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Inductors

1. Core Relations​

  • Voltage: v(t) = L · (di / dt)
  • Energy stored: E = ½ · L · I²
  • Impedance: Z = jωL
Inertia for Current

Think of an Inductor like a Heavy Flywheel inside a water pipe.

  • It takes pressure (Voltage) to get it spinning (Current).
  • Once spinning, it doesn't want to stop.
  • If you cut the flow instantly, the momentum creates a massive pressure spike (Flyback).

2. Physics & Operation​

Current in an inductor cannot change instantaneously. If the drive (voltage) is removed, the inductor will generate whatever voltage is needed (even thousands of volts) to keep the current flowing across the gap. This is the Flyback Kick.

Interactive: The Inductive Kick​

Charge the coil and release to see the voltage spike.

Inductive Flyback Demonstration

Hold to build field. Release to see the High Voltage Spike.

3. Frequency Behavior​

The Rules of Thumb:

  • DC (f=0): Z is Zero. Acts like a Short Circuit (Wire).
  • High Freq: Z is High. Acts like an Open Circuit.

This is the exact opposite of a Capacitor.

04. Phase Relationship

Phase: V leads I by 90°

VITime →

Voltage (Green) must exist across the inductor before Current (Red) can start ramping up.

"ELI the ICE man"

  • Voltage (E) leads Current (I) by 90°.
  • You must apply Voltage before Current can start ramping up.

4. Common Uses​

Switching Regulators (Buck/Boost)​

Used very often in modern power systems. The inductor stores energy during the "On" cycle and releases it to the load during the "Off" cycle.

Filtering (Chokes)​

  • Series Choke: Blocks high-frequency noise from entering a circuit.
  • Ferrite Bead: A lossy inductor that turns RF noise into heat.

Transformers​

Two coupled inductors. Used to step voltage up/down or isolate grounds.

5. Core Types & Selection​

The material inside the coil determines how much energy it can hold before it "saturates" (stops working).

TypeMaterialPros/ConsBest Application
FerriteMnZn / NiZnHigh Permeability. Low losses.
Con: Hard Saturation (Inductance falls off a cliff).		Switch-Mode Power (Discontinuous), Signal Filtering.
PowderIron / AlloySoft Saturation. Inductance drops gracefully.
Con: Higher core losses.		High-Current Power (Continuous Mode).
Air CoreAir / PlasticNo Saturation. Perfect linearity.
Con: Huge physical size for low inductance.		RF Circuits, Tuned Radios.

6. RL Time Constants​

Just like RC circuits, Inductors have a time constant when paired with a resistor.

  • Time Constant: τ = L / R
  • Current Rise: I(t) = (V / R) · (1 - e-t/τ)

Key Takeaway: Current takes time to ramp up. Lower Resistance = Slower Ramp (Higher τ).

  • Contrast with Caps: Capacitors charge slower with Higher resistance. Inductors charge slower with Lower resistance (because L/R).

7. Switch-Mode Basics (The "Integrator")​

While Capacitors smooth out Voltage, Inductors smooth out Current.

The Buck Converter (Step-Down)​

This is the primary use case for inductors in digital hardware.

  1. Switch ON: Voltage is applied. Current ramps up linearly (V = L·di/dt). Energy is stored in the magnetic field.
  2. Switch OFF: Field collapses. The Inductor acts as a source, pushing current through the diode to the load.
  3. Result: The output sees a smooth average DC voltage, even though the input was chopped pulses.
Design Choice
  • Ferrite Drum: Better for High Ripple / Discontinuous mode.
  • Powder Core: Better for Low Ripple / Continuous mode (handles DC bias better).

8. Real-World Parasitics​

DCR (DC Resistance)

Real wire has resistance.

  • Effect: Simple I²R heating.
  • Trade-off: Thicker wire = Lower DCR but larger size.
SRF (Self-Resonance)

Windings are close together, creating tiny Inter-winding Capacitance.

  • Above SRF: The inductor stops blocking noise and acts like a Capacitor (passes high freq!).
  • Rule: Always operate well below the SRF.

9. Non-Ideal Properties (The "Gotchas")​

A. Saturation Current (Isat)​

The most dangerous spec.

  • Concept: The magnetic core can only hold so much flux. Once full, it acts like Air.
  • The Danger: Inductance drops to near zero instantly. Current spikes massively, potentially blowing up your MOSFET.
  • Rule: Never exceed Isat, even for a microsecond.

B. Audible Noise ("Coil Whine")​

  • Magnetostriction: The magnetic field physically squeezes the core material.
  • At certain frequencies (2kHz - 20kHz), the core vibrates like a speaker, creating an audible whine.
  • Fix: Use molded inductors (solid block) or shift switching frequency above 20kHz.

C. EMI (Electromagnetic Interference)​

  • Shielded Inductors: Have a magnetic housing to keep the field inside.
  • Unshielded: Cheaper, but spew magnetic field lines everywhere, inducing noise in nearby traces.
Layout Tip

Never route sensitive signal traces under an inductor! It acts like a transformer primary and will inject noise into your signal.