Magnetic Materials B-H Curve Simulator

The B-H relationship is fundamentally non-linear and hysteretic, but a key derived property is the permeability (μ), which relates B and H. The initial permeability is the slope of the B-H curve at the origin.

Here, $B$ is magnetic flux density [T], $H$ is magnetic field strength [A/m], $\mu_0$ is the permeability of free space ($4\pi \times 10^{-7}$ H/m), and $\mu_r$ is the dimensionless relative permeability, which is material-specific and varies with H and temperature.

The total power lost per unit volume in a magnetic core when subjected to an alternating magnetic field is predicted by the Steinmetz equation. It separates loss into hysteresis and eddy current components.

$P_{core}$ is core loss per volume [W/m³], $f$ is frequency [Hz], and $B$ is the peak flux density [T]. $k_h$ and $\alpha$ are material constants for hysteresis loss, representing the area of the B-H loop. $k_e$ is the constant for eddy current loss, which depends on material resistivity and lamination thickness.

High-Frequency Power Converters: Ferrite cores, with their high resistivity and low eddy current loss, are essential for switch-mode power supplies and EV chargers operating above 10 kHz. Engineers use B-H curves like the ones in this simulator to select a ferrite grade that minimizes core loss at the operating frequency and temperature.

Power Transformers & Motors: Laminated silicon steel sheets (often 0.35mm thick) are the workhorse material for 50/60 Hz transformers and industrial motors. The simulator shows its high saturation flux density (~1.8 T), allowing compact designs, but its core loss must be carefully managed through material grade and lamination.

Current Sensors & Magnetic Shielding: Permalloy (a nickel-iron alloy) exhibits extremely high permeability, as you can see in the simulator. This makes it perfect for current transformer cores and shielding sensitive electronics from stray magnetic fields, as it easily channels magnetic flux away.

Inductors for EMI Filters: Powdered iron or sendust cores offer a distributed air gap, preventing saturation in high-DC-bias applications like power line inductors. Their B-H curve in the simulator would show a more "slanted" loop, reflecting lower permeability but higher saturation tolerance.

When you start using this tool, there are several pitfalls that beginners in CAE often fall into. The first is not taking catalog permeability values at face value. For example, even if a permalloy's initial permeability is listed as "80,000", that's under extremely weak magnetic fields. At actual design flux densities, say 0.5T, the permeability drops significantly as you can see in the tool's "Permeability μr-H Curve". If you judge solely based on catalog values thinking "high permeability means it's fine", you might end up needing a much larger magnetizing current than anticipated.

The second point is that the relationship between frequency and loss is not simple. Looking at the Steinmetz equation $P_{core}= k_h f B^\alpha + k_e f^2 B^2$, eddy current losses increase with the square of frequency, so you might think ferrite is the only choice for high frequencies. However, even with actual ferrites, above a few MHz, another component called "residual loss"—where the magnetic field changes too fast for magnetization to keep up—becomes non-negligible. Understand that this tool is primarily for capturing trends in the low to mid-frequency range.

The third point is not to overlook the effects of temperature. If you increase the temperature in the tool, you'll see the saturation flux density $B_s$ of ferrite decreases. For instance, if a switching power supply core heats up to 100°C, a design based on room temperature values could lead to saturation and inrush current, potentially causing failure. Conversely, the coercivity of silicon steel may decrease with rising temperature, sometimes reducing hysteresis losses. Always keep in mind that simulations assume room temperature, and develop the habit of considering them alongside the thermal design of the actual device.

Magnetic Materials is a fundamental topic in engineering and applied physics. This interactive simulator lets you explore the key behaviors and relationships by directly manipulating parameters and observing real-time results.

By combining numerical computation with visual feedback, the simulator bridges the gap between abstract theory and physical intuition — making it an effective learning tool for students and a rapid-verification tool for practicing engineers.