■ Overview

Magnetic components are indispensable elements in switch-mode power supplies (SMPS) because they enable energy storage, voltage conversion, filtering, and isolation functions while maintaining excellent efficiency and a compact size.

In actual applications, due to the air gap and fringe effect of the magnetic core, leakage flux can reach adjacent metals such as the heat sink, the copper layer of the substrate, or other conductors.

This causes eddy currents to be generated inside the metal, which causes additional losses and changes in the inductance.

In this article, we analyze the effect of adjacent metals on eddy current losses and inductance changes using finite element analysis (FEA), and also introduce various methods to reduce these effects.

■ Preface

Inductors, including coupled inductors and trans-inductor voltage regulators (TLVRs), are key components in switch-mode power supplies.

Generally, magnetic cores with an air gap are used to prevent core saturation and improve energy storage capacity.

Because the core material has a much higher permeability than air, most of the magnetic flux remains inside the core, but the fringe flux generated around the air gap is part of the magnetic flux It causes leakage into the surrounding space.

At this time, if metal is present nearby, the leaked magnetic flux can induce eddy currents inside the metal, resulting in additional losses and reduced efficiency.

The decrease in efficiency is caused by additional eddy current losses and increased current ripple, because the eddy currents generate a reverse magnetic field that substantially reduces the inductance.

Finite Element Analysis (FEA) simulations were performed to analyze these issues and explore possible solutions.

Figure 1a is an example of a magnetic component with an air gap, used to explain the theory in this article.

This structure consists of a ferrite magnetic core (gray), one air gap, and two windings (orange).

On the other hand, in Figure 1b, to represent the copper layer typically present on a substrate, an additional copper layer (green) with a thickness of 200 µm was placed above and below the core.


■ Generation of eddy currents and the resulting reduction in inductance

In the FEA simulation, high-frequency AC excitation was applied to one winding, and the other winding was left open (no current) so that the effects of eddy currents on self-inductance, mutual inductance, and leakage inductance could be observed, respectively.

Figure 2 shows the distribution of magnetic flux density (B-field) in the air region above the core.

Figures 2a and 2b show the case where there is no adjacent copper layer and the case where a copper layer is included, respectively.

Because copper has high electrical conductivity, leakage flux is blocked from passing through the copper layer and spreading into the upper air region, and as a result, leakage flux in the surrounding air region is significantly reduced.


If the right-hand rule is applied to the magnetic flux distribution in Figure 2a, it can be confirmed that counterclockwise eddy currents are induced in the upper copper layer, as shown in Figure 3.

The strongest eddy currents appear at the top of the air gap of the core, because more magnetic flux leaks into the surrounding air space in that area.

In addition, strong eddy currents are generated on the upper part of the winding that is closer to the source of the current.


Figure 4a shows an observation sheet (pink) for observing the B-field.

Figure 4b is a B-field distribution graph showing that leakage flux is suppressed by the copper layer.


Figure 5 shows the magnetic flux density (B-field) measured along the white dashed line path in the center of the core shown in Figure 4b.

Since only one winding is excited, the B-field in the core section (0 < distance < 3 mm) connected to the excited winding represents the total magnetic flux related to self-inductance.

On the other hand, the B-field in the section connected to the unexcited winding (3 mm < distance < 6 mm) represents the mutual flux related to mutual inductance.

The orange curve shows the case with a copper layer, and the blue curve shows the case without a copper layer, respectively.

It can be observed that while the mutual magnetic flux remains almost unchanged, the total magnetic flux decreases significantly because the leakage magnetic flux is reduced when the copper layer is present.


To investigate the effect of the distance between the copper layer and the magnetic core on the inductance, the upper copper layer was placed at a position 100µm above the winding and the lower copper layer was placed at a position 900µm below the winding.

The simulated inductance values, including self-inductance (L11), mutual inductance (L12), leakage inductance (Lk1), and coupling coefficient (k), are summarized in Table 1 based on one case.


As can be seen in Table 1, the upper copper layer has a greater effect on leakage inductance and magnetic inductance because it is located closer to the magnetic core and winding than the lower copper layer.

When both copper layers are present, the self-inductance decreases by 17.7% and the leakage inductance decreases by 73.0%.

When such a reduced inductance value is applied to a 4-phase TLVR-based buck converter with a duty cycle of 0.15, the current ripple can increase by up to 50%.

As can be seen in Figure 3, the strongest eddy currents occur above the air gap of the core and above the excited winding.

To evaluate the individual effects of these eddy currents on the change in inductance, a groove was introduced into the copper layer at the corresponding location as shown in Figure 6.


Figure 7 shows the B-field distribution for two grooved copper layer configurations.


In Figure 7a, the flux linkage between the two core sections is significantly improved, increasing the mutual flux, which can be seen in Table 2.


In Figure 7b, the flux leakage into the air region above the winding increases significantly, and as a result, it can be seen in Table 3 that the amount of leakage increases.

Since the entire copper layer serves to reduce leakage flux, adding grooves only to the top of the winding provides only limited improvement.


■ Strategies to Mitigate Eddy Current Effects in Adjacent Metals

▶ Reduction in air gap length
As mentioned earlier, there are two main reasons why efficiency decreases due to eddy currents generated in adjacent metals.

The first is that current ripple increases due to the decrease in inductance, and the second is that additional losses occur due to eddy currents generated in surrounding metal parts.

The first method to improve inductance is to reduce the length of the air gap in the core.

Reducing the core air gap reduces magnetic reluctance, which can generate more magnetic flux, and as a result, increases inductance.

In addition, by allowing the magnetic flux to be better concentrated inside the core material, leakage flux into the surrounding air region can be reduced, and accordingly, eddy currents and associated losses in adjacent conductive structures can be mitigated (Figure 8).


Table 4 illustrates simulation results comparing inductance values for two different core air gap lengths (lg).

When the air gap increases from 0.15 mm to 0.25 mm, the total inductance increases by 37.2% and the mutual inductance increases by 40.1%.

The eddy current losses reduced by this method are shown in Table 5. However, a disadvantage of this method is that the saturation current of the inductor may be lowered.


▶ Removal of the dominant copper layer
When adjacent conductors are multiple copper layers inside the substrate, one way to reduce eddy current losses is to reduce the copper area of the sublayer closest to the winding and magnetic core.

The closer the copper layer is to the winding, the stronger the magnetic flux it receives, and as a result, a larger eddy current is induced.

For example, as shown in Figure 9, a method to remove the bottom copper layer of the upper substrate can be applied.


Figure 10 shows the eddy current density occurring in eight copper sublayers.

As can be seen in the figure, sublayer 8 (lowest layer) has the strongest eddy current, and sublayer 1 (top layer) has the weakest eddy current.

The direction of the eddy current is influenced not only by the original magnetic flux generated in the winding but also by the eddy current generated in the adjacent copper sublayer.

When the copper layer is thin, it cannot completely block the magnetic flux generated in the winding, so some of the magnetic flux passes through the upper layer and can induce eddy currents in the upper copper layer as well.

On the other hand, if the copper layer is sufficiently far from the winding or if the adjacent lower layer is thick enough to block the magnetic flux, the influence of the magnetic flux generated in the winding is almost negligible.

In such cases, the eddy currents generated in the copper layer are mainly induced by the currents in adjacent copper layers.

For example, as can be seen in Figure 11, in the copper region of sublayer 8 located directly above the winding, the eddy current flows in the opposite direction to the winding current, but in sublayer 4, the eddy current flows in the same direction as the winding current.


Figure 12 compares the current density of the upper substrate measured along the direction of the black arrow indicated in Figure 10.

Here, orange represents the case where there are 8 copper sublayers, and blue represents the case where there are 7 copper sublayers.

If the 8th sublayer is removed, the eddy current decreases to zero because there is no copper in that layer, which helps reduce eddy current losses as shown in Table 5.

However, the current density of the 7th, 6th, and 5th sublayers increases significantly compared to the case where there are 8 copper layers.

This is because strong eddy currents are induced in the remaining layers as the 8th lower layer, which was blocking the magnetic flux generated in the winding, is removed.

Therefore, this method helps reduce eddy current losses but does not help increase inductance.

▶ Increase switching frequency
Another way to reduce the effects of eddy currents is to increase the switching frequency.

Increasing the switching frequency reduces current ripple, and as a result, eddy current losses are also reduced (Table 5). When Method 1, Method 2, and Method 3 are applied together, the maximum efficiency of the converter improves from 87.4% to 89%, and the full-load efficiency increases from 86.7% to 87.2%.


■ Effect of Top Inductor Air Gap on µModule® Regulator Performance

The LTM4680 is a step-down µModule regulator supporting up to 16 VINs, providing dual 30A or single 60A outputs and featuring a digital PMBus® interface.

This device is provided in a small BGA package measuring 16 mm × 16 mm × 7.82 mm.

The LTM4700 is a product that offers higher current capacity, supports dual 50A or single 100A outputs, and is available in a BGA package measuring 15mm × 22mm × 7.87mm.

Both products are designed to provide excellent performance in a variety of applications. To achieve excellent efficiency with a small package size, a ferrite core inductor with an air gap is integrated into the top of the package.

Figure 13 shows a 3D model of the LTM4700 package.

If a heatsink or additional PCB is placed close to the top of the module, the inductance and overall efficiency may decrease due to the eddy current effect described earlier.

To reduce these effects, a method of machining grooves into the metal plane of the heatsink as shown in Figure 14 can be applied.

In addition, if a multilayer PCB is placed near the top surface of the LTM4700 or LTM4680, removing the main copper layer can further reduce eddy current losses.

As an alternative, increasing the switching frequency can be considered, but this should be taken into account as it may increase switching losses.


■ Conclusion

In this article, we analyzed the cause of the decrease in power system efficiency due to eddy currents generated when magnetic components are placed near conductive materials.

These induced currents not only cause additional losses but also reduce effective inductance, resulting in increased current ripple and higher AC losses.

Finite Element Analysis (FEA) simulations were performed to evaluate this phenomenon. Three mitigation strategies for efficiency improvement were also proposed.

The first method is to reduce the length of the core air gap, the second is to remove the main copper region, and the third is to increase the switching frequency.

Reducing the core air gap can simultaneously address the reduction in inductance and eddy current losses, but there is a trade-off in that the saturation current of the inductor may be lowered.

The remaining two methods focus mainly on reducing losses caused by eddy currents.

The content presented in this article can be applied to the design of LTM4700 and LTM4680, and various strategies can be used to mitigate the effects of eddy currents when they occur in actual applications.

※ Author Introduction
Min Gao is a senior engineer in product applications who earned a Ph.D. in electrical engineering from Florida State University in Tallahassee, Florida. He later joined Analog Devices in California in 2025 as an application engineer.
YT (Ye) Tang joined Analog Devices in February 2021 as a staff engineer in charge of product applications. Currently, I work as a design engineer and application engineer at the µModule® group, developing high-power current point-of-load (POL) converters for data centers, optical communications, and various markets. I am also focusing on research to reduce the size and increase the power density of POL switching power supplies by utilizing the latest FET and coupled inductor technologies.
Ling Jiang is a Senior Manager for Product Applications. He received his Ph.D. in Electrical Engineering from the University of Tennessee in Knoxville, Tennessee, in 2018. After graduation, he joined the Power Products Group at Analog Devices in the California Bay Area and currently serves as a Senior Manager supporting µModule® products for various market applications. He also contributes to the definition and design of high-density µModule regulators.