Calculate and visualize B-H hysteresis loops, core loss (Steinmetz equation), and permeability μr-H curves for soft iron, silicon steel, ferrite, and permalloy in real time.
Parameters
Material Selection
Peak magnetic field H_max [A/m]
A/m
Temperature T [°C]
°C
Frequency
Results
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Saturation Bs [T]
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Remanence Br [T]
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Coercivity Hc [A/m]
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Max μr
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Coreloss [W/kg]
B-H Hysteresis Loop
Theory & Key Formulas
Core loss (per unit volume):
$$P_{core}= k_h f B^\alpha + k_e f^2 B^2$$
1st term: Hysteresis loss ($k_h, \alpha$ are material constants)
Second term: eddy-current loss ($k_e$ depends on resistivity and lamination thickness)
Design Notes
Ferrite cores are essential for high-frequency power transformers (10kHz+). Laminated silicon steel sheets (0.35mm) are for commercial frequency only. Permalloy has ultra-high permeability (μr>50000) and is used for current sensors and magnetic shielding.
What exactly is a B-H curve? I see it's the main chart in this simulator.
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Basically, it's the "fingerprint" of a magnetic material. It shows how the magnetic flux density (B) inside the material responds to an applied magnetic field (H). The simulator plots this relationship, and you'll see it forms a loop. Try moving the "Peak magnetic field H_max" slider above—you'll see the loop grow wider and taller as you apply a stronger field.
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Wait, really? Why is it a loop and not just a line? And what's that other chart showing "Core Loss"?
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Great question! The loop shape, called hysteresis, shows that the material "remembers" where it's been—it takes energy to magnetize and demagnetize it. That wasted energy is the core loss. The second chart calculates that loss using the famous Steinmetz equation. For instance, in a power transformer, this loss turns into heat. Switch the material type to "Silicon Steel" and watch how its loss compares to "Ferrite" at the same H_max.
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So, permeability is shown as a separate curve too. Is higher permeability always better? And does the "Temperature T" slider affect it?
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Not always! High permeability, like in Permalloy, is great for sensitive sensors. But it often saturates at a lower B, meaning it can't handle strong magnetic fields. Temperature is critical—it directly changes a material's magnetic properties. Slide the temperature control and watch the Ferrite's permeability drop sharply as you heat it up, a common challenge in power electronics design.
Physical Model & Key Equations
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.
$$B = \mu H = \mu_0 \mu_r H$$
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.
$$P_{core}= k_h f B^\alpha + k_e f^2 B^2$$
$P_{core}$ 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.
Frequently Asked Questions
Switch between soft iron, silicon steel, ferrite, and permalloy in the material selection dropdown, or adjust parameter sliders such as saturation flux density Bs and coercivity Hc. The loop shape and permeability curve will update in real time.
The Steinmetz equation is generally accurate in the practical frequency range of 50 Hz to several kHz, but errors may occur depending on the material and flux density amplitude. At high frequencies or high flux densities, the ratio of hysteresis loss to eddy current loss changes, so please use the results as reference values.
The B-H loop may not be plotted up to the saturation region. Increase the maximum value of H or set Bs higher in the material parameters. Since permeability is calculated from the slope of the B-H curve, both the linear and saturation regions are required.
Since this uses ideal material parameters for theoretical values, actual devices may exhibit errors of 10–30% due to winding stray capacitance, temperature dependence, and processing strain. Particularly at high frequencies or large amplitudes, the deviation from measured values becomes larger, so please use this as a design guideline.
Real-World Applications
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.
Common Misconceptions and Points to Note
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.
What is Magnetic Materials?
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.