Air-core solenoid (Wheeler)
| L (µH) | = (r²·N²) / (9r + 10ℓ) — all in inches |
|---|---|
| SI form | L = μ₀ · N² · A / ℓ (for long solenoid) |
| r | Coil radius |
| ℓ | Coil length |
| N | Number of turns |
Multilayer (Wheeler)
| L (µH) | = (0.8·a²·N²) / (6a + 9ℓ + 10c) |
|---|---|
| a | Mean radius (in) |
| ℓ | Winding length (in) |
| c | Winding depth (in) |
Toroid
| L (H) | = μ₀ μ_r · N² · A_e / ℓ_e |
|---|---|
| A_e | Effective cross-section area |
| ℓ_e | Mean magnetic path length |
| A_L | Core-specific factor: L (nH) = A_L · N² |
Design notes
- Adding ferromagnetic core increases L by μ_r (hundreds to thousands for ferrite).
- Saturation current I_sat: above it, the core loses permeability and L drops sharply.
- For RF, air-core is preferred for highest Q and zero saturation.
- Self-resonant frequency (SRF) is where parasitic capacitance makes the coil look like a capacitor.
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