JP2984108B2 - DC superposition inductance calculator - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to an apparatus for calculating the inductance of a magnetic material excited by a current obtained by superimposing an alternating current on a direct current, such as a smoothing choke of a switching power supply.

[0002]

2. Description of the Related Art The calculation of a magnetic field has been performed by approximating by a difference method or a finite element method based on the Maxwell equation, and dividing a magnetic component to be calculated into minute regions.

Here, the difference method and the finite element method will be described. "Finite element method of electrical engineering" (Takayoshi Nakata,
Norio Takahashi, Morikita Publishing).

In order to perform a magnetic field calculation, it is necessary to solve equation (1) among the following basic equations. In general, equation (4) is often solved by adding equations (2) and (3) to facilitate the handling of variables.

RotH = J (1) H: magnetic field strength (A / m), J: current density (A / m ² ) where H and J represent vectors.

B = μH (2) B: magnetic flux density (Wb / m ² ), μ: magnetic permeability B and H represent vectors.

B = rotA (3) A: Vector potential (Wb / m) Note that B and A represent vectors.

(Rotν · rotA) = J (4) ν (= 1 / μ): magnetic resistivity A and J represent vectors.

However, since equation (4) is a partial differential equation, it is extremely difficult to directly solve it. Therefore, the solution is performed using some approximation, and there is a difference method or a finite element method as the method. Hereinafter, these approximation methods will be specifically described. Note that for simplicity, equation (4) is
It is handled in a dimensional field (x and y coordinates only).

The equation in the two-dimensional field of the equation (4) is

[0011]

(Equation 1)

In a two-dimensional field, the magnetic flux densities are B _X and B _Y
Vector potential has only an _AZ component. In addition, the current is flowing in an infinite length in the Z direction. In the following description, _AZ is simply written as A.

"Difference method" In the difference method, as shown in FIG. 10, a region to be calculated is divided into a grid, and the vector potential _AZ is Taylor-expanded at each grid point to obtain an equation (5) Is a method of calculating numerical values by using the relational expression of the potential of the lattice points close to each other. Specifically, when a second-order Taylor expansion is performed around a point (i, j) shown in FIG.

[0014]

(Equation 2)

## EQU1 ## Here, h _x and h _y are distances between lattices. Using equations (5) and (6), for i and j,

[0016]

(Equation 3)

The following equation is obtained. J (i, j),
Since h _x , h _y , ν _y (= 1 / μ _y ) and ν _x (= 1 / μ _x ) are given as calculation conditions, the remaining values of A are unknown. If the equation (7) is established for each grid point by the same means, a simultaneous equation having an element of the total number of grid points can be obtained. However, in practice, the lattice point at the boundary portion at the far end of the current source is set to A = 0 and is treated as a known value, so that a simultaneous equation with a reduced number of elements is solved.

Of the above procedures, a procedure for dividing into grids, a procedure for calculating simultaneous equations, and a procedure for obtaining H and B from the obtained value of A using the equations (2) and (3) are performed by a computer. The input of the value of A, material constants ν _x , ν _y , current conditions, etc. are determined by the operator.

"Finite element method" The finite element method is a method in which a region to be calculated is divided into minute regions called elements, and the distribution of vector potentials A in the elements is approximated by a simple function for analysis. . Although there is no limitation on the shape of the element, for example, a triangle as shown in FIG. 11 is often used. Each vertex of the triangle is called a node, and consecutive numbers are assigned, and elements are also consecutively numbered.

Now, equation (5) is

[0021]

(Equation 4)

In other words, if A is a true solution satisfying the equation, f (A) = 0. A represents a vector. If A is an approximate solution A ', then f (A') = R. Note that A 'represents a vector. If A ′ is determined such that 積分 Rdxdy, which is the integral (sum) of R over the entire calculation target area, is minimized, A = A ′ can be obtained. Therefore, when weighting integration is performed by introducing a weighting function for each element, an actual operation can be performed and A 'can be obtained quantitatively.

∬R · Wdxdy = 0 (8) It is generally called the finite element method that a function called an interpolation function is introduced into the weight function W. The potential of any point in an element is a function of the potential of those nodes

[0024]

(Equation 5)

Where N _i is the interpolation function. If it is triangular elements shown in FIG. 11, for example with respect to the node _{i, N i = (1 /} 2S) × (b i + c i x + d i y) S: area of the triangle _{b i = x j y k -x} k y _j c _i = y _j −y _k d _i = x _k −x _j (10) Equation (8) is specifically

[0026]

(Equation 6)

## EQU2 ## When the equation (11) is partially integrated,

[0028]

(Equation 7)

## EQU1 ## In this equation (12),

[0030]

(Equation 8)

Is replaced by the differentiation of the interpolation function. The derivative of the interpolation function is easily obtained by equation (10), and ∂N _i / ∂x = c _i / 2SＳN _i / ∂y = d _i / 2S. In this way, simultaneous equations can be established for one element from equation (12) by the number of nodes constituting the element. For each element, a simultaneous equation based on the equation (12) is established and superimposed on nodes shared between adjacent elements, and finally a simultaneous equation having an element of the total number of nodes is obtained. An approximate solution A 'can be obtained by solving this simultaneous equation. However, in practice, the potential of the node at the boundary portion at the far end of the current source is set to A = 0 and is treated as a known value, so that a simultaneous equation with a slightly reduced number of elements is solved.

Of the above procedures, a procedure for dividing into elements, a procedure for calculating simultaneous equations, and a procedure for obtaining H and B from the obtained value of A by the equations (2) and (3) are performed by a computer. The input of the value of A, the material constants ν _x , ν _y , current conditions, etc. are determined by the operator.

As described above, the difference method and the finite element method have been described for a two-dimensional field. However, it is possible to solve a three-dimensional field by a similar procedure.

Using this method to calculate the magnetic field of a magnetic component excited by a current obtained by superimposing an alternating current on a direct current as shown in FIG. A general method is to divide and calculate according to the current value that changes every moment. This is because it is necessary to calculate in consideration of the influence of the eddy current generated inside the magnetic material by the AC component of the DC superimposed current. At this time, the magnetic characteristics of the magnetic component are generally non-linear with hysteresis in a DC superimposed state. Therefore, the magnetic properties must be corrected according to the magnetic field strength or the magnetic flux density calculated every minute time, and iterative calculations must be performed for the same current value (for example, IEEJ Transactions on Engineering, Vol. 109, No. 6).
Pp. 247-254, 1989, "Analysis of Hysteresis Loss by Finite Element Method," Masato Enozono, Koji Ikeshita, and JP-A-2-232773. In other words, iterative calculation for the nonlinearity of the material and iterative calculation for the current to change with time are necessary, and the total number of iterative calculations required to perform the simulation by calculating the DC superimposed state is as follows.
The total number of iterations is estimated as follows: (number of iterations related to non-linearity) × (number of iterations related to time change of current).

[0035]

In the case of calculating a DC superimposed state using the above method, for example, if the number of repetitive calculations related to non-linearity is 10 and the number of repetitive calculations related to time change of current is 12, the total repetition rate is calculated. The number of calculations is 120 (= 10
× 12). The total number of repeated calculations of 120 times is a general number and is not particularly large.

The DC superposition characteristic generally means a change in inductance value when the frequency and amplitude of the AC component of the DC superposition current are kept constant and the DC component is continuously changed. It is usually necessary to perform calculations assuming a plurality of. Therefore, when a plurality of DC component values are assumed, the total amount of calculation further increases, and becomes a value obtained by multiplying the assumed number of DC current values by the above-described iterative calculation. As described above, there is a problem that a large amount of calculation is required to use the magnetic field calculation.

Therefore, it is extremely difficult to perform such calculations with a small computer in a short time, so a large computer capable of performing high-speed processing is required. On the other hand, in order to obtain DC bias characteristics without performing a magnetic field calculation, it has been necessary to estimate from a measured value of a magnetic component having a similar shape or to manufacture at least one prototype. In addition, if the prototype does not have the desired DC superimposition characteristics, it is necessary to repeat the trial production, and the period and cost for this are enormous.

An object of the present invention is to provide an inductance calculating apparatus for calculating the DC bias characteristics of a magnetic component with a small amount of calculation without producing a prototype in order to solve the above problems.

[0039]

According to a first aspect of the present invention, there is provided an inductance calculating apparatus for calculating an inductance of a magnetic member which is excited by a current obtained by superimposing an alternating current on a direct current. Based on the initial magnetization characteristics of the magnetic material (40) having the same demagnetizing coefficient as the same material as the material and the geometric information of the magnetic member, the magnetic field of each minute region of the magnetic member with respect to the DC current component is determined. A first magnetic flux density calculating means (1) for calculating the flux density (B _DC ); the magnetic flux density (B _DC ) calculated by the first magnetic flux density calculating means (1) is the same material as the magnetic member; Ah
Each micro territory based on the incremental magnetic permeability of the magnetic material in the that shape
Geometric increment permeability and the magnetic member of each minute area of the magnetic member; incremental permeability determination means for determining an incremental magnetic permeability of the band
The second magnetic flux density and magnetic to calculate the magnetic flux density and magnetic field strength with respect to the alternating current component of the magnetic member (30) on the basis of the information
Field strength calculation means (1); and second magnetic flux density and magnetic field
Calculating means (1) for calculating an inductance (L) of the magnetic member (30) based on the magnetic flux density and the magnetic field strength calculated by the strength calculating means (1). Symbols in parentheses indicate corresponding elements or items in the embodiment shown in the drawings and described later.

[0040]

According to this, the constant determining means (1) determines the constant of the magnetic member calculated from the initial magnetization characteristics of the magnetic material (40) formed of the same material as the magnetic member (30) and having a shape having a minimal demagnetizing coefficient. The material constant (μ _Zi ) is determined based on the magnetic flux density (B _DC ) for the DC current component and the incremental magnetic permeability (μ) of the magnetic material (40), and the calculating means (1) calculates the material constant (μ _Zi ).
The inductance (L) of the magnetic member (30) is calculated based on the magnetic flux density (B _AC ) for the alternating current component of the magnetic member (30) calculated from the above.

Accordingly, the DC superimposition characteristics of the magnetic member (30) having an arbitrary shape made of one magnetic material (40) can be accurately calculated without particularly manufacturing the magnetic member (30). The period is shortened.

Also, since a single calculation can be performed in a relatively short time even with a small computer, a calculation level can be set for a plurality of material properties and shapes. The optimum material and shape can be determined. Other objects and features of the present invention will become apparent from the following description of embodiments with reference to the drawings.

[0043]

FIG. 1 shows an outline of the configuration of a computer 10 according to an embodiment of the present invention. The computer 10 has a CPU that performs overall control.
1, a ROM in which a control program is stored 2, a RAM temporarily used by the control program 3, an internal system bus for exchanging data between devices 4, a memory for storing various information 5, an interactive graphic terminal 20 I / F (interface) that connects the system bus 4
And an operation display section 7 for inputting instructions from the operator and displaying predetermined information. In FIG.
The magnetic component 30 to be calculated is shown. This magnetic part 3
0 is a so-called choke core used in a switching power supply. Reference numerals 31 and 32 denote magnetic members made of ferrite, and reference numeral 33 denotes a coil portion obtained by winding a magnetic member 31 with a conductive wire. Reference numeral 34
Is a non-magnetic spacer inserted to provide a gap between the magnetic members 31 and 32. By changing the thickness of the spacer 34, direct current superposition can be varied and used in a linear region.

FIG. 3 shows a flow chart of the CPU 1 for explaining the processing operation for calculating the DC superposition characteristic of the magnetic component (choke core) 30.

When the power is turned on, the processing mode and the like are initialized (step 1: hereinafter, the word "step" is omitted in parentheses), and the input is read (2). The input to be read are the initial magnetization characteristics, the incremental permeability, the DC component value of the DC superimposed current, the AC component value, and the like of the ring-shaped sample 40 made of the same material as the magnetic component (choke core) 30.

The initial magnetization characteristics of the ring-shaped sample 40 are shown in FIG.
The measurement is performed using a DC magnetometer as shown in FIG. That is, the electric field strength H (A / m) is as follows: H = NI / l (13) N: number of turns of the conductor, I: DC current value by DC power supply, l:
The magnetic flux density B (wb / m ² ) is obtained from the magnetic path length of the sample 40, and the magnetic flux density B (wb / m ² ) is obtained from the output value obtained by integrating the measured voltage by the integrating circuit. FIG. 5 shows the measurement results of the initial magnetization characteristics (the relationship between the electric field strength H and the magnetic flux density B).

Next, the measurement of the incremental magnetic permeability of the ring-shaped sample 40 will be described. First, the DC superimposition characteristic of the ring-shaped sample 40 is measured using a DC superimposition characteristic measuring device (not shown) described in JIS (C-2514).
FIG. 6 shows the measurement results. The vertical axis is inductance L
(ΜH), the horizontal axis is the value I of the DC component of the DC superimposed current
_DC (A) is shown. The effective value of the AC component of the DC superimposed current when measured in this embodiment the frequency is 1.0mA was 1.0kH _Z. From the value of the inductance L, the incremental magnetic permeability μ _Z is obtained by calculation. That is,
The incremental magnetic permeability μ _Z is as follows: μ _Z = π × R × L / (μ ₀ × N ² × Ae) (14) π: Pi, R: Average straight diameter (m) of the ring sample 40, μ ₀ : magnetic permeability in vacuum (H / m), N: number of turns of the conductor Ae: sectional area (m ² ) of the ring sample 40. Further, the magnetic field strength H (A / m) in the ring sample 40 generated by the DC current component from the DC component value I _DC of the DC superimposition by the following equation is: H = N × I _DC / (π × R). (15) _IDC is converted to magnetic flux density B from the relationship between the magnetic field intensity of the initial magnetization characteristics and the magnetic flux density measured earlier from the value of the magnetic field strength. The result is shown in FIG. The value of the magnetic flux density means the magnetic flux density generated in the ring sample 40 by the DC component of the DC superimposed current.

The reason why the incremental magnetic permeability and the magnetic flux density are obtained by the calculation is that the sample has a ring shape and the demagnetizing coefficient is negligible, and is measured from a magnetic component (choke core) 30. With a large measurement error.

Returning to the flowchart of FIG. When the input is read, other mode processing is performed until a start instruction is given by the operator (3, 4). Other mode processing includes, for example, a range designation at the time of mesh division described later. When there is a start instruction, geometric information obtained by dividing the magnetic component (choke core) 30 into minute regions is read using the interactive graphic terminal 20, and stored in the memory 5 (5, 6). In this embodiment, since the finite element method is used for the magnetic field calculation in this embodiment, the division is performed into triangular elements called meshes as shown in FIG. FIG. 8 is a sectional view taken along the line CC of FIG.
It is a sectional view, and division information in a space P1-P2-P3-P4-P1 surrounding a magnetic component (choke core) 30 is read. The space surrounding the magnetic component (choke core) 30 is specified by the operation display unit 7. If the difference method is used for the magnetic field calculation, equally-spaced division called a difference grid is performed.

Next, a magnetic field calculation is performed based on the geometric information, the initial magnetization characteristics obtained in step 2 and the DC component value of the DC superimposed current (7). Since the initial magnetization characteristics used in this case have a non-linearity with respect to the magnetic field strength as shown in FIG.
A nonlinear iterative calculation such as the Rapson method (described in the above-mentioned “Finite Element Method of Electrical Engineering”, page 200 (described by Takayoshi Nakata and Norio Takahashi, Morikita Publishing)) is performed. The magnetic field strength and the magnetic flux density are obtained starting from an appropriate initial magnetic permeability value μ, and when the values match the values shown in FIG. 5, the calculation is terminated. The iterative calculation is performed by changing the value μ until the desired accuracy is achieved. In the present embodiment, convergence was achieved by ten repetitive calculations. Thereby, the magnetic flux density B _DC of each minute region with respect to the DC current component is calculated.

Next, the obtained magnetic component (choke core)
The incremental magnetic permeability μ _Zi of each minute region is determined from the magnetic flux density B _DC of each minute region inside the 30 using the relationship between the incremental magnetic permeability μ _Z and the magnetic flux density shown in FIG. 7 (8). Specifically, the results of the incremental magnetic permeability μ _Z and the magnetic flux density obtained by the input reading in step 2 are approximated by an appropriate function and stored in advance, and the magnetic flux density B _DC of each minute region obtained in step 7 is stored. Next, the incremental magnetic permeability μ _Zi is determined by this function. In this embodiment, the approximation is made by a cubic function.

Next, from the incremental magnetic permeability μ _Zi of each minute region, the geometric information obtained in step 5 and the AC current component value of the DC superimposed current read in step 2, the same magnetic field calculation method as performed in step 7 The calculation is performed only once using (9). The reason why the calculation only needs to be performed once is that the influence of the eddy current generated by the alternating current component is added to the value of the incremental magnetic permeability μ _Zi . Therefore, here, the effective value and frequency of the AC component of the DC superimposed current applied to the magnetic component (choke core) 30 are the effective value (1) of the AC component of the DC superimposed current when the incremental permeability of the ring sample 40 is measured. .0 mA)
And it is made to coincide with the measurement conditions and frequency (1.0kH _Z). As a result, the magnetic flux density B _AC corresponding to the alternating current component
And the magnetic field strength H _AC is obtained.

Next, the magnetic flux density B corresponding to the AC current component
_{From the AC} and the magnetic field strength H _{AC, a} target DC superimposition characteristic (inductance value) is obtained from the following equation (16) (10).

L = ∫B _AC · H _AC dv / I _AC ² (16) dv: volume of each element The integration area is the entire calculation area. The variable used in the calculation in step 9 is vector potential A (Wb
/ M), it is calculated by equation (17). L = ∫A · J _AC dv / I _AC ² (17) where J _AC is the current density (A / m) of the divided small area of the coil.
² ) The integration area is the coil part where the current flows.

Next, an instruction for iterative calculation, that is, step 2
It is checked whether or not iterative calculation has been performed by the number of DC current components I _DC inputted in (11). If the number of DC current components has not been reached, the process returns to step 5 and the following processes (5 to 11) are executed. When iterative calculation is performed for the number of DC current components, the relationship between the DC current component I _DC (A) and the inductance (μH) is obtained from the point sequence data (the mark in the figure is a calculated value) as shown in FIG. It is displayed on the operation display section 7 (12). Note that the solid line in the figure shows the actually measured values of the magnetic component (choke core) 30 experimentally manufactured for comparison.

In this embodiment, the repetitive calculation of the magnetic field calculation performed in step 7 is performed 10 times, and the magnetic field calculation performed in step 9 is performed once, and a total of 11 magnetic field calculations are performed for the DC component of one superimposed DC current. The inductance was calculated. In order to obtain all the calculated values shown in FIG.
The calculation time was about 10 minutes for the workstation SP / 1 manufactured by N Company.

[0057]

According to the DC superposition inductance calculating apparatus of the present invention, the DC superposition characteristic of the magnetic member (30) having an arbitrary shape made of one magnetic material (40) is especially manufactured by trial production of the magnetic member (30). Calculation with high accuracy without
Prototyping costs and periods are reduced.

Further, since a single calculation can be performed in a relatively short time even with a small computer, a calculation level can be set for a plurality of material properties and shapes, and a predetermined DC superimposition characteristic required in the design of equipment can be obtained. The optimum material and shape can be determined.

[Brief description of the drawings]

FIG. 1 is an inductance calculator 1 according to an embodiment of the present invention.
FIG. 3 is a block diagram showing a configuration of a 0.

Fig. 2 Magnetic components to be calculated (choke core)
FIG.

FIG. 3 is a flowchart showing a processing operation of a CPU 1 shown in FIG.

FIG. 4 is a block diagram showing a schematic configuration of a DC magnetometer for measuring initial magnetization characteristics of a ring-shaped sample 40;

5 is a graph showing initial magnetization characteristics (relationship between electric field strength H and magnetic flux density B) measured by the DC magnetometer shown in FIG.

FIG. 6 is a graph showing a measurement result of a DC superposition characteristic of a ring-shaped sample 40, wherein the vertical axis represents an inductance L (μ);
H), the horizontal axis represents the value I _DC (A) of the DC component of the DC superimposed current.

FIG. 7 is a graph showing a relationship between a magnetic flux density B of a ring-shaped sample 40 and an incremental magnetic permeability (μ).

8 is a cross-sectional view of the magnetic component (choke core) 30 shown in FIG.

FIG. 9 is a graph showing the relationship between the direct current component I _DC (A) of the magnetic component (choke core) 30 and the inductance (μH), where the circles indicate calculated values and the solid lines indicate measured values. Show.

FIG. 10 is a plan view showing an example of division by a difference method.

FIG. 11 is a plan view showing an example of division by the finite element method.

FIG. 12 is a timing chart showing a state in which an alternating current is superimposed on a direct current.

[Explanation of symbols]

1: CPU (first magnetic flux density calculating means, second magnetic flux density calculating means, constant determining means, calculating means) 2: ROM 3: RAM 4: System bus 5: Memory 6: I / F 7: Operation display section 10 : Computer 20: Interactive graphic terminal 30: Magnetic component (magnetic member) 40: Ring sample (magnetic material)

──────────────────────────────────────────────────続 き Continued on the front page (72) Inventor Kenji Umezu 20-1 Shintomi, Futtsu City Nippon Steel Corporation Technology Development Division (72) Inventor Hiroo Kaneko 5-10-1 Fuchinobe Sagamihara City New Nippon Steel Corporation Electronics Research Laboratory (58) Fields surveyed (Int. Cl. ⁶ , DB name) G01R 27/26 G01R 33/12

Claims (1)

(57) [Claims] 1. An inductance calculating apparatus for calculating an inductance of a magnetic member excited by a current obtained by superimposing an alternating current on a direct current, comprising: a magnetic material having the same material as the magnetic member and having a shape having a minimal demagnetizing coefficient; A first magnetic flux density calculating means for calculating a magnetic flux density of each minute region of the magnetic member with respect to a direct current component based on the magnetization characteristics and geometric information of the magnetic member; a magnetic flux calculated by the first magnetic flux density calculating means Density and magnetic material
Incremental magnetic permeability determining means for determining the incremental magnetic permeability of each minute region based on the incremental magnetic permeability of a magnetic material having the same material and having a demagnetizing coefficient of a minimum ; an increment of each minute region of the magnetic member Permeability and geometry of magnetic members
A second magnetic flux density and a magnetic field strength calculating means for calculating a magnetic flux density and a magnetic field strength for an alternating current component of the magnetic member based on the information ; and a magnetic flux density calculated by the second magnetic flux density and the magnetic field strength calculating means
And calculating means for calculating the inductance of the magnetic member based on the magnetic field strength .