A magnetic hysteresis loop is the closed B-H curve that maps how a ferromagnetic material retains magnetization after an external field is removed, representing the exact amount of energy dissipated as heat during each AC magnetization cycle. In a real circuit or installation, this loop dictates whether your power transformer runs cool or melts down, whether your switching power supply achieves 90% efficiency, and whether a relay armature drops out cleanly or stays magnetically stuck. Think of hysteresis like the internal friction of stretching a stiff rubber band; energy is lost as heat every time you stretch and release it, and that thermal penalty must be managed in your design.
Most hobbyists and junior engineers confuse hysteresis loss with magnetic saturation or eddy currents. Saturation is the absolute ceiling of flux density (the flat top of the loop), while eddy currents are losses caused by circulating electrical currents inside the core material. Hysteresis, strictly speaking, is the energy cost of physically realigning magnetic domains inside the crystal lattice of the core every single AC cycle.
The Anatomy of the B-H Curve and Critical Data Points
To make material decisions, you need to read a B-H (Flux Density vs. Magnetic Field Strength) datasheet graph. The shape of this loop tells you everything about how the material will behave under load.
The total area enclosed by the hysteresis loop represents the energy lost per unit volume per cycle. A "fat" loop means high core loss; a "skinny" loop means high efficiency.
Worked Example: Quantifying Core Loss at 60Hz vs 100kHz
Let’s calculate the actual thermal penalty of hysteresis loop magnetism using the Steinmetz equation, which approximates hysteresis power loss: Ph = kh · f · Bmaxn. Here, f is frequency, Bmax is peak flux density, and kh and n are material-specific constants.
Material: M-6 Grain-Oriented Silicon Steel.
Parameters: f = 60 Hz, Bmax = 1.5 Tesla.
Result: The narrow hysteresis loop and high resistivity of the laminated steel yield a core loss of roughly 1.2 W/kg. The transformer runs warm but manageable.
Material: TDK PC40 Manganese-Zinc Ferrite.
Parameters: f = 100,000 Hz, Bmax = 0.2 Tesla (we lower Bmax to keep losses in check).
Result: Despite the frequency being 1,666 times higher, the ultra-skinny hysteresis loop of the ferrite keeps the core loss at approximately 150 W/kg (or ~300 kW/m³).
The Fatal Mistake: If you attempted to use M-6 Silicon Steel at 100kHz, the hysteresis loss would scale linearly with frequency, resulting in over 2,000 W/kg of heat generation. The core would literally glow red and melt the bobbin within seconds. This numeric reality is why we switch core materials as frequency increases.
Where You Meet Hysteresis in Practice
You will encounter the effects of the hysteresis loop in four primary bench and jobsite scenarios:
- Switch-Mode Power Supplies (SMPS): In flyback or forward converters, the core is driven through all four quadrants of the B-H loop (or two quadrants in single-ended topologies). The hysteresis loss directly subtracts from your overall efficiency and dictates your heatsink sizing.
- EMI Chokes and Common Mode Filters: Here, you actually want a lossy material. A wide hysteresis loop at high frequencies (like Nickel-Zinc ferrite) absorbs high-frequency noise and dissipates it as harmless heat rather than reflecting it back down the line.
- Relays and Contactors: If the armature steel has too high a remanence (Br), the magnetic field won't collapse fast enough when the coil is de-energized. The relay will chatter or fail to drop out, keeping a high-voltage load energized—a critical safety hazard.
- Audio Output Transformers: In tube amplifiers, the hysteresis loop introduces non-linear distortion at low signal levels because the B-H curve is not perfectly linear near the origin. High-permeability, highly annealed silicon steel (like M6) is used to minimize this crossover distortion.
Core Material Decision Tree
Stop guessing which toroid or E-core to order. Use this decision path to select the exact material grade based on your operating frequency and application.
| Operating Frequency | Application Goal | Material Class | Concrete Pick / Part Series |
|---|---|---|---|
| 50Hz / 60Hz | Mains isolation, heavy power transformers | Grain-Oriented Silicon Steel | AK Steel M-6 or M-4 Laminations |
| 400Hz - 10kHz | Audio transformers, aerospace power, high-current inductors | Amorphous / Nanocrystalline Metal | Hitachi Metglas or Finemet (e.g., Hitachi FT-3H) |
| 10kHz - 2MHz | SMPS transformers, PFC chokes, resonant converters | Manganese-Zinc (MnZn) Ferrite | TDK PC40 (General) or TDK PC95 (High-Efficiency) |
| 2MHz - 500MHz | EMI suppression, RF chokes, antenna baluns | Nickel-Zinc (NiZn) Ferrite | Fair-Rite 43 (Broadband) or Fair-Rite 61 (HF) |
| DC to 100kHz | DC-DC buck/boost inductors (needs high DC bias without saturation) | Powdered Iron / Sendust | Magnetics Kool Mµ (Sendust) or Micrometals -26 (Iron Powder) |
What People Commonly Confuse With Hysteresis
To troubleshoot magnetic components effectively, you must isolate hysteresis from its two sibling losses:
1. Hysteresis vs. Eddy Current Loss: Hysteresis is the friction of magnetic domains flipping. Eddy currents are actual electrical loops induced inside the core material by the changing flux (Faraday's Law). You reduce hysteresis by picking a "softer" material. You reduce eddy currents by increasing the material's electrical resistance (ferrites are basically ceramics) or by slicing the core into insulated laminations (silicon steel). Total core loss is the sum of both.
2. Hysteresis vs. Saturation: Hysteresis happens continuously during normal AC operation and generates steady heat. Saturation is a hard limit; when you push the core past Bsat, the inductance collapses to near zero. If you confuse the two, you might try to fix an overheating inductor by adding more turns (which lowers flux density and fixes hysteresis heating), but if the core is actually saturating due to high DC bias, adding turns won't save your switching transistor from a current spike.
Frequently Asked Questions
Can I measure the hysteresis loop on my bench?
Yes. You can build a simple B-H curve tracer using a function generator, a power amplifier, a primary drive winding, and a secondary sense winding connected to an RC integrator circuit. Feed the primary current (proportional to H) into the X-axis of an oscilloscope, and the integrated secondary voltage (proportional to B) into the Y-axis. You will see the live hysteresis loop on the screen.
Does hysteresis affect DC circuits?
In a pure, steady DC circuit, hysteresis loss is zero because the magnetic field is not changing. However, in DC-DC converters (like a buck converter), the current is constantly rippling (AC superimposed on DC), meaning the core is traversing a minor hysteresis loop on every switching cycle, generating heat.
Why do relays sometimes stick even when power is removed?
This is caused by high remanence (Br) in the relay's armature steel. The hysteresis loop is too "wide," leaving residual magnetism that physically holds the contacts closed. In precision DC relays, manufacturers use materials with low coercivity or add a small physical non-magnetic gap (like a brass pin) to the armature to force the flux to drop to zero.
For further reading on magnetic material properties and core loss curves, refer to the All About Circuits chapter on Magnetic Hysteresis and the TDK Electronics Ferrite Cores catalog for exact B-H curve datasheets.
