Inductors

Inductors are the third fundamental passive component, after resistors and capacitors. They store energy in a magnetic field and resist changes in current — where a capacitor fights changes in voltage, an inductor fights changes in current. This complementary behaviour makes them natural partners for filtering, and their energy-storage property makes them the heart of every switching power supply.

How They Work

An inductor is a coil of wire. Run current through it and it creates a magnetic field. Change the current and the magnetic field changes, inducing a voltage that opposes the change — this is Faraday's law of electromagnetic induction, and Lenz's Law gives the direction. The key relationship:

V = L × (dI/dt)

V — voltage across the inductor (volts)
L — inductance (henrys, H)
dI/dt — rate of change of current (A/s)

If current isn't changing, voltage across an ideal inductor is zero — it looks like a short circuit to steady DC. Rapidly changing current produces a large voltage. This is why you can never just switch off an inductive load (motor, relay coil, solenoid) without handling the stored energy — the collapsing magnetic field generates a voltage spike that can exceed the supply voltage by 10× or more and destroy switching transistors instantly.

Inductance Units

Unit	Symbol	Value	Typical use
Henry	H	1 H	Mains-frequency chokes, audio crossovers
Millihenry	mH	0.001 H	Audio inductors, power line filters
Microhenry	µH	10⁻⁶ H	Switching supply inductors (typical: 4.7–470 µH)
Nanohenry	nH	10⁻⁹ H	RF circuits, PCB trace inductance

Types

Type	Core material	Inductance range	Frequency range	Best use
Air core	None	nH – µH	RF, VHF, UHF	RF inductors, VCOs, filters above 1 MHz. No saturation, lowest loss.
Ferrite core	Ferrite	nH – mH	kHz – MHz	EMI chokes, switching supply inductors, RF transformers
Powdered iron toroid	Iron powder	µH – mH	DC – MHz	Switching supplies — handles high DC current without saturating
Laminated iron	Silicon steel	mH – H	DC – kHz	Mains-frequency transformers, audio output transformers
Multilayer chip	Ferrite (SMD)	nH – µH	MHz – GHz	Surface-mount RF, decoupling beads

RL Time Constant

Like the RC time constant for capacitors, the RL time constant τ = L/R determines how fast current rises in an inductor circuit:

Energising: I(t) = (V/R) × (1 - e^(-t/τ))
De-energising: I(t) = I₀ × e^(-t/τ)

τ = L / R   (seconds, when L is in henrys and R in ohms)

Time elapsed	Current (% of final value, energising)
1τ	63.2%
2τ	86.5%
3τ	95.0%
5τ	99.3% — considered fully energised

Example: L = 10 mH, R = 100Ω
τ = 0.01 / 100 = 0.0001 s = 100 µs
Fully energised in ~500 µs (5τ)

Combining Inductors

Series (assuming no mutual coupling):
  L_total = L1 + L2 + L3 ...    (same rules as resistors)

Parallel:
  1/L_total = 1/L1 + 1/L2 + ...  (same rules as resistors in parallel)

Two in parallel: L_total = (L1 × L2) / (L1 + L2)

If inductors are physically close, their magnetic fields can couple — the effective inductance changes depending on whether the fields aid or oppose. PCB layout matters: inductors near each other can interact in ways that are hard to predict without measurement.

Key Specifications

Spec	What it means	Why it matters
Inductance (L)	Nominal value, usually ±10–20%	Sets filter frequency, energy storage
DCR (DC resistance)	Resistance of the wire winding	Causes voltage drop and power loss at high current — pick low DCR for power supplies
Saturation current (Isat)	Current at which inductance drops by 20–30%	Exceed it and the inductor stops working — in a switching supply this can be destructive
RMS current rating	Max continuous current for thermal limit	Copper heating limit — different from Isat
SRF (self-resonant frequency)	Frequency at which parasitic capacitance resonates with L	Above SRF the component behaves capacitively — use below SRF
Q factor	Ratio of reactance to resistance at a given frequency	High Q = low loss, important for RF and oscillator circuits

Common Applications

Switching Power Supplies (Buck Converter)

Operation:
  ON:  switch closes → current ramps up through L → energy stored
  OFF: switch opens → inductor maintains current through diode → energy released to output

Inductor value (approximate for buck converter):
  L = (Vin - Vout) × D / (f × ΔI)

  D = duty cycle = Vout/Vin
  f = switching frequency
  ΔI = desired ripple current (typically 20-40% of I_out)

EMI Filtering

A choke (inductor in series with the power line) presents high impedance to high-frequency noise, blocking it from entering the circuit. Ferrite beads are a single-turn version — very effective for suppressing high-frequency noise on power rails and signal lines. The common-mode choke on PC power cords and USB cables prevents conducted emissions.

LC Resonant Circuit

Resonant frequency: f₀ = 1 / (2π√LC)

Example: L = 100 µH, C = 100 pF
f₀ = 1 / (2π × √(0.0001 × 0.0000000001))
f₀ = 1 / (2π × 10⁻⁷) ≈ 1.59 MHz  ← RF tuning range

Inductive Kickback — Why It Matters

Every inductive load needs a flyback diode (also called a freewheeling or snubber diode) across it when switched with a transistor:

Without the diode: when transistor turns off, coil produces spike of
-50V, -100V, or more, destroying the transistor in microseconds.
With the diode: spike clamped to one diode drop above VCC (safe).

This applies to any relay, motor, solenoid, or contactor coil. It's one of those things you learn once the hard way and never forget.

References

• Horowitz & Hill — The Art of Electronics, 3rd ed. Chapters 1, 9
• Erickson & Maksimovic — Fundamentals of Power Electronics
• Coilcraft — Inductor Terms Glossary ↗
• Electronics-Tutorials — Inductors ↗