Litz Wire

How litz wire works

Send DC through a round wire and the current spreads itself evenly across the whole cross-section, because nothing favours one part of the copper over another. Switch to high-frequency AC and that uniform picture falls apart. The alternating current sets up an alternating magnetic field, and inside the conductor that changing field induces eddy currents. Lenz's law makes those eddy currents oppose the flow in the centre and reinforce it at the rim, so the net current crowds into a thin shell at the surface. This is the skin effect, and it means the inside of a fat wire is carrying almost nothing — you paid for the copper but it's dead weight.

Litz wire's trick is disarmingly simple to state and surprisingly hard to manufacture. Split the one fat conductor into dozens or hundreds of thin strands, each thinner than the depth the skin effect reaches into copper. Inside a strand that thin, the skin effect has nothing to crowd against — the current already fills it uniformly. But that alone is not enough, because a strand sitting on the outside of the bundle still sees a different magnetic environment than one buried in the centre, so the outer strands would hog the current. The fix is transposition: the strands are not merely twisted, they are woven so that each individual strand spirals from the surface to the core and back again, over and over, along the length of the cable. Averaged over any reasonable length, every strand spends the same fraction of its journey on the outside and the same fraction in the middle.

That equal exposure does two jobs at once. It forces the strands to share the total current equally — so the bundle behaves like one large conductor with current spread uniformly, which is exactly what you wanted and exactly what the skin effect denied you. And because the strands swap places constantly, the magnetic coupling between them averages out, which also cancels the proximity effect — the current crowding that one conductor's field imposes on its neighbours. The payoff is an AC-to-DC resistance ratio that can stay close to 1 at frequencies where a solid wire of the same copper area would show a ratio of 3, 5, or worse.

The governing physics: skin depth and AC resistance

The single most important number is the skin depth δ — the depth at which the current density has fallen to 1/e (about 37%) of its surface value:

             ┌──────────────┐
   δ  =  √ ( ──────────────── )        [metres]
             │  π · f · μ · σ │
             └──────────────┘

  f = frequency (Hz)
  μ = permeability  = μ0·μr  (copper: μr ≈ 1, μ0 = 4π×10⁻⁷ H/m)
  σ = conductivity  (annealed copper ≈ 5.8×10⁷ S/m)

Convenient form for copper at 20 °C:

  δ_copper ≈ 66 / √f      (mm, with f in Hz)
           ≈ 0.066 / √f   (mm, with f in MHz)

Run the numbers and the motivation for litz wire becomes obvious:

  f = 50 Hz      →  δ ≈ 9.3 mm   (mains; skin effect barely matters)
  f = 20 kHz     →  δ ≈ 0.47 mm
  f = 100 kHz    →  δ ≈ 0.21 mm
  f = 500 kHz    →  δ ≈ 0.093 mm
  f = 1 MHz      →  δ ≈ 0.066 mm

At 100 kHz the current lives in the outer 0.21 mm of any copper. A solid 1.6 mm (about AWG 14) wire has a radius of 0.8 mm — nearly four skin depths — so most of its copper is wasted. The AC resistance ratio for a round solid conductor, often written F_R = R_AC / R_DC, is governed by the parameter ξ = (radius)/δ. For a single isolated strand of diameter d, a widely used approximation for the skin-effect contribution is:

  F_R(skin)  ≈  1 + (1/768)·(d/δ)⁴    for  d/δ ≲ 2  (thin-strand regime)

So keep each strand under one skin depth (d ≲ δ) and the skin penalty
per strand is a fraction of a percent.

The proximity term is what the transposition kills. Following the standard Dowell / Ferreira treatment used in power-electronics design, the total per-unit-length AC loss in a winding splits into a skin part and a proximity part, and for a bundle of n strands the proximity loss scales roughly with the square of the magnetic field the bundle sits in and with the number of layers it presents. Transposing the strands makes every strand see the same average field, so the cross-terms that would otherwise add up cancel. The headline design rule for choosing the strand diameter is simply:

  Choose strand diameter d  such that  d / δ  ≈ 0.5 to 1
  Then pick strand count n  to hit the copper area you need:
       A_copper = n · (π/4) · d²
  And accept a fill-factor penalty: bundle area is larger than
  the copper area by the insulation + packing overhead (~30 to 60%).

Worked example: a 100 kHz transformer winding

Suppose you are winding the primary of a 200 W switch-mode transformer running at 100 kHz and you need 0.5 mm² of copper to keep DC and conduction losses reasonable. Compare a solid wire to litz.

Target copper area:   A = 0.5 mm²
Operating frequency:  f = 100 kHz  →  δ ≈ 0.21 mm

OPTION A — solid wire
  Equivalent diameter for 0.5 mm²:  d = √(4A/π) = 0.80 mm
  Radius / skin depth:   0.40 mm / 0.21 mm ≈ 1.9
  Skin-effect ratio:     R_AC/R_DC ≈ 1.2 to 1.3 (skin alone)
  Add proximity in a real winding and the ratio climbs further
  → much of the copper is idle; the wire runs hot.

OPTION B — litz wire
  Strand diameter:       0.10 mm (AWG 38)  →  d/δ ≈ 0.48  ✓
  Area per strand:       (π/4)(0.10)² = 7.85×10⁻³ mm²
  Strands needed:        0.5 / 7.85×10⁻³ ≈ 64 strands
  Build:                 64/38 litz (64 strands of AWG 38)
  R_AC/R_DC (transposed) ≈ 1.05 to 1.15
  → nearly all copper is active; the winding runs cool.

The litz winding does cost more: it carries 64 enamel coats instead of one, so its overall bundle diameter is larger (lower fill factor), and the wire itself is several times the price per kilogram of equivalent magnet wire. But the loss reduction is real money in a power supply — cutting winding loss from, say, 6 W to 2 W in a 200 W converter lifts efficiency by about two percentage points and removes the heat you would otherwise have to sink. Above a few hundred watts that trade almost always favours litz at this frequency.

Strand-size selection table

A practical cheat-sheet for round copper litz, "strand thinner than one skin depth" as the design target:

Frequency	Skin depth δ (copper)	Max useful strand dia.	Typical AWG strand	Common build
20 kHz	0.47 mm	~0.40 mm	AWG 26	Coarse litz / heavy stranded
50 kHz	0.30 mm	~0.25 mm	AWG 30	e.g. 40/30 litz
100 kHz	0.21 mm	~0.15 mm	AWG 36–38	e.g. 64/38 litz
250 kHz	0.13 mm	~0.10 mm	AWG 40	e.g. 100/40 litz
500 kHz	0.093 mm	~0.06 mm	AWG 44	e.g. 200/44 litz
1 MHz	0.066 mm	~0.05 mm	AWG 46–48	Fine litz (manufacturing limit)
3 MHz+	0.038 mm	impractically thin	—	Consider foil / tubing / planar instead

Note how the strand gets finer and the strand count climbs as frequency rises. Around 1–3 MHz the strands become so fine that handling, enamel-to-copper ratio, and residual bundle-level proximity loss erode the benefit — which is why MHz-class RF and very-high-frequency power converters often abandon litz for solid tubing, copper foil, or planar PCB windings.

Construction, fill factor, and termination

Real litz is built in stages. Individual enamelled strands are first twisted into small primary bundles; several primary bundles are twisted into secondary bundles; and so on, sometimes through three or four levels, until the final cable is assembled. The hierarchical twisting is what produces true transposition rather than a simple parallel rope. Manufacturers describe a build with notation like "5×5×5/40", meaning 5 groups of 5 groups of 5 strands of AWG 40 (125 strands total), or simply "64/38" for a single-operation bundle of 64 AWG-38 strands.

A few numbers that bite in practice:

• Fill factor. Even perfectly packed round strands fill only π/(2√3) ≈ 90.7% of their bounding area, and litz never reaches that. Counting enamel and the looseness of twisting, the effective copper fill of a litz bundle is typically 60% to 75% of the bundle's cross-section — meaningfully worse than a solid wire's ~100% or a foil's near-100%. That lost fill is the price of beating the skin effect.
• Enamel grade. Strand insulation is a thin enamel film — commonly polyurethane (Grade 1/2/3 by thickness) or polyurethane-nylon, rated to a temperature class such as 155 °C (Class F) or 180 °C (Class H). Self-soldering ("solderable") grades are designed so a hot iron burns the film off at the joint, avoiding a separate stripping operation.
• Serving. Heavier litz is often wrapped (served) in nylon, silk, or a Nomex/Mylar tape to hold the bundle and add a layer of mechanical and dielectric protection.
• Termination is the classic failure point. Every strand must connect at the ends, or the unterminated strands carry no current and the effective copper drops. Builders solder in a hot pot, crimp, or fusing-weld the ends; a poorly tinned termination where a third of the strands never wet with solder is a common, hard-to-spot defect that silently raises resistance and creates a hot joint.

Where litz wire is used

Application	Typical frequency	Why litz
Switch-mode power supply transformers	50–500 kHz	Cuts winding loss, lifts efficiency, removes heat from the magnetics
Induction cooktops & induction heating	20–100 kHz	Work coil carries tens of amps; solid wire would overheat from skin + proximity loss
Wireless / inductive charging coils (Qi, EV pads)	85 kHz–6.78 MHz	High coil current at HF; litz keeps coil Q high and the pad cool
Resonant LLC & PFC inductors	50–300 kHz	High ripple current at the switching frequency
RF tank / antenna-matching inductors (LF/MF)	100 kHz–2 MHz	Maximises inductor Q in the long/medium-wave bands
Electric-vehicle traction & motor windings (some)	1–20 kHz (PWM harmonics)	Reduces AC copper loss from inverter-driven high-frequency content
MRI gradient & some medical/sensor coils	kHz–MHz	Low, predictable AC resistance for coil quality factor

The induction cooktop is the most everyday example: the work coil under the glass runs at roughly 20–50 kHz and carries enough current that a single solid conductor would dissipate far more heat in itself than it couples into the pan. The pan is supposed to get hot — the coil is not. Litz keeps the coil's own AC resistance low so the energy ends up in your food, not in the cooktop.

Litz vs solid, stranded, foil and tubing

	Litz wire	Solid round wire	Plain stranded (touching)	Copper foil	Copper tubing
Beats skin effect	Yes (strands < δ)	No	No (strands merge electrically)	Partly (thin in one axis)	Partly (only the wall conducts)
Beats proximity effect	Yes (transposed)	No	No	Poor in stacked layers	No
Copper fill factor	Low (60–75%)	Highest (~100%)	High (~85–90%)	Near 100%	Wall only
Cost per kg of copper	Highest	Lowest	Low	Moderate	Moderate
Best frequency band	~20 kHz–1 MHz	DC–low kHz	DC–low kHz	High kHz–low MHz (wide thin)	HF/VHF (RF coils)
Termination effort	High (tin every strand)	Trivial	Easy	Easy (tab/solder)	Easy (braze)
Typical home	SMPS, induction, wireless power	Mains wiring, low-f windings	Flexible low-f cables	Planar transformers, busbars	MRI, transmitter tank coils

Common misconceptions and pitfalls

• "Stranded wire is litz wire." The single most common error. Ordinary stranded or rope-lay wire has strands that touch each other electrically; the moment they touch they behave as one fat conductor and the skin effect comes straight back. Litz requires individually insulated strands and genuine transposition. A strand-count alone tells you nothing.
• "More strands is always better." Adding strands lowers the AC penalty but erodes copper fill. Past the optimum, the rising DC resistance from lost copper overtakes the falling AC loss, and total resistance climbs again. There is a frequency-dependent optimum strand count, given by the standard litz design formulas (e.g. Sullivan's optimisation).
• "Litz helps at 50/60 Hz." Skin depth in copper at mains frequency is ~9 mm, so anything short of a busbar barely sees the skin effect. Litz is pointless — and counterproductive because of the fill penalty — below roughly 10 kHz. It earns its keep at high frequency, not high current at low frequency.
• "Just twisting solid wires makes litz." Twisting helps, but without insulation between strands they short together, and without true multi-level transposition the inner and outer strands still carry unequal current. Both insulation and transposition are mandatory.
• "The bundle-level proximity effect goes away too." Transposition cancels the proximity effect between strands, but the whole bundle still sits in the winding's external field. If you stack many litz turns in a multi-layer winding, the bundle as a unit still experiences proximity loss from neighbouring turns and from the gap-field near a transformer core. Good magnetics design (interleaving, gap placement, layer count) still matters — litz is not a licence to ignore winding geometry.
• "A few un-tinned strands at the joint don't matter." They do. Strands that fail to wet during soldering carry no current, so the effective copper area drops and the working strands run hotter and at higher resistance. Hot-pot tinning and post-solder inspection exist precisely to avoid this silent loss.