AC-Winding-Resistance Calculation of Toroidal Inductors with Solid-Round-Wire and Litz-Wire Winding Based on Complex Permeability Modeling^†

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this paper, a modified Dowell’s method – based on the complex permeability and iterative calculations – is proposed and thoroughly documented for calculating the frequency-dependent AC resistance of solid-round- and Litz-wire toroidal inductor windings. The computed results across a wide range of frequencies up to 1 MHz emphasize good agreement with finite-element analysis results. Three air-core toroidal windings with both solid-round and Litz wires have been manufactured, and their AC resistances have been measured by using an LCR meter from 1 kHz to 1 MHz.  Satisfactory agreement between measured AC resistances and the calculated ones has been provided, especially for densely-wound inductors. Although being an extended version of the authors’ ICEMS-2022-conference previous paper, the present paper is self-consistent, well-organized, soundly-written and with original and pertinent outcomes. Hence, there are no requests to be addressed to the authors for paper improvement. 

Author Response

Thank you very much for taking the time to review this manuscript. We are uploading our updated manuscript with yellow highlighting indicating changes.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The paper considers the evaluation of winding losses due to alternating current in a wide frequency range. The losses are affected by skin and proximity effects. 

The paper is a follow-up of a conference paper and it provides a step-by-step methodology based on the use of complex permeability and Ollendorf formula.

Despite the issue is rather old (Dowell's formulas are about fifty years old) and covered in a number of useful textbooks, cf. M. Kazimierczuk, High‐Frequency Magnetic Components, 

J. Wiley & Sons for example, it still attracts much attention of the engineering community. 

Analytical solutions are rarely feasible and even for the simplest geometries the computations are lengthy and complicated, https://www.mdpi.com/1996-1073/12/18/3584 as an example.

Therefore the researchers use FEM computations as reference, as it is also done in this paper. 

Despite some deviations, of the order of 15%-20%, between the results from FEM and complex-permeability approaches are noticeable, they can be attributed to crude assumptions e.g. concering the unchanged values of parameters used in numerical computation.

 

This is certainly a very useful engineering work, which should be accepted "as it is".

minor typo, title of subsection 4.2 should be "Iterative" 

 

Author Response

Thank you very much for taking the time to review this manuscript. We are uploading our point-by-point response to the comments (below) and updated manuscript with yellow highlighting indicating changes.

Comment1: The title of subsection 4.2 should be "Iterative" 

Response 1: Thank you for your careful comment. We have corrected the mistyped title.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

A method for calculating the frequency-dependent winding resistance of toroidal inductor windings with Litz-wire as well as solid-round wire has been presented in this paper, it is an interesting topic, and the results are virified by both FEA and experiment. Following is some suggestions:

1) Can you include a comparison of the theoretical calculation values in the section 5.2 to be compared with the experimental results?

2) Will uneven coil winding in the prototype affect the calculation results? Because both theoretical calculations and finite elements are based on the premise of uniform distribution.

Author Response

Thank you very much for taking the time to review this manuscript. We are uploading our point-by-point response to the comments (below) and updated manuscript with yellow highlighting indicating changes.

Comment 1: Can you include a comparison of the theoretical calculation values in the section 5.2 to be compared with the experimental results?

Response 1: Thank you for pointing this out. We agree with adding values of the calculation and measurement and have added these in Table 3.

Comment 2: Will uneven coil winding in the prototype affect the calculation results? Because both theoretical calculations and finite elements are based on the premise of uniform distribution.

Response 2: We agree with your comment. The distribution of the wires can cause uncertainty in the calculation. Uneven winding can occur especially in a loosely wound winding while densely wound winding can make more even winding. The proximity effect among wires is not significant, compared with the skin effect in the loosely wound winding, which can be seen in Figure 5. Therefore, the uneven distribution of wires cannot make a substantial error between the calculation and the measurement from the author's point of view. 

Author Response File: Author Response.pdf