Winding Losses in Transformers and Inductors

Winding losses in transformers and inductors comprise resistive losses from DC and alternating currents, with skin effect and proximity effect increasing the loss associated with high-frequency current. This article explains the mechanisms, compares Litz wire, solid round wire, rectangular wire, foil and PCB windings, and gives design and validation guidance for engineers specifying power magnetics.

The discussion applies primarily to power transformers, switched-mode power-supply inductors, resonant magnetics and wireless power-transfer coils. The underlying conductor physics also applies to signal and RF components, but their selection additionally depends on bandwidth, impedance, quality factor and self-resonance. This article develops an original explanatory note by Pablo Blázquez, Power Electronics Engineer at Frenetic.

Key Takeaways

Winding-loss reduction requires the current waveform, conductor dimensions and magnetic-field distribution to be considered together.

Separate the DC current component from AC harmonics. Apply the winding resistance appropriate to each frequency rather than multiplying the complete current by one high-frequency resistance.
Copper skin depth at 20 °C is approximately 8.52 mm at 60 Hz and 0.209 mm at 100 kHz. Skin depth describes current penetration; it is not a boundary beyond which current becomes zero.
Proximity loss depends on neighbouring conductors, winding-section ampere-turns and gap-fringing fields. Total layer count alone does not determine the loss.
Litz wire needs individually insulated strands and suitable transposition and bundle construction. Strand insulation alone does not equalise current or remove proximity loss.
Foil, rectangular wire and PCB windings can provide useful copper utilisation, but thickness, field orientation, layer arrangement and parallel-path current sharing determine their AC performance.
Validate the complete design for winding and core loss, hot-spot temperature, leakage inductance, capacitance, manufacturability and insulation requirements.

Understanding Winding Losses

Winding losses convert electrical energy into heat in conductors and their terminations. They affect conversion efficiency, temperature rise and the operating margin of the insulation system. In high-frequency power magnetics, DC resistance alone does not describe the complete winding loss. [1, 2]

DC resistance and the low-frequency baseline

For a uniform conductor, DC resistance R_DC, in Ω, depends on conductor resistivity ρ, in Ω·m, conductor length l, in m, and copper cross-sectional area A, in m². Eq. (1) is the starting point; actual winding resistance also includes terminations and any additional conductor length introduced by twisting. [1, 2]

R_{DC} = \rho\frac{l}{A} \tag{1}

If the current distribution remains approximately uniform, winding loss is I_rms²R_DC, where I_rms is the total RMS current in A. At higher frequencies, skin and proximity effects produce non-uniform current density, so the effective resistance associated with the AC current increases. Both effects are illustrated schematically in Figure 1. [1]

Schematic illustration comparing skin effect and proximity effect in winding conductors — Figure 1. Skin effect and proximity effect redistribute current and increase AC winding loss.

Current harmonics and AC resistance

Converter winding currents are frequently non-sinusoidal. For a linear conductor-loss model at a specified temperature and winding excitation, their loss can be calculated by separating the DC component and summing the losses of the AC harmonics, as in Eq. (2). The AC resistance used for each harmonic must represent the actual winding arrangement and its associated proximity fields. [1, 3]

P_{w} = I_{DC}^{2}R_{DC} + \sum_{n=1}^{\infty} I_{n,rms}^{2}R_{AC}(nf_{1}) \tag{2}

Here P_w is winding loss in W, I_DC is the average current in A, I_n,rms is the RMS amplitude of harmonic n in A, f₁ is the waveform fundamental frequency in Hz, and R_AC(nf₁) is the effective winding resistance in Ω at that harmonic frequency. The dimensionless harmonic index n starts at one. All resistance values must correspond to the temperature being evaluated.

R_AC already includes the ordinary resistive contribution for its AC current component. Do not add I_rms²R_DC to Eq. (2), because that would count part of the loss twice. For multiwinding components with different current waveforms and phases, use a coupled loss model that accounts for their combined field rather than assuming each winding has an excitation-independent AC resistance. [1, 2]

For a defined sinusoidal excitation, the AC-resistance factor F_R compares AC resistance with DC resistance at the same temperature, as shown in Eq. (3). A resistance factor is not itself a complete thermal or efficiency result: the current spectrum and absolute resistance also matter. [1, 2]

F_{R}(f) = \frac{R_{AC}(f)}{R_{DC}} \tag{3}

Skin Losses

Skin effect is the redistribution of alternating current within a conductor caused by its own changing magnetic field. As frequency rises, current density becomes greater near the surface and lower towards the interior, increasing AC resistance relative to the uniform-current case. [1]

Skin depth and its limits

Skin depth δ, in m, is given by Eq. (4), where f is sinusoidal frequency in Hz and µ is the conductor’s absolute magnetic permeability in H/m. Use the permeability of the conductor, not the permeability of the transformer core. For copper, µ is approximately the permeability of free space, µ₀ ≈ 4π × 10⁻⁷ H/m. [1, 2]

\delta = \sqrt{\frac{\rho}{\pi f\mu}} \tag{4}

For a thick conductor with an approximately flat surface, current-density magnitude falls to 1/e of its surface value after one skin depth. This exponential approximation is most useful when conductor dimensions and surface radius of curvature are large relative to δ. Current does not abruptly stop at that depth; small round wires require the appropriate cylindrical solution for accurate resistance prediction. [1, 2]

Copper examples at 60 Hz and 100 kHz

Using copper resistivity ρ = 1.72 × 10⁻⁸ Ω·m at 20 °C in Eq. (4) gives δ ≈ 8.52 mm at 60 Hz and δ ≈ 0.209 mm at 100 kHz. The original approximate values of 8.5 mm and 0.21 mm are therefore appropriate. [2]

For the original 1 mm diameter copper-wire example, the radius is 0.5 mm, or approximately 2.40 skin depths at 100 kHz. Current is appreciably non-uniform, but describing nearly the entire interior as inactive is too strong. The actual loss depends on the continuous cylindrical current distribution and, in a winding, on additional proximity fields. Do not estimate the loss by simply deleting all copper more than one skin depth below the surface.

Copper resistivity increases with temperature. Eq. (4) therefore predicts a greater skin depth at higher temperature, while Eq. (1) predicts greater DC resistance. Recalculate both resistance and AC redistribution at the intended operating temperature; a larger skin depth is not evidence of lower total winding loss. [1, 2]

Reducing the relevant conductor dimension can limit skin-effect loss. The suitable solution may be finer solid wire, correctly arranged parallel conductors, Litz wire, thin foil or PCB copper. Selection must also account for the external magnetic field, copper fill, conductor length and termination resistance. [1, 2]

Proximity Losses

Proximity effect is current redistribution caused by alternating magnetic fields from other conductors or other parts of the magnetic assembly. These fields induce eddy currents that add to the useful current in some regions and oppose it in others, increasing resistive loss. Even a shield or inactive winding section carrying no net terminal current can dissipate power in an alternating field. [1, 3]

Winding layers and magnetic-field distribution

In an unsplit multilayer winding, accumulated ampere-turns can create a strong field across successive layers. Magnetomotive force, or MMF, is the algebraic sum of winding current multiplied by turn count. Proximity-loss prediction depends on the field at each conductor, its dimensions, operating frequency and the location of zero-field surfaces. [1, 3]

Some one-dimensional winding models contain a contribution that increases approximately with the square of an effective layer or section parameter. This does not establish a universal rule that four physical layers produce 16 times the loss of one layer. Changing layer count can also change turns per layer, conductor dimensions, DC resistance, winding breadth and the MMF distribution. Compare complete designs under explicitly defined conditions. [1, 3]

Techniques for reducing proximity loss

The most effective measures reduce the field acting on the copper or reduce the dimensions over which it can drive circulating currents. Apply them together rather than treating insulation thickness or conductor shape as an independent cure. [1, 2]

Winding interleaving: split primary and secondary windings into correctly connected sections so that opposing load ampere-turns reduce field build-up. A primary–secondary–primary arrangement is one possible construction, not a guarantee of a fixed loss reduction.
Fewer effective layers: distribute the required turns over suitable winding breadth or divide the winding into sections. Check the resulting conductor length, copper fill and manufacturability.
Appropriate conductor dimensions: use strand diameter or foil thickness suitable for the local field and current spectrum, not only for the fundamental-frequency skin depth.
Controlled spacing: position conductors to manage the actual field, especially near gaps. Ordinary insulation prevents electrical contact but does not shield a conductor from an alternating magnetic field.
Correct Litz construction: combine fine insulated strands with suitable transposition and bundle construction. Individual strands still experience proximity fields and associated loss.

Transformer interleaving often reduces leakage inductance as well as winding loss, but can increase primary-to-secondary capacitive coupling and the number of insulation interfaces. In resonant converters, leakage inductance may be an intentional circuit parameter. Optimise the winding against converter operation, common-mode noise and insulation requirements rather than always seeking maximum interleaving. [1, 3]

Gap-fringing fields in inductors and flyback magnetics

A discrete core gap produces a local fringing field that can induce substantial loss in nearby turns. This is particularly important in energy-storage inductors and flyback magnetic components, where proximity loss cannot be assessed solely from neighbouring-turn fields. Moving copper away from the gap is an established mitigation, but the required spacing depends on the actual gap and winding geometry. [2]

Litz wire does not eliminate this problem. A highly localised field can act over a length shorter than the strand-transposition pattern, reducing the benefit of twisting. Include the gap, conductor position and field orientation in the model, and inspect local hot spots rather than relying only on average winding temperature. [2]

Wire Types and Their Impact on Winding Losses

Conductor type determines the available copper area, current-path geometry, insulation arrangement and manufacturing options. No conductor family has a universal frequency limit or an inherent guarantee of low AC loss: compare candidate constructions using their actual dimensions, winding fields and current waveforms. [1, 2, 3]

Litz Wire

Litz wire comprises many individually insulated strands arranged so that their positions within the conductor change along its length. Fine strands reduce strand-level skin effect, while suitable transposition helps equalise induced voltages and current sharing between strands. Simply twisting a large group of insulated wires does not necessarily prevent bundle-level skin effect. Figure 2 retains the original Litz-wire illustration. [1, 2]

Strand insulation interrupts direct electrical paths between neighbouring strands along the conductor, but it does not reduce the magnetic field itself. Transposition and bundle construction address unequal flux linkage; strand diameter limits the eddy-current loss within each strand. Both strand-level and bundle-level effects must therefore be considered. [2]

The original 100 kHz rule-of-thumb calculation gives 2δ ≈ 0.417 mm, rounded to 0.42 mm. That arithmetic is correct, but choosing any strand diameter below 0.42 mm does not establish a low-loss winding. Sullivan and Zhang’s simplified design method operates in a range where strand diameter is no greater than approximately one skin depth and also considers turn count, winding breadth, strand count and construction. [2]

Litz wire can be effective in resonant converters and power-transfer coils, but its additional insulation, interstrand spaces and twisted conductor length reduce copper utilisation and can increase DC resistance. Terminations must connect the intended strands reliably. Compare total hot winding loss and production cost with solid-wire and foil alternatives rather than selecting Litz solely from a frequency table. [1, 2]

Rectangular Wires

Rectangular wire can use winding space efficiently and provide a large copper area within a controlled profile. Its AC performance depends on thickness and orientation relative to the magnetic field, not simply on having more surface area than round wire. A thick rectangular conductor can still suffer substantial skin and proximity loss. [1]

Assess bend regions, edge current crowding, layer arrangement and termination geometry. Insulation is necessary for electrical separation, but magnetic-field management still requires suitable positioning and winding construction. Figure 3 shows the original rectangular-wire inductor.

Inductor illustration showing a winding made with rectangular wire — Figure 3. Rectangular-wire inductor; conductor thickness and field orientation influence AC loss.

Round Wires

Solid round wire remains a practical conductor for mains-frequency magnetics and many switched-mode designs. Its suitability depends on diameter relative to skin depth, winding arrangement, current and allowable temperature rise. A sufficiently fine solid conductor can remain useful at high frequency; there is no universal rejection threshold at 10 kHz or 20 kHz. [1, 2]

Large-diameter wire becomes less effectively utilised as skin effect increases, while neighbouring turns add proximity loss. Parallel insulated wires can provide the required copper area with smaller individual diameters, but they must experience sufficiently similar flux linkage to avoid circulating currents. Parallel connection alone does not guarantee equal current sharing. Figure 4 retains the original round-wire illustration. [1]

Illustration of round winding-wire conductors — Figure 4. Round winding wire; diameter, placement and parallel-path arrangement determine its high-frequency suitability.

Foil Conductors

Foil provides a wide, thin conductor that can supply substantial copper area without a large thickness. It is useful for suitable low-turn-count, high-current windings, but thin foil does not automatically eliminate proximity loss. The field distribution can concentrate current on one face, and successive foil turns can experience very different fields. [1, 3]

Choose foil thickness together with winding breadth, turns, section arrangement and insulation. Splitting a thick conductor into parallel insulated foils does not necessarily reduce loss if the foils occupy different field positions and are connected together at their ends: unequal induced voltages can drive circulating currents. Figure 5 retains the original foil-conductor illustration. [1]

Illustration of foil conductors used for magnetic-component windings — Figure 5. Foil conductors require suitable thickness, layer arrangement and parallel-path current sharing.

PCB and Planar Windings

PCB and other planar windings provide controlled flat-conductor geometry and repeatable layer arrangements. They are subject to the same skin and proximity mechanisms as other conductors. Copper thickness, track width, layer ordering, vias, terminations and gap-fringing exposure all influence loss. [3]

Interleaving can reduce the effective winding-section MMF, but may increase capacitive coupling. Parallel layers require deliberate current-sharing analysis; more copper layers are not automatically beneficial. Select a planar construction for its complete electrical, thermal, mechanical and production requirements rather than assuming that it is always lower-loss or lower-cost than wire-wound magnetics. [1, 3]

Table 1 summarises the selection considerations. The entries are qualitative design guidance, not guaranteed loss rankings or fixed operating-frequency bands. [1, 2, 3]

Conductor type	Potential advantage	Main AC-loss limitation	Selection and cost considerations	Application context
Solid round wire	Simple construction and readily available wire sizes	Skin effect in larger diameters; proximity loss in the winding field	Compare diameter, hot DCR, layer arrangement and termination cost	Mains magnetics and suitable switched-mode windings
Rectangular wire	Controlled profile and useful copper utilisation	Thickness, orientation and local current crowding	Check bending, insulation integrity, tooling and conductor availability	Power inductors and suitable high-current windings
Foil conductor	Large copper area with limited thickness	Layer proximity loss, edge effects and unequal parallel-path flux linkage	Compare foil thickness, sectioning, insulation and termination process	Suitable low-turn-count, high-current windings
Litz wire	Fine strands and transposition can reduce AC loss	Strand proximity loss, bundle effects and imperfect current sharing	Specify strand diameter, count, construction, overall dimensions and terminations	Resonant magnetics and power-transfer coils where justified by loss analysis
PCB or planar winding	Controlled geometry, low profile and repeatable construction	Layer proximity loss, gap fields, vias and parallel-layer current sharing	Compare stack-up, copper thickness, board area, insulation and production volume	Integrated and low-profile power magnetics

Table 1. Conductor selection considerations for winding-loss control.

Design and Selection Checklist

Define the operating envelope before choosing a catalog component or releasing a custom winding specification. Nominal inductance, current rating and DCR do not establish high-frequency loss or hot-spot temperature in the final assembly.

Electrical and thermal requirements

Record topology, switching or resonant frequency range, duty-ratio range and current waveforms for every winding. Include DC, RMS and peak currents at relevant load and input conditions.
Compare DCR at a stated temperature and obtain AC-loss data or a model appropriate to conductor geometry and waveform. Distinguish typical simulations from guaranteed acceptance limits.
Check inductance, tolerance, DC-bias behaviour and saturation margin separately from winding heating. Include core loss in the total magnetic-component thermal budget.
Specify allowable winding hot-spot and core temperatures under the intended ambient, mounting, airflow and enclosure conditions. Average current density alone is not a thermal qualification.
Compare leakage inductance, interwinding capacitance and frequency response with their measurement connections and test conditions defined. Preserve any parasitic inductance intentionally used by the converter.

Catalog versus custom magnetics

A catalog component is appropriate when its documented electrical, thermal, mechanical and insulation limits fit the application. Ask for the current waveform and cooling assumptions behind loss or temperature-rise data. Do not treat a DC thermal current rating as proof of acceptable switching-frequency performance.

Use custom magnetics when required winding ratios, leakage, isolation, profile or thermal performance cannot be met adequately by standard parts. Control turn count, winding order, conductor construction, gap location, insulation, terminations and critical dimensions in the drawing. Agree acceptance tests, traceability and change-notification requirements before qualifying an alternative supplier.

Qualification and safety

Loss optimisation must preserve the intended insulation function. Specify working voltage, transient stress, required insulation system, creepage, clearance and winding-to-core separation for the final equipment. A dielectric withstand test alone does not establish the permissible continuous working voltage.

Confirm that conductor enamel, Litz serving, tapes, bobbin materials and PCB dielectric belong to the intended approved construction where approval is required. Verify the exact component and construction covered by supplier documentation. Interleaving or changing insulation thickness can affect safety, capacitance, leakage and production tolerances simultaneously.

Predicting and Measuring Winding Loss

Analytical models, field simulation and measurements answer different parts of the design problem. Use them together to estimate the loss distribution and verify performance in the actual converter and thermal environment. [1, 2, 4]

Analytical and numerical methods

Dowell-type methods remain useful for approximately one-dimensional layered winding fields. Litz-specific models can include strand dimensions, turn count, winding breadth and construction. Their assumptions must match the geometry; a simple model is valuable when its scope is respected, not obsolete merely because numerical software is available. [1, 2]

Use finite-element analysis when local gap fields, conductor edges or non-uniform field distributions materially affect the result. FEMM supports two-dimensional magnetic analysis and single-frequency AC solutions; it is not a general three-dimensional solver. Define conductor connectivity, conductivity, excitation phase and adequate mesh resolution near conductor surfaces. Its AC excitation quantities use peak amplitudes rather than RMS values. [4]

For non-sinusoidal excitation, evaluate the relevant harmonic contributions with a model valid over that frequency range. A two-dimensional model may not capture termination, end-turn or three-dimensional current-sharing effects. Check mesh convergence and the difference between the modelled geometry and the manufactured winding before relying on the predicted loss. [2, 4]

Bench validation

Measure DC resistance with a suitable four-wire connection and record winding temperature. For impedance measurements, compensate the fixture and document frequency, excitation amplitude, winding connections and bias conditions. A measured equivalent series resistance can include magnetic and dielectric contributions as well as copper loss; it is not automatically the isolated winding resistance.

In transformer short-circuit tests, the measured loss includes the losses of the participating windings and any residual contributions from the test arrangement. Use a sufficiently low-inductance short and interpret the result with the applicable equivalent circuit rather than assigning all measured resistance to one winding.

Finally, operate production-representative samples with the intended waveform and cooling. Compare measured input-output loss, component temperatures and local hot spots with the model, allowing for measurement uncertainty. Check operating extremes and relevant transient conditions, then refine the conductor arrangement or loss model where discrepancies are significant.

Conclusion

Winding losses depend on both the current waveform and the spatial distribution of the magnetic field. Skin depth provides an essential conductor-dimension reference, but proximity fields, gap fringing, winding sections and parallel-path current sharing often determine whether a practical construction performs well.

Select solid wire, rectangular wire, foil, Litz or planar conductors by comparing complete designs at operating temperature. Use analytical models within their assumptions, add field simulation where geometry requires it, and validate total loss, hot spots, parasitics and insulation in the final assembly.

FAQ

These answers address common winding-loss questions when designing or purchasing power transformers and inductors.

What are winding losses in transformers and inductors?

Winding losses are electrical power dissipated in winding conductors and their terminations. They include the loss associated with the DC current component and with alternating current. At higher frequencies, skin and proximity effects redistribute current and increase effective resistance. Accurate prediction therefore requires the current waveform, operating temperature and actual winding geometry.

What is the skin depth of copper at 100 kHz?

Using copper resistivity at 20 °C, skin depth at 100 kHz is approximately 0.209 mm. It describes the characteristic penetration of alternating current, not a sharp boundary beyond which current is zero. Compare this value with strand diameter or conductor thickness, then include proximity fields and the current spectrum when estimating winding loss.

Do proximity losses increase with the square of the number of winding layers?

Some simplified winding models contain a contribution related to the square of an effective layer or section parameter. This is not a universal relationship for total physical layer count. Loss also depends on conductor dimensions, winding breadth, frequency, interleaving and current. Compare the complete field distribution rather than assuming four layers always produce sixteen times the loss.

How should Litz wire be selected for a high-frequency winding?

Specify strand diameter, strand count, bundle construction, overall dimensions and termination requirements. Fine insulated strands reduce strand-level skin effect, while suitable transposition helps control unequal induced voltages and current sharing. Strand insulation does not block magnetic fields. Compare total loss, copper utilisation and cost against solid-wire or foil alternatives under the actual current waveform.

Are foil and rectangular conductors always better than round wire?

No conductor shape is universally better. Foil and rectangular wire can provide useful copper area and controlled dimensions, but their AC loss depends on thickness, field orientation, layer arrangement and current sharing. Fine round wire can remain suitable at high frequency. Select the construction from calculated hot loss, thermal performance, insulation and manufacturing requirements.

How can proximity losses be reduced in power magnetics?

Reduce the magnetic field acting on the conductor or reduce the dimensions over which it drives circulating currents. Suitable measures include transformer winding interleaving, fewer effective layers, correctly constructed Litz wire and moving copper away from discrete gaps. Preserve insulation requirements and check leakage inductance and capacitance, because a loss improvement can change other circuit parameters.

How to Minimise AC Winding Losses in Power Magnetics

Use this procedure to compare conductor and winding arrangements, then validate the selected construction. It complements topology-specific magnetic design and the safety assessment of the final equipment.

Compare and validate a low-loss winding construction for power transformers and inductors.

Define the current waveforms and operating range
Record switching or resonant frequency range, duty ratio, DC current, RMS current and peak current for every winding. Include operating extremes and determine the harmonic content relevant to loss prediction.
Calculate resistance and skin depth
Calculate DC resistance and skin depth using conductor properties at the intended temperature. Compare skin depth with strand diameter or conductor thickness, without treating it as a sharp current boundary or a complete selection rule.
Compare conductor constructions
Evaluate solid round wire, rectangular wire, foil, Litz and planar options as applicable. Compare copper area, conductor dimensions, insulation, available winding space, terminations, current sharing and manufacturing cost.
Reduce field build-up and gap exposure
Evaluate winding breadth, sectioning and effective layer count. Identify discrete-gap fringing fields and reposition conductors where useful. Do not assume that a fixed layer-count ratio predicts the loss change.
Evaluate interleaving and parasitic trade-offs
For transformers, compare correctly connected interleaving arrangements. Check winding loss together with leakage inductance, capacitive coupling and the converter requirements. Preserve any intentionally specified leakage inductance.
Confirm insulation and production requirements
Check working voltage, transient stress, creepage, clearance, insulation materials and termination construction. Specify controlled dimensions, acceptance tests and supplier documentation for the exact catalog or custom component.
Model, measure and qualify the winding
Use analytical models within their assumptions and field simulation where the geometry requires it. Verify resistance, parasitics, operating loss and local temperatures on production-representative samples under the intended waveform and cooling conditions.

References

The following documents support the conductor-loss mechanisms, analytical methods and simulation limitations cited in the text. Undated documents are identified without assigning an unverified publication year.