Power Electronics

Core Loss

Q: How do you separate hysteresis loss from eddy-current loss in a core?

The classical loss-separation method measures total core loss at several frequencies while holding peak flux density constant, then plots the per-cycle loss (total loss divided by frequency) versus frequency. Hysteresis loss is proportional to frequency, so it contributes a constant per-cycle term, while eddy-current loss is proportional to frequency squared, so it contributes a term that rises linearly with frequency on the per-cycle plot. The y-intercept gives the hysteresis component and the slope gives the eddy-current (and excess) component. In practice the Bertotti three-term model adds an excess or anomalous loss term proportional to frequency to the power 1.5, which captures domain-wall dynamics that the two-term classical model misses, especially in grain-oriented silicon steel.

Q: Why does core loss rise so steeply with flux density?

The Steinmetz equation models core loss per unit volume as Pv = k times f to the power alpha times Bpeak to the power beta, where beta is typically between 2.0 and 3.0 for ferrites and powdered iron. Because beta is well above 1, halving the peak flux density Bpeak reduces core loss by a factor of roughly 2 to the power beta, so a 2x reduction in flux can cut core loss by 4 to 8 times. This is why designers add turns or increase core cross-section to lower Bpeak rather than accept the heating. Near saturation the loss exponent climbs further and the curve becomes very steep, which is one reason cores are operated well below their saturation flux density at high frequency.

Q: How does core loss change when you move from 100 kHz to several MHz?

Hysteresis loss scales roughly linearly with frequency while eddy-current loss scales with the square of frequency, so above a material-dependent crossover the eddy-current term dominates and total loss climbs faster than linearly. To stay efficient at higher frequency, designers reduce peak flux density and switch to higher-resistivity materials. NiZn ferrites and low-permeability powdered-iron mixes work into the tens of MHz, whereas MnZn ferrites are usually limited to roughly 1 to 3 MHz before loss and reduced resistivity make them impractical. Manufacturers publish loss-versus-frequency curves at fixed Bpeak that let you read the usable band directly.

/kor laws/

Power dissipated as heat inside a magnetic core when it is driven by an alternating magnetic field, the unavoidable penalty paid by every transformer, inductor, and choke. It is the sum of two mechanisms: hysteresis loss, which comes from the energy enclosed by the B-H loop on each cycle, and eddy-current loss, which comes from circulating currents induced in the conductive core material. Core loss depends strongly on frequency, peak flux density, and the choice of ferrite or powdered-iron material, and it sets the thermal limit on how hard a magnetic component can be pushed. Engineers predict it with the empirical Steinmetz equation and manage it by lowering peak flux, raising material resistivity, and selecting a core mix matched to the operating frequency.

Category: Power Electronics

Mechanisms: Hysteresis + Eddy-Current

Typical Limit: ~100 to 500 mW/cm³

How Magnetic Cores Dissipate Power

When a magnetic core is taken around its B-H loop by an alternating excitation, it does not return all of the stored energy to the circuit. The area enclosed by the hysteresis loop represents energy converted to heat on every cycle as magnetic domains realign against internal friction; this hysteresis component scales directly with operating frequency. Simultaneously, the changing flux induces voltages within the core itself, and because real core materials have finite resistivity, those voltages drive circulating eddy currents that dissipate power resistively. Eddy-current loss scales with the square of frequency, so it grows much faster than hysteresis loss as the excitation speeds up.

For high-frequency RF and switch-mode magnetics, the core material is chosen specifically to suppress eddy currents. Laminated silicon steel is split into thin insulated sheets to break up current paths at mains and audio frequencies, while above roughly 100 kHz designers move to ferrites, whose ceramic structure has resistivity many orders of magnitude higher than metal alloys. Powdered-iron and other distributed-gap cores embed metal particles in an insulating binder, giving a built-in distributed air gap that further limits eddy currents and improves permeability stability versus DC bias.

Core loss is not just an efficiency line item; it is a thermal constraint. The dissipated power raises core temperature, which in turn shifts permeability and saturation flux density and can drive thermal runaway if loss rises faster with temperature than the core can shed heat. Manufacturers therefore publish core loss as power per unit volume (mW/cm³) at specified frequency and peak flux density, and a practical design keeps the resulting temperature rise within roughly 40 to 50 °C above ambient.

The Steinmetz and Loss-Separation Models

Steinmetz equation (volumetric loss):
P_v = k × f^α × B_peak^β (mW/cm³)

Loss separation (per unit volume):
P_v ≈ k_h·f·B_peak^β + k_e·f²·B_peak² + k_ex·f^1.5·B_peak^1.5
(hysteresis term + classical eddy-current term + excess/anomalous term)

Where: α ≈ 1.1 to 1.7, β ≈ 2.0 to 3.0, f = frequency, B_peak = peak flux density (T or mT), k, k_h, k_e, k_ex = material coefficients from datasheet curve fits.

Example: an MnZn power ferrite at f = 100 kHz, B_peak = 100 mT typically gives P_v ≈ 80 to 120 mW/cm³ near 25 °C, dropping to a minimum around 80 to 100 °C.

Material Selection by Frequency and Loss

Core Material	Useful Frequency	Relative Permeability μ_r	Resistivity	Loss Character	Typical Use
Laminated SiFe steel	50 Hz to 10 kHz	2,000 to 40,000	~0.5 µΩ·m	Low f, high B; eddy loss limited by lamination	Mains transformers
MnZn ferrite	10 kHz to 3 MHz	1,500 to 15,000	~1 to 20 Ω·m	Low loss at 100 kHz class; falls off in MHz	SMPS transformers
NiZn ferrite	1 MHz to 300 MHz	10 to 1,500	10⁵ to 10⁷ Ω·m	High resistivity tames eddy loss at VHF	RF chokes, EMI beads
Powdered iron	10 kHz to 100 MHz	10 to 100	Distributed-gap, insulated grains	Higher hysteresis loss; very stable vs. bias	RF inductors, PFC chokes
Sendust / MPP	10 kHz to 5 MHz	14 to 550	Distributed-gap alloy	Low loss, soft saturation, good DC bias	Filter and output chokes

Common Questions

Frequently Asked Questions

How do you separate hysteresis loss from eddy-current loss in a core?

Measure total loss at several frequencies at a fixed B_peak, then plot per-cycle loss (P/f) versus frequency. Hysteresis is constant per cycle (the y-intercept) while the eddy-current term rises linearly with f (the slope). The Bertotti model adds an excess term proportional to f^1.5 to capture domain-wall dynamics the two-term classical fit misses, notably in grain-oriented steel.

Why does core loss rise so steeply with flux density?

The Steinmetz exponent β is typically 2.0 to 3.0, so loss scales as B_peak^β. Halving B_peak cuts loss by roughly 2^β, a factor of 4 to 8. That is why designers add turns or enlarge the core cross-section to lower flux rather than tolerate the heating, and why cores run well below saturation where the exponent climbs even higher.

How does core loss change from 100 kHz to several MHz?

Hysteresis loss grows roughly linearly with frequency but eddy-current loss grows with f², so above a material crossover the eddy term dominates and total loss climbs faster than linearly. Designers lower B_peak and switch to higher-resistivity materials: NiZn ferrites and low-μ powdered iron reach tens of MHz, while MnZn ferrites typically cap out near 1 to 3 MHz.

Related Terms

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