Electronics & Magnetics
Planar Transformer & PCB Spiral Coil Inductance Calculator
Model planar spiral inductor trace inductance ($L$), high-frequency skin depth ($\delta$), Dowell proximity effect AC copper resistance ($R_{ac}$), and vector Archimedean track layout for high-density power converters.
1. Input Parameters
Total concentric or spiral turns on a single PCB copper layer.
Core center leg clearance window diameter.
Width of the spiral planar conductor.
Dielectric clearance between adjacent concentric tracks.
Power converter operating frequency (GaN/SiC: 100 kHz - 2 MHz).
2. Calculation Results
Spiral Inductance ($L_{coil}$)
0.00 µH
Copper Skin Depth ($\delta$)
0.0 µm
Outer Diameter ($d_{out}$)
0.0 mm
AC Resistance Ratio ($R_{ac}/R_{dc}$)
1.00 (Low Loss)
Total Conductor Length
0.0 cm
DC Resistance ($R_{dc}$)
0.0 mΩ
3. Dynamic Visualizer & CAM Preview
4. Engineering Notes & Physics Specifications
Planar PCB Magnetics & Dowell High-Frequency Eddy Current Loss:
- Modified Harold-Wheeler Inductance Formula: For planar circular/polygonal spirals: $L = \frac{\mu_0 N^2 d_{avg} c_1}{2} \left(\ln\left(\frac{c_2}{\rho}\right) + c_3 \rho + c_4 \rho^2\right)$, where fill factor $\rho = \frac{d_{out} - d_{in}}{d_{out} + d_{in}}$.
- Copper Skin Depth: High-frequency alternating currents crowd to the conductor perimeter: $\delta = \sqrt{\frac{\rho_{cu}}{\pi f \mu_0}}$. At 250 kHz, copper skin depth is $\approx 130\,\mu\text{m}$. If foil thickness $t_{cu} > 2\delta$, AC resistance escalates rapidly.
- Proximity Effect & Dowell Interleaving: Multi-layer planar windings suffer severe eddy currents induced by adjacent layers. Primary/secondary interleaving (P-S-P-S) reduces the Dowell porosity factor, dropping $R_{ac}/R_{dc}$ from $> 8.0$ down to $< 1.3$.
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