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Calculate impedance, stored energy, Q factor, and self-resonant frequency for any inductor.
XL = 2πfL — Inductive Reactance vs Frequency
An ideal inductor stores energy in its magnetic field and opposes changes in current. Its impedance XL = 2πfL increases linearly with frequency — at DC it acts as a short circuit, at high frequencies it blocks current. This frequency-dependent behavior is what makes inductors essential in filters, oscillators, and power supplies.
Real inductors have DC resistance (DCR) from the wire winding, which causes power loss as heat. The Q factor (quality factor) measures how 'ideal' the inductor is: Q = XL/DCR. Higher Q means lower losses. Ferrite-core inductors typically have Q = 20–80, while air-core inductors used in RF circuits can reach Q > 200.
Every inductor also has parasitic capacitance between its turns, forming an unintended LC circuit. This creates a self-resonant frequency (SRF) above which the inductor behaves like a capacitor. For reliable operation, always use inductors well below their SRF — a good rule is to stay below SRF/3.
Inductive Reactance (XL)
XL = 2πfLStored Energy
E = ½LI²Inductor formulas:
Inductive reactance: XL = 2πfL (Ω)
Impedance: Z = √(R² + XL²)
Energy stored: E = ½ × L × I² (Joules)
Voltage across L: VL = L × dI/dt
Air-core coil (Wheeler):
L(µH) = (r² × N²) / (9r + 10l)
r = coil radius (inches), l = coil length (inches), N = turns| Inductance | 1kHz | 10kHz | 100kHz | 1MHz | Application |
|---|---|---|---|---|---|
| 1µH | 6.3mΩ | 63mΩ | 0.63Ω | 6.3Ω | RF choke, VHF |
| 10µH | 63mΩ | 0.63Ω | 6.3Ω | 63Ω | SMPS filter |
| 100µH | 0.63Ω | 6.3Ω | 63Ω | 630Ω | EMI filter |
| 1mH | 6.3Ω | 63Ω | 630Ω | 6.3kΩ | Audio crossover |
| 10mH | 63Ω | 630Ω | 6.3kΩ | 63kΩ | Line filter |
| 100mH | 630Ω | 6.3kΩ | 63kΩ | 630kΩ | Power supply choke |
Vin=12V, Vout=24V, D=0.5, f=100kHz:
L = Vin×D / (f×ΔI) = 12×0.5 / (100k×0.5) = 120µH → use 150µH standard
Target: XL > 10× load impedance at 1MHz. Load = 5Ω
XL needed > 50Ω → L > 50/(2π×1e6) = 8µH → use 10µH CMC
Real inductors have DC resistance (DCR) — check the datasheet for power loss. Saturation current (Isat): inductance drops sharply above this — size L for peak current. Core material matters: ferrite (SMPS), iron powder (lower frequency), air core (RF, no saturation). For SMPS: choose L so ΔI_L ≈ 20–40% of I_out for best efficiency.
Did you know? Inductors store energy in a magnetic field and resist changes in current — the dual of capacitors which resist changes in voltage. Together, they form the LC resonant circuit used in virtually every radio, TV tuner, and wireless transceiver ever built.