Planar Coil Inductance Calculator

Planar Coil Inductance Formula:

\[ L = \frac{\mu_0 \times N^2 \times d_{avg}}{2} \times \left(\ln\left(\frac{2.46}{\phi}\right) + 0.2 \phi^2\right) \]

Inductance (L):

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1. What is a Planar Coil Inductance Calculator?

Definition: This calculator estimates the inductance of a planar (flat) spiral coil based on its physical dimensions and number of turns.

Purpose: It helps electrical engineers and hobbyists design planar coils for applications like wireless charging, RFID, and PCB inductors.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L = \frac{\mu_0 \times N^2 \times d_{avg}}{2} \times \left(\ln\left(\frac{2.46}{\phi}\right) + 0.2 \phi^2\right) \]

Where:

\( L \) — Inductance (henrys)
\( \mu_0 \) — Permeability of free space (4π×10⁻⁷ H/m)
\( N \) — Number of turns
\( d_{avg} \) — Average diameter of the coil (meters)
\( \phi \) — Fill factor (ratio of inner to outer diameter)

Explanation: The formula accounts for the coil geometry and the logarithmic relationship between the fill factor and inductance.

3. Importance of Planar Coil Inductance Calculation

Details: Accurate inductance calculation is crucial for designing efficient wireless power transfer systems, RF circuits, and other applications where precise inductance values are needed.

4. Using the Calculator

Tips: Enter the number of turns, average diameter in meters, and fill factor (default 0.5). Fill factor must be between 0 and 1.

5. Frequently Asked Questions (FAQ)

Q1: What is the fill factor (φ)?
A: The fill factor is the ratio of inner diameter to outer diameter of the coil (φ = d_inner/d_outer). It affects how "tightly wound" the coil is.

Q2: How do I calculate average diameter?
A: Average diameter is (d_outer + d_inner)/2, where d_outer is the outer diameter and d_inner is the inner diameter of the coil.

Q3: What's a typical fill factor value?
A: Common values range from 0.3 to 0.7. The default of 0.5 is a good starting point for many designs.

Q4: How accurate is this formula?
A: This is an approximation that works well for typical planar coils. For precise designs, consider electromagnetic simulation.

Q5: What if my coil isn't circular?
A: This formula is for circular planar coils. Square or rectangular coils require different formulas.