Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This manuscript proposes a modified Jiles–Atherton (J–A) hysteresis model aimed at improving the representation of minor loops by introducing an excitation-dependent parameterization and implementing the model as a SPICE-compatible macromodel. The topic is relevant to the modeling of magnetic components for circuit-level simulation, and the combination of hysteresis modeling with practical SPICE implementation is of interest to both the magnetics and power electronics communities.

The manuscript is generally well organized, and the proposed approach is technically sound. The numerical and waveform-based validations indicate that the modified model can better reproduce minor-loop behavior than the conventional J–A formulation. However, several methodological and clarity issues should be addressed to strengthen the scientific rigor, reproducibility, and physical interpretation of the work. The manuscript can be considered for publication after  moderate revisions addressing the points below.

1,The manuscript introduces an excitation-dependent parameter using a quantity denoted as Bpp​, described as a peak-to-peak magnetic flux density. However, Eq. (15) defines this quantity as the time-averaged absolute value of B(t) over one period. This definition does not correspond to the conventional peak-to-peak value.This mismatch between nomenclature and mathematical definition may confuse readers and raises questions about the physical interpretation of the parameter dependence.

2, The parameter extraction procedure appears to rely mainly on manual tuning using a SPICE-based parameter adjustment tool. While this may be acceptable for engineering practice, the manuscript would benefit from a clearer and more systematic description of the extraction workflow.

3,The validation is primarily based on visual comparison of hysteresis loops and transient waveforms. While these comparisons are informative, they remain qualitative. To strengthen the validation, the authors are encouraged to include at least one quantitative metric, such as:Area error of the hysteresis loop; Root-mean-square error between measured and simulated waveforms; Harmonic distortion or spectral error for transient responses. Even a limited quantitative comparison would substantially improve the objectivity of the performance assessment.

4, The manuscript acknowledges that effects such as eddy currents, frequency dependence, and temperature variations are not considered. However, the limitations of the proposed approach are not sufficiently discussed in the main text. The authors should more explicitly state: The intended operating frequency range;The excitation conditions under which the model is expected to be valid, Whether the proposed modification primarily targets quasi-static or low-frequency hysteresis behavior.

Such clarification will help readers understand the practical boundaries of the model.

Author Response

Many thanks for providing a useful feedback! The explanations for specific comments are below.

Comment 1: The manuscript introduces an excitation-dependent parameter using a quantity denoted as Bpp​, described as a peak-to-peak magnetic flux density. However, Eq. (15) defines this quantity as the time-averaged absolute value of B(t) over one period. This definition does not correspond to the conventional peak-to-peak value.This mismatch between nomenclature and mathematical definition may confuse readers and raises questions about the physical interpretation of the parameter dependence.

Response 1: The equation for Bpp is correct. SPICE doesn’t provide a direct way to get the peak-to peak value. The time denoted by T is not a period but transient simulation. This equation represent the output voltage of the ideal full wave rectifier that may be represented by ideal diode bridge and ideal ripple filter. The T is replaced by Tsim to avoid mixing its value with period. Added more explanations around line 254. The new number of equation in the revised version is (16).

Comment 2: The parameter extraction procedure appears to rely mainly on manual tuning using a SPICE-based parameter adjustment tool. While this may be acceptable for engineering practice, the manuscript would benefit from a clearer and more systematic description of the extraction workflow.

Response 2: A short description of the extraction procedure added in the Section 4.1 near the Lines 284-298.

Comment 3: The validation is primarily based on visual comparison of hysteresis loops and transient waveforms. While these comparisons are informative, they remain qualitative. To strengthen the validation, the authors are encouraged to include at least one quantitative metric, such as:Area error of the hysteresis loop; Root-mean-square error between measured and simulated waveforms; Harmonic distortion or spectral error for transient responses. Even a limited quantitative comparison would substantially improve the objectivity of the performance assessment.

Response 3: The paper contains numerical comparison of the simulated and measured data.

• BH-loops area numerically compared in the Table 2 (third column)

• RMSE between simulated and measured waveforms computed in Table 4.

• Harmonics amplitudes are compared in the Table 3.

Comment 4: The manuscript acknowledges that effects such as eddy currents, frequency dependence, and temperature variations are not considered. However, the limitations of the proposed approach are not sufficiently discussed in the main text. The authors should more explicitly state: The intended operating frequency range;The excitation conditions under which the model is expected to be valid, Whether the proposed modification primarily targets quasi-static or low-frequency hysteresis behavior.

Response 4: Added note in the end of Section 2.2 (Lines 117-123) and in the Conclusion (Line 408).

Reviewer 2 Report

Comments and Suggestions for Authors

Introduction is well-organized and the references are properly chosen. Section 2 describes the theoretical aspect regarding the JA model and the circuit model simulation considered. Here, all the aspects are clearly indicated. In Section 3 the discussion is about the improvements of the JA models. Here, I suggest an elaborated discussion about the procedures used for fitting the mentioned parameters (Cminor, Cmajor, γ). In Figure 11 the major and the minor loops are not symmetrical for the axis? At the beginning of Section 4 there are presented the JA model parameters for 5 materials, but after that the results are only for the Epcos N87 core. Please explain if the other materials do not provide correct data or indicate in a table to shorten the results.

Author Response

Many thanks for providing a useful feedback! The explanations for specific comments are below.

 

Comment 1: Here, I suggest an elaborated discussion about the procedures used for fitting the mentioned parameters (Cminor, Cmajor, γ).

 

Response 1: Added a paragraph describing the parameter extraction procedure in the Section 4.1 around Lines 284-298

 

Comment 2: In Figure 11 the major and the minor loops are not symmetrical for the axis?

 

Response 2: Possible zero shift is taken in the account while the raw measurement data conversion to digital form.

 

Comment 3: At the beginning of Section 4 there are presented the JA model parameters for 5 materials, but after that the results are only for the Epcos N87 core. Please explain if the other materials do not provide correct data or indicate in a table to shorten the results.

 

Response 3: All considered materials provide correct results. The simulation and measurement data for other materials mentioned in the Table 1 are uploaded via Zenodo as the supplementary data and could be accessed from the Data Availability Statement section. Added the note around the Line 416.

Reviewer 3 Report

Comments and Suggestions for Authors

Several aspect can be highlighted, as follows:

1. The proposed theoretical approach is consistent with the magnetic circuits hypothesis, namely: uniform magnetic flux distribution on the corss-sectional surface, no flux disperssion,  extremely narrow airgap (Lg), etc. Otherwise, in the airgap region the flux is fringe outwards, effectively increasing the cross-sectional area occupied by the field lines. All these hypothesis are absent in the introductory part of the research.
2. Figure 1 is missing the reference direction for the two currents i1(t) and i2(t). Consequently, there is no means to know the reference direction for the magnetomotive force (mmf) when Ampere's circuital law is later applied to get Eq. (5).
3. In Eq. (5),  index '0' is not necessary, not being previoulsy considered in (2). Consequently, k = 1, 2. The sum notation is useless.
4. In (1), if the current is function of time, the magnetic field strength (in the left-hand side) should be a function of time.
5. At least one bibiographical referencesshould be indicated for the summary of classical Jiles-Atherton formalism.
6. The proposed modified Jiles-Atherton model is difficult to follow using the actual Spice circuit diagrams and command lines, as shown in Figs. 2, 3, 4, and 5. A flowchart would be more illustrative and easy to understand and interpret by the reader.
7. How are the 'convergence helper' resitors sized, and how they affect result accuracy and convergence?
8. To make the paper self-contained, it would be briefly mention in what consist "power law dependency". Similarly, how is the Hausdorff distance defined?
9. At the point they are mentioned in the text, there is no description of the experimental model used to obtain the experimental data shown in Figure 8 nor the conditions in which the experiments were carried out. The experimental model is described later in the manuscript.
10. The equation of line 224 (page 10) is not dimensionally homogeneous. Inside the two parenthesis a dimensionless quantity, i.e., 1 is added to a voltage. The left-hand side a voltage equals a ratio of two voltages in the right-hand side of the equation.
11. If there are two ferrite materials have, probably "relative" - not specified by the author, permittivities of 1700 and 1500, that implies the use of LINEAR materials. Hence, there is no point in modeling any nonlinear B-H characteristic or hysteresis loop.
12. In Table 2 the unit of measurement for the Hausdorff distance (d) is not specified.
13. How is the so-called 'transient' regime generated for the results shown in Figure 16. Apparently, there is not 'transient', but a a distorted periodical (nonsinusoidal) regime, as also confirmed by the waveforms plotted in Figure 17.
14. The supposed improvement of the Jiles-Atherton model consist in a smoother 'zero crossing' in Figure 16, but with a significanly larger maximum value. Then, in what consist the actual advancement or novelty proposed in the paper?

Comments on the Quality of English Language

The English text is affected by many grammar errors and inconsistencies, too many to be enumerated in this review report.

Author Response

Many thanks for providing a useful feedback! The explanations for specific comments are below.

 

Comment 1: The proposed theoretical approach is consistent with the magnetic circuits hypothesis, namely: uniform magnetic flux distribution on the cross-sectional surface, no flux dispersion,  extremely narrow airgap (Lg), etc. Otherwise, in the airgap region the flux is fringe outwards, effectively increasing the cross-sectional area occupied by the field lines. All these hypothesis are absent in the introductory part of the research.

 

Response 1: Thanks for pointing this. Added note on the model restrictions in the Introduction around Line 45-49.

 

Comment 2: Figure 1 is missing the reference direction for the two currents i1(t) and i2(t). Consequently, there is no means to know the reference direction for the magnetomotive force (mmf) when Ampere's circuital law is later applied to get Eq. (5).

Response 2: The Section 2.1 containing the mentioned Figure was removed by request of another reviewer.

 

Comment 3: In Eq. (5),  index '0' is not necessary, not being previously considered in (2). Consequently, k = 1, 2. The sum notation is useless.

Response 3: The Section 2.1 containing Equation (5) was removed by request of another reviewer.

 

Comment 4: In (1), if the current is function of time, the magnetic field strength (in the left-hand side) should be a function of time.

Response 4: The equation corrected. The new equation number after removing of the Section 2.1 is (10).

 

Comment 5: At least one bibliographical references should be indicated for the summary of classical Jiles-Atherton formalism.

Response 5: Added a citations [16,17] of the original D.Jiles and D.Atherton paper.

 

Comment 6: The proposed modified Jiles-Atherton model is difficult to follow using the actual Spice circuit diagrams and command lines, as shown in Figs. 2, 3, 4, and 5. A flowchart would be more illustrative and easy to understand and interpret by the reader.

Response 6: Added functional block diagrams explaining circuits (Figures 3 and 12)

 

Comment 7: How are the 'convergence helper' resistors sized, and how they affect result accuracy and convergence?

Response 7: There is no common method to numerically estimate the convergence helpers for SPICE. The values of convergence helpers are selected according recommendation from [19]. Added note around Line 139.

 

Comment 8: To make the paper self-contained, it would be briefly mention in what consist "power law dependency". Similarly, how is the Hausdorff distance defined?

Response 8: The equations (12) and (13) for power law added around Line 204. Hausdorff distance definition added around Line 311. Added citation [34] explaining Hausdorff distance computation method.

 

Comment 9: At the point they are mentioned in the text, there is no description of the experimental model used to obtain the experimental data shown in Figure 8 nor the conditions in which the experiments were carried out. The experimental model is described later in the manuscript.

Response 9: Added link for measurement data used for preparation of this plot (Figure 9 in the revised version) around Line 237.

 

Comment 10: The equation of line 224 (page 10) is not dimensionally homogeneous. Inside the two parenthesis a dimensionless quantity, i.e., 1 is added to a voltage. The left-hand side a voltage equals a ratio of two voltages in the right-hand side of the equation.

Response 10: The page 10 and line 224 contained no equations. Please explain more in details. Did you mean the Line 201 in the paper version before revision? It is the only place where 1 is added to voltage. It is not equation, but SPICE code. The v(C) represents the virtual voltage for coefficient C expressed as the complex dependency. Representing any other values including dimensionless as the virtual voltage is a common practice when designing SPICE macromodels. This code entry is replaced by circuit diagram (Figure 11) according the request of another reviewer.

 

Comment 11: If there are two ferrite materials have, probably "relative" - not specified by the author, permittivities of 1700 and 1500, that implies the use of LINEAR materials. Hence, there is no point in modeling any nonlinear B-H characteristic or hysteresis loop.

Response 11: All considered materials show the nonlinear behavior. The measurement data for all materials are uploaded via Zenodo and could be accessed from Data Availability Statement section. I have specified the initial magnetic permittivity only to distinguish two materials of unknown manufacturer and give it a name, because there was no possibility to identify the origin of these two materials. The specification of mu removed from the Table 1 to avoid possible confusion.

 

Comment 12: In Table 2 the unit of measurement for the Hausdorff distance (d) is not specified.

Response 12: This value is dimensionless. The Table 2 header is corrected.

 

Comment 13: How is the so-called 'transient' regime generated for the results shown in Figure 16. Apparently, there is not 'transient', but a a distorted periodical (nonsinusoidal) regime, as also confirmed by the waveforms plotted in Figure 17.

Response 13: Initial intention was to follow the SPICE specification where transient simulation (TRAN) means time-domain analysis. The term “transient” replaced by “time domain” or “waveform” in the Section 4.2 to avoid possible confusion.

 

Comment 14: The supposed improvement of the Jiles-Atherton model consist in a smoother 'zero crossing' in Figure 16, but with a significantly larger maximum value. Then, in what consist the actual advancement or novelty proposed in the paper?

 

Response 14: Added paragraph in Section 3.1 explaining the disadvantages of the existing modified magnetic hysteresis models (Lines 212-226) and Figure 8. Added legend for Figure 19. Added note in Conclusion (Line 387-390). Here are the detailed explanations of changes made.

 

The basic J.-A. model shows a step at zero crossing at the low excitation level which is totally incorrect result. The proposed model with four parameters provides a good match with measured waveform (see the circles – measured time domain data points, and blue solid line – simulated data in the Figure 18) The mismatch of the peak value appear only for a simplified form of the proposed model (solid green line in Figure 18). But the simplified model still provide a good match of the waveform shape. The peak value mismatch for simplified model (using BetaA=0) still be acceptable for practical usage, because the shape of the waveform still be good reproducible, and the ferrite core parameters may vary from sample to sample up to 25% according documentation from manufacturer. The previous research [13,23,25] only proposes to introduce dependency of the model parameters on the flux density amplitude, but don’t consider its integration with circuit simulation tools. The approach proposed by [13] cannot be implemented without patching of the simulation software core. Power law dependency proposed by [23] always requires four additional parameters. The power law functions may cause convergence problems for some SPICE implementations. The Figure 18 was corrected to avoid possible confusion about high mismatch.

 

Reviewer 4 Report

Comments and Suggestions for Authors

Review of manuscript entitled “Improved Jiles-Atherton Magnetic Core Model and Its SPICE Implementation”

Manuscript purpose and benefits are clear. Proposed correction term will be useful in SPICE modeling. More explanations and definitions must be provided before publication. In my opinion a larger Introduction is needed, more details on testing setup and deeper discussion on the results must be provided. Major improvements recommendations are:

1) Jiles-Atherton is a magnetic hysteresis model, but all the time it is defined as Ferromagnetic Core Model.

2) sub-section “2.1. Winding Model Equations” is not very useful and can be removed.

3) In section “3. Improved Jiles-Atherton Ferromagnetic Core Model” must be included the main J-A equation for B or M calculation.

4) What is the testing frequency and frequency range? High harmonic behavior must be explained and pointed somehow. Table 3 results comes from nowhere.

5) More resent works on JA models for different applications which will give the applicability field of the current model must be provided.

6) Equation on page 10 must be written with an equation editor. Do not use * for multiplication. All equation parameters must be defined after the equation.

7) English must be polished. There are strange expressions as “The most distant points of the measured and measured loops is located on the loop tips.”

Comments on the Quality of English Language

English must be polished. There are strange expressions as “The most distant points of the measured and measured loops is located on the loop tips.” 

Author Response

Many thanks for providing a useful feedback! The explanations for specific comments are below.

Comment 1: Jiles-Atherton is a magnetic hysteresis model, but all the time it is defined as Ferromagnetic Core Model.

Response 1: The naming corrected in the Introduction and body text.

Comment 2: sub-section “2.1. Winding Model Equations” is not very useful and can be removed.

Response 2: Section 2.1 removed.

Comment 3: In section “3. Improved Jiles-Atherton Ferromagnetic Core Model” must be included the main J-A equation for B or M calculation.

Response 3: Added Jiles-Atherton ODE, equation (8)

Comment 4: What is the testing frequency and frequency range? High harmonic behavior must be explained and pointed somehow. Table 3 results comes from nowhere.

Response 4: The test conditions are the same as for waveform measurement. Added note around Line 367.

Comment 5: More resent works on JA models for different applications which will give the applicability field of the current model must be provided.

Response 5: Added citations [3,6-8] considering power electronics simulation tasks.

Comment 6: Equation on page 10 must be written with an equation editor. Do not use * for multiplication. All equation parameters must be defined after the equation.

Response 6: The equation on page 10 is not equation, but SPICE netlist code entry. It is converted to Figure 11 that shows how to modify the B2 source. This would allow to avoid confusion.

Comment 7: English must be polished. There are strange expressions as “The most distant points of the measured and measured loops is located on the loop tips.”

Response 7: Grammar revised through the entire text. The paper will be submitted to the author services after the final review round if necessary.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have substantially improved the manuscript. Quantitative validation has been added, the extraction workflow is clarified, and applicability limitations are now stated.

Only a minor conceptual clarification remains regarding the definition of BppB_{pp}Bpp​. Although the authors clarified its implementation, the terminology “peak-to-peak” may still be misleading since the definition corresponds to a rectified averaging amplitude indicator. A brief clarification in the text would eliminate potential ambiguity.

After this minor refinement, the manuscript is suitable for publication.

Author Response

Comments 1: Only a minor conceptual clarification remains regarding the definition of Bpp Although the authors clarified its implementation, the terminology “peak-to-peak” may still be misleading since the definition corresponds to a rectified averaging amplitude indicator. A brief clarification in the text would eliminate potential ambiguity.

Response 1: Agree. Added a note around Line 265.

Reviewer 3 Report

Comments and Suggestions for Authors

In general, the author has provided pertinent responses. The second manuscript version has been improved to a satisfactory degree.

There still is an open issue: the first review concern no. 10.

Here, the author requested additional clarifications, as follows:

Clarification 1: "The page 10 and line 224 contained no equations. Please explain more in details."

Answer 1: Please refer to the attached screen capture of the manuscript (file 'Clarifications.pdf', page 1) that would certainly be helpful in locating the relationship in question.

Clarification 2: "Did you mean the Line 201 in the paper version before revision? It is the only place where 1 is added to voltage.".

Answer 2: Of course, it was the first manuscript version (the one "before revision"), because it was the only version available at that moment. Line 201, mentioned by the author, does not contain any addition of "1", as one can check in the second attached screen capture (file 'Clarifications.pdf' page 2).

Since the aforemention relationship is still present in the second manuscript version (the revised version), please comment on its homogeneity (volts in the left-hand-side must equal volts on the righ-hand side).

Comments for author File: Comments.pdf

Comments on the Quality of English Language

The English text is acceptable with respect to the paper's content understanding.

Author Response

Comments 1: There still is an open issue: the first review concern no. 10. Since the aforemention relationship is still present in the second manuscript version (the revised version), please comment on its homogeneity (volts in the left-hand-side must equal volts on the righ-hand side).

Response 1: Thanks for providing a clarification. The Line 201 was not an equation, but SPICE code entry. The v(C) was a virtual voltage representing dependency of C parameter. It is a common practice to represent non-voltage parameter as virtual voltages when designing compact models and macromodels. This code entry was replaced by Figure 11 by request of another reviewer to avoid possible confusion. This figure shows how to modify the equation defined voltage source.

Reviewer 4 Report

Comments and Suggestions for Authors

In my opinion, improvements made by the Author are reasonable.

The last left is some grammar editing and text formatting issues.

Also Introduction can be extended with more details on considered models (lines 27-30) and their particular case applications for special magnetic materials modeling.

In general, I recommend the publication of the manuscript.

Comments on the Quality of English Language

English must be polished. There are strange expressions as “The most distant points of the measured and measured loops is located on the loop tips.” 

Author Response

Comments 1: Also Introduction can be extended with more details on considered models (lines 27-30) and their particular case applications for special magnetic materials modeling.

Response 1: Introduction extended around lines 28-37. Added references [16-21] considering application of the mentioned models.

Comments 2: English must be polished. There are strange expressions as “The most distant points of the measured and measured loops is located on the loop tips.” 

Response 2: The grammar in entire text and this particular sentence was revised. The article will be uploaded to the author services after the final review round if still be necessary. This particular sentence fixed in Line 336.