Spiral Coil Inductance Calculator

Spiral Coil Inductance Formula:

\[ L = \frac{\mu_0 \times N^2 \times d_{avg}}{2} \times \left(\ln\left(\frac{8 d_{avg}}{w}\right) - 2\right) \]

Inductance (L):

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1. What is a Spiral Coil Inductance Calculator?

Definition: This calculator estimates the inductance of a spiral coil based on the number of turns, average diameter, and width of the coil.

Purpose: It helps electrical engineers and hobbyists design spiral coils for applications like RFID antennas, wireless charging, and RF circuits.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ L = \frac{\mu_0 \times N^2 \times d_{avg}}{2} \times \left(\ln\left(\frac{8 d_{avg}}{w}\right) - 2\right) \]

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)
\( w \) — Width of the coil (meters)

Explanation: The formula accounts for the geometry of the spiral coil and the magnetic field it generates.

3. Importance of Spiral Coil Inductance Calculation

Details: Accurate inductance calculation is crucial for designing efficient RF circuits, antennas, and wireless power transfer systems.

4. Using the Calculator

Tips: Enter the number of turns (integer), average diameter (in meters), and width (in meters). All values must be > 0.

5. Frequently Asked Questions (FAQ)

Q1: What is μ₀ (mu-zero)?
A: It's the permeability of free space, a fundamental physical constant equal to 4π×10⁻⁷ H/m.

Q2: How do I measure average diameter?
A: Average diameter is (outer diameter + inner diameter) / 2 of the spiral coil.

Q3: What's a typical width for spiral coils?
A: Width typically ranges from 0.1 mm to several millimeters, depending on the application.

Q4: What affects spiral coil inductance most?
A: Inductance is most sensitive to the number of turns (N² factor) and average diameter.

Q5: Is this formula accurate for all spiral coils?
A: This provides a good estimate for planar spiral coils. Accuracy decreases for very thick or non-circular spirals.