H(r)=c1I0(kr); When the radius of the circular cross-section ferrite core r = R, Substitute the boundary condition of r = R into H(r) = c1I0(kr) to obtain the unknown coefficients Based on the unknown coefficients c1 and c2, the exact solution of the Bessel equation of the imaginary quantity is obtained, which is expressed as: The magnetic field strength calculation model is expressed as: Wherein, Γ represents the gamma function, R1 and R2 represent the outer radius and inner radius of the circular cross-section ferrite core, respectively.

7. The method for calculating the magnetic permeability of a circular cross-section ferrite core in a toroidal inductor according to claim 6, characterized in that: Specifications of circular cross-section ferrite cores include: average circumference of circular cross-section ferrite cores, number of core winding turns, area of ​​circular cross-section, outer radius and inner radius.

8. The method for calculating the magnetic permeability of a circular cross-section ferrite core in a toroidal inductor according to claim 6, characterized in that: Based on the Maxwell equations, the correlation formula between the electric field strength and the magnetic field strength is obtained; based on the correlation formula and the magnetic field strength calculation model, the electric field strength calculation model is obtained, including: Based on Maxwell's equations, the relationship between electric field strength and magnetic field strength is obtained, which is expressed as: Based on the correlation formula and the magnetic field strength calculation model, the electric field strength calculation model is obtained, which is expressed as: Wherein, I1(kr) represents the first-order imaginary Bessel function of the first kind.

9. The method for calculating the magnetic permeability of a circular cross-section ferrite core in a toroidal inductor according to claim 8, characterized in that: The complex power of the toroidal inductor is calculated by integrating the magnetic field intensity and electric field intensity at each radial position on the circular cross-section ferrite core, expressed as: S=∫∫∫σ|E| 2 dV+jω(∫∫∫μ|H| 2 dV-∫∫∫ε|E| 2 dV)。 10. The method for calculating the magnetic permeability of a circular cross-section ferrite core in a toroidal inductor according to claim 9, characterized in that: Acquisition of magnetic permeability prediction model, including: The toroidal inductor is equivalent to an equivalent circuit of resistance and inductance in series. Based on the equivalent resistance and equivalent inductance in the equivalent circuit, the equivalent permeability calculation model is obtained, which is expressed as: μ c =μ′-jμ”; Based on the relationship between the equivalent inductance L and the real part μ′ of the magnetic permeability, the real part expression is obtained, which is expressed as: Based on the relationship between the equivalent resistance R and the imaginary part μ" of the magnetic permeability, the imaginary part expression is obtained, which is expressed as: The power of the toroidal inductor satisfies: S = I 2 (R+jωL); Based on the real part expression, imaginary part expression and the conditions satisfied by the power of the toroidal inductor, the real part Re(S) and imaginary part Im(S) of the complex power are obtained, which can be expressed as: Re(S) = I 2 R,Im(S)=I 2 ωL; Substituting the real and imaginary parts of the complex power into the equivalent permeability calculation model, the permeability prediction model is obtained, which is expressed as: Among them, μ c represents the magnetic permeability, S represents the complex power of the toroidal inductor to be tested, Im(S) and Re(S) represent the imaginary part and the real part of the complex power respectively, j represents the imaginary unit; l, N and A represent the average circumference, number of turns and cross-sectional area of ​​the circular cross-section ferrite core respectively, ω and I represent the supply frequency and effective value of the supply current respectively.

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