What Is Transposed Litz Wire and Why It Beats Ordinary Stranded Wire

Transposed litz wire is a high-frequency conductor made of many insulated thin copper strands, each of which, during stranding, successively occupies every position across the bundle cross-section. This periodic rearrangement (transposition) equalizes the current distribution among the strands and suppresses the skin effect and the proximity effect at frequencies from 10 kHz to 2 MHz. Not every wire made of many thin strands is litz wire, and not every litz wire works: the difference between "just 125 strands twisted together" and a properly built 5×5×5 is a factor of 2 to 3 in AC resistance at the operating frequency.

Let's work through it step by step: why this happens, where the rule of "no more than five bundles per operation" comes from, why the classic seven-bundle stranding (6 around 1) is a compromise from the last century, and how to calculate the weight of the finished product before it goes into production.

Why litz wire is needed at all

At DC there is no problem: the electrons distribute evenly across the wire cross-section and the resistance is given by a high-school-level formula:

The trouble starts at AC. The current stops flowing uniformly and is pushed toward the surface of the conductor — this is the skin effect. The thickness of the layer in which the current density drops by a factor of e from its surface value is called the skin depth:

For copper, in simplified form:

The specific numbers worth keeping in mind:

The table makes it clear right away: at 100 kHz a solid wire thicker than 0.4 mm already works inefficiently — the center carries almost no current. You could take a single thin 0.1 mm wire, but then there isn't enough cross-section for the required current. So the answer is: take many thin wires, each in enamel insulation, and connect them in parallel. That is the idea behind litz wire.

A practical rule for choosing the elementary strand diameter:

At d = 2δ the increase in AC resistance over DC due to the skin effect at the level of a single strand is about 8%; at d = δ it is under 1%. This is the upper bound. Real constructions often go lower — down to d ≈ 0.5δ — when the dominant effect at the operating frequency is not the skin effect but the proximity effect.

But a "pile" of thin strands alone is not enough. If you simply gather them into a bundle without the right geometry, the skin-effect problem is replaced by a second one — the proximity effect. The magnetic field of neighboring strands in the same bundle (internal proximity) and the magnetic field of neighboring coil turns (external proximity) induce eddy currents in every strand. The result: some strands heat up more than others, the AC resistance of the whole bundle rises, and we are back where we started.

Naively splitting a solid conductor into thin strands — without transposition and without taking the diameter below the skin depth — makes things worse, not better.

The reason lies in how proximity losses are calculated in the first place. By the classic Dowell formula for a winding, they grow not with the total copper cross-section but with the number of conductor "layers" across the magnetic field of the coil. A solid 5×5 mm bus bar is one layer. A matrix of 25 strands of 1×1 mm in the same volume is already five layers. The magnetic field passing through the winding induces eddy currents in each layer in turn, and the losses add up.

Specific numbers (S. Zurek, Encyclopedia Magnetica, a winding at 10 kHz):

At 1 mm strands the gain from reducing the skin effect does not yet offset the loss from the increased number of layers — on balance it is worse than a solid bus bar. At 0.5 mm strands it is already better. And so on — each further reduction in diameter wins back more.

Two important practical consequences:

1. The elementary strand diameter must be chosen much smaller than δ, not merely ≤ 2δ. Formally the limit d = 2δ applies to the skin effect of a single strand; to fight the proximity effect in real windings you often have to go down to d ≈ 0.3–0.5δ.
2. These numbers apply to parallel, non-transposed strands — that is, to what you get from "wild" stranding without a systematic change of positions. Proper transposition suppresses not the proximity effect itself (which cannot be eliminated completely) but the circulating currents between strands, and that cuts the total losses by a large factor.

Hence the key takeaway: transposition and the right strand diameter are not alternatives but mandatory conditions at the same time. One without the other works poorly.

There is also a reverse estimate for the designer. The maximum number of strands worth combining into a single bundle without further transposition is the number at which the bundle diameter still fits within 2δ:

where k_pack ≈ 0.75–0.85 for dense packing of round strands. If the calculation calls for more, simple stranding will not do — it is time for the next stage.

The transposition principle: why every strand must "go everywhere"

Transposition is the systematic change of the position of each individual strand within the bundle along the length of the wire. In an ideally built litz wire, every strand, over one full lay length, occupies in turn all possible positions in the cross-section: center, middle layer, outer layer.

Why this is needed physically: a strand at the center of the bundle links one magnetic flux, a strand at the edge links another. If the positions are static, different EMFs are induced in the strands, a potential difference arises, and circulating currents begin to flow through the parallel-connected strands — currents that do nothing useful and only heat the copper. When each strand has in turn visited every point of the cross-section, the integral flux linkages equalize, the potential difference between strands tends to zero, the circulating currents are suppressed, and the current distributes evenly.

A typical lay length for realizing the effect is 15–20 diameters of an individual strand; this parameter cannot be neglected, since the quality of the transposition and the Q factor of the future coil depend directly on it.

The lay length must be neither too long nor too short. Too long (>30 diameters) — the strand does not manage to change positions over the characteristic length of a coil turn; the transposition is formally present but in fact does not work. Too short (<10 diameters) — the lay angle becomes steep, the strand length grows (and with it the DC resistance), the enamel insulation is deformed, and there is a risk of microcracks and turn-to-turn breakdown. Sullivan's calculations for a typical transformer on an EC70 core show an optimum lay around 12 mm for a 0.1 mm strand — that is, the same ~15 diameters.

An important nuance: "wild" stranding (all strands in one pass on an ordinary twisting machine without a pay-off system) does not provide transposition. The strands in it are randomly jumbled but do not pass through all positions with equal probability. Some strands stay in the center, some stay outside. The strand lengths come out different, which by itself kills the high-frequency characteristics: the longer strands have higher inductance, less current flows through them, and more flows through the short ones — so the cross-section is again used unevenly.

True transposition is achieved only by multi-stage stranding: first n₁ strands are stranded into a first-stage sub-bundle, then n₂ such sub-bundles into a second-stage bundle, and so on. This is denoted as 5×5, 3×4×5, 5×5×5, etc. The first figure is the number of strands in the smallest sub-bundle, the last is the number of top-level sub-bundles.

The rule of five: why 3, 4, 5 are fine but 6, 7 are not

This is where it gets most interesting and counterintuitive. There is a magic number — five. It rigidly limits how many elements can be combined at each stranding stage.

The geometric rationale

Take round elements of equal diameter and pack them as tightly as possible:

• 3 elements — an equilateral triangle, all three on the periphery, no center;
• 4 elements — a square or rhombus, all four on the periphery, no center;
• 5 elements — a pentagon with an empty center, all five equidistant from the axis;
• 6 elements — either a regular hexagon with an empty center (mechanically unstable) or 5 in a ring + 1 in the center;
• 7 elements — 6 in a ring + 1 in the center, a concentric layout.

In the first three cases all the elements are in a geometrically equivalent position relative to the bundle's axis of symmetry. Simple twisting guarantees that each of them works through all angular positions equally, and that is enough: within such a bundle there is no "center" position to fight over.

Starting at six, a center appears. And the problems begin.

Mechanics: why 6 around 1 is an unstable construction

Six bundles with no central strand is a construction that, under tension on the drum or during rewinding, collapses: one of the outer bundles falls into the center and the other five close around it. The result is effectively 5+1, and with broken geometry: the bundle that "fell in" has a shorter length than the five outer ones. The equality of strand lengths is broken — and so is the transposition.

You can put an inert filler in the center (an aramid cord, fiberglass), but this adds diameter, mass and cost without improving electrical efficiency — which defeats the whole purpose.

Electrics: why 7 bundles (6+1) lose to 5

With seven, everything seems stable: six bundles concentrically around one central one. Structurally sound. But electrically the central bundle always loses out. It sits in a zone where the magnetic field of the outer bundles pushes less current into it, and it is itself shielded from the external field. As a result the central bundle carries less current than each of the six outer ones — this is the manifestation of a bundle-level skin effect.

Simple twisting does not solve the problem: rotation about the axis does not move the central bundle out of the center. To genuinely transpose 7 bundles you need an additional stranding stage at the next level, which moves not individual strands but whole sub-bundles between radial positions. This is exactly the point of a multi-stage construction such as 5×5, 5×5×5, etc.

The measured effect

Sullivan's group at Dartmouth (Thayer School of Engineering) directly compared three variants of 125 strands of 0.16 mm diameter on an Agilent 4294A impedance analyzer:

1. Simple stranding 125×0.16 mm — the worst result.
2. Construction 5×25/0.16 mm (first stage — wild stranding of 25 strands, then 5 sub-bundles with true transposition) — a middling result.
3. True litz wire 5×5×5/0.16 mm — the best result.

The difference in the AC-resistance factor is a multiple. At the same copper mass and the same outer diameter, the third construction works at frequency 2 to 3 times more efficiently than the first. What this means in practical units: a 20 kW induction-heater coil wound with "simple" litz wire dissipates about 400 W in the copper, while a properly transposed one dissipates 150–200 W. That 200 W difference means either a smaller heatsink and a quiet fan, or, over two units a year, as much saved electricity as the litz wire itself costs.

It is useful to understand here that variant No. 2 (a wild first stage plus proper transposition afterward) is exactly how commercial litz wires are built in practice. Bringing every stage down to an ideal ≤5 elements is economically justified only at ultra-high frequencies and for small strand counts. For typical applications around 20–200 kHz, a wild primary bundle of 15–30 thin strands followed by proper ×3/×4/×5 stages delivers 80–90% of the electrical performance of a full 5×5×5 at a multiple lower production cost.

This bears directly on the coil's Q factor. Per Elektrisola, for a real winding the following relation holds:

Switching from "wild" stranding of 125 strands to a properly transposed construction at 100 kHz lowers F_R by roughly a factor of three, which for a coil with the same L and N turns means a tripling of the Q factor without a single extra gram of copper. Switching from "wild" stranding of 125 strands to a properly transposed construction at 100 kHz lowers F_R by roughly a factor of three, which for a coil with the same L and N turns means a tripling of the Q factor without a single extra gram of copper.

The practical takeaway for the designer

The rule reads: at each transposing stage, combine no more than 5 elements. The first (innermost) stage of thin enamelled wires is a separate story — there a wild stranding of 15–30 strands is permissible. But from the second stage on, factor the count into multiples from {3, 4, 5}:

Avoid 6 and 7 on transposing stages. The first, innermost stage, however, is built differently — and here it is important not to confuse the two.

In the first stage, up to 60 thin enamelled wires are stranded together into a single bundle at once. Geometrically this is not "3, 4, 5" — the strands settle into a chaotic packing with no clearly defined center and no layers. But transposition is present there too, only it is statistical. Thanks to the twisting and the dense random packing, each strand, over a length of several lays, passes through all radial positions within the bundle — now at the center, now at the periphery, now in between. Per Elektrisola this is called a "statistically homogeneous distribution of the single wires across the litz wire cross section." In Diada's TU (ДСГТ.685660.019ТУ, clause 1.3.7) this requirement is stated explicitly.

An important nuance fixed in the TU: at the first stage, a regular geometric stranding of 6, 7 or 8 strands is categorically prohibited. The reason is exactly the one discussed above: such constructions leave the central conductor without transposition.

In commercial marking and order specifications, the breakdown by stranding stages is not used. The form of notation accepted in the industry and in the TU is N×d, where N is the total number of strands and d is the diameter of a single wire in millimeters. Examples from Diada's TU:

• Litz PET (ПЭПЭТ-155-М) 500×0,1 — 500 strands × 0.1 mm under a PET-film serving.
• Litz 200 оА2 (ПЭВоА2-200-М) 500×0,224 — 500 × 0.224 mm, 200 °C, double Arselon serving.
• LitzPr F (ПЭФ-Пр-155-М) 460×0,071 2×2 — rectangular 460 × 0.071 mm, 2×2 mm cross-section, PTFE.

The order of the factors affects the geometry of the finished product — with 3×4×5 the triple occupies the center, with 4×3×5 the quadruple does. For rectangular forming ("square litz wire," which gains up to 20% in the winding-window fill factor) sequences with an even number of elements on the top stage are preferred.

Where litz wire stops working

Litz wire is not a universal solution at all frequencies. There are two ceilings, above which it either does not help or gets in the way.

The upper frequency limit is the inter-strand capacitance. Each pair of adjacent strands, insulated by a thin layer of enamel, is a parallel-plate capacitor. Above 1–2 MHz this capacitor begins to effectively "short" the adjacent strands with AC bypassing the enamel, the transposition loses its point, and the litz wire starts to behave like a single solid thick conductor — that is, poorly. Above about 5 MHz one no longer uses litz wire but hollow conductors (copper tubing) or special film constructions.

The lower efficiency limit is when the skin effect is not critical enough to justify the cost. At 50 Hz the skin depth in copper is 9 mm, and ordinary copper bus bars work fine without any transposition. Litz wire at power frequency is used only where there are either very large currents in dense busbars (in which case the Roebel transposed conductor is used in turbogenerator windings) or higher harmonics that heat an ordinary wire badly.

A separate headache is end termination. Each strand must be reliably connected to a common point, otherwise the current distributes unevenly: some strands end up "disconnected" and some are overloaded. Poor termination with uneven tinning can degrade the performance of even a perfectly built litz wire by 20–30%. That is why the leads use either hot tinning in a flux bath (strands of self-fluxing enamelled wire tin themselves when heated above 380 °C) or special end-face contact terminals.

How much it weighs: the formulas

When a customer asks "how much will 200 meters of 3×4×5 litz wire from 0.2 mm wire weigh," you need a quick and accurate answer. Here is a working calculation scheme.

Step 1: the mass of one elementary strand

An elementary strand is an enamelled wire of diameter d (over the enamel) with a copper diameter d_Cu. The linear mass:

In practice the enamel contributes 2–4% to the mass; for a quick estimate it is often accounted for by a correction factor k_enamel ≈ 1.03.

Example: 0.20 mm copper, enamel up to 0.22 mm → m₁ ≈ 0.290 g/m.

Step 2: the length increase due to stranding

Each stranding stage adds geometric length to the strand: the strand does not run straight along the axis of the finished wire but along a helical path. The length-increase factor for one stage:

At the standard ratio p_i/D_i ≈ 15 the factor comes out around 1.02 — that is, the strand is 2% longer than the axis. At each subsequent stage the effect accumulates — the factors multiply:

In Diada's TU for high-frequency winding wires (ДСГТ.685660.019ТУ, clause 1.3.8) the upper bound of this factor is normalized directly: no more than 1.03 for round wires and no more than 1.05 for rectangular ones.

Step 3: the resulting linear mass

One meter of finished litz wire contains not L = 1 m of strand but L · K_Σ meters. So the total mass of the strands is:

If there is outer insulation (a film serving, a polyamide braid, PVC or PU extrusion), its linear mass is added. In total, the mass of one meter of finished wire is:

A worked example: 60×0.20

Litz wire 60×0,20 (0.20 mm copper, enamel up to 0.22 mm, no outer insulation):

• m₁ ≈ 0.290 g/m
• K_Σ per the TU norm for round wire = 1.03
• M ≈ 60 · 0.290 · 1.03 = 17.9 g/m, or 17.9 kg per 1000 m

For a 0.3 mm polyurethane jacket over a bundle of ≈2.0 mm diameter, about another 2.5 g/m is added → a total of ≈20.5 g/m.

A second example: 125×0.2 with a silicone jacket

Now the same 0.2 mm strand, but 125 of them with an extruded silicone jacket (ρ ≈ 1.2 g/cm³) 0.4 mm thick. The bundle diameter is about 2.8 mm.

• N · m₁ = 125 · 0.290 = 36.25 g/m
• K_Σ = 1.03 → M_strands = 36.25 · 1.03 ≈ 37.3 g/m
• M_insul = π·(3.6² − 2.8²)/4 · 1.2 ≈ 4.8 g/m
• Total ≈ 42 g/m, or 42 kg per 1000 m

A useful rule of thumb: in such constructions pure copper makes up roughly 80–85% of the wire mass excluding the outer jacket. Everything else is enamel, the technological length increase from stranding, and the air gaps between strands.

Where it is used and what it gives in real numbers

The main consumers of transposed litz wire today are four segments, each with its own frequency windows:

• Induction heating (metalworking, hardening, HF brazing, induction cooktops): 10–100 kHz, currents up to hundreds of amperes. Litz wire reduces losses in the inductor by a factor of 2 to 5 compared with a solid tube.
• Wireless charging (the Qi standard, automotive WPT systems): 85–205 kHz. The window fill factor and the Q factor are critical — which is why flat or profiled litz wire is often used.
• SiC/GaN power converters (EV on-board chargers, PFC, LLC resonant stages): 50–500 kHz and higher. Switching to litz wire raises OBC efficiency by 0.5–1.5 percentage points — 50–150 W saved on an 11 kW charger.
• Instrumentation and high-Q resonant circuits (MRI coils, HF generators, radio transmitters): 100 kHz to several MHz.

Historically litz wire appeared in the 1920s alongside the first medium-wave radio transmitters; in the 1940s it went into ultrasonic equipment, and in the 1950s into the chokes of VHF receivers. Mass use in power electronics is a phenomenon of the last two decades: as long as converter frequencies stayed at a few kilohertz, ordinary wires were enough.

What to specify when ordering litz wire

To sum up all of the above — before releasing a job to production, it is worth fixing five parameters:

1. Operating frequency — sets the maximum allowable elementary strand diameter (d ≤ 2δ).
2. Required copper cross-section — sets the number of strands and the stranding construction.
3. Stranding structure — the factoring of N into multiples from {3, 4, 5}, with no sixes or sevens on any transposing stage.
4. Lay length of each stage — 15–20 diameters of the corresponding bundle, fixed in the process sheet.
5. Type of outer covering — determined by the service conditions (temperature, environment, mechanics).

Once all five parameters are agreed, you can compute the DC resistance, estimate the AC resistance at the operating frequency, calculate the mass, price it out, and put it into production.

Frequently asked questions

What is transposed litz wire in simple terms?

It is a high-frequency conductor made of many insulated thin copper strands, each of which, during stranding, successively occupies every position across the bundle cross-section — both inner and outer. This periodic rearrangement (transposition) equalizes the current distribution among the strands and suppresses the skin effect and the proximity effect at frequencies from 10 kHz to 2 MHz.

How does transposed litz wire differ from ordinary multi-strand wire?

In ordinary stranding such as 6×1, 19×1, or 37×1, the strands run along the wire in fixed positions and the induced eddy currents are distributed unevenly — electrically such a wire behaves like a single thick strand. In transposed litz wire each strand passes through every position in turn, so all strands carry current equally. The difference in AC resistance at the operating frequency is a factor of 2 to 3.

What is the "rule of five" in litz wire construction?

The rule of five is an empirical manufacturing principle: in a single pass on the stranding machine you can combine no more than five bundles, otherwise the packing geometry breaks down and the strands do not pass through every position evenly. That is why the canonical constructions are 3×N, 4×N, 5×N, 3×3×3, 4×4×4, 5×5×5 and their hierarchical combinations, built up from "allowed" bundles of no more than five.

Why is seven-bundle stranding (6×1 or 7×1) worse than transposed?

In a 6×1 or 7×1 construction the central strand is surrounded by six peripheral strands and is geometrically locked in place — it cannot be "brought to the outside" in a single stranding operation. The transposition is incomplete: the central strand operates under different conditions than the peripheral ones. Such a construction is acceptable up to about 50 kHz; above that it is noticeably worse than a fully transposed construction (5×5×5, 3×5×5, etc.) in AC resistance.

How do you calculate the mass of finished litz wire per kilometer of length?

Mass of 1 km of litz wire excluding insulation: m = ρCu · N · π · (d/2)² · klay, where ρ_Cu = 8.96 g/cm³ is the density of copper, N is the total number of copper strands, d is the elementary strand diameter, and k_lay = 1.03–1.05 is the strand lay factor. To this mass you add the mass of the enamel on the strands and of the outer insulation (PTFE, polyimide, Arselon, PET) from the standard tables.