Litz Wire
Litz Wire: Theoretical Foundations
Principle of Litz Wire
Professor, why can Litz wire reduce AC losses?
By twisting together multiple thin insulated strands, the diameter of each strand is made smaller than the skin depth $\delta$, thereby suppressing the skin effect and proximity effect.
If the strand diameter $d_{strand}$ is sufficiently smaller than $\delta$:
Is the twisting method also important?
The purpose of twisting is to ensure each strand passes through all positions equally within the conductor cross-section (transposition). Incomplete twisting leads to uneven current distribution among strands (circulating currents), increasing losses. The hierarchical structure of bundle twisting (Type 1, 2, 3) is important.
Summary
- $d_{strand} < \delta$ — Condition for skin effect suppression
- Twisting (Transposition) — Equalization among strands
- Applications — High-frequency transformers, wireless power transfer coils
The Invention of Litz Wire—Bundles of Thin Wires that Supported Early 20th Century Wireless Telegraphy
Litz wire originates from the German word "Litzendraht" (stranded wire) and was first used in the early 1900s for the transmitting coils of high-frequency wireless communication (spark-gap transmitters). The idea of insulating and twisting thin wires to suppress increased high-frequency resistance due to the skin effect was born from practical necessity during the Marconi wireless telegraph era. Modern applications in wireless power transfer (WPT) and high-frequency inductors are examples of a 100-year-old technology returning to the cutting edge in a new form.
Computational Methods for Litz Wire
Litz Wire Modeling in FEM
Modeling hundreds of strands individually must be tough, right?
Individual strand models are accurate but computationally expensive. Practically, a homogenized model is used.
- JMAG: Automatically calculates equivalent properties of Litz wire using the FEM Coil function.
- COMSOL: Sets equivalent conductivity using the Homogenized Multi-Turn Coil feature.
- Extended Dowell's Formula: Analytically calculates the AC resistance factor $F_r$ from strand diameter, number of strands, and twist pitch.
How do you handle circulating current losses?
Circulating current losses due to imperfect twisting are difficult to capture in homogenized models. JMAG has a method using a "partial model" that individually models a representative few strands to evaluate circulating currents.
Summary
- Homogenized Model — Practical. ~90% accuracy.
- Individual Strand Model — High accuracy but high cost.
- Circulating Currents — Additional losses when twisting is imperfect.
FEM for Litz Wire—How to Model Tens of Thousands of Thin Wires
Litz wire has a structure bundling tens to tens of thousands of thin wires. Faithfully modeling all strands leads to an enormous mesh and computational failure. A practical approach is the "homogenization method," which replaces the structure with an equivalent anisotropic conductivity tensor considering the volume fill factor and orientation of the strands, allowing analysis with macroscopic FEM. The accuracy of this homogenized model depends on the number of strands, twist count, and frequency; errors increase at high frequencies, requiring careful judgment of its applicable range.