Inductor equivalent circuit model, inductor simulation method, equivalent circuit model creation method, and program

Abstract

The present disclosure addresses the problem of accurately representing an AC loss in an inductor even if a current on which a DC current is superposed flows to the inductor. An inductor equivalent circuit model (100) comprises a ladder circuit (10) including a first ladder circuit (11) and a second ladder circuit (12). The first ladder circuit (11) is a circuit for representing a first loss component of the AC loss of the inductor, the first loss component being proportional to the square of an effective value of an AC current (iac). An input current (i) is input to the first ladder circuit (11). The second ladder circuit (12) is a circuit for representing a second loss component of the AC loss of the inductor, the second loss component being proportional to the β power of the effective value of the AC current (iac). A current ((i-Idc)β(Idc) / 2), of a power of a value obtained as a result of the AC current (iac) being divided by an exponent β which is divided by 2, is input from a current source (120) to the second ladder circuit (12). The exponent β in the second loss component is a function of a DC current (Idc).

Description

Inductor equivalent circuit model, inductor simulation method, equivalent circuit model creation method, and program

[0001] The present disclosure relates to an equivalent circuit model of an inductor, a method for simulating an inductor, a method for creating an equivalent circuit model, and a program.

[0002] Non-Patent Document 1 describes an equivalent circuit model of an inductor for SPICE simulation.

[0003] In the equivalent circuit model of Non-Patent Document 1, in order to describe the loss in an inductor, the loss in the inductor is expressed as the sum of a component proportional to the square of the effective value of the AC current (hereinafter referred to as the "first term") and a component proportional to the β power (β is a constant) of the effective value of the AC current (hereinafter referred to as the "second term"). The first term is expressed by a Cauer circuit (hereinafter referred to as the "first Cauer circuit"), and the second term is expressed by a combination of a Cauer circuit (hereinafter referred to as the "second Cauer circuit") and an ideal transformer.

[0004] In the equivalent circuit model of Non-Patent Document 1, the resistance values ​​of the resistive elements and the inductances of the inductive elements in each stage of the first Cauer circuit, as well as the resistance values ​​of the resistive elements and the inductances of the inductive elements in each stage of the second Cauer circuit, are determined using fitting by a genetic algorithm (GA).

[0005] In the equivalent circuit model of Non-Patent Document 1, the loss in the inductor is calculated as the sum of the losses in the resistive elements in each stage of the first Cauer circuit and the sum of the losses in the resistive elements in each stage of the second Cauer circuit.

[0006] Yuki Sato, Cauer-Equivalent Circuit for Inductors Considering Hysteresis Magnetic Properties for SPICE Simulation, IEEETRANSACTIONS ON POWER ELECTRONICS, VOL. 35, NO. 9, SEPTEMBER 2020, p.9663-9670

[0007] The equivalent circuit model in Non-Patent Document 1 has a problem in that when a current superimposed with a DC current flows through an inductor, the calculated loss (AC loss) may deviate from the actual measurement.

[0008] An object of the present disclosure is to accurately represent AC loss in an inductor even when a current with a DC current superimposed thereon flows through the inductor.

[0009] An equivalent circuit model of an inductor according to one aspect of the present disclosure includes a ladder circuit of resistive elements and inductive elements for representing the inductance and AC loss of the inductor when an input current in which a DC current is superimposed on an AC current flows through the inductor. The ladder circuit includes a first ladder circuit and a second ladder circuit. The first ladder circuit is a circuit for representing a first loss component of the AC loss of the inductor that is proportional to the square of the effective value of the AC current. The input current is input to the first ladder circuit. The second ladder circuit is a circuit for representing a second loss component of the AC loss of the inductor that is proportional to the β power of the effective value of the AC current. A current raised to the power of a value obtained by dividing the AC current by an exponent β by 2 is input to the second ladder circuit from a current source. The exponent β of the second loss component is a function of the DC current. The resistance value of the resistive element and the inductance value of the inductive element in the first ladder circuit are obtained by performing a first fitting. In the first fitting, fitting is performed so that the frequency characteristics of the real part of the impedance of the first ladder circuit match the frequency characteristics of a first equivalent resistance, and so that the frequency characteristics of the imaginary part of the impedance of the first ladder circuit match the frequency characteristics of the actually measured value of the inductance of the inductor. The first equivalent resistance determines the first loss component. The first loss component is obtained from an actual measurement of the AC loss of the inductor under a condition where the DC current is zero. The resistance value of the resistive element and the inductance value of the inductive element in the second ladder circuit are obtained by performing a second fitting. The second fitting is performed so that the frequency characteristics of the real part of the impedance of the second ladder circuit match the frequency characteristics of a second equivalent resistance of the inductor, and so that the frequency characteristics of the imaginary part of the impedance of the second ladder circuit match the frequency characteristics of the actually measured value of the inductance of the inductor. The second equivalent resistance determines the second loss component. The second loss component is obtained from an actual measurement of the AC loss of the inductor under a condition where the DC current is zero.

[0010] An inductor simulation method according to one aspect of the present disclosure is a method for calculating inductor characteristics using a computer with a simulation model including an equivalent circuit model of the inductor. The simulation model includes the equivalent circuit model and a current source. The equivalent circuit model includes a ladder circuit of resistive elements and inductive elements for representing the inductance and AC loss of the inductor when an input current in which a DC current is superimposed on an AC current flows through the inductor. The ladder circuit includes a first ladder circuit and a second ladder circuit. The first ladder circuit is a circuit for representing a first loss component of the AC loss of the inductor that is proportional to the square of the effective value of the AC current. The input current is input to the first ladder circuit. The second ladder circuit is a circuit for representing a second loss component of the AC loss of the inductor that is proportional to the β power of the effective value of the AC current. A current of a power of a value obtained by dividing the AC current by an exponent β by 2 is input to the second ladder circuit from a current source. The power exponent β of the second loss component is a function of the DC current. The resistance value of the resistive element and the inductance value of the inductive element in the first ladder circuit are obtained by performing a first fitting. In the first fitting, fitting is performed so that the frequency characteristics of the real part of the impedance of the first ladder circuit match the frequency characteristics of a first equivalent resistance, and so that the frequency characteristics of the imaginary part of the impedance of the first ladder circuit match the frequency characteristics of the actually measured value of the inductance of the inductor. The first equivalent resistance determines the first loss component. The first loss component is obtained from an actual measurement of the AC loss of the inductor under a condition where the DC current is zero. The resistance value of the resistive element and the inductance value of the inductive element in the second ladder circuit are obtained by performing a second fitting. In the second fitting, fitting is performed so that the frequency characteristics of the real part of the impedance of the second ladder circuit match the frequency characteristics of a second equivalent resistance of the inductor, and the frequency characteristics of the imaginary part of the impedance of the second ladder circuit match the frequency characteristics of the actually measured value of the inductance of the inductor. The second equivalent resistance determines the second loss component.The second loss component is obtained from an actual measurement of the AC loss of the inductor under a condition where the DC current is 0. The simulation method includes a loss calculation step in which the AC loss of the inductor is calculated using a resistance value of the resistive element in the first ladder circuit, a current flowing through the resistive element in the first ladder circuit, a resistance value of the resistive element in the second ladder circuit, and a current flowing through the resistive element in the second ladder circuit.

[0011] A method for creating an equivalent circuit model according to one aspect of the present disclosure is a computer-executable method for creating an equivalent circuit model of an inductor. The equivalent circuit model includes a ladder circuit of resistive elements and inductive elements for representing the inductance and AC loss of the inductor when an input current in which a DC current is superimposed on an AC current flows through the inductor. The ladder circuit includes a first ladder circuit and a second ladder circuit. The first ladder circuit is a circuit for representing a first loss component of the AC loss of the inductor that is proportional to the square of the effective value of the AC current. The input current is input to the first ladder circuit. The second ladder circuit is a circuit for representing a second loss component of the AC loss of the inductor that is proportional to the β power of the effective value of the AC current. A current raised to the power of a value obtained by dividing the AC current by an exponent β by 2 is input to the second ladder circuit from a current source. The exponent β of the second loss component is a function of the DC current. The method for creating an equivalent circuit model includes a first ladder circuit calculation step and a second ladder circuit calculation step. In the first ladder circuit calculation step, a first fitting is performed to determine the resistance value of the resistive element and the inductance value of the inductive element in the first ladder circuit. In the first fitting, fitting is performed so that the frequency characteristics of the real part of the impedance of the first ladder circuit match the frequency characteristics of a first equivalent resistance of the inductor, and so that the frequency characteristics of the imaginary part of the impedance of the first ladder circuit match the frequency characteristics of the actually measured value of the inductance of the inductor. The first equivalent resistance determines the first loss component. The first loss component is determined from an actual measurement of the AC loss of the inductor under a condition where the DC current is zero. In the second ladder circuit calculation step, a second fitting is performed to determine the resistance value of the resistive element and the inductance value of the inductive element in the second ladder circuit. In the second fitting, fitting is performed so that the frequency characteristics of the real part of the impedance of the second ladder circuit match the frequency characteristics of the second equivalent resistance of the inductor, and so that the frequency characteristics of the imaginary part of the impedance of the second ladder circuit match the frequency characteristics of the actual measured value of the inductance of the inductor.The second equivalent resistance determines the second loss component, which is obtained from an actual measurement of the AC loss of the inductor under the condition that the DC current is zero.

[0012] A program according to one aspect of the present disclosure causes one or more processors to execute the method for creating an equivalent circuit model.

[0013] FIG. 1 is a flowchart of a method for creating an equivalent circuit model according to an embodiment of the present disclosure. FIG. 2 is a circuit diagram of an example of an inductor targeted by the equivalent circuit model. FIG. 3 is a graph showing AC current characteristics of measured values ​​of AC loss in the inductor when AC current flows through the inductor. FIG. 4 is an explanatory diagram showing a ladder circuit included in the equivalent circuit model. FIG. 5 is a graph showing frequency characteristics of measured values ​​of inductance of the inductor. FIG. 6 is a graph showing calculation results of frequency characteristics of a first equivalent resistance of the inductor and frequency characteristics of the real part of the impedance of a first ladder circuit included in the equivalent circuit model. FIG. 7 is a graph showing frequency characteristics of a second equivalent resistance of the inductor and frequency characteristics of the real part of the impedance of a second ladder circuit included in the equivalent circuit model. FIG. 8 is a graph showing DC current characteristics of the inductance of the inductor. FIG. 9 is a graph showing AC current characteristics of measured values ​​of AC loss in the inductor when AC current flows through the inductor. Fig. 10 is a graph showing the AC current characteristics of the measured AC loss in the inductor when an input current consisting of a 10 A DC current superimposed on an AC current flows through the inductor of the same. Fig. 11 is a graph showing the AC current characteristics of the measured AC loss in the inductor when an input current consisting of a 20 A DC current superimposed on an AC current flows through the inductor of the same. Fig. 12 is a graph showing the AC current characteristics of the measured AC loss in the inductor when an input current consisting of a 30 A DC current superimposed on an AC current flows through the inductor of the same. Fig. 13 is a graph showing the DC current characteristics of the power exponent β. Fig. 14 is a graph comparing the measured AC loss of the inductor of the same when an input current consisting of a 10 A DC current superimposed on an AC current flows, the AC current characteristics of the AC loss at each frequency calculated using the same equivalent circuit model, and the AC current characteristics of the AC loss at each frequency calculated using a comparative example.Fig. 15 is a graph comparing measured AC losses of the inductor of the same when an input current consisting of a 10 A DC current superimposed on an AC current is input, the AC loss characteristics at each frequency calculated using the same equivalent circuit model, and the AC loss characteristics at each frequency calculated using a comparative example. Fig. 16 is a graph comparing measured AC losses of the inductor of the same when an input current consisting of a 20 A DC current superimposed on an AC current is input, the AC loss characteristics at each frequency calculated using the same equivalent circuit model, and the AC loss characteristics at each frequency calculated using a comparative example. Fig. 17 is a graph comparing measured AC losses of the inductor of the same when an input current consisting of a 20 A DC current superimposed on an AC current is input, the AC loss characteristics at each frequency calculated using the same equivalent circuit model, and the AC loss characteristics at each frequency calculated using a comparative example. Fig. 18 is a graph showing a comparison of measured values ​​of AC loss of the inductor of the same when an input current in which a DC current of 30 A is superimposed on an AC current is input, the AC current characteristics of AC loss at each frequency calculated using the same equivalent circuit model, and the AC current characteristics of AC loss at each frequency calculated using a comparative example. Fig. 19 is a graph showing a comparison of measured values ​​of AC loss of the inductor of the same when an input current in which a DC current of 30 A is superimposed on an AC current is input, the AC current characteristics of AC loss at each frequency calculated using the same equivalent circuit model, and the AC current characteristics of AC loss at each frequency calculated using a comparative example.

[0014] Hereinafter, an equivalent circuit of an inductor, a method for simulating an inductor, a method for creating an equivalent circuit model, and a program according to an embodiment of the present disclosure will be described with reference to the accompanying drawings.

[0015] (1) Embodiment An equivalent circuit model 100 of an inductor, a method for creating the equivalent circuit model 100, and a method for simulating an inductor according to this embodiment will be described with reference to FIGS. 1 to 19. FIG. 1 is a flowchart of the method for creating the equivalent circuit model 100 according to this embodiment. The method for creating the equivalent circuit model 100 according to this embodiment is realized, for example, by a computer including one or more processors executing a program.

[0016] The equivalent circuit model 100 of the inductor of this embodiment is ａｃ DC current I ｄｃ This is an equivalent circuit model for expressing the characteristics of an inductor 90 (see FIG. 2) when an input current i on which an AC current i is superimposed flows through the inductor 90. ａｃ " refers to a current that flows in the opposite directions alternately at regular intervals (a current whose average value is 0 and whose current value changes periodically; a sinusoidal wave current, a triangular wave current, etc.). ｄｃ " means a current whose value is constant (constant current).

[0017] (1.1) AC Loss of Inductor Generally, AC loss Pc in the inductor 90 when a current flows through the inductor 90 can be expressed as a loss due to the resistance of the copper wire 91 of the inductor 90, a loss due to eddy current loss in the core 92 of the inductor 90, and a loss due to hysteresis loss in the core 92. In this embodiment, the AC loss Pc of the inductor 90 is expressed by the following equation (1), where f is the AC current i ａｃ is the frequency of R ａｃ is the AC resistance of the copper wire 91, and K １ , K. ２、 α1 and α2 are constants (parameters specific to each inductor 90), and I ｒｍｓ is the AC current i ａｃ is the effective value of

[0018]

[0019] In equation (1), the first term on the right side (effective value I ｒｍｓThe component proportional to the square of the AC current (hereinafter also referred to as the "first loss component") represents the loss due to the resistance of the copper wire 91 and the loss due to the eddy current loss in the core 92. In addition, in the formula (1), the second term on the right side (effective value I ｒｍｓ The component proportional to the β power of (hereinafter also referred to as the “second loss component”) represents the loss due to the hysteresis loss of the core 92.

[0020] In this embodiment, as shown in equation (1), the exponent β of the second loss component is calculated by multiplying the DC current I ｄｃ This introduces a DC current dependency into the AC loss Pc of the inductor 90.

[0021] In this way, in the method for creating the equivalent circuit model 100 of the inductor, P Ｃ is the AC loss of the inductor 90, f is the AC current i ａｃ The frequency of R ａｃ is the AC resistance of the copper wire 91, K １ , K. ２、 α1 and α2 are constants, I ｒｍｓ AC current i ａｃ The effective value of I ｄｃ is a DC current, the AC loss Pc of the inductor 90 is expressed by equation (1) (step ST1).

[0022] (1.2) Constant K in the constant calculation formula (1) １ , K. ２、 α1 and α2 are DC currents I ｄｃ This can be determined by fitting the frequency characteristics of the actual measured value of AC loss Pc of inductor 90 measured under the condition of .times. ...

[0023] Specifically, the DC current I ｄｃ Under the condition of .times. ... ｒｍｓ AC current i ａｃ is passed through the inductor 90, and the AC loss Pc at that time is measured (actual measurement). This measurement is performed at various values ​​of frequency f (here, 1.6 MHz, 2.7 MHz, 5.8 MHz, 7.7 MHz, and 9.8 MHz) and various effective values ​​I ｒｍｓ (Here, peak current value = √2 × effective value Iｒｍｓ The measurements were performed at various currents (1 A, 2 A, 3 A, 5 A, 6 A, 7 A, 8 A, 9 A, and 10 A). Figure 3 shows the measured values ​​of AC loss Pc of inductor 90 obtained in this manner. The measured values ​​of AC loss Pc of inductor 90 can be measured, for example, according to the capacitive cancellation method described in the reference document (Japanese Patent Laid-Open Publication No. 2022-38455) or using a BH analyzer.

[0024] In this way, in the method for creating the equivalent circuit model 100 of the inductor, the DC current I ｄｃ Under the condition of .times. ...

[0025] Then, at each value of frequency f, K is set so that the curve expressed by equation (1) matches the frequency characteristics of the measured AC loss Pc of the inductor 90. １ , K. ２、 α1, α2, β(I ｄｃ = 0) as a fitting parameter. As the fitting algorithm, for example, CMA-ES (Covariance Matrix Adaptation Evolution Strategy) can be adopted.

[0026] 3 shows graphs G1 to G5 of a plurality of curves (solid lines) indicating fitting results. Graphs G1 to G5 are graphs of curves when the value of frequency f is 1.6 MHz, 2.7 MHz, 5.8 MHz, 7.7 MHz, and 9.8 MHz, respectively. Through this fitting, the constant K １ , K. ２、 α1, α2, β(I ｄｃ The constant K １ , K. ２、 The values ​​of α1 and α2 are shown.

[0027]

[0028] In this way, the method for creating the equivalent circuit model 100 of the inductor includes the constant calculation step ST3. In the constant calculation step ST3, the DC current I ｄｃUnder the condition that is 0, multiple curves expressed by equation (1) for multiple values ​​of frequency f are fitted to the frequency characteristics of the measured values ​​of the AC loss Pc of the inductor at the corresponding values ​​of frequency f, so that the constant K １ , K. ２、 The values ​​of α1 and α2 are calculated.

[0029] (1.3) Ladder Circuit Next, in the method for creating the equivalent circuit model 100 of the inductor, the AC current i ａｃ DC current I ｄｃ A ladder circuit 10 (see FIG. 4) of resistive and inductive elements is defined to represent the inductance and AC loss of the inductor 90 when an input current i superimposed with flows through the inductor 90. Then, various measured values ​​of the inductor 90 are used to determine the circuit constants of the ladder circuit 10 (steps ST4 to ST10). This allows an equivalent circuit model 100 that represents the characteristics of the inductor 90 of interest to be obtained.

[0030] In the equivalent circuit model 100 of the inductor of this embodiment, the ladder circuit 10 includes a first ladder circuit 11 and a second ladder circuit 12 as shown in FIG.

[0031] The first ladder circuit 11 is configured to generate a first loss component (AC current i ａｃ The effective value of I ｒｍｓ This is a circuit for representing a component proportional to the square of

[0032] As shown in FIG. 4, the first ladder circuit 11 includes a resistor R ｊ (j=1 to M; M is an integer of 2 or more) and inductance element L ｊ In the first ladder circuit 11, the first-stage series circuit is connected between a pair of input terminals 111 and 112. In the first ladder circuit 11, the inductance element L ｊ The next-stage series circuit is connected between both ends of the first ladder circuit 11. An input current i is input to an input terminal 111 of the first ladder circuit 11.

[0033] The second ladder circuit 12 is configured to generate a second loss component (AC current i ａｃ The effective value of Iｒｍｓ This is a circuit for representing the component proportional to the β power of

[0034] As shown in FIG. 4, the second ladder circuit 12 includes a resistor R ｈｊ (j=1 to N; N is an integer of 2 or more) and inductance element L ｈｊ In the second ladder circuit 12, the first-stage series circuit is connected between a pair of input terminals 121 and 122. However, in the second ladder circuit 12, the resistance element R ｈ１ The resistance value of the resistor element R ｈ１ By expressing the second ladder circuit 12 so as not to include the resistor element R ｈ１ In the second ladder circuit 12, the resistance value of the inductance element L ｈｊ The next-stage series circuit is connected between both ends of the second ladder circuit 12. The input terminal 121 of the second ladder circuit 12 receives an AC current i ａｃ (= i - I ｄｃ ) to the exponent β(I ｄｃ ) divided by 2 to the power of the current (i-I ｄｃ ) β（Ｉｄｃ）／２ is entered.

[0035] (1.3.1) First Ladder Circuit Calculation Step The method for creating the equivalent circuit model 100 of the inductor includes a first ladder circuit calculation step ST4 (see FIG. 1). In the first ladder circuit calculation step ST4, the circuit constants of the first ladder circuit 11 are calculated. The "circuit constants of the first ladder circuit 11" refer to the resistance element R ｊ (j=1 to M) Each resistance value and inductance element L ｊ (j=1 to M) are the inductance values ​​of the respective ladder circuits 11. In the first ladder circuit calculation step ST4, the number of stages M of the first ladder circuit 11 is determined.

[0036] Specifically, in the first ladder circuit calculation step ST4, the DC current I ｄｃ Under the condition of =0, the impedance Z of the first ladder circuit 11 １ (f) real part Re{Z １ (f)} and the first equivalent resistance R that determines the first loss component. Ｅ１The frequency characteristics of the １ (f) Imaginary part Im{Z １ Fitting (first fitting) is performed so that the frequency characteristics of {(f)} match the frequency characteristics of the actually measured value of the inductance of the inductor 90. As the fitting algorithm, for example, CMA-ES can be adopted.

[0037] Here, "first equivalent resistance R Ｅ１ " is the coefficient of the first term on the right side of equation (1) and is expressed by the following equation (2).

[0038]

[0039] FIG. 5 also shows a graph G10 indicating the frequency characteristics of the measured inductance of the inductor 90.

[0040] In the fitting (first fitting) in the first ladder circuit calculation step ST4, the impedance Z of the first ladder circuit 11 calculated by a circuit simulator such as SPICE is １ (f) real part Re{Z １ (f)} and the frequency characteristic of the imaginary part Im{Z １ (f)} is expressed by the first equivalent resistance R Ｅ１ The circuit constants of the first ladder circuit 11 (resistance element R ｊ The respective resistance values ​​and inductance element L ｊ The fitting can be performed using the respective inductance values ​​as fitting parameters.

[0041] In FIG. 6, the first equivalent resistance R Ｅ１ Graph G100 showing the frequency characteristic (i.e., equation (2)) of the first ladder circuit 11 obtained by fitting, and １ (f) real part Re{Z １ Graphs G101 to G108 show the results of calculating the frequency characteristics of the filter (f) when the number of stages M is 1, 2, 4, 6, 7, 8, 9, and 10, respectively.

[0042] As shown in FIG. 6, as the number of stages M of the first ladder circuit 11 increases, the first equivalent resistance R Ｅ１ The frequency characteristics of the first ladder circuit 11 can be reproduced up to a high frequency f. On the other hand, the calculation load increases as the number of stages M of the first ladder circuit 11 increases. Therefore, the number of stages M of the first ladder circuit 11 is set to a value that is proportional to the frequency of the target AC current i. ａｃ In the example of FIG. 6, for example, the frequency f of the target AC current i ａｃ If the frequency f of the first ladder circuit 11 is about 1 MHz, the number of stages M of the first ladder circuit 11 may be about 8. ａｃ If the frequency f is about 10 MHz, the number of stages M of the first ladder circuit 11 may be about 10 stages.

[0043] In this way, in the method for creating the equivalent circuit model 100 of this embodiment, the circuit constants of the first ladder circuit 11 (resistance element R ｊ The respective resistance values ​​and inductance element L ｊ The inductance values ​​of the first ladder circuit 11 are calculated. １ (f) can be calculated.

[0044] (1.3.2) Second Ladder Circuit Calculation Step The method for creating the equivalent circuit model 100 of the inductor includes a second ladder circuit calculation step ST5 (see FIG. 1). In the second ladder circuit calculation step ST5, the circuit constants of the second ladder circuit 12 are calculated. The "circuit constants of the second ladder circuit 12" refer to the resistance element R ｈｊ (j=1 to N) Each resistance value and inductance element L ｈｊ (j=1 to N) are the inductance values ​​of the respective resistor elements R ｈ１ The resistance value of is 0. In the second ladder circuit calculation step ST5, the number of stages N of the second ladder circuit 12 is determined.

[0045] Specifically, in the second ladder circuit calculation step ST5, the DC current I ｄｃ Under the condition of .times. ... ２ (f) real part Re{Z ２ (f)} and the second equivalent resistance R that determines the second loss component.Ｅ２ The frequency characteristics of the ２ (f) Imaginary part Im{Z ２ (f)} and the frequency characteristics of the measured inductance of the inductor 90 (see FIG. 5) are matched. As the fitting algorithm, for example, CMA-ES can be used.

[0046] Here, "second equivalent resistance R Ｅ２ " can be calculated based on the second term on the right side of equation (1) and expressed by the following equation (3): where T is the AC current i ａｃ This is the cycle.

[0047]

[0048] To explain in detail, the DC current I ｄｃ The second loss component when ρ = 0 is calculated by the second equivalent resistance R Ｅ２ and the second equivalent resistance R Ｅ２ Current flowing through i = i ａｃ This can be expressed as one period integral of the product of

[0049]

[0050] Then, by transforming this equation (4), the second equivalent resistance R Ｅ２ The following equation (3) is obtained:

[0051] In the fitting (second fitting) in the second ladder circuit calculation step ST5, the impedance Z of the second ladder circuit 12 calculated by a circuit simulator such as SPICE is calculated. ２ (f) real part Re{Z ２ (f)} and the frequency characteristic of the imaginary part Im{Z ２ (f)} is expressed by the second equivalent resistance R Ｅ２ The circuit constants of the second ladder circuit 12 (resistance element R ｈｊ The respective resistance values ​​and inductance element L ｈｊ The fitting can be performed using the respective inductance values ​​as fitting parameters.

[0052] In FIG. 7, the second equivalent resistance R Ｅ２ Graph G200 showing the frequency characteristic (i.e., equation (3)) of the second ladder circuit 12, and the impedance Z ２ (f) real part Re{Z ２ Graphs G201 to G207 show the results of calculating the frequency characteristics of {(f)}. Graphs G201 to G207 are graphs when the number of stages N is 2, 3, 4, 5, 6, 8, and 10, respectively.

[0053] As shown in FIG. 7, as the number of stages N of the second ladder circuit 12 increases, the second equivalent resistance R Ｅ２ The frequency characteristics of the second ladder circuit 12 can be reproduced up to a high frequency f. On the other hand, the calculation load increases as the number of stages N of the second ladder circuit 12 increases. Therefore, the number of stages N of the second ladder circuit 12 is set to a value that is proportional to the frequency of the target AC current i. ａｃ In the example of FIG. 7, for example, the frequency f of the target AC current i ａｃ If the frequency f of the second ladder circuit 12 is about 1 MHz, the number of stages N of the second ladder circuit 12 may be about 7. ａｃ If the frequency f is about 10 MHz, the number of stages N of the second ladder circuit 12 may be about 10 stages.

[0054] In this way, in the method for creating the equivalent circuit model 100 of this embodiment, the circuit constants of the second ladder circuit 12 (resistance element R ｈｊ The respective resistance values ​​and inductance element L ｈｊ The inductance values ​​of the second ladder circuit 12 are calculated. ２ (f) can be calculated.

[0055] (1.3.3) Circuit Constants of Ladder Circuit Table 2 shows the circuit constants of the first ladder circuit 11 and the second ladder circuit 12 determined for the inductor 90 of interest.

[0056]

[0057] As described above, the method for creating the equivalent circuit model 100 of the inductor includes the first ladder circuit calculation step ST4 and the second ladder circuit calculation step ST5.

[0058] In the first ladder circuit calculation step ST4, the first fitting is performed to calculate the resistance element R ｊ Resistance value of the inductance element L ｊ In the first fitting, the impedance Z of the first ladder circuit 11 is calculated. １ The frequency characteristics of the real part of (f) and the first equivalent resistance R of the inductor 90 Ｅ１ The frequency characteristic (Equation (2)) of the first ladder circuit 11 is satisfied, and the impedance Z １ Fitting is performed so that the frequency characteristics of the imaginary part of (f) match the frequency characteristics of the actually measured value of the inductance of the inductor 90. Ｅ１ determines the first loss component. The first loss component is the DC current I ｄｃ It can be obtained from the actual measurement of the AC loss Pc of the inductor 90 under the condition that

[0059] More specifically, in the first ladder circuit calculation step ST4, the first fitting is performed to calculate the resistance elements R ｊ Resistance values ​​of (j=1 to M) and inductance elements L of the 1st to Mth stages ｊ In the first fitting, the impedance Z of the first ladder circuit 11 is calculated. １ The frequency characteristics of the real part of (f) and the first equivalent resistance R Ｅ１ and the impedance Z of the first ladder circuit 11. １ Fitting is performed so that the frequency characteristics of the imaginary part of (f) match the measured value of the inductance of the inductor 90.

[0060] In the second ladder circuit calculation step ST5, the resistance element R ｈｊ Resistance value of the inductance element L ｈｊ In the second fitting, the impedance Z of the second ladder circuit 12 is calculated. ２The frequency characteristics of the real part of (f) and the second equivalent resistance R of the inductor 90 Ｅ２ The frequency characteristic (Equation (3)) of the second ladder circuit 12 is satisfied, and the impedance Z ２ Fitting is performed so that the frequency characteristics of the imaginary part of (f) match the frequency characteristics of the actually measured value of the inductance of the inductor 90. Ｅ２ determines the second loss component. The second loss component is the DC current I ｄｃ It can be obtained from the actual measurement of the AC loss Pc of the inductor 90 under the condition that

[0061] More specifically, in the second ladder circuit calculation step ST5, the second fitting is performed to calculate the resistance elements R ｈｊ and the resistance values ​​of the 1st to Nth stage inductance elements L ｈｊ In the second fitting, the impedance Z of the second ladder circuit 12 is calculated. ２ The frequency characteristics of the real part of (f) and the second equivalent resistance R Ｅ２ and the impedance Z of the second ladder circuit 12. ２ Fitting is performed so that the frequency characteristics of the imaginary part of (f) match the measured value of the inductance of the inductor 90.

[0062] (1.4) Introducing DC Current Dependence The method for creating the inductor equivalent circuit model 100 further includes a DC current dependency introducing step (ST6 to ST8). ｄｃ If the component is included, the direct current I ｄｃ The inductance of the inductor 90 changes depending on the DC dependency. This is introduced into the equivalent circuit model 100 of the inductor by the DC dependency introducing step.

[0063] In the method for creating the inductor equivalent circuit model 100 of this embodiment, the DC dependency introducing step includes a first introducing step and a second introducing step.

[0064] In the first introduction step, DC current dependency is introduced into the circuit constants of the first ladder circuit 11. In the method for creating the equivalent circuit model 100 of the inductor according to the present embodiment, in the first introduction step, the first-stage inductance element L １ This introduces DC current dependency into the inductance value of the inductance element L of the first ladder circuit. １ The inductance value of DC current I ｄｃ (step ST8).

[0065] In the second introduction step, DC current dependency is introduced into the circuit constants of the second ladder circuit 12. In the method for creating the equivalent circuit model 100 of the inductor according to the present embodiment, in the second introduction step, the first-stage inductance element L ｈ１ This introduces DC current dependency into the inductance value of the inductance element L of the first stage series circuit of the second ladder circuit. ｈ１ The inductance value of DC current I ｄｃ (step ST8).

[0066] Specifically, first, the DC current I ｄｃ The inductance of the inductor 90 when an input current having a superimposed current I flows through the inductor 90 is expressed as ｄｃ Next, the magnitude of the DC current I ｄｃ The measured inductance value when DC current I = 0 is used as a reference, and the measured inductance value is normalized. ｄｃ DC current I in the range of 0 to 50 A ｄｃ The graph plots points representing the measured normalized inductance when the magnitude of the current is changed in increments of 5 A.

[0067] Then, the approximate expression g(I ｄｃ ) is calculated (step ST7). ｄｃ ) is also shown. In the example of FIG. ｄｃ ) is expressed by the following equation (5).

[0068]

[0069] The inductance element L of the first ladder circuit 11 １ Inductance value L １ (I ｄｃ ) into the DC current I ｄｃ Measured value L when = 0 １ (I ｄｃ = 0) (575 nH in the example of Table 2), the DC current I is calculated as shown in the following equation (6). ｄｃ It is expressed as a function of .

[0070]

[0071] Similarly, the inductance element L of the first stage of the second ladder circuit 12 ｈ１ Inductance value L ｈ１ (I ｄｃ ) into the DC current I ｄｃ Measured value L when = 0 ｈ１ (I ｄｃ = 0) (542 nH in the example of Table 2), the DC current I is calculated as shown in the following equation (7). ｄｃ It is expressed as a function of .

[0072]

[0073] As a result, the inductance element L １ and the inductance value of the inductance element L of the first stage of the second ladder circuit 12 ｈ１ The DC current dependency is introduced into the inductance value (step ST8).

[0074] In the following, the impedance Z of the first ladder circuit 11 １ In (f), the first stage inductance element L １ The DC current dependency is introduced into Z １ (f, I ｄｃ ) and the impedance Z of the second ladder circuit 12 is expressed as ２ In (f), the first stage inductance element L ｈ１ The DC current dependency is introduced into Z ２ (f, I ｄｃ ) is written as

[0075] (1.5) Power Exponent The method for creating the equivalent circuit model 100 of the inductor further includes a power exponent calculation step ST10.

[0076] In the exponent calculation step ST10, the DC current dependency is introduced into the exponent β of the second loss component. In other words, the exponent β is calculated by ｄｃ It is expressed as a function of .

[0077] In the method for creating the equivalent circuit model 100 of the inductor according to this embodiment, the AC current i ａｃ DC current I ｄｃ The actual measured value Pc(f,I) of AC loss in the inductor 90 when the input current i on which ｄｃ , I ｒｍｓ ) and the impedance Z of the first ladder circuit 11 calculated in step ST8 １ (f, I ｄｃ ) and the impedance Z of the second ladder circuit 12 ２ (f, I ｄｃ ) and the calculated value of AC loss (the right side of equation (8)).

[0078]

[0079] Specifically, a certain frequency f and a certain effective value I ｒｍｓ AC current i ａｃ A direct current I of a magnitude ｄｃ The input current i on which the DC current I is superimposed is passed through the inductor 90, and the AC loss Pc at that time is measured (actually measured). ｄｃ Under the condition that the magnitude of is constant, various values ​​of frequency f (here, 1.6 MHz, 2.7 MHz, 5.8 MHz, 7.7 MHz, 9.9 MHz) and various effective values ​​I ｒｍｓ This measurement is carried out at various DC currents I ｄｃ The magnitude of (here, I ｄｃ 9 to 12 show the measured values ​​of AC loss Pc of the inductor 90 obtained in this way. ｄｃ 10 shows the case where the DC current I ｄｃ11 shows the case where the DC current I ｄｃ 12 shows the case where the DC current I ｄｃ = 30A.

[0080] And, the direct current I ｄｃ For each of the cases where the DC current I is 0 A, 10 A, 20 A, and 30 A, a curve showing the AC current characteristics of the AC loss Pc of the inductor 90 is obtained by fitting at each value of the frequency f based on equation (8). ｄｃ is a power of 0 β(I ｄｃ =0), DC current I ｄｃ is the power exponent β(I ｄｃ = 10A), DC current I ｄｃ is the power exponent β(I ｄｃ =20A), DC current I ｄｃ is the power exponent β(I ｄｃ =30A) are calculated. As the fitting algorithm, for example, CMA-ES can be used.

[0081] 9 to 12 also show graphs of multiple curves (solid lines) indicating the fitting results. Graphs G401 to G405 in Fig. 9 are graphs of curves when the frequency f is 1.6 MHz, 2.7 MHz, 5.8 MHz, 7.7 MHz, and 9.9 MHz, respectively. Similarly, graphs G411 to G415 in Fig. 10, graphs G421 to G425 in Fig. 11, and graphs 431 to 435 in Fig. 12 are graphs of curves when the frequency f is 1.6 MHz, 2.7 MHz, 5.8 MHz, 7.7 MHz, and 9.9 MHz, respectively.

[0082] And various DC currents I ｄｃ (Here, I ｄｃ = 0A, 10A, 20A, 30A) is calculated as ｄｃ β(I ｄｃ ) to find an approximate expression.

[0083] This allows us to calculate the power exponent β as a function of the DC current I ｄｃ It can be expressed as a function of

[0084] In this way, the AC current i ａｃ DC current I ｄｃ It is possible to create an equivalent circuit model 100 that represents the characteristics of the inductor 90 when an input current i with a superimposed current flows through the inductor 90. Furthermore, the created equivalent circuit model 100 can be used to calculate the characteristics (AC loss, etc.) of the inductor 90.

[0085] (1.6) Simulation of Inductor Characteristics The inductor simulation method of this embodiment is a method of calculating the characteristics of the inductor 90 using a computer and a simulation model including the created equivalent circuit model 100. As shown in FIG. 4 , the simulation model includes a current source 120.

[0086] In the simulation method of this embodiment, the total loss P ｔｏｔａｌ can be obtained by performing a time domain analysis (time integration) of the loss using the following equation (9).

[0087]

[0088] However, i ｊ is the j-th resistance element R of the first ladder circuit 11 ｊ is the current flowing through the ｈｊ is the j-th resistance element R of the second ladder circuit 12 ｈｊ 4. Pdc is the DC current I ｄｃ The coefficient γ of the second term in equation (9) is expressed by the following equation (10):

[0089]

[0090] The value of γ is determined by the equation (3) when the input current i is a sinusoidal current (i ａｃ =√2×I ｒｍｓ × cosωt), the DC current I ｄｃ Second equivalent resistance R when Ｅ２ Based on the following equation (11) representing the DC current I ｄｃ Second equivalent resistance R when is not 0 Ｅ２ ' and the second equivalent resistance R Ｅ２The ratio (γ = R Ｅ２ ' / R Ｅ２ ) can be obtained from the following equation (12).

[0091]

[0092] As described above, the simulation method of this embodiment includes a loss calculation step. In the loss calculation step, the resistance element R ｊ (j=1 to M), the resistance value of the resistance element R ｊ Current i flowing through ｊ (j=1 to M), the resistance element R in the second ladder circuit 12 ｈｊ (j=2 to N) and the resistance value of the resistance element R ｈｊ Current i flowing through ｈｊ (j=2 to N) to calculate the AC loss Pc of the inductor 90.

[0093] 14 to 19 show the DC current I ｄｃ 14 and 15 show the measured values ​​of the AC loss Pc of the inductor 90 when the DC current I is 10 A, 20 A, and 30 A, respectively, and the calculation results (solid lines) of the AC loss Pc calculated using a simulation model including the inductor equivalent circuit model 100 of this embodiment. ｄｃ 16 and 17 show the case where the DC current I ｄｃ 18 and 19 show the case where the DC current I ｄｃ is 30A. Graphs G11 to G13 in Fig. 14, graphs G21 to G23 in Fig. 16, and graphs G31 to G33 in Fig. 18 are graphs of calculation results when the values ​​of frequency f are 1.6 MHz, 2.7 MHz, and 5.8 MHz, respectively. Graphs G14 and G15 in Fig. 15, graphs G24 and G25 in Fig. 17, and graphs G34 and G35 in Fig. 19 are graphs of calculation results when the values ​​of frequency f are 7.7 MHz and 9.9 MHz, respectively.

[0094] 14 to 19 also show the calculation results (dashed lines) of AC loss Pc calculated using the equivalent circuit model of Non-Patent Document 1 (hereinafter also referred to as the "comparison example"). Graphs G911 to G913 in FIG. 14, graphs G921 to G923 in FIG. 16, and graphs G931 to G933 in FIG. 18 are graphs of calculation results when the frequency f is 1.6 MHz, 2.7 MHz, and 5.8 MHz, respectively. Graphs G914 and G915 in FIG. 15, graphs G924 and G925 in FIG. 17, and graphs G934 and G935 in FIG. 19 are graphs of calculation results when the frequency f is 7.7 MHz and 9.9 MHz, respectively.

[0095] As can be seen from FIGS. 14 to 19, according to the equivalent circuit model 100 of the inductor of this embodiment, the DC current I ｄｃ Even when the input current i having the superimposed current flows through the inductor 90, the AC loss Pc in the inductor 90 can be accurately represented.

[0096] (2) Modifications The above embodiment is merely one of various embodiments of the present disclosure. The above embodiment can be modified in various ways depending on the design, etc., as long as the object of the present disclosure can be achieved. Furthermore, functions similar to the method for creating the equivalent circuit model 100 according to the above embodiment may be embodied in a computer program, a computer program product including a computer program, a non-transitory recording medium on which a computer program is recorded, or the like. A (computer) program according to one aspect is a program that causes one or more processors to execute the above method for creating the equivalent circuit model 100.

[0097] (3) Aspects As can be seen from the above-described embodiments and modifications, the present specification discloses the following aspects.

[0098] The equivalent circuit model (100) of the inductor of the first aspect is ａｃ ) to DC current (I ｄｃThe present invention provides a ladder circuit (10) of resistive elements and inductive elements for representing the inductance and AC loss (Pc) of an inductor (90) when an input current (i) on which an AC current (Pc) is superimposed flows through the inductor (90). The ladder circuit (10) includes a first ladder circuit (11) and a second ladder circuit (12). The first ladder circuit (11) represents the AC current (i) superimposed on the AC loss (Pc) of the inductor (90). ａｃ ) effective value (I ｒｍｓ The first ladder circuit (11) receives an input current (i). The second ladder circuit (12) calculates the AC loss (Pc) of the inductor (90) by dividing the AC loss (i ａｃ ) effective value (I ｒｍｓ The second ladder circuit (12) is a circuit for representing the second loss component proportional to the β power of the AC current (i ａｃ ) is the current ((i-I ｄｃ ) β（Ｉｄｃ）／２ ) is input from the current source (120). The exponent β in the second loss component is ｄｃ ) in the first ladder circuit (11). ｊ ) resistance value and inductance element (L ｊ The inductance value of the first ladder circuit (11) is calculated by performing a first fitting. １ (f)) and the frequency characteristic of the real part of the first equivalent resistance (R Ｅ１ ) frequency characteristics of the first ladder circuit (11) and the impedance (Z １ Fitting is performed so that the frequency characteristics of the imaginary part of the first equivalent resistance (R Ｅ１ ) determines the first loss component. The first loss component is the DC current (I ｄｃ The AC loss (Pc) of the inductor (90) is determined by measuring the AC loss (Pc) of the inductor (90) under the condition that the resistance element (R ｈｊ ) resistance value and inductance element (L ｈｊThe inductance value of the second ladder circuit (12) is calculated by performing a second fitting. ２ (f)) and the frequency characteristic of the real part of the second equivalent resistance (R Ｅ２ ) frequency characteristics of the second ladder circuit (12) and the impedance (Z １ Fitting is performed so that the frequency characteristics of the imaginary part of the second equivalent resistance (R Ｅ２ ) determines the second loss component. The second loss component is the DC current (I ｄｃ ) is determined by measuring the AC loss (Pc) of the inductor (90) under the condition that the AC loss (Pc) is zero.

[0099] According to this aspect, the DC current (I ｄｃ It is possible to accurately represent the AC loss (Pc) in the inductor (90) when an input current (i) on which the input current (i) is superimposed flows through the inductor (90).

[0100] The second aspect of the inductor simulation method is a method for calculating the characteristics of an inductor (90) using a computer with a simulation model including an equivalent circuit model (100) of the inductor. The simulation model includes the equivalent circuit model (100) and a current source (120). The equivalent circuit model (100) calculates the characteristics of an AC current (i ａｃ ) to DC current (I ｄｃ The present invention provides a ladder circuit (10) of resistive elements and inductive elements for representing the inductance and AC loss (Pc) of an inductor (90) when an input current (i) on which an AC current (Pc) is superimposed flows through the inductor (90). The ladder circuit (10) includes a first ladder circuit (11) and a second ladder circuit (12). The first ladder circuit (11) represents the AC current (i) superimposed on the AC loss (Pc) of the inductor (90). ａｃ ) effective value (I ｒｍｓ The first ladder circuit (11) receives an input current (i). The second ladder circuit (12) calculates the AC loss (Pc) of the inductor (90) by dividing the AC loss (i ａｃ) effective value (I ｒｍｓ The second ladder circuit (12) is a circuit for representing the second loss component proportional to the β power of the AC current (i ａｃ ) is the current ((i-I ｄｃ ) β（Ｉｄｃ）／２ ) is input from the current source (120). The exponent β in the second loss component is ｄｃ ) in the first ladder circuit (11). ｊ ) resistance value and inductance element (L ｊ The inductance value of the first ladder circuit (11) is calculated by performing a first fitting. １ (f)) and the frequency characteristic of the real part of the first equivalent resistance (R Ｅ１ ) frequency characteristics of the first ladder circuit (11) and the impedance (Z １ Fitting is performed so that the frequency characteristics of the imaginary part of the first equivalent resistance (R Ｅ１ ) determines the first loss component. The first loss component is the DC current (I ｄｃ The AC loss (Pc) of the inductor (90) is determined by measuring the AC loss (Pc) of the inductor (90) under the condition that the resistance element (R ｈｊ ) resistance value and inductance element (L ｈｊ The inductance value of the second ladder circuit (12) is calculated by performing a second fitting. ２ (f)) and the frequency characteristic of the real part of the second equivalent resistance (R Ｅ２ ) frequency characteristics of the second ladder circuit (12) and the impedance (Z １ Fitting is performed so that the frequency characteristics of the imaginary part of the second equivalent resistance (R Ｅ２ ) determines the second loss component. The second loss component is the DC current (I ｄｃThe loss is calculated by measuring the AC loss (Pc) of the inductor (90) under the condition that the resistance element (R ｊ ) in the first ladder circuit (11), ｊ ) current (i ｊ ), the resistive element (R ｈｊ ) and the resistance value of the resistive element (R ｈｊ ) current (i ｈｊ ) to calculate the AC loss (Pc) of the inductor (90).

[0101] According to this aspect, the direct current (I ｄｃ When an input current (i) on which a superimposed current (Pc) flows through the inductor (90), it is possible to accurately determine the AC loss (Pc) in the inductor (90).

[0102] In the inductor simulation method of the third aspect, in the second aspect, the first ladder circuit (11) includes a resistive element (R ｊ ) and an inductance element (L ｊ The first ladder circuit (11) has M stages (M is an integer of 2 or more) of series circuits with the inductance element (L ｊ The inductance element (L) of the first ladder circuit (11) is connected to the next series circuit. １ ) is the inductance value of the DC current (I ｄｃ ) is a function of

[0103] According to this aspect, the direct current (I ｄｃ When an input current (i) on which a superimposed current (Pc) flows through the inductor (90), it is possible to accurately determine the AC loss (Pc) in the inductor (90).

[0104] In the inductor simulation method of the fourth aspect, in the second or third aspect, the second ladder circuit (12) includes a resistive element (R ｈｊ ) and an inductance element (L ｈｊThe second ladder circuit (12) has N stages (N is an integer of 2 or more) of series circuits with the inductance element (L ｈｊ The second ladder circuit (12) is configured by connecting the resistor element (R ｈ１ The resistance value of the inductance element (L) of the first stage series circuit of the second ladder circuit (12) is 0. ｈ１ ) is the inductance value of the DC current (I ｄｃ ) is a function of

[0105] According to this aspect, the direct current (I ｄｃ When an input current (i) on which a superimposed current (Pc) flows through the inductor (90), it is possible to accurately determine the AC loss (Pc) in the inductor (90).

[0106] The fifth aspect of the method for creating an equivalent circuit model is a method for creating an equivalent circuit model (100) of an inductor. The equivalent circuit model (100) is a method for creating an equivalent circuit model (i ａｃ ) to DC current (I ｄｃ The present invention provides a ladder circuit (10) of resistive elements and inductive elements for representing the inductance and AC loss (Pc) of an inductor (90) when an input current (i) on which an AC current (Pc) is superimposed flows through the inductor (90). The ladder circuit (10) includes a first ladder circuit (11) and a second ladder circuit (12). The first ladder circuit (11) represents the AC current (i) superimposed on the AC loss (Pc) of the inductor (90). ａｃ ) effective value (I ｒｍｓ The first ladder circuit (11) receives an input current (i). The second ladder circuit (12) calculates the AC loss (Pc) of the inductor (90) by dividing the AC loss (i ａｃ ) effective value (I ｒｍｓ The second ladder circuit (12) is a circuit for representing the second loss component proportional to the β power of the AC current (i ａｃ ) is the current ((i-I ｄｃ ) β（Ｉｄｃ）／２ ) is input from the current source (120). The exponent β in the second loss component is ｄｃ) is a function of the resistance element (R ｊ ) resistance value and inductance element (L ｊ In the first fitting, the impedance (Z １ (f)) and the frequency characteristic of the real part of the first equivalent resistance (R Ｅ１ ) frequency characteristics of the first ladder circuit (11) and the impedance (Z １ Fitting is performed so that the frequency characteristics of the imaginary part of the first equivalent resistance (R Ｅ１ ) determines the first loss component. The first loss component is the DC current (I ｄｃ The AC loss (Pc) of the inductor (90) is calculated by measuring the AC loss (Pc) of the inductor (90) under the condition that the AC loss (Pc) of the inductor (90) is 0. In the second ladder circuit calculation step (ST5), the second fitting is performed to calculate the AC loss (Pc) of the resistor element (R ｈｊ ) resistance value and inductance element (L ｈｊ In the second fitting, the impedance (Z ２ (f)) and the frequency characteristic of the real part of the second equivalent resistance (R Ｅ２ ) frequency characteristics of the second ladder circuit (12) and the impedance (Z １ Fitting is performed so that the frequency characteristics of the imaginary part of the second equivalent resistance (R Ｅ２ ) determines the second loss component. The second loss component is the DC current (I ｄｃ ) is determined by measuring the AC loss (Pc) of the inductor (90) under the condition that the AC loss (Pc) is zero.

[0107] According to this aspect, the direct current (I ｄｃIt is possible to create an equivalent circuit model (100) of an inductor that can accurately represent AC loss (Pc) in an inductor (90) when an input current (i) on which AC loss (Pc) is superimposed flows through the inductor (90).

[0108] The method for creating an equivalent circuit model of the sixth aspect is the same as the fifth aspect, and further includes a constant calculation step (ST3). In the constant calculation step (ST3), a constant K is calculated by performing a third fitting based on the following equation (1) that represents the frequency characteristic of the AC loss (Pc) of the inductor (90): １ , K. ２、 The values ​​of α1 and α2 are calculated. In the third fitting, the DC current (I ｄｃ Under the condition that the frequency characteristic of the AC loss (Pc) of the inductor (90) at the corresponding frequency (f) is 0, fitting is performed so that the curves expressed by the formula (1) for the multiple frequency (f) values ​​match the frequency characteristics of the actual measured value of the AC loss (Pc) of the inductor (90) at the corresponding frequency (f) values. Ｃ is the AC loss of the inductor (90), and f is the AC current (i ａｃ ) frequency, R ａｃ is the AC resistance of the copper wire (91) in the inductor (90), K １ , K. ２、 α1 and α2 are constants, I ｒｍｓ is the AC current (i ａｃ ) effective value, I ｄｃ is the DC current.

[0109]

[0110] According to this aspect, the direct current (I ｄｃ It is possible to create an equivalent circuit model (100) of an inductor that can accurately represent AC loss (Pc) in an inductor (90) when an input current (i) on which AC loss (Pc) is superimposed flows through the inductor (90).

[0111] In the method for creating an equivalent circuit model of the seventh aspect, in the sixth aspect, the first ladder circuit (11) is ｊ ) and an inductance element (L ｊ The first ladder circuit (11) has M stages (M is an integer of 2 or more) of series circuits with the inductance element (Lｊ ) and the next-stage series circuit is connected between both ends of the resistor elements (R ｊ ) and the resistance values ​​of the 1st to Mth inductance elements (L ｉ In the first fitting, the impedance (Z １ (f)) and the first equivalent resistance (R Ｅ１ ) frequency characteristics of the first ladder circuit (11) and the impedance (Z １ Fitting is performed so that the frequency characteristics of the imaginary part of (f)) match the frequency characteristics of the actually measured value of the inductance of the inductor (90).

[0112]

[0113] According to this aspect, the direct current (I ｄｃ It is possible to create an equivalent circuit model (100) of an inductor that can accurately represent AC loss (Pc) in an inductor (90) when an input current (i) on which AC loss (Pc) is superimposed flows through the inductor (90).

[0114] The method for creating an equivalent circuit model of the eighth aspect is the same as the seventh aspect, but further includes a first introduction step (ST8). In the first introduction step (ST8), an inductance element (L １ ) is the inductance value of the DC current (I ｄｃ ) as a function of

[0115] According to this aspect, the direct current (I ｄｃ It is possible to create an equivalent circuit model (100) of an inductor that can accurately represent AC loss (Pc) in an inductor (90) when an input current (i) on which AC loss (Pc) is superimposed flows through the inductor (90).

[0116] In the method for creating an equivalent circuit model of the ninth aspect, in any one of the sixth to eighth aspects, the second ladder circuit (12) includes a resistor element (R ｈｊ ) and an inductance element (L ｈｊThe second ladder circuit (12) has N stages (N is an integer of 2 or more) of series circuits with the inductance element (L ｈｊ The second ladder circuit (12) is configured by connecting the resistor element (R ｈ１ ) has a resistance value of 0. In the second ladder circuit calculation step (ST5), the second fitting is performed to calculate the resistance values ​​of the second to Nth resistance elements (R ｈｊ ) and the resistance values ​​of the 1st to Nth stage inductance elements (L ｈｊ In the second fitting, the impedance (Z ２ (f)) and the frequency characteristic of the real part of the second equivalent resistance (R Ｅ２ ) frequency characteristics of the second ladder circuit (12) and the impedance (Z ２ Fitting is performed so that the frequency characteristics of the imaginary part of (f)) match the frequency characteristics of the actually measured value of the inductance of the inductor (90).

[0117]

[0118] where T is the AC current (i ａｃ ) period.

[0119] According to this aspect, the direct current (I ｄｃ It is possible to create an equivalent circuit model (100) of an inductor that can accurately represent AC loss (Pc) in an inductor (90) when an input current (i) on which AC loss (Pc) is superimposed flows through the inductor (90).

[0120] The method for creating an equivalent circuit model of the tenth aspect is the same as the ninth aspect, but further includes a second introduction step (ST8). In the second introduction step (ST8), an inductance element (L ｈ１ ) is the inductance value of the DC current (I ｄｃ ) as a function of

[0121] According to this aspect, the direct current (I ｄｃIt is possible to create an equivalent circuit model (100) of an inductor that can accurately represent AC loss (Pc) in an inductor (90) when an input current (i) on which AC loss (Pc) is superimposed flows through the inductor (90).

[0122] A program according to an eleventh aspect causes one or more processors to execute the method for creating an equivalent circuit model according to any one of the fifth to tenth aspects.

[0123] 100 Equivalent circuit model 10 Ladder circuit 11 First ladder circuit R ｊ Resistance element L ｊ Inductance element Z １ (f) Impedance i ｊ Resistance element R ｊ Current flowing through 12 Second ladder circuit R ｈｊ Resistance element L ｈｊ Inductance element Z ２ (f) Impedance i ｈｊ Resistance element R ｈｊ Current flowing through 120 Current source 90 Inductor 91 Copper wire 92 Core R Ｅ１ First equivalent resistance R Ｅ２ Second equivalent resistance i Input current i ａｃ AC current I ｒｍｓ Effective value f Frequency I ｄｃ DC current Pc AC loss ST3 Constant calculation process ST4 First ladder circuit calculation process ST5 Second ladder circuit calculation process ST8 First introduction process, second introduction process

Claims

1. An equivalent circuit model of an inductor, the equivalent circuit model comprising a ladder circuit of resistance elements and inductance elements for representing the inductance and AC loss of the inductor when an input current in which a DC current is superimposed on an AC current flows through the inductor, the ladder circuit comprising: a first ladder circuit for representing a first loss component of the AC loss of the inductor that is proportional to the square of the effective value of the AC current, the first ladder circuit receiving the input current; and a second ladder circuit for representing a second loss component of the AC loss of the inductor that is proportional to the β power of the effective value of the AC current, the second ladder circuit receiving a current that is a power of the AC current divided by 2 from a current source, the power β of the AC current being a function of the DC current, the resistance value of the resistance element and the inductance value of the inductance element in the first ladder circuit being an equivalent circuit model of an inductor, wherein the resistance value of the resistive element and the inductance value of the inductance element in the second ladder circuit are determined by fitting such that the frequency characteristics of the real part of the impedance of the first ladder circuit match the frequency characteristics of a first equivalent resistance that determines the first loss component obtained from actual measurement of the AC loss of the inductor under the condition that the DC current is 0, and the frequency characteristics of the imaginary part of the impedance of the first ladder circuit match the frequency characteristics of the actual measured value of the inductance of the inductor; and the resistance value of the resistive element and the inductance value of the inductance element in the second ladder circuit are determined by fitting such that the frequency characteristics of the real part of the impedance of the second ladder circuit match the frequency characteristics of a second equivalent resistance that determines the second loss component obtained from actual measurement of the AC loss of the inductor under the condition that the DC current is 0, and the frequency characteristics of the imaginary part of the impedance of the second ladder circuit match the frequency characteristics of the actual measured value of the inductance of the inductor.

2. A method for simulating an inductor, using a computer to calculate characteristics of an inductor using a simulation model including an equivalent circuit model of the inductor, wherein the simulation model includes the equivalent circuit model and a current source, and the equivalent circuit model comprises a ladder circuit of resistance elements and inductance elements for representing the inductance and AC loss of the inductor when an input current in which a DC current is superimposed on an AC current flows through the inductor, and the ladder circuit includes: a first ladder circuit for representing a first loss component of the AC loss of the inductor that is proportional to the square of the effective value of the AC current, the first ladder circuit receiving the input current, and a second ladder circuit for representing a second loss component of the AC loss of the inductor that is proportional to the β power of the effective value of the AC current, the second ladder circuit receiving a current that is a power of the AC current divided by 2, the second ladder circuit receiving from the current source, and wherein the power β of the second loss component is a function of the DC current, the resistance value of the resistive element and the inductance value of the inductance element in the first ladder circuit are determined by fitting such that the frequency characteristics of the real part of the impedance of the first ladder circuit match the frequency characteristics of a first equivalent resistance that determines the first loss component determined from actual measurement of the AC loss of the inductor under the condition that the DC current is zero, and that the frequency characteristics of the imaginary part of the impedance of the first ladder circuit match the frequency characteristics of the actual measured value of the inductance of the inductor; the resistance value of the resistive element and the inductance value of the inductance element in the second ladder circuit are determined by fitting such that the frequency characteristics of the real part of the impedance of the second ladder circuit match the frequency characteristics of a second equivalent resistance that determines the second loss component determined from actual measurement of the AC loss of the inductor under the condition that the DC current is zero, and that the frequency characteristics of the imaginary part of the impedance of the second ladder circuit match the frequency characteristics of the actual measured value of the inductance of the inductor;The simulation method includes a loss calculation step of calculating the AC loss of the inductor using a resistance value of the resistive element in the first ladder circuit, a current flowing through the resistive element in the first ladder circuit, a resistance value of the resistive element in the second ladder circuit, and a current flowing through the resistive element in the second ladder circuit.

3. The inductor simulation method according to claim 2, wherein the first ladder circuit comprises M stages (M is an integer of 2 or more) of series circuits of resistance elements and inductance elements, and the next stage series circuit is connected between both ends of the inductance element in the previous stage series circuit, and the inductance value of the inductance element in the first stage series circuit of the first ladder circuit is a function of the DC current.

4. The inductor simulation method according to claim 2 or 3, wherein the second ladder circuit comprises N stages (N is an integer of 2 or greater) of series circuits of resistance elements and inductance elements, with the next stage series circuit connected between both ends of the inductance element in the previous stage series circuit, with the resistance value of the resistance element in the first stage series circuit being 0, and the inductance value of the inductance element in the first stage series circuit of the second ladder circuit being a function of the DC current.

5. A computer-implemented method for creating an equivalent circuit model of an inductor, wherein the equivalent circuit model comprises a ladder circuit of resistance elements and inductance elements for representing the inductance and AC loss of the inductor when an input current in which a DC current is superimposed on an AC current flows through the inductor, the ladder circuit comprising: a first ladder circuit for representing a first loss component of the AC loss of the inductor that is proportional to the square of the effective value of the AC current, the first ladder circuit receiving the input current; and a second ladder circuit for representing a second loss component of the AC loss of the inductor that is proportional to the β power of the effective value of the AC current, the second ladder circuit receiving a current that is a power of the AC current divided by 2 from a current source, the power β of the second loss component being a function of the DC current, the method for creating the equivalent circuit model comprising: a first ladder circuit calculation step of determining a resistance value of the resistive element and an inductance value of the inductance element in the first ladder circuit by performing fitting so that the frequency characteristics of the real part of the impedance of the first ladder circuit match the frequency characteristics of a first equivalent resistance that determines the first loss component determined from actual measurement of the AC loss of the inductor under a condition where the DC current is zero, and so that the frequency characteristics of the imaginary part of the impedance of the first ladder circuit match the frequency characteristics of the actual measured value of the inductance of the inductor; and a second ladder circuit calculation step of determining a resistance value of the resistive element and an inductance value of the inductance element in the second ladder circuit by performing fitting so that the frequency characteristics of the real part of the impedance of the second ladder circuit match the frequency characteristics of a second equivalent resistance that determines the second loss component determined from actual measurement of the AC loss of the inductor under a condition where the DC current is zero, and so that the frequency characteristics of the imaginary part of the impedance of the second ladder circuit match the frequency characteristics of the actual measured value of the inductance of the inductor. How to create an equivalent circuit model.

6. P Ｃ is the AC loss of the inductor, f is the frequency of the AC current, R ａｃ is the AC resistance of the copper wire in the inductor, K １ , K. ２、 α1 and α2 are constants, I ｒｍｓ the effective value of the AC current, I ｄｃ is the DC current, and based on the following equation (1) which represents the frequency characteristic of the AC loss of the inductor, Under the condition that the DC current is 0, fitting is performed so that a plurality of curves expressed by the formula (1) for a plurality of frequency values ​​and the frequency characteristics of the actually measured values ​​of the AC loss of the inductor at the corresponding frequency values ​​match each other, thereby obtaining the constant K １ , K. ２、 The method for creating an equivalent circuit model according to claim 5 , further comprising a constant calculation step of determining values ​​of α1 and α2.

7. The first ladder circuit comprises M stages (M is an integer of 2 or more) of series circuits of resistance elements and inductance elements, with a next stage series circuit connected between both ends of an inductance element in a previous stage series circuit, and the first ladder circuit calculation step determines the resistance values ​​of the resistance elements in the 1st to Mth stages and the inductance values ​​of the inductance elements in the 1st to Mth stages by performing fitting so that the frequency characteristics of the real part of the impedance of the first ladder circuit match the frequency characteristics of the first equivalent resistance expressed by the following equation (2) and so that the frequency characteristics of the imaginary part of the impedance of the first ladder circuit match the frequency characteristics of the actually measured value of the inductance of the inductor. Here, R Ｅ１ The method for creating an equivalent circuit model according to claim 6 , wherein: is the first equivalent resistance.

8. The method for creating an equivalent circuit model according to claim 7, further comprising a first introduction step of expressing the inductance value of the inductance element of the first stage series circuit of the first ladder circuit as a function of the DC current.

9. The second ladder circuit comprises N stages (N is an integer of 2 or more) of series circuits of resistance elements and inductance elements, and is configured by connecting a next stage series circuit between both ends of an inductance element in a previous stage series circuit, with the resistance value of the resistance element in the first stage series circuit being 0, and the second ladder circuit calculation step determines the resistance values ​​of the resistance elements in the second to N stages and the inductance values ​​of the inductance elements in the first to N stages by performing fitting so that the frequency characteristics of the real part of the impedance of the second ladder circuit match the frequency characteristics of the second equivalent resistance expressed by the following equation (3) and so that the frequency characteristics of the imaginary part of the impedance of the second ladder circuit match the frequency characteristics of the actually measured value of the inductance of the inductor. Here, R Ｅ２ 9. The method for creating an equivalent circuit model according to claim 6, wherein: is the second equivalent resistance, and T is a period of the AC current.

10. The method for creating an equivalent circuit model according to claim 9, further comprising a second introduction step of expressing the inductance value of the inductance element of the first stage series circuit of the second ladder circuit as a function of the DC current.

11. A program that causes one or more processors to execute the method for creating an equivalent circuit model according to any one of claims 5 to 10.

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