Planar Transformer & PCB Spiral Coil Magnetics: CAM Vector Prepress Guide

Master the engineering physics of planar PCB magnetics. Eliminate high-frequency proximity losses in multi-layer GaN/SiC power converters with optimized trace geometries and mathematical spiral vector cutpaths.

1. High-Density Planar PCB Magnetics Overview

Planar Transformers and Inductors replace bulky wire-wound magnetic components with flat copper spiral traces integrated directly into multi-layer printed circuit boards (4 to 32 layers). Planar magnetics offer exceptional thermal dissipation, repeatable leakage inductance, sub-millimeter low profiles, and high power densities ($> 50\text{ W/cm}^3$) in modern resonant LLC converters.

2. Wheeler Inductance & Geometric Formulation

Planar Circular Spiral Inductance:
  L = (mu0 * N^2 * d_avg * c1 / 2) * [ ln(c2 / rho) + c4 * rho^2 ]   [Henry]

Where:
  N     = Total number of concentric spiral turns
  d_avg = Average spiral diameter ( (d_in + d_out) / 2 )
  rho   = Fill factor ( (d_out - d_in) / (d_out + d_in) )

3. High-Frequency Eddy Currents & Dowell AC Resistance

At high switching frequencies ($100\text{ kHz} - 3\text{ MHz}$), skin and proximity effects force current toward conductor surfaces and outer layer boundaries:

Copper Skin Depth:
  delta = sqrt( rho_cu / (pi * f_sw * mu0) )   [m]

To eliminate extreme AC copper losses ($R_{ac}/R_{dc} > 5$), multi-layer PCB stackups must utilize interleaved primary-secondary layers (e.g. P1-S1-P2-S2) and keep individual copper foil thickness $t_{cu} \le 2\delta$.