A magnetic hysteresis loop is a closed B-H curve that maps the lag between an applied magnetizing force (H) and the resulting magnetic flux density (B) inside a ferromagnetic material. In practical circuit design, this loop dictates how much electrical energy is wasted as heat (core loss) and determines whether a material is better suited for a high-efficiency power transformer or a permanent magnet that resists demagnetization. When you push alternating current through an inductor, the magnetic domains inside the core material physically rotate to align with the field. Think of these domains like heavy furniture on a carpet: pushing it moves it, but when you stop pushing, friction prevents it from sliding back to its exact starting point. You have to apply force in the opposite direction just to get it back to zero. That molecular "friction" is hysteresis, and it generates heat every single AC cycle.
Decoding the B-H Curve and Material Properties
To read a hysteresis loop, you need to understand three critical coordinates on the graph. The horizontal axis is the magnetizing force (H, measured in Amperes per meter), which is driven by your coil current. The vertical axis is the flux density (B, measured in Tesla), which is the resulting magnetic field inside the core.
- Saturation ($B_{sat}$): The point where pushing more current (H) yields almost no increase in flux density (B). The core is "full."
- Retentivity ($B_r$): The residual magnetism left in the core when the applied current drops to zero.
- Coercivity ($H_c$): The reverse magnetizing force required to force the residual flux density back down to zero.
The physical area enclosed by the loop represents the energy lost as heat per cycle per unit volume. Engineers categorize materials into "soft" (narrow loop, low loss) and "hard" (wide loop, high retention) based on these metrics. Below is a spec-sheet comparison of common magnetic materials you will encounter in power electronics and magnetics design.
| Material | Typical Application | Coercivity ($H_c$) | Retentivity ($B_r$) | Loop Area (Relative) |
|---|---|---|---|---|
| M19 Grain-Oriented Silicon Steel | 50/60Hz Mains Transformers | ~10 A/m | ~1.2 T | Very Narrow |
| MnZn Ferrite (e.g., TDK N87) | Switchmode PSU (100kHz+) | ~15 A/m | ~0.4 T | Narrow |
| Alnico 5 | Sensors, Low-Speed Motors | ~50,000 A/m | ~1.2 T | Wide |
| N42 Neodymium (NdFeB) | BLDC Motors, Permanent Magnets | ~900,000 A/m | ~1.3 T | Extremely Wide |
Calculating Hysteresis Loss: A Worked Numeric Example
While the generalized Steinmetz equation ($P_v = C_m \cdot f^\alpha \cdot B^\beta$) is used for high-frequency ferrite datasheets, the most fundamental way to calculate hysteresis loss for standard mains frequencies relies directly on the physical area of the loop. The energy dissipated per cycle is exactly equal to the area of the B-H loop.
Let us calculate the hysteresis power loss for a custom 60 Hz mains transformer core using standard M6 silicon steel.
- Identify the Loop Area: From the manufacturer's B-H curve for M6 steel at a peak flux density ($B_{max}$) of 1.5 Tesla, the area of the hysteresis loop is approximately 250 Joules per cubic meter (J/m³). This means 250 J of heat is generated in one cubic meter of steel per AC cycle.
- Determine Core Volume: We are using an EI core stack that measures 0.005 cubic meters (5 liters).
- Identify Frequency: The mains frequency ($f$) is 60 Hz (60 cycles per second).
The formula for total hysteresis power loss ($P_h$) is:
$P_h = \text{Loop Area} \times \text{Volume} \times \text{Frequency}$
Plugging in our real-world values:
$P_h = 250 \text{ J/m}^3 \times 0.005 \text{ m}^3 \times 60 \text{ Hz}$
This 75W is pure heat generated solely by the molecular friction of the magnetic domains flipping back and forth. In a 1000W transformer, a 75W core loss represents a 7.5% efficiency hit before you even account for copper ($I^2R$) winding losses. This is exactly why high-efficiency designs push $B_{max}$ down to 1.2T or use thinner, higher-grade grain-oriented steel to shrink that loop area.
Where You Meet This in Practice
You interact with the consequences of the hysteresis loop every time you design or repair electromagnetic hardware. Here is how it manifests across different domains:
- Mains Transformers and Inductors: You want the narrowest possible loop. A narrow loop means low coercivity, allowing the core to magnetize and demagnetize with minimal energy waste. This is why transformer cores are made of specialized silicon steel rather than generic iron.
- Relays and Contactors: The armature core must have extremely low retentivity ($B_r$). If the loop is too wide, the core will remain slightly magnetized when the coil is de-energized. This residual magnetism can cause a relay to "stick" closed or delay the drop-out time, which is a critical safety hazard in motor control circuits.
- Switchmode Power Supplies (SMPS): At frequencies above 50 kHz, standard steel loops become useless. Ferrite ceramics are used because their high electrical resistance limits eddy currents, and their specific chemical doping keeps the hysteresis loop narrow even when flipped millions of times per second.
- Data Storage and Security: Magnetic stripe cards and hard drive platters rely on materials with a very wide hysteresis loop (high coercivity). This ensures that the written data (the magnetic orientation) is not accidentally erased by stray magnetic fields from nearby speakers or motors.
Hysteresis Loss vs. Eddy Current Loss: Clearing the Confusion
The most common mistake hobbyists and junior engineers make is confusing hysteresis loss with eddy current loss. Both occur in the magnetic core, both generate heat, and both are lumped together under the term "core losses" or "iron losses." However, their physical mechanisms and mitigation strategies are entirely different.
Hysteresis loss is caused by the internal friction of magnetic domains. It scales linearly with frequency ($f$). To reduce it, you must change the chemical composition of the material (e.g., adding silicon to steel) to make the domains easier to flip.
Eddy current loss is caused by the changing magnetic field inducing actual circulating electrical currents within the bulk conductive core material. These currents flow through the resistance of the iron, generating $I^2R$ heat. Eddy losses scale with the square of the frequency ($f^2$). To reduce them, you do not change the chemistry; you change the physical geometry by slicing the core into thin, insulated laminations or using non-conductive ferrite ceramics.
Frequently Asked Questions
Can a hysteresis loop be completely eliminated?
No. As long as a material is ferromagnetic, there will always be some domain friction. However, specialized amorphous metals (like Metglas) have loops so narrow that their hysteresis losses are a fraction of standard silicon steel, making them ideal for high-efficiency distribution transformers.
Why does my inductor get hot even with no load attached?
If an inductor or transformer is connected to an AC source, the core is cycling through its hysteresis loop continuously. The heat you feel is the core loss (hysteresis plus eddy currents) driven by the excitation voltage, entirely independent of the secondary load current.
Where can I find B-H curve data for specific parts?
Manufacturers like TDK, Magnetics Inc., and Cogent provide detailed B-H curves and Steinmetz coefficients in their core databooks. For fundamental physics and baseline material curves, the Georgia State HyperPhysics database and All About Circuits are excellent starting points. For deeper AC circuit analysis, Electronics Tutorials provides solid worked examples of loop area calculations.
