Single Layer Coil Calculator

The Formula

The formula for calculating the inductance of a single layer coil is:

\[L = \frac{N^2 * r^2}{(9 * r) + (10 * l)}\]

Where:

• L: Inductance (in Henries, H)
• N: Number of turns
• r: Radius of the coil (in meters, m)
• l: Length of the coil (in meters, m)

Calculation Steps

1. Convert the coil diameter and length from millimeters to meters
2. Calculate the radius (r) by dividing the diameter by 2
3. Apply the formula: L = (N² * r²) / ((9 * r) + (10 * l))
4. Convert the result from Henries (H) to microhenries (µH) by multiplying by 1,000,000

Example Calculation

Let's calculate the inductance for a coil with these parameters:

• Diameter: 20 mm
• Length: 50 mm
• Number of turns: 100

1. Convert to meters:

Diameter = 20 mm = 0.02 m

Length = 50 mm = 0.05 m

2. Calculate radius:

r = 0.02 / 2 = 0.01 m

3. Apply the formula:

\[L = \frac{100^2 * 0.01^2}{(9 * 0.01) + (10 * 0.05)} = 1.96 * 10^{-5} H\]

4. Convert to µH:

\[L = 1.96 * 10^{-5} * 1,000,000 = 19.6 µH\]

Limitations and Considerations

While this calculator provides a good approximation, it's important to note:

• The formula assumes an ideal coil and doesn't account for factors like wire thickness or spacing between turns.
• It's most accurate for coils where the length is greater than 0.8 times the diameter.
• Real-world inductance may vary due to factors like core material, nearby metal objects, and manufacturing tolerances.

For more precise calculations or complex coil designs, consider using specialized software or consulting with an electronics engineer.