Comparison of Loss in Single-Layer and Multi-Layer Windings with a DC Current Component

A common technique for reducing losses in high frequency windings is to use multiple conductor layers, each thin compared to a skin depth. This can be effective, but single-layer windings can also be advantageous for high frequency windings because their ac resistance goes up proportional to the square root of frequency, whereas the ac resistance of multi-layer windings can be proportional to the square of frequency. A general comparison of multi-layer and single-layer windings for applications with significant dc current shows that multi-layer windings can be effective in reducing loss in these applications, but achieving lower loss than a single-layer winding may require a large number of layers and may only produce a small improvement in loss