Inductor Design Calculator

The Inductance Formula and Core Material Effects

This formula is the fundamental relationship governing inductor design. Because inductance scales with the square of the turn count, doubling the number of turns quadruples the inductance — but also quadruples the DC resistance and winding losses. Core permeability acts as a linear multiplier: a ferrite core with μ_r = 2000 achieves the same inductance as an air-core coil with 44 times fewer turns (the square root of 2000). This is why high-permeability cores are essential in power electronics, where bulk and winding resistance both directly impact efficiency.

Air cores have μ_r = 1 and are used where absolute linearity matters — RF tank circuits, precision measurement equipment, and high-current chokes where any core saturation would be catastrophic. Ferrite cores (μ_r typically 100 to 15,000) dominate switching power supply inductors from a few kilohertz to several megahertz; their low eddy current losses make them efficient at high frequencies. Powdered iron cores (μ_r typically 10 to 90) have a distributed air gap throughout the material, giving them gradual soft saturation and good DC bias performance, making them preferred for output filter chokes that carry significant DC current. Laminated silicon steel is used at 50/60 Hz mains frequency, where its high permeability and saturation flux density allow compact transformer and reactor construction despite the higher core losses that would make it unusable at switch-mode frequencies.

Q Factor, Self-Resonant Frequency, and Saturation Current

The quality factor Q = ωL / R_s describes how effectively an inductor stores reactive energy compared to the resistive energy it dissipates in one cycle. Here ω = 2πf is the angular frequency and R_s is the equivalent series resistance of the winding and core losses combined. A high-Q inductor wastes little power and presents a sharply defined impedance — critical in resonant filters, oscillators, and impedance-matching networks. Q is not constant: it rises with frequency as the inductive reactance grows, peaks, then falls as skin effect and core losses increase faster than the reactance. The frequency of peak Q is the sweet spot for most RF applications.

Every inductor has a self-resonant frequency (SRF) where the parasitic winding capacitance resonates with the inductance. Above the SRF, the component looks capacitive, not inductive — a critical concern for RF chokes and bypass inductors. Tight winding increases inter-turn capacitance and lowers the SRF, while bank winding and section winding techniques are used to maximise SRF in high-frequency applications. The saturation current I_sat is the DC current at which permeability drops to a defined fraction (typically 20-30%) of its zero-current value, reducing inductance by the same fraction. Power inductor datasheets specify both the thermal rating (where winding resistance causes excessive heating) and I_sat; the design must satisfy both. Operating a switching converter inductor beyond its I_sat rating causes the inductance to collapse, sending peak currents through the switch far beyond the design point and frequently destroying it.

Practical Turns Calculation and Winding Considerations

In practice, inductors are designed from the core manufacturer's A_L value — the inductance per turn squared in nH/turn² — which already incorporates the core geometry and material permeability into a single convenient parameter. The required turns count is simply N = √(L / A_L), rounded up to the nearest integer. For example, a 100 μH inductor on a core with A_L = 160 nH/turn² requires N = √(100,000 / 160) = 25 turns. The actual inductance after winding should be verified with an LCR meter, as A_L tolerances can be ±20% on standard ferrite grades.

Wire gauge selection balances DC resistance (thinner wire = higher resistance = more copper loss) against physical fit (thicker wire may not fit the required turns in the available winding window). The winding window utilisation factor, typically 0.3 to 0.5 for hand-wound toroidal inductors and up to 0.7 for machine-wound bobbins, determines the maximum conductor cross-section. A common starting point is to allow a current density of 2 to 4 A/mm² in the conductor, then check that the resulting wire gauge and turn count fit in the core's window area. Litz wire — a bundle of individually insulated thin strands — reduces skin effect losses at high frequencies and is worth the added cost in any inductor operating above about 100 kHz where skin depth becomes comparable to solid wire radius.

Worked Examples

Example 1 — 100 μH buck converter output inductor. Target: 100 μH at 3 A peak on a T50-26 iron powder core (A_L = 31 nH/turn²). N = √(100 000 / 31) = 57 turns. At 3 A the stored energy is 0.5 × 100 × 10⁻⁶ × 3² = 0.45 mJ. Use #22 AWG (2 A/mm² at 3 A) wound evenly around the toroid.

Example 2 — 10 μH RF choke at 10 MHz. On a T37-6 (air-yellow) core, A_L ≈ 3.0 nH/turn². N = √(10 000 / 3) = 58 turns. At 10 MHz, X_L = 2π × 10⁷ × 10 × 10⁻⁶ = 628 Ω — plenty of isolation. Self-resonant frequency sits around 30 MHz; keep operating frequency well below.

Example 3 — Core saturation check. A 3C95 ferrite core (B_sat ≈ 380 mT at 100 °C) wound with 20 turns carries 5 A peak through l_e = 40 mm. B = μ₀ × μ_r × N × I / l_e = 4π × 10⁻⁴ × 2 500 × 20 × 5 / 0.040 = 1.96 T. Deep in saturation — either add an air gap, reduce N, or pick a lower-μ material.

Example 4 — Gapped E-core for high-DC-bias. A 500 μH inductor carrying 10 A DC on an E25 N87 ferrite core (A_e = 52 mm²). Without gap, B = 4π × 10⁻⁴ × 2 200 × 30 × 10 / 0.0573 = 14.5 T — absurd. Introduce a 1 mm air gap: effective μ_r drops to ~57, N rises to ~200, B = 0.44 T — safely under B_sat. Gapping trades turns count for DC-bias headroom.

Common Pitfalls

• Ignoring DC bias. Manufacturer A_L is specified at zero bias. At full operating current, effective permeability can drop 30–60%, and inductance with it. Always read the bias-vs-μ curve.
• Choosing ferrite at mains frequency. Ferrites saturate at 300–500 mT; silicon steel reaches 1.5–2 T. Use steel laminations for 50/60 Hz power transformers, ferrite for 20 kHz+.
• Skipping the air gap in storage inductors. Every flyback/buck inductor needs a gap to store energy without saturating. Ungapped ferrite E-cores saturate almost immediately under DC bias.
• Tight bifilar winding for low SRF. Adjacent turns form capacitors. For high-SRF chokes, use spaced winding or section winding (Litz-style banks) to keep inter-turn capacitance low.
• Skin effect at HF. Above ~100 kHz, current crowds to the wire surface. At 1 MHz in copper, skin depth ≈ 0.066 mm — anything thicker than 0.13 mm benefits from Litz wire.

Frequently Asked Questions

Why does my measured inductance differ from calculated? Core A_L tolerance is typically ±20% for ferrite, ±10% for iron powder. Also, LCR meters typically measure at 1 kHz; core μ_r can shift at operating frequency. Verify at the actual working frequency if precision matters.

How do I pick between toroid and E-core? Toroids have low EMI (closed magnetic path) and no air gap — best for filters and chokes. E-cores accept gaps easily (for DC bias) and are faster to wind on a bobbin — preferred for power transformers and flybacks.

Can I just use more turns to add safety margin? No. More turns raises copper loss by N²/N = N (resistance goes up linearly with length), and raises B by N (flux goes up linearly with NI). You save nothing on saturation while wasting power. Better to upsize the core.

What kills inductors in practice? Core saturation from transient overcurrent (cycle-by-cycle current limit needs to act faster than the inductor collapses), thermal runaway (copper losses heat core, which reduces μ, which raises current, which raises losses), and insulation breakdown from dv/dt in switch-mode applications.

Is ferrite safe at cold temperatures? Yes, but permeability rises at low T — so inductance grows and saturation current drops. Worst case for saturation is often cold startup at full load.

Related Calculators

For the wider power-electronics toolkit, try the Transformer Sizing Calculator, Impedance Calculator, and Frequency Calculator for resonant-circuit design. For basic AC analysis the Ohm's Law Calculator and Power Calculator are the foundation. Browse the full Electronics category for more.

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