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REVIEW 3 major objections 7 minor 8 references

Analysis of Skin Effect in High Frequency Isolation Transformers

T0 review · 3 major / 7 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Skin effect raises AC winding resistance and lowers leakage inductance as frequency rises, and the paper reports that winding shape and layout alone can vary these parasitics by up to 400-fold and 13-fold at the same magnetizing inductance.

desk verdict The 400x claim is physically impossible (type-c resistance sits below the DC floor for AWG18-equivalent foil), so the paper's headline numbers are not credible, even though the qualitative skin-effect trends are standard. read the letter →

arxiv 1910.01983 v1 pith:O5KMUEVC submitted 2019-08-15 physics.ins-det eess.SPphysics.acc-ph

Mohamad Saleh Sanjarinia , Sepehr Saadatmand , Pourya Shamsi , Mehdi Ferdowsi This is my paper · ORCID
classification physics.ins-deteess.SPphysics.acc-ph
keywords skineffecteddycurrentsleakageinductanceACwindingresistancehigh-frequencytransformerfiniteelementmethodfoilwindingsveryhighfrequencypowerconversion
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper simulates a 1:1 high-frequency isolation transformer in four winding styles—round wire, square wire, overlaid foil, and spaced foil—at 20 kHz and 20 MHz to see how the skin effect changes parasitic behavior. It argues that skin effect crowds current toward conductor surfaces, so as frequency rises the winding AC resistance increases and the leakage inductance decreases. It also reports that, at the same magnetizing inductance, the winding arrangement and conductor shape can move leakage inductance by roughly 13 times and AC resistance by 400 times, giving designers a wide lever for tuning loss and resonance. This matters for very-high-frequency converters using fast SiC and GaN switches, where knowing leakage inductance and winding resistance is needed to maintain efficiency and avoid unwanted oscillation.

What carries the argument

The central object is the skin depth, $\delta=\sqrt{\rho/(\pi \mu_0 f)}$, which sets how thin the effective current-carrying shell becomes at 20 MHz. The finite-element simulations produce current-density and magnetic-field distributions for each winding arrangement, and leakage inductance is obtained from the volume integral $L_{\text{leakage}}=\iiint H\cdot B\,dv\,/\,I_{\text{primary}}^2$ taken over the window with the secondary short-circuited. Foil windings work because a thin, wide conductor oriented along the field carries current with less surface crowding, and the overlaid pattern (type c) prevents eddy-current loops from forming.

What would settle it

Measure AC resistance and leakage inductance of the four winding arrangements on the same EE core at 20 MHz with an impedance analyzer and compare them with the simulated values; the claim fails if the reported ordering and rough magnitude—especially the roughly 400-fold lower resistance of the overlaid foil winding—are not reproduced.

Watch

Extended reading notes

Core claim

On the paper's own terms, the discovery is a quantitative finite-element comparison: at 20 MHz, the round-wire design has AC resistance 80.637 mΩ, the square-wire design 73.377 mΩ, the overlaid foil design 0.19381 mΩ, and the spaced foil design 6.7345 mΩ, while leakage inductance ranges from 3.8030 nH to 51.765 nH. The authors read this as showing that geometry, not just frequency, controls skin-effect losses: overlaid foil conductors keep the current path spread out and suppress eddy-current circulation, whereas round and square wires confine current to thin surface shells. Because the magnetizing inductance stays nearly the same across designs (about 397–422 nH), the parasitic differences are attributed to winding topology. The paper's general conclusion is that the skin effect increases AC resistance and decreases leakage inductance with frequency, with the overlaid-foil winding showing that trend only weakly because its structure largely cancels the eddy-current mechanism.

Load-bearing premise

The quantitative comparisons rest on the finite-element simulation being accurate at 20 MHz; the paper does not provide a mesh-convergence check, an experimental measurement, or a comparison with a standard closed-form resistance formula, so a wrong field solution would shift every reported ratio.

Editorial extensions

If this is right

  • A converter designer can reduce winding AC loss by roughly two orders of magnitude at 20 MHz by switching from AWG18 round wire to overlaid foil windings, at the cost of higher leakage inductance.
  • Leakage inductance can be tuned over a 13-fold range without changing magnetizing inductance, so the same core can be wound to place the parasitic where a resonant tank needs it.
  • Square conductors of the same cross-sectional area as round wire show a slightly weaker skin effect, so conductor shape alone is a small but usable loss lever.
  • The frequency-response curves imply that wire-wound transformers change parasitic values markedly between 20 kHz and 20 MHz, while foil-wound transformers remain comparatively stable.
  • Because magnetizing inductance stays near 400 nH across all four designs, the observed parasitic differences are attributable to winding geometry rather than to changes in the core.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • An immediate testable extension would be to wind the four geometries on a physical EE core and measure impedance from 20 kHz to 20 MHz; the paper's 400-fold resistance claim would survive only if the foil winding's advantage persists after terminal and lead resistances are included.
  • The same skin-effect logic suggests litz-wire designers could reduce loss by using square or shaped strands rather than round strands, since the simulations show a weaker skin effect in square conductors; the paper notes the possibility but does not test a litz bundle.
  • If leakage inductance can be varied 13-fold at fixed magnetizing inductance, one could co-design the transformer as the resonant inductor of a ZVS or ZCS tank, shrinking the converter by removing a separate inductor—an implication the paper points toward but does not build.
  • Because core loss at 20 MHz grows steeply with flux density under the reported Steinmetz fit, the 400-fold winding-resistance improvement may matter less than core loss in a full converter, so foil-winding choice should be weighed against total loss rather than winding loss alone.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 7 minor

Summary. The paper reports a finite-element method (FEM) study of skin effect in a 1:1 high-frequency isolation transformer with four winding configurations: AWG18 circular wires, square wires of equivalent cross-section, overlaid foil windings (type c), and non-overlaid foil windings (type d). For each configuration, the authors present current-density and magnetic-field distributions at 20 kHz and 20 MHz, and tabulate magnetizing inductance, leakage inductance, and winding AC resistance at both frequencies, along with frequency sweeps. The stated central claims are that skin effect increases AC winding resistance and decreases leakage inductance with frequency, and that for a nearly constant magnetizing inductance the winding topology can vary leakage inductance by up to 13 times and AC resistance by up to 400 times.

Significance. If the quantitative results were reliable, the comparison of winding topologies at very high frequency would be practically useful for designers of SiC/GaN-based converters, where parasitic inductance and winding loss are critical. The study is not circular: no parameters are fitted to the reported outputs, and the inductance and resistance values are taken directly from FEM solutions of Maxwell's equations. The qualitative observation that conductor shape and winding arrangement affect leakage inductance and AC resistance is consistent with textbook physics. However, the quantitative findings, especially the headline '400 times lower AC resistance,' are compromised by a physically impossible value in the tables and by the complete absence of mesh-convergence or validation evidence.

major comments (3)
  1. [III-B, Tables III and IV] The AC resistance reported for type (c) violates the DC floor for the stated geometry. All winding types are described as having cross-sectional area equivalent to AWG18 (0.823 mm²) with 5 turns per winding. Using the mean turn length implied by Table II (about 18 mm), copper resistivity, and series-connected turns gives R_DC ≈ 1.84 mΩ, which matches type (a) at 20 kHz (1.8264 mΩ). Type (c) reports 0.10297 mΩ at 20 kHz and 0.19381 mΩ at 20 MHz, both well below the DC resistance of the same conductor material and cross-section. No skin effect, eddy-current redistribution, or FEM post-processing error can produce a resistance below the DC value for a series-connected winding of fixed total conductor volume. This indicates an error in the FEM model definition for type (c), such as inadvertently shorting foil turns in parallel or misinterpreting the post-processed quantity. Consequently, the abstract and conclusion claims of 'up to 400 times' lower AC resistance, and any comparison involving type (c), are unsupported and must be re-derived after correcting the model.
  2. [III-B, paragraph after Table IV] The claim that the skin-effect trend is observable in all transformer types 'except type c' is contradicted by the paper's own tables. For type (c), the leakage inductance decreases from 13.451 nH at 20 kHz to 13.2631 nH at 20 MHz, and the AC resistance increases from 0.10297 mΩ to 0.19381 mΩ. Both changes are in the same direction as the stated skin-effect trend, albeit smaller in magnitude than for the wire conductors. The accompanying explanation that the structure of type (c) 'cancel[s] the skin effect and prevent[s] the eddy current to flow' is also inconsistent with a resistance that nearly doubles over the frequency range. Please reconcile the text with the data or provide a corrected interpretation.
  3. [III-A and III-B, FEM methodology] The manuscript provides no information on the FEM solver, mesh density, element order, boundary conditions, or convergence criteria, and it includes no validation of the simulation setup against an analytical benchmark (e.g., Dowell's formula for a foil winding) or against measurement. Given that Table IV contains a physically impossible resistance for type (c), the accuracy of all reported numbers, including the leakage-inductance ratios and the frequency-response curves in Fig. 11, is called into question. The authors should add a mesh-convergence study and at least one validation case demonstrating that the FEM model reproduces a known AC resistance and leakage inductance before the quantitative comparisons can be accepted.
minor comments (7)
  1. [II, Eq. (3)] Equation (3) is garbled: the symbols '𝜄𝜔' and '𝜔𝜔' are unclear, and the expression for AC resistance is dimensionally inconsistent as printed. It should be rewritten, for example as R_ac = ρ l / (w δ) with δ = sqrt(ρ/(π μ0 f)), to make the skin-depth dependence explicit.
  2. [III, before Eq. (5)] The text says 'Equation (4) shows the relation between magnetic energy and leakage inductance,' but the displayed equation is numbered (5). Please renumber or fix the cross-reference.
  3. [Table I] Table I is difficult to parse because the three flux-density values and the three core-loss values are not clearly aligned in separate columns. Please reformat so each pair is unambiguous.
  4. [Tables III and IV] The line breaks in the manuscript text make the table entries hard to associate with their rows. Please ensure the actual published tables have clear row and column separation.
  5. [Conclusion] The conclusion states that the comparisons are made 'for the same value of the magnetizing inductance,' but Table III shows magnetizing inductances ranging from 397.08 to 422.14 nH, a spread of about 6%. Please qualify this statement.
  6. [Abstract and throughout] Minor language issues include 'at presence of eddy currents' (should be 'in the presence of'), 'trans former ration' (should be 'ratio'), and inconsistent capitalization of 'KHz'/'kHz' and 'MHZ'/'MHz'.
  7. [Section II] The FEM software and solver type are not identified. Please state the tool (e.g., ANSYS Maxwell, COMSOL, or another package), the element type, and the mesh settings used for the 20 MHz and 20 kHz simulations.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: central results are direct FEM outputs, not fitted or self-referential predictions.

full rationale

The paper's central claims are that skin effect increases AC winding resistance and decreases leakage inductance, and that winding topology can vary leakage inductance and AC resistance by up to 13x and 400x for the same magnetizing inductance. These claims are read directly from finite-element field solutions of Maxwell's equations; no parameter is fitted to the reported leakage inductance or AC resistance values, and no equation defining one target quantity in terms of another target quantity is used to generate the tables. Equation (3) is a standard skin-depth/winding-loss relation used for motivation, and equation (5) is the standard magnetic-energy definition used to post-process leakage inductance from simulated H and B fields; neither embeds the paper's conclusions as inputs. The self-citations [2]–[5] provide background on VHF converters and control techniques, but they are not load-bearing for the skin-effect, leakage-inductance, or AC-resistance results. The '400 times' and '13 times' ratios are direct comparisons of simulated Table III/IV entries, so they are reported observations from the simulation rather than predictions forced by construction. The paper's stated limitation about lack of material performance data above 20 MHz and the absence of mesh-convergence or experimental validation are correctness and reproducibility concerns, not circularity. Even if the type-c AC resistance values are physically implausible for the stated geometry, that would indicate a modeling or post-processing error, not circular derivation.

Assumptions & free parameters 0 free parameters · 3 assumptions · 0 invented entities

No new entities are introduced. All components are standard transformer elements. The only nonstandard element is the claim that foil type c cancels eddy currents, which is a behavioral claim, not an entity.

assumptions (3)
  • domain assumption The FEM solver accurately solves Maxwell's equations for the 3D transformer geometry with the specified mesh and material properties.
    The paper reports FEM results without a mesh convergence study or comparison with analytical solutions or measurements; all quantitative claims depend on this assumption.
  • domain assumption The Fair-Rite 67 material B-H curve and Steinmetz coefficients are valid at 20 MHz.
    The text itself notes that 'over 20 MHz lack of material performance data is a challenging issue,' yet simulations at 20 MHz rely on the datasheet B-H curve and core loss constants from [7] and [8].
  • standard math The standard skin depth formula and equivalent circuit definitions (Eqs. 1-5) apply to this geometry.
    The paper uses textbook formulas for core area, core loss, winding loss, and leakage inductance, which are standard background results.

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Cite this review

Pith. "Pith review of Analysis of Skin Effect in High Frequency Isolation Transformers." pith.science (2026). https://pith.science/paper/O5KMUEVC

@misc{pith2026191001983,
  author       = {Pith},
  title        = {Pith review of: Analysis of Skin Effect in High Frequency Isolation Transformers},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/O5KMUEVC}},
  note         = {Machine review of arXiv:1910.01983}
}
read the original abstract

In this paper, a high frequency transformer with different conductors and winding arrangements, at presence of eddy currents and skin effect, is studied. By using different winding structures, and conductor types, such as circular, square shaped, and foil wires, the skin effect in the windings is studied and current density within the conductors at a high frequency of 20 MHz and a lower frequency of 20 kHz are investigated using finite element method (FEM) simulation. Moreover, magnetic field distribution in the transformers at 20 MHz is obtained and displayed. Also, magnetizing inductance, leakage inductance and AC winding resistance for all of the transformer types are found and compared, and frequency response for the transformers are obtained and shown. Lastly, based on the results, the skin effect increases the AC winding resistance and decreases the leakage inductance as the frequency increases. Furthermore, different winding arrangements, conductors, and transformer types show a wide range of parasitic and loss behavior, which enable the designers to compromise between various parameters in different applications, especially new fast switches such as SiC and GaN.

Figures

Figures reproduced from arXiv: 1910.01983 by the authors.

Figure 2
Figure 2. The 3D EE transformer core (a) (b) (c) (d) [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Side and front views of the EE core. a) Front view of the block set. b) Side view of the block set. c) Front view of the EE core. d) Side view of the EE core. Side views show the depth of the cores. TABLE II Dimensions of the [PITH_FULL_IMAGE:figures/full_fig_p002_3.png] view at source ↗
Figure 4
Figure 4. Different winding arrangements of the transformer [PITH_FULL_IMAGE:figures/full_fig_p002_4.png] view at source ↗
Figures from the paper (7 more)
Figure 6
Figure 6. Figure 6: Current density distribution (J) in the windings of the transformer for type (a) and (b) of the [PITH_FULL_IMAGE:figures/full_fig_p003_6.png]
Figure 7
Figure 7. Figure 7: Defined cutline across the conductors on the primary at the right [PITH_FULL_IMAGE:figures/full_fig_p003_7.png]
Figure 5
Figure 5. Figure 5: shows the current density distribution in the circular and the square wires during the full load working of the transformer. As it is clear, in center parts of the wires, the current density is very low, but at the parts near the surface the current density is much hig…
Figure 8
Figure 8. Figure 8: Current density norm (A/mm2 ) across the defined cutline in [PITH_FULL_IMAGE:figures/full_fig_p004_8.png]
Figure 6
Figure 6. Figure 6: In Fig. 6 it is clear that [PITH_FULL_IMAGE:figures/full_fig_p004_6.png]
Figure 10
Figure 10. Figure 10: Magnetic field strength (A/mm) at 20 MHz. a) Windings with the AWG18 circular shape conductors b) Windings with the square shape conductors with the same cross sectional area to the AWG18. c) Type (I) of windings with foil conductors. d) Type (II) of windings with foi…
Figure 11
Figure 11. Figure 11: Leakage inductance and winding AC resistance at different frequencies. a) Windings with the AWG18 circular shape conductors b) Windings with the square shape conductors with the same cross sectional area to the AWG18. c) Type (I) of the windings with the foil conducto…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

8 extracted references · 7 canonical work pages

  1. [1]

    Opportunities and Challenges in Very High Frequency Power Conversion

    Perreault, David J., et al. “Opportunities and Challenges in Very High Frequency Power Conversion.” 2009 Twenty -Fourth Annual IEEE Applied Power Electronics Conference and Exposition , 2009, doi:10.1109/apec.2009.4802625

    work page arXiv 2009

  2. [2]

    Design and Development of Very High Frequency Resonant DC –DC Boost Converters

    Shamsi, Pourya, and Babak Fahimi. “Design and Development of Very High Frequency Resonant DC –DC Boost Converters.” IEEE Transactions on Power Electronics , vol. 27, no. 8, 2012, pp. 3725 –3733., doi:10.1109/tpel.2012.2185518

    work page arXiv 2012

  3. [3]

    Robust Backstepping Control of Synchronverters under Unbalanced Grid Condition,

    S. Yazdani and M. Ferdowsi, “Robust Backstepping Control of Synchronverters under Unbalanced Grid Condition,” 2019 IEEE Power and Energy Conference at Illinois (PECI), 2019

    work page 2019

  4. [4]

    Voltage Sensorless Control of a Three-Phase Standalone Inverter Based on Internal Model Control,

    S. Yazdani and M. Ferdowsi, “Voltage Sensorless Control of a Three-Phase Standalone Inverter Based on Internal Model Control,” 2018 IEEE Energy Conversion Congress and Exposition (ECCE), 2018

    work page 2018

  5. [5]

    Hardware Co -simulation of Voltage Sensorless Current Control Based on Internal Model Principle,

    S. Yazdani and M. Ferdowsi, “Hardware Co -simulation of Voltage Sensorless Current Control Based on Internal Model Principle,” 2018 IEEE Energy Conversion Congress and Exposition (ECCE), 2018

    work page 2018

  6. [6]

    Design of Le akage Inductance in Resonant DC -DC Converter for Electric Vehicle Charger,

    J.-M. Choi, B.-J. Byen, Y.-J. Lee, D.-H. Han, H.-S. Kho, and G.-H. Choe, “Design of Le akage Inductance in Resonant DC -DC Converter for Electric Vehicle Charger,” IEEE Transactions on Magnetics, vol. 48, no. 11, pp. 4417– 4420, 2012

    work page 2012

  7. [7]

    C. W. T. McLyman, Transformer and inductor design handbook . CRC Press, 2017

    2017

  8. [8]

    Available: https://www.fair-rite.com/67-material-data-sheet/

    Fair -rite products c rop, 67 material datasheet, Costa Mesa, CA, USA [online]. Available: https://www.fair-rite.com/67-material-data-sheet/

    work page

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