Planar Inductor Calculator
Design PCB spiral inductors using Modified Wheeler/Mohan formulas.
What is a Planar Inductor?
A Planar Inductor is an inductive coil etched directly onto a flat surface, such as a PCB or silicon chip. Instead of wire wrapped around a core, it uses a spiral trace of copper.
They are fundamentally important in modern electronics, appearing in RFID tags (as the antenna), NCF cards, wireless chargers, and RF integrated circuits (RFICs) where bulky external components are impossible to use.
Inductance Formulas (Wheeler & Mohan)
Calculating the inductance of a flat spiral is complex. This tool uses the Modified Wheeler Formula approximation, which is accurate within 5% for most standard geometries.
L ≈ K₁µ₀n²davg / (1 + K₂ρ)
Key Parameters
- n: Number of turns. Inductance increases with the square of turns (n²).
- davg: Average diameter = (Dout + Din) / 2.
- ρ: Fill Ratio = (Dout - Din) / (Dout + Din). How "full" the spiral is.
Practical Applications
- RFID / NFC: The large square spiral on an access card is actually a planar inductor tuned to 13.56 MHz.
- Wireless Charging (Qi): The receiver and transmitter coils are essentially large planar inductors designed for magnetic coupling.
- RF Filters: Creating compact LC filters directly on the PCB to remove unwanted frequencies.
FAQ
Square vs Circular Spirals?
Circular spirals have the highest Q-factor (lowest resistance for a given inductance) because they have the shortest trace length. However, Square spirals are much easier to draw and manufacture on standard PCBs.
Does the ground plane affect inductance?
Yes, significantly. If there is a solid ground plane directly underneath the inductor, it acts like a "shorted turn" transformer, drastically reducing the inductance and Q-factor. You must remove the copper (courtyard) under the coil on all layers.
What is Self-Resonance?
Planar inductors have capacitance between the spiral turns. At high enough frequencies (SRF), this capacitance resonates with the inductance, and the component stops acting like an inductor. Always optimize trace spacing to push SRF higher.