How does the Sullivan formula choose optimal Litz strand diameter?

The Sullivan (1999) equation balances DC conduction loss against high-frequency eddy current proximity loss in multi-layer windings. As the number of effective layers m increases, strand diameter must be reduced significantly below the skin depth to prevent excessive proximity heating.

What is the packing factor for Litz wire outer diameter buildup?

The unserved bundle diameter follows OD = 1.154 × √N × d_enamel × k_stage, where k_stage accounts for cable stranding slack (1.00 for single stage, 1.03 for 2 stages, 1.05 for 3+ stages). Outer servings such as nylon yarn or extruded TIW add an additional 0.06 mm to 0.35 mm.

Litz Wire Calculator — Optimal Strand Diameter & Window Fit

Hi, I'm a power electronics engineer.

Unlike generic wire charts that only list AWG tables, this Litz Wire Calculator actively solves the coupled trade-off between strand diameter, proximity loss factor $F_R$, and physical bobbin fit in the transformer window.

You can lock individual parameters (like available strand stock or strand count) to see their immediate impact on copper loss and window utilization.

Conductor Technology:

Winding Window Space (Shared Window)

Window Width Ww (mm)

Window Height Hw (mm)

Number of Turns (N)

Conductor Specification & Insulation

Outer Serving Type

Enamel Insulation Grade (IEC 60317)

Strand Diameter d (mm)

Strand Count N

Electrical & Thermal Parameters

Operating Frequency f (kHz)

RMS Current I_rms (A)

Target Current Density J (A/mm²)

Winding Temperature T_op (°C)

Proposed Spec 375/0.100 (25 × 3 × 5) Standard SKU: LZ-375-0100-SN

Outer Diameter (OD) 2.72 mm Strand wire: ⌀0.100 mm

AC Loss Factor F_R (AC/DC) 3.92× Skin depth δ: 0.240 mm

Copper Loss P_Cu 19.50 W R_AC = 60.2 mΩ (R_DC = 15.4 mΩ)

Conductor Cross-Section & Current Density Adaptive Cross-Section

Window Build Utilization WARNING

82.7 % (≤ 80% Safe)

0 % Warn: 80 Max: 100

Ratio of total winding build thickness W_build to usable window width W_usable.

AC Proximity Factor (F_R) FAIL

3.9 × (≤ 1.6 Optimal)

1 × Warn: 1.6 Max: 2.5

AC resistance multiplier due to proximity and skin effect (Dowell).

Current Density (J) PASS

6.1 A/mm² (Target: 6 A/mm²)

0 A/mm² Warn: 6.8999999999999995 Max: 8.100000000000001

Actual RMS current density in bare copper cross-section.

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Winding Health & Diagnostics

1 Notice

TIP

Alternative Conductor Recommendation

On this shared core window, switching to Planar PCB Coil yields a 60% reduction in AC copper loss (7.70 W vs. 19.50 W).

Recommendation: Switch to the Planar PCB Coil tab to evaluate detailed winding parameters.

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Compare 5 Conductor Technologies on Shared Window

Shared Window Evaluation · Dowell 1D Loss Comparison

Conductor Technology	Proposed Spec	R_DC (mΩ)	F_R (×)	R_AC (mΩ)	Loss P_Cu (W)	Cu Fill (Ku)	Build Util (%)	Window Fit	Action
Litz Wire Active	375/0.100 (25 × 3 × 5)	15.4	3.92×	60.2	19.50 W	27.2%	83%	⚠ TIGHT	Active
Solid / Multifilar Wire	2filar × ⌀1.37 mm	13.3	29.95×	398.9	129.24 W	27.2%	48%	✓ PASS
Flat / Edgewise Wire	2.97 × 0.99 mm (Edgewise)	14.2	16.72×	236.6	76.65 W	27.2%	62%	✓ PASS
Copper Foil	23.4 mm × 126 µm	13.7	4.94×	67.5	21.87 W	27.2%	54%	✓ PASS
Planar PCB Coil	12-Layer Stackup, 3 oz (28.0 mm trace)	16.1	1.48×	23.8	7.70 W	27.2%	95%	⚠ TIGHT

Physics & Formulas: High-Frequency Litz Wire

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Sullivan-Zhang Strand Optimization (1999)

d_opt = δ(T) · (πη/4)^-1/4 · [3/(5m² - 1)]^1/4

Determines the optimal single strand diameter balancing DC conduction and proximity AC eddy loss based on skin depth δ(f, T) and layer count m.

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Litz Wire Bundle Outer Diameter (OD)

OD_total = 1.154·√N·d_enamel·k_stage + ΔD_serving

Calculates total bundle diameter including stage twisting packing dilation factor k_stage (1.00 - 1.05) and outer serving insulation thickness.

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Industrial Cabling Breakdown

N_total = N_primary × m₁ × m₂ ...

Decomposes total strand count into real-world manufacturing cabling stages (primary bundle of 7-60 strands, followed by 3-, 4-, or 5-strand secondary operations).

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Modified Dowell Proximity Factor

m_eff = m_layers · √(0.65 · N_strands)

Maps multi-strand twisted bundles into an equivalent number of conductive foil layers for 1D Dowell high-frequency eddy loss calculation.

Litz Wire Winding & Window Fit Calculator