Inductors and Chokes in Power Electronics: Working Principle, Core Materials, Inductance Formulas & SMPS Design

Inductors are passive magnetic components that store energy in a surrounding magnetic field when electric current flows through their windings. Unlike capacitors which resist changes in voltage, inductors resist changes in current, making them essential for DC-DC buck/boost converters, EMI suppression chokes, and resonant LLC tanks.

1. Fundamental Electromagnetics & Governing Equations

The operation of an inductor is governed by Faraday’s Law of Induction and Lenz’s Law. The voltage induced across an inductor is proportional to the time rate of change of current:

V(t) = L * (di / dt)

Where L is inductance in Henries (H). The energy stored in the magnetic field is given by:

E = 0.5 * L * I^2 [Joules]

2. Physical Inductance Calculation for Coils

For a solenoidal coil of N turns wound over an effective magnetic cross-sectional area A_e (m^2) with mean magnetic path length l_m (m) and core relative permeability mu_r:

L = (mu_0 * mu_r * N^2 * A_e) / l_m

Where mu_0 = 4 * pi * 1e-7 H/m (permeability of free space). For gapped ferrite cores, the air gap length l_g predominantly controls total magnetic reluctance, preventing early DC flux saturation.

3. Critical Engineering Parameters: Isat vs Irms

• Saturation Current (Isat): The instantaneous DC current at which the core flux density approaches B_sat, causing inductance to drop typically by 20% or 30%. Operating beyond Isat causes inductance collapse and switch damage.