Transformer Proximity Effect Calculator

Understanding High-Frequency Proximity Effect in Transformers

At high switching frequencies (100 kHz to 2 MHz) in switch-mode power supplies (flyback, LLC, phase-shifted full-bridge), standard DC copper resistance calculations severely underestimate winding losses. While the skin effect drives current toward the surface of an isolated conductor, the proximity effect—induced by the magnetic field generated by adjacent conductor turns and layers—forces current into narrow filaments, causing AC resistance to multiply by $5\times$ to $50\times$.

Dowell's 1D Analytical Formulation

P.L. Dowell (1966) derived the classical closed-form 1D eddy-current equation for multi-layer windings. The AC-to-DC resistance factor $F_R = R_{ac} / R_{dc}$ is formulated as:

Where:

• $\xi = \frac{h}{\delta} \sqrt{\eta}$: Normalized conductor thickness relative to skin depth $\delta$ scaled by layer porosity $\eta$.
• $m$: Number of layers in a winding portion where magnetomotive force (MMF) builds up continuously.
• $\delta = \sqrt{\frac{\rho}{\pi f \mu_0}}$: Skin depth of annealed copper at operating temperature $T$.
• $\eta = \frac{N_l \cdot d_w}{b_w}$: Porosity factor representing the copper fill width along the bobbin traverse $b_w$. For round wire, Dowell replaces round conductors with equivalent square foils of thickness $h = d_w \sqrt{\pi / 4} \approx 0.8862 d_w$.

The Dominance of the $m^2$ Factor

Notice that the proximity term scales with $(m^2 - 1)$. In a 4-layer primary winding ($m = 4$), the term $(4^2 - 1) = 15$ multiplies the proximity loss. If the winding is interleaved in a sandwich configuration (Primary - Secondary - Primary, or P-S-P), the MMF resets to zero at the boundary, halving $m$ from 4 to 2. This reduces $(m^2 - 1)$ from 15 down to 3—a $5\times$ reduction in proximity-induced eddy losses!