Linearity of inductors and magnetic cores Which of the following inductors behaves most linearly with current over a wide range (i.e., exhibits negligible magnetic saturation and constant inductance)?

Introduction / Context:
Inductor linearity concerns whether inductance remains approximately constant as current varies. Core materials with nonlinear B–H characteristics (and saturation) cause inductance to change with magnetizing current, whereas an air core avoids such nonlinearity.

Given Data / Assumptions:

• Compare air versus ferromagnetic and ferrimagnetic cores.
• Operation over moderate AC or DC bias without special gapping.
• Linearity measured by stability of L with current.

Concept / Approach:

Air has μr ≈ 1 and a strictly linear relationship between B and H (no saturation). Ferromagnetic cores (iron, steel, alloys) have high μr but nonlinear B–H curves and saturate at finite flux density, making L current-dependent. Ferrites are more linear than metallic irons at high frequency but still exhibit finite permeability and saturation.

Step-by-Step Reasoning:

Verification / Alternative check:

Data sheets for power inductors show inductance roll-off with DC bias for cored parts; air-core RF coils maintain L across current until resistive and geometric effects dominate.

Why Other Options Are Wrong:

• Cast iron, sheet steel, iron alloys: high μr but saturate; L varies with current.
• Ferrites: better linearity at RF but still magnetically saturable; not as linear as air.

Common Pitfalls:

Confusing higher μr (more inductance) with linearity; high μr cores give compact inductors but introduce nonlinearity and saturation limits.

Final Answer:

Air-cored inductor