Litz wire consists of multiple individually insulated strands woven or braided together in a precise geometric pattern. This construction is engineered to minimize high-frequency losses caused by the skin effect and proximity effect, making it an essential component in high-frequency custom transformers and inductors.
Understanding the skin effect
The skin effect is the tendency of high-frequency alternating current ($AC$) to distribute itself unevenly within a conductor, forcing current density to concentrate near the outer surface (the "skin"). This reduces the effective cross-sectional area of the conductor, leading to a significant increase in $AC$ resistance ($R_{\text{ac}}$) and power losses.
The depth to which the current penetrates is known as the skin depth ($\delta$). For copper at 70°C, it can be approximated using the formula:
$$\delta = \frac{66}{\sqrt{f}}$$
Where $\delta$ is the skin depth in millimeters ($\text{mm}$) and $f$ is the operating frequency in Hertz ($\text{Hz}$).
Skin depth at typical frequencies
| Frequency ($f$) | Skin depth ($\delta$) | Max recommended strand gauge |
|---|---|---|
| 10 kHz | 0.660 mm | AWG 22 (0.644 mm) |
| 50 kHz | 0.295 mm | AWG 28 (0.321 mm) |
| 100 kHz | 0.209 mm | AWG 32 (0.202 mm) |
| 250 kHz | 0.132 mm | AWG 36 (0.127 mm) |
| 500 kHz | 0.093 mm | AWG 38 (0.101 mm) |
| 1 MHz | 0.066 mm | AWG 40 (0.079 mm) |
The proximity effect in custom transformers
While the skin effect looks at an isolated conductor, the proximity effect occurs when multiple current-carrying conductors are packed closely together, such as in transformer windings. The magnetic field generated by adjacent wires distorts the current distribution within each strand, causing severe current crowding and localized overheating.
In multi-layer transformer windings, the proximity effect is often the dominant source of high-frequency loss, causing the $AC$-to-$DC$ resistance ratio ($R_{\text{ac}}/R_{\text{dc}}$) to spike exponentially if improper wire configurations are chosen.
Litz wire construction styles
Litz wire is classified into different types based on how the strands are bundled, twisted, and insulated:
| Type | Construction | Best suited for |
|---|---|---|
| Type 1 | Single bunching of insulated strands | Low to medium frequencies, simple inductors |
| Type 2 | Bundles of Type 1 twisted together | Medium power transformers, high frequency |
| Type 3 | Braided or woven configuration | High-power, high-frequency switch-mode transformers |
| Type 4 | Bundles served with nylon or silk textile yarn | Applications requiring extra mechanical protection |
Engineering framework for litz wire selection
To choose the right litz wire for custom transformer configurations, implement this systematic approach:
- Determine operating frequency ($f$): Identify the fundamental switching frequency and major harmonics of your design.
- Calculate maximum strand diameter ($d_{\text{max}}$): Ensure that the individual strand diameter is less than or equal to the skin depth ($d \le \delta$). For high efficiency, select a diameter matching $d \approx 0.5\delta\text{–}0.8\delta$.
- Calculate required total copper area ($A_{\text{total}}$): Determine the overall conductor cross-section based on your continuous current ($I_{\text{rms}}$) and target current density (typically $3\text{–}5\,\text{A/mm}^2$).
- Calculate required number of strands ($N$): Divide total copper area by individual strand area:
$$N = \frac{A_{\text{total}}}{A_{\text{strand}}}$$
- Evaluate winding window constraints: Factor in the litz packing density and outer diameter expansion due to individual strand insulation coatings and outer serving jackets.
Manufacturing & processing considerations
- Termination and soldering: Polyurethane-insulated strands can be directly soldered using a high-temperature solder bath ($380\text{–}430^\circ\text{C}$), which melts away the insulation layers cleanly. For higher thermal classes (e.g., polyimide coatings), mechanical or chemical stripping is required before crimping or welding.
- Bending limits: Avoid tight bends that can crush individual internal strands, causing voltage breakdowns and unequal current distribution across bundles.
- Fill factor limits: Litz wire has a lower copper fill factor ($0.50\text{–}0.65$) than solid magnet wire due to air gaps between bundles. Account for this reduced volume allocation during early bobbin and winding window geometries.