Comprehensive Guide to PCB Coil Inductance Calculation
Printed Circuit Board (PCB) planar inductors are widely utilized in modern RF circuits, wireless power transfer systems, NFC antennas, and DC-DC converters due to their low profile, repeatability, and cost-effectiveness.
Understanding PCB Planar Inductors
Unlike traditional wire-wound inductors, PCB coils are etched directly onto the copper layers of a circuit board. Their electrical performance relies heavily on geometric properties such as trace width, track spacing, number of turns, and overall outer and inner diameters. Accurate modeling requires accounting for magnetic flux linkage and high-frequency phenomena like the skin effect.
Formula Used
This calculator employs modified Wheeler and Mohan empirical expressions tailored for planar spiral inductors. For circular spirals, the inductance $L$ in nanohenries is estimated using:
$$L = \frac{\mu_0 \cdot N^2 \cdot d_{avg} \cdot c_1}{2} \cdot \left( \ln\left(\frac{c_2}{\rho}\right) + c_3 \cdot \rho + c_4 \cdot \rho^2 \right)$$
Where $N$ represents the number of turns, $d_{avg}$ is the average diameter, $\rho$ is the fill ratio, and $c_1$ through $c_4$ are layout-dependent geometric coefficients.
How to Use This Calculator
Follow these simple steps to obtain accurate inductance results:
- Select your preferred coil geometry (Circular, Square, or Hexagonal).
- Input your coil parameters including number of turns, outer dimensions, and inner dimensions.
- Specify copper track dimensions, spacing, and the operating frequency.
- Click the Calculate Inductance button to view instantaneous computed metrics right above the form.