Magnetic Materials
Magnetic materials are used in RF and power electronics to make inductors, transformers, ferrite beads, and circulators. Understanding their properties is essential for choosing the right core material.
Relative Permeability (\(\mu_r\))
Permeability \(\mu_r\) relates the magnetic flux density to the applied field: \(B = \mu_r\mu_0 H\). High \(\mu_r\) increases inductance but also limits useful frequency range (permeability drops at high frequencies).
Ferrites
Ferrites are ceramic magnetic materials with high resistivity (minimising eddy current losses at RF). They are used in:
- Ferrite beads — suppress high-frequency noise on power lines and signal traces by presenting high impedance above a target frequency.
- Ferrite cores — increase inductance of RF chokes and RF transformers, particularly below 50 MHz.
- Circulators and isolators — exploit the non-reciprocal properties of magnetised ferrite (Faraday rotation) to route signals directionally.
Core Saturation
At high flux densities, magnetic cores saturate — \(\mu_r\) collapses, inducing harmonics and power loss. Always verify that peak flux density is below the saturation flux density \(B_{sat}\) of the chosen material under worst-case conditions.
Core Loss
Core loss (hysteresis + eddy current losses) is characterised by the complex permeability \(\mu = \mu' - j\mu''\). The loss factor \(\mu''/\mu'\) (analogous to \(\tan\delta\)) increases with frequency. Ferrite materials are categorised by their intended frequency range (e.g. MnZn ferrites for <5 MHz, NiZn for 1–100 MHz).
Toroidal Cores and the AL Method
A toroid concentrates almost all of its flux inside the ring, so its inductance is set by the core's published inductance factor \(A_L\) (in nH per turn²) rather than by the coil geometry. The inductance is then simply \(L = A_L N^2\), and the turns needed for a target inductance are \(N = \sqrt{L/A_L}\). Because inductance scales with the square of the turns, a couple of extra turns move the value a lot. Powdered-iron cores have a low \(A_L\) and a high saturation flux for stable, high-Q RF inductors; ferrite cores offer a far higher \(A_L\) for compact chokes and wideband transformers but saturate sooner — so verify the peak flux density \(B_{peak}=V_{rms}\sqrt2/(2\pi f N A_e)\) against \(B_{sat}\) as above.