Rectangular litz wire: when and why forming pays off
Rectangular litz wire is transposed litz wire formed into a rectangular cross-section in a single pass together with its insulation, which raises winding-window fill by 15–20% compared with round litz wire of the same copper cross-section. Forming is needed where the core slot geometry (Planar E32, a hairpin slot, a toroidal PFC coil) does not accept round strands well, and where every percent of window fill turns into watts of efficiency or millimeters of device size.
Rectangular litz wire is a distinct class of winding wire with its own economics. Through +20% winding-window fill it converts that simple geometry into specific watts of efficiency, grams of core, and millimeters of device size. There are alternatives on the market — hairpin windings, continuously transposed cable (CTC), Roebel bars, planar windings on multilayer PCBs — and to make the right decision you need to know where each one works and where it does not replace rectangular litz. This article works through the economics of +20% on real converters, five application classes with concrete gains, five competing technologies, the link to typical cores, and the full ordering process — from window dimensions to finished wire. The physics of the rectangular cross-section itself (anisotropy, aspect ratio, fill geometry) is covered in detail in the long article on choosing a litz-wire grade and is not repeated here.
1. From geometry to money: +20% fill in watts of efficiency
The figure "+20% window fill" sounds dull until you translate it into money and watts. Let's work through two examples from different application classes — power electronics and industrial induction heating.
1.1 Example: the PFC inductor in an 11 kW EV OBC
Inputs. An on-board charger for an electric vehicle, 11 kW, 400 V, 85 kHz switching frequency, PFC inductor on an ETD59 core (window 44×8 mm, magnetic volume 37 cm³). The winding has 35 turns carrying 20 A RMS.
Round litz scenario. At 85 kHz the skin depth δ ≈ 0.22 mm, so we choose a 0.1 mm strand; the strict Sullivan optimum is 735 strands, 5.77 mm² of copper. The finished litz wire in a PET jacket comes out to about 4.2 mm outer diameter. The turns fit into the window with a fill factor η ≈ 0.60: 35 turns × π·2.1² = 485 mm², out of the 352 mm² of bobbin-free window area — copper fill of about 34%. With a DC resistance RDC ≈ 4.3 mΩ/m and a mean turn length of 220 mm, the copper loss I²·R·FR = 20² · 0.0043 · 7.7 · 1.15 = 30 W.
Rectangular litz scenario. The same wire — 735 strands of 0.1 mm — is formed into a 4.7×3.2 mm cross-section (aspect ratio 1.47:1, sized to the ETD59 window). The window fill factor is now η ≈ 0.82. At the same turn count, free space appears, and we can afford to increase the copper cross-section by 35% — using 990 strands instead of 735, for 7.78 mm² of copper in a 5.5×3.7 mm cross-section. DC resistance drops to 3.2 mΩ/m and copper loss to 22 W.
The economics. An 8 W difference on one of the OBC's six windings is 48 W in total across the device. At an average of 4000 operating hours per year for a single EV (estimated from European WLTP data), that is 190 kWh per season. Across a fleet of 100,000 cars, that is 19 GWh per year — equivalent to the output of a small 3 MW thermal plant running continuously. In money, at a tariff of 5 rubles/kWh, that is 95 million rubles of net energy savings. In terms of mass: every 8 W of copper loss removed lets you shrink the OBC heatsink by 0.1 kg — 10 kg across a fleet of 100 cars, which then carry payload instead of metal.
An alternative scenario is to not increase the copper but shrink the core instead. With the same round 735×0.1 mm litz packed rectangularly, the turns fit a 35×7 mm window instead of 44×8. That allows switching from ETD59 to ETD44 — 18 cm³ of magnetic volume instead of 37, with ferrite mass down 50%. Core loss at the same flux density falls in proportion to volume: at 100 W/dm³ (typical for 3C95 at 85 kHz) that saves another 19 W.
Which of the two scenarios to choose depends on what is more critical: efficiency or compactness. For stationary charging stations, the first. For mobile, on-board systems, the second. Rectangular litz gives the engineer both options; round litz gives neither.
Takeaway. "+20% window fill," translated to an EV OBC, is either 8 W of copper per winding or 50% of core mass. Choosing between those two bonuses is exactly the engineering decision that rectangular litz enables.
Model of the PFC winding in an 11 kW OBC: 35 turns, 20 A RMS, 85 kHz, 6 windings per device. Drag the sliders — the figures recompute in real time. Copper loss in round litz is computed as I²·R·FR·Kiso; in rectangular litz, with −27% from fill. The bonus of returning ferrite mass is not included here — that is a separate scenario, and it can be unwound in the other direction (shrinking the core by −50% instead of removing loss).
1.2 Second example: an induction heater for HF surface hardening
Let's take a radically different class — a 40 kW industrial induction heater at 30 kHz for surface hardening the journal of an engine crankshaft. The inductor is a flat round coil 250 mm in diameter, 12 turns.
Round litz wire. At 30 kHz the skin depth δ ≈ 0.37 mm, so a 0.15 mm strand (strictly less than δ/2). At a design current of 180 A RMS and a current density of 6 A/mm² (water cooling), the copper cross-section is 30 mm² — 1697 strands in a 1700×0,15 construction. The finished round litz wire in a polyimide jacket is about 8 mm in diameter. At 12 turns the inductor stands 100 mm tall — beyond the convenient geometry for most hardening rigs, where the gap between inductor and workpiece is critical.
Rectangular litz wire. The same wire is formed into a 9.5×5.5 mm cross-section (ratio 1.7:1). The inductor height drops to 66 mm — minus 34%. But the key point in this application is not size, it is field uniformity over the workpiece. With a round inductor the turns leave ring-shaped gaps where the field is locally weaker by 15–25%, and the surface hardening comes out uneven — with bands of different hardness. With rectangular litz the turns sit edge to edge, the field over the inductor becomes nearly uniform, and the case depth along the journal surface is stable, with no more than 5% deviation across the whole working zone.
For a hardening shop, that means cutting the scrap rate on hardened-layer geometry from a typical 3–5% to a fraction of a percent. On a program of 50,000 shafts per year, that is tens of millions of rubles of annual savings, and the payback on switching from a round inductor to a rectangular one is measured in quarters, not years.
Two economic stories — the OBC and induction hardening — show that the benefit of rectangular litz is different in different applications. Sometimes it is pure efficiency, sometimes process quality, sometimes device size. There is no universal "+20% efficiency": you have to run the numbers for each job separately, and the figure in actual money can turn out to be several times larger than the difference in wire price.
2. Five applications where forming gives a multiplied payback
Rectangular litz wire does not win everywhere. There are five applications where the payback is multiplied, and a few more where forming gives an indirect bonus.
2.1 Qi wireless charging and automotive WPT systems (SAE J2954)
The Qi specification (WPC 1.3) and SAE J2954 for electric vehicles set tight coil dimensions: diameter 100–500 mm, winding thickness no more than 5–8 mm. At 85 kHz the strand must be ≤ 0.1 mm and the strand count runs into the hundreds. Round litz wire of that construction gives a cross-section diameter of 4–5 mm, and on a standard 10-turn flat coil the total winding thickness exceeds the allowed envelope.
A flat rectangle of 6×3.2 mm solves the problem at once: the coil height fits within 3.5 mm plus the ferrite backing. This is not a percentage optimization, it is a go/no-go: without forming the coil simply does not fit the envelope.
2.2 PFC and LLC inductors in power electronics
A typical PFC inductor in an 11 kW OBC is an ETD49 or ETD59 core with 30–40 turns. We just worked through the numbers: +8 W of efficiency or −50% of core mass. For production parts with annual volumes of 10,000+, that is tens of millions of rubles of difference in material cost and hundreds of millions in operating losses at the end user.
LLC resonant converters in 3 kW 48 V server power supplies (AI farms, hyperscale data centers) at 250–500 kHz are the same story in even sharper form: copper loss at such frequencies makes up as much as 40% of all transformer loss, and rectangular litz removes 25–35% of it, where the round equivalent physically does not fit into the window of a PQ core of the required inductance.
2.3 Induction heaters and domestic cooktops
A 3.5 kW induction cooktop is a flat coil 180 mm in diameter and 2.5 mm tall. Field uniformity over the working surface is set by turn density, and rectangular litz in such coils gives more uniform flux: round turns leave gaps between them where the field is locally weaker, and heating of the cookware along the radius comes out non-uniform.
For industrial HF-hardening inductors in the 50 kW class, the same picture has a different emphasis: there, what matters is not size but the copper loss of the inductor, which sets the heat dumped into the cooling-circuit water. Switching from a tubular inductor to rectangular litz in a multi-turn design cuts copper loss by a factor of 3–5.
2.4 MRI coils and RF windings for precision instrumentation
Magnetic resonance imaging requires coils with the highest possible Q factor at frequencies from 20 to 300 MHz. Rectangular litz in such geometry gives two bonuses: dense turn packing raises inductance per unit volume, and tight contact with the coolant reduces local heating under pulsed loading. The gradient coils of modern scanners (Siemens, GE, Philips) use rectangular litz wire precisely — and that is a separate, heavily proprietary technology.
2.5 Hybrid windings for EV traction motors
Since 2023, a new class of solutions has appeared in IEEE papers (Applied Sciences, 2023, MDPI) and from Elektrisola: a hairpin winding in the stator slot + rectangular litz wire in the end turns. The idea is that in the slot, where the magnetic field is comparatively uniform, the solid rectangular hairpin bar gives maximum slot fill factor and is automated on the assembly line, while in the end turns, where the field is sharply non-uniform and proximity-effect losses are catastrophic, rectangular litz is used — it removes those losses while keeping packing density.
For traction motors on 800 V SiC-inverter platforms, this solution gives an efficiency gain of 0.5–1.5 percentage points over a pure hairpin design — at the same motor volume. On a 150 kW traction motor, that is 750–2250 W of heat not generated, a direct addition to the EV's range.
3. Alternatives to rectangular litz — and the limits of each
Understanding the alternatives matters not for competition, but to avoid using rectangular litz where it is not the best choice. Five technologies it is regularly confused with or compared to:
3.1 Hairpin windings (solid rectangular magnet wire)
This is a solid rectangular copper bar bent into a U like a hairpin (hence the name) — a single conductor, no transposition, usually in enamel or polyimide varnish. Used in the traction motors of Tesla, BMW, and the VW ID series.
Where it wins. A fill factor up to 0.85 — on par with rectangular litz. High assembly automation: the U-shaped blank is inserted into the slot and laser-welded at the stator crown. Mechanical stiffness — a built-in structural advantage in motors with high centrifugal loads.
Where it loses. Above 1–2 kHz the copper loss grows quadratically with frequency per Dowell's equation. The SiC inverters of traction motors run at 10–40 kHz, and the AC/DC resistance ratio of a hairpin winding paired with such an inverter reaches 3–5. That is exactly where the hybrid hairpin+litz designs came from — to cover the hairpin's weak spot in the end turns.
3.2 Continuously transposed cable (CTC)
This is a large power transposed winding of 5–55 individually insulated rectangular strands, transposed along the length at a constant pitch. Used in power transformers from 100 kVA to hundreds of MVA, including the windings of grid autotransformers.
Where it wins. Currents from hundreds of amps to kiloamps at the industrial frequency of 50/60 Hz. A proven technology with half a century of history.
Where it loses. It does not scale down: CTC strands are rectangular conductors 2–10 mm on a side, and their cross-section is sized for the industrial frequency with a skin depth of 9 mm. Above 500 Hz the CTC stops working — the strands become "electrically thick" and the skin effect returns. CTC is never used for switching converters.
3.3 Roebel bars
A Roebel transposed conductor is 20–100 flat varnished copper bars stacked and transposed in a special helical pattern and pressed into a single plate. Used in the windings of power-station turbogenerators — Mitsubishi, GE, Siemens Energy, ENE (Russia).
Where it wins. Megawatt power levels, currents up to 20 kA, century-long service life under continuous operation. A unique technology for power generation at large stations.
Where it loses. Each plate is assembled by hand with high precision — output is measured not in meters per hour but in pieces per day. Economically unjustified for currents below a kiloamp and frequencies above 400 Hz.
3.4 Planar PCB windings
This is when the transformer or inductor winding is made of copper traces in a multilayer PCB. Used in low-profile DC/DC converters of 10–500 W, LED drivers, and server point-of-load (POL) converters.
Where it wins. Absolute repeatability — every coil is identical to the previous one to PCB tolerance. Full assembly automation, zero manual operations. Ultra-low profile — down to 2–3 mm total module height.
Where it loses. Limited copper cross-section — 35–105 µm per layer, at most 6–10 layers, totaling 0.3–1 mm² of copper. It will not carry currents above 20–30 A. And, crucially: above 500 kHz the board begins to suffer from the same skin and proximity effects as a solid wire — the traces become electrically "thick" and losses rise. For high-power, simultaneously high-frequency tasks a planar winding is not suitable.
3.5 Compacted stranded wire
This is a bundle of thin copper strands with no individual insulation, pressed to reduce the gaps between strands. Cheap, flexible, mechanically strong. Used in the cable industry for power cables.
Where it wins. Several times cheaper than litz wire at the same copper cross-section. Excellent flexibility.
Where it loses. No individual strand insulation — which means no transposition at all: the whole bundle acts as one thick conductor. Above 1 kHz losses rise rapidly and the wire becomes electrically identical to a solid one. Useless for winding production in switching electronics.
3.6 Summary table
| Technology | Frequencies | Currents | Key advantage | Limit of use |
|---|---|---|---|---|
| Hairpin winding | 50 Hz – 2 kHz | 50–500 A | Assembly automation | AC-loss disaster at f > 10 kHz |
| Continuously transposed cable (CTC) | 50–400 Hz | 100 A – 5 kA | Proven technology for transformers | Does not work at switching frequencies |
| Roebel bar | 50–60 Hz | 1–20 kA | Megawatt power levels | Manual assembly, cost |
| Planar PCB winding | 100 kHz – 1 MHz | up to 20 A | Full automation, low profile | Limited copper cross-section |
| Compacted stranded wire | DC – 1 kHz | depends on cross-section | Cheap, flexible | No transposition |
| Rectangular litz | 1 kHz – 2 MHz | 5–200 A per turn | Density + transposition at once | Aspect ratio up to 3.5:1 |
The niche of rectangular litz wire is high frequencies, medium currents, critical density — exactly where all the other technologies fail at the same time.
An engineering map in frequency × current coordinates (both axes logarithmic, from 10 Hz to 10 MHz and from 0.1 A to 100 kA). Seven colored zones are the operating areas of each technology. Black dots are real applications: Qi charging, OBC, server LLC, induction cooktop, MRI coil, turbogenerator. Click a chip for solo mode; the other zones dim. You can see that the niche of rectangular litz is a narrow band of "high frequencies + medium currents," where every alternative either falls short or overheats.
4. Mapping to typical cores: which rectangle for which window
The optimal cross-section of rectangular litz wire is computed for the specific core window, but the high-volume production types have characteristic proportions that are useful to know as a starting point.
ETD series (34 / 39 / 44 / 49 / 54 / 59). Cores with a central round limb and a rectangular window for SMPS transformers and resonant converters. The windows have aspect ratios from 2.5:1 in the smaller sizes to 5.5:1 in the ETD59. A typical litz cross-section is 2:1 or 3:2, with two or three rows of turns across the window height.
PQ series (20 / 26 / 32 / 35 / 40 / 50). Compact cores for high-frequency LLC resonant and server-class DC/DC converters. The window is close to square (1.3:1). The optimal litz cross-section is close to 1:1, a square or slightly elongated rectangle. 3×3 or 4×3 with a 0.1 mm strand is often used.
RM series (6 / 8 / 10 / 12 / 14). Cores for small inductances and instrument transformers. The window is close to square with rounded corners. A 1:1 litz cross-section, typical sizes 1,5×1,5, 2×2.
Planar series (Planar E14 / E22 / E32 / E38 / E43 / E58 / E64). Flat cores for low-profile converters. The window is very wide and low, with an aspect ratio from 3:1 to 4:1. The litz is formed to a ratio of 3:1…3.5:1 — the upper limit of our process. Typical cross-sections: 6×2, 9×3.
Toroidal cores (T series, PFC inductors). A toroid has no window in the sense an E-core does: the winding lies around the ring, and fill is set by the circumference and the winding thickness. Rectangular litz gives no benefit here, and we recommend a round cross-section — more in the section "When to choose round, when rectangular" of the long article.
Switch cores — the window geometry and recommended litz aspect ratio rebuild. On the left (orange), round turns in hexagonal packing; on the right (teal), rectangular turns of the same copper cross-section. A toroid has no window as such, and rectangular forming gives no benefit — for toroids we recommend round litz.
For practical sizing of the cross-section for a specific winding, a simple formula works to first order:
- b — height of the rectangular litz cross-section, mm
- Hwindow — core window height, mm
- tbobbin — bobbin flange thickness, mm
- Nrows — number of winding rows across the height
The width of the second side is computed from the number of turns per row and the window width. The exact calculation, accounting for interlayer insulation, bobbin clearance, and tolerances, is done when the order is processed — iteratively, checking FR at the operating frequency through the Dowell model.
5. Quality control of formed litz wire
After forming, rectangular litz wire differs from round not only in shape but in its profile of possible defects. Our in-house QC checks five parameters beyond those standard for round wire.
1. Tolerance on the cross-section sides. Per our TU DSGT.685660.019 (clause 1.3.2), the tolerance on a rectangle side is ±0.1 mm for cross-sections up to 5 mm and ±0.15 mm for cross-sections of 5–10 mm. Inspection is by caliper or optical micrometer every 10 m of wire at acceptance.
2. Squareness of the cross-section. The rectangle diagonals must match to within 0.05 mm per side. A deviation signals incorrect tool alignment or uneven bundle tension during forming.
3. Jacket uniformity after forming. Visual inspection of the film serving for tears or "gaps" on the long sides of the rectangle. With single-pass forming together with the insulation (see section 4.2 of the long article), the jacket must lie evenly; tears are grounds for stopping the batch and analyzing the cause.
4. Dielectric strength after forming. Per GOST R IEC 60317 — an AC test at 50 Hz, 1–2 kV for 1 minute, depending on the insulation class. Forming must not reduce the breakdown voltage by more than 10% relative to comparable round litz wire.
5. Retention of DC resistance. Per our TU (clause 1.3.8), the strand-length increase coefficient KΣ for a rectangular cross-section is no more than 1.05. In practice this means the DC resistance per meter of finished wire must not exceed the calculated value by more than 5% — we measure this directly before shipping each spool.
For customers who need laboratory cross-section verification from metallographic analysis — a typical requirement in aerospace assemblies, medical equipment, MRI coils, and precision research rigs — we arrange a metallographic micro-section of the first sample at a partner metallography laboratory. The procedure is standard: a length of finished litz wire is cut, embedded in epoxy compound, polished to a mirror finish, and photographed under a microscope with digital processing. The report covers the strand count in the cross-section, their integrity, the integrity of each strand's varnish insulation, the uniformity of the outer jacket, and the exact geometric dimensions of the rectangle. This is not a routine operation of our shop QC but a separate service, quoted as a separate line in the specification on request. Turnaround is about a week, and the cost usually pays for itself in confidence at series launch.
6. Common selection mistakes — so you don't repeat them
Over decades of working with litz wire we have seen five recurring scenarios where the engineer made a sub-optimal decision on cross-section shape. We have gathered them here so the reader can recognize their own situation in advance.
Mistake 1. "Rectangular in a toroid." A ring core and a rectangular shape are a combination that only works in one direction. A toroid has no window in the usual sense: the winding lies radially from the inner to the outer diameter, and rectangular litz gives no packing density (on the contrary, it creates wedge-shaped gaps between turns near the inner diameter). For toroidal geometry the right choice is round litz wire, and our catalog says so plainly.
Mistake 2. "A square on an elongated window." If a core has a 60×15 mm window (4:1 ratio), a 5×5 mm square litz will fill it worse than a 5×2.5 mm rectangle of the same copper cross-section. The first gives a fill of 0.5, the second 0.75. A common mistake is choosing the litz shape "out of habit," without tying it to the geometry of the specific window.
Mistake 3. "Rectangular without transposition is just as good." The market sometimes offers a "rectangular twist" from non-specialist manufacturers — they take a bundle of parallel strands (without multi-stage transposition by the rule of five) and crimp it into a rectangle. The wire looks like rectangular litz and is noticeably cheaper. Above 10 kHz such wire works many times worse than genuine transposed litz — skin and proximity effects are not suppressed. We come across such cases in tenders and try to explain the difference to customers before they buy from a competitor and end up with a winding that falls short of the design efficiency.
Mistake 4. "Let's save and take round." In the other direction: in a project where density and window fill are critical (Qi charging, OBC, PFC inductor), engineers sometimes choose round litz "to save money." At a price difference of 10–15%, round wire will give up 0.5–2% in efficiency in the finished device — that is, in production those 10% of savings on wire turn into tenfold losses in energy at the end user, plus a heavier core, plus a larger enclosure volume. Rounding the budget "on material" without accounting for the product's life cycle is a classic specifier's mistake.
Mistake 5. "Let's order the series straight away, no trial length." For standard round-litz grades with proven geometry, that is reasonable. For rectangular litz on new tooling, it is risky: nothing guarantees that on your specific coil with your specific bobbin a 4.2×3.1 mm cross-section will lie the way it does in the design model. A trial length of 10–20 meters after the tooling is made takes a week and costs next to nothing, yet lets you catch any discrepancies before they reach a 1000-meter series. We deliberately propose this step and recommend not skipping it.
7. The ordering process: from window geometry to series production
Unlike round litz wire, where ordering comes down to picking a catalog item, rectangular litz has a six-step sequence. We have refined it over dozens of projects.
Switching frequency, RMS current, turn count, core type (or window dimensions), insulation requirements. Ideally — waveforms from LTspice / PLECS / Simulink. At best — a 3D model of the bobbin.
Optimal strand diameter per Sullivan, strand count, stranding layout. In parallel we size the rectangle to your window. The result is a preliminary specification: grade per TU, cross-section, length.
We send the calculated RDC, FR, losses, and mass. If the prediction meets the brief, we sign off. If not, we discuss alternatives (a different cross-section, insulation, sometimes a different core series).
Forming tool for your cross-section. The machine is designed with interchangeable tooling — a custom cross-section costs no more than a "standard" one, with no expensive separate setup.
10–20 m of wire + full QC on 5 parameters (section 5). The sample ships to your address; you wind a trial coil and measure inductance, Q factor, and losses on your bench.
The main batch after the trial length is confirmed. For urgent jobs we run it in parallel with another order and shift schedules within reason. There is no lower volume limit: from 50 m for R&D to industrial volumes.
Total from brief to series batch: 3–5 weeks. For pilot projects of 10–50 meters — 2 weeks. We do not recommend skipping step 5 (trial length): it takes a week, costs next to nothing, and protects against mistakes across thousands of meters.
Order quantity. We have no lower volume limit. We make trial batches from 50 meters for research work and prototypes, and single-piece batches of 1–5 m for dissertations and graduation projects — as part of our cooperation with universities and research groups. On certain especially interesting cases (new construction types, experimental geometries that extend our own experience), we run the trial length at our own cost, in exchange for the right to add the results to our database and use them anonymized in publications.
Summary
Rectangular litz wire is not "round wire, but flattened" — it is an engineering tool with its own economics, applications, and alternatives. Its niche is high frequencies plus medium currents plus critical packing density — an area where none of the competing technologies delivers all three properties at once. On a specific EV OBC it is 8 W of efficiency or 50% of core mass; on Qi charging it is the question of whether the winding fits the envelope or not; on an MRI coil it is the Q factor that determines the quality of the medical image.
If you are designing a device in this niche, send us the core window geometry, frequency, current, and environmental requirements. We calculate, sign off, fabricate the tooling, make the trial length, and launch the series. Engineering discipline, not slogans.
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