Table of Contents
Helical Coil Inductance
A helical coil (solenoid) stores energy in a magnetic field when current flows through it. The inductance depends on the number of turns squared, the cross-sectional area, and inversely on the length. Inductors are fundamental components in filters, oscillators, transformers, and energy storage systems.
The simple solenoid formula assumes uniform field inside the coil, which is most accurate when the coil is much longer than its diameter (L/D > 2). For shorter coils, corrections are needed. Air-core inductors are used at high frequencies, while ferrite cores increase inductance at lower frequencies.
Solenoid Formula
Design Parameters
| Parameter | Effect on Inductance |
|---|---|
| Double turns (N) | 4x inductance |
| Double radius | 4x inductance |
| Double length | 0.5x inductance |
| Add ferrite core | 100-10000x inductance |
Frequently Asked Questions
Why does inductance scale with N squared?
Each turn contributes to the magnetic field, and each turn also links with the total flux from all turns. The flux linkage is N times the flux from N turns, giving N × N = N² dependence. This is why doubling the number of turns quadruples the inductance.
What is the self-resonant frequency?
Every real inductor has parasitic capacitance between turns. At the self-resonant frequency, this capacitance resonates with the inductance, and the component behaves like a resistor rather than an inductor. Above this frequency, the component becomes capacitive. Coils must be used well below their self-resonant frequency.