Eddy Current Losses Scale With the Square of Sheet Thickness, Forcing Transformers to Use Laminations

A solid copper wire channels electricity efficiently from one end to the other because the voltage pushes in a single direction. But place a solid block of iron inside an alternating magnetic field, and the physics invert. The block ceases to be a conduit and becomes a dead short.

This is the fundamental paradox of alternating current transformers. They rely on iron cores to guide magnetic flux between their primary and secondary coils, because iron carries magnetism thousands of times better than air. However, iron is also an electrical conductor.

When the alternating magnetic field surges back and forth through the core, it induces a voltage inside the iron itself, just as it does in the copper windings. Because the solid iron block forms a closed conductive loop, this voltage drives massive, swirling electrical currents.[3]

Engineers call these circular flows "eddy currents," and they are entirely parasitic. They contribute nothing to the transformer's output, instead converting electrical energy directly into waste heat through the iron's natural electrical resistance.[3]

If grid operators attempted to run a substation transformer with a solid steel core, the resulting eddy currents would generate catastrophic heat. The core would glow red hot, melt its copper windings, and destroy the equipment within minutes.

The mathematics of the square law

The sheer scale of this heating problem comes down to the geometry of the core and the unforgiving mathematics of electrical power. According to Faraday's law of induction, the voltage induced around a loop is directly proportional to the cross-sectional area of that loop.

In a solid block of steel, the available cross-sectional area is massive, which induces a correspondingly high voltage. Meanwhile, the electrical resistance of that same block is extremely low, because resistance drops as the cross-sectional area of a conductor increases.

Power dissipation equals voltage squared divided by resistance. Because the induced voltage scales with the core's thickness, and that voltage is then squared in the power equation, the resulting heat generation scales with the square of the material's thickness.

"The eddy current loss is proportional to the square of the lamination thickness," notes a 2024 engineering analysis from All About Circuits. "To minimize the core losses, the laminations should be as thin as possible."

This square-law relationship means that doubling the thickness of a conductive core does not merely double the waste heat; it quadruples it. Conversely, slicing the material into thinner segments offers an exponential reduction in parasitic power loss.

The lamination solution

The solution to this thermal runaway was pioneered in 1886 by William Stanley, who designed the first practical commercial transformer for George Westinghouse. Stanley realized that the magnetic core did not need to be a single, continuous block of metal.[1][4]

Instead of casting a solid core, Stanley built his transformer from a stack of thin, E-shaped iron plates. By slicing the core parallel to the magnetic field, he preserved the pathway for the magnetic flux while severely restricting the pathway for the electrical currents.[1][4]

Crucially, each individual sheet—or lamination—must be electrically insulated from its neighbors. If the plates touch bare metal to bare metal, the eddy currents simply bridge the gap, treating the stacked assembly as a single solid block and generating the same catastrophic heat.[3]

Modern manufacturers coat each steel sheet with a microscopic layer of inorganic varnish or glass-like silicate. This insulation forces the induced eddy currents to circulate strictly within the confines of a single, millimeter-thin sheet, drastically reducing the loop area.[3]

The mathematical payoff is immense. If a solid 54-millimeter core is replaced by a stack of 200 insulated sheets, each 0.27 millimeters thick, the voltage inside each sheet drops by a factor of 200. Because the loss scales with the square of the thickness, the total eddy current heat plummets by a factor of 40,000.[2]

Grain-oriented electrical steel

Today, the global power grid relies almost entirely on a specialized material known as grain-oriented electrical steel, or GOES. Metallurgists carefully roll and heat-treat this steel to align its microscopic crystal grains in a single direction, maximizing its magnetic permeability.

While the grain alignment minimizes the energy required to flip the magnetic field, the physical thickness of the GOES sheets remains the sole defense against eddy currents. Standard utility transformers typically utilize sheets between 0.23 and 0.30 millimeters thick.

"Reducing thickness from 0.35 mm to 0.23 mm reduces eddy current losses by approximately 57 percent," details a 2026 technical review from Industrial Monitor Direct. This aggressive scaling explains why high-efficiency designs push for the thinnest possible gauges.

However, engineers cannot slice the steel infinitely thin. As the sheets shrink toward 0.20 millimeters, they become fragile, expensive to roll, and difficult to stack without bending. More importantly, the insulating coating begins to consume a larger percentage of the core's total volume.

This ratio is known as the stacking factor. If the insulation takes up 5 percent of the space, the core is only 95 percent steel, which reduces its overall magnetic capacity. Manufacturers must constantly balance the square-law benefits of thinner sheets against the physical realities of the stacking factor.

The cost of silicon alloying

Beyond lamination thickness, metallurgists employ a secondary defense against eddy currents by altering the chemistry of the steel itself. By alloying the iron with approximately 3 percent silicon, they fundamentally change the material's electrical properties.

"Grain oriented silicon steel is a type of electrical steel containing approximately 3 percent silicon, which improves magnetic performance and reduces electrical losses," explains a 2026 specification guide from Moopec. The silicon acts as an impurity that disrupts the flow of electrons.

This disruption significantly increases the bulk electrical resistivity of the metal. Because eddy current power loss is inversely proportional to the material's resistivity, the silicon addition directly throttles the amount of current that the induced voltage can push through the sheet.

Yet, like lamination thickness, silicon alloying carries a strict mechanical penalty. Pushing the silicon content beyond 3.5 percent makes the steel incredibly brittle, causing it to crack and shatter during the cold-rolling processes required to achieve the 0.23-millimeter target thickness.

Consequently, transformer design remains trapped in a narrow optimization window. Engineers must extract the maximum electrical resistance from the silicon alloy without destroying the steel's ability to be rolled into the microscopic sheets demanded by the square-law equation.

The high-frequency limit

The square-law equation contains another punishing variable: frequency. The classical eddy current loss formula dictates that waste heat scales not only with the square of the thickness, but also with the square of the alternating current's frequency.

At the standard grid frequencies of 50 or 60 Hertz, 0.23-millimeter steel laminations keep eddy currents well under control. But modern electronics, such as computer power supplies and electric vehicle chargers, operate at frequencies ranging from 20,000 to over 100,000 Hertz.

At 100,000 Hertz, the frequency multiplier is millions of times higher than on the grid. Even the thinnest practical steel laminations would instantly overheat. The square-law math simply breaks down the utility of conductive metals at high switching speeds.

To survive these environments, engineers abandon steel entirely and use ferrite cores. Ferrites are ceramic compounds made from iron oxides that carry magnetic flux but feature extremely high electrical resistivity. Because they barely conduct electricity, they suppress eddy currents without needing to be laminated at all.

The design of every magnetic power device is a continuous negotiation with Faraday's law. Whether through microscopic laminations or ceramic insulators, engineers must continuously break the electrical circuits that the magnetic fields are desperately trying to close.