How Does the Magnetic Field Penetrate Shielding Materials? Analysis and Comparison

Why is Magnetic Field Shielding a Challenge?

Magnetic field shielding is one of the more complex issues in electromagnetic engineering. Unlike the electric field, which can be relatively easily blocked with conductive or insulating layers, the magnetic field has the ability to penetrate many materials, which makes its effective attenuation much more difficult.

The main difficulties arise from the fact that the magnetic field does not interact directly with electric charges, but with flowing currents and magnetic moments. Therefore, materials used for shielding must not only conduct current but also respond appropriately to changes in the field, which in practice means the need to consider many physical and structural parameters.

Typical metal shields, made of foil or sheet, effectively attenuate the magnetic field thanks to their high conductivity and the skin effect, which limits the penetration of the field to a very thin surface layer of the material. Unfortunately, such solutions are rigid and not very flexible, which in many modern applications, such as wearable electronics or flexible circuits, is a significant drawback.

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Fig. 1. Metal PCB shield

Therefore, shielding materials with conductive fibers, which offer flexibility and easy adaptation to different shapes, are gaining more and more importance. However, their operation is more complex and requires a detailed understanding of the mechanisms of magnetic field penetration through their structure.

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Fig. 2 Flexible conductive material

Shielding Materials with Conductive Fibers – An Alternative to Metals

Magnetic shields made of metals such as copper or aluminum, although very effective, have significant limitations. Their rigidity and lack of flexibility make them not always easy to apply in modern, often complex electronic designs or in devices requiring flexible protective materials.

In response to these challenges, shielding materials based on conductive fibers have been developed. These are usually metallized fibers or fibers coated with a layer of metal, formed into meshes or fabrics that create light, flexible, and easily adaptable shields. Such solutions are increasingly used in wearable electronics, the automotive industry, and telecommunications, where both shielding properties and user comfort are required.

Conductive fibers form a lattice of short, closed meshes that are responsible for attenuating the magnetic field. However, their operation is much more complex than that of uniform metal shields. The effectiveness depends not only on the conductivity of the metal itself but also on its spatial arrangement, the size of the openings between fibers, and the electrical parameters of the structure itself.

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Fig. 3. EMC Tent

Additionally, internal parameters such as resistance (R'), inductance (L'), and capacitance (C') of this fibrous structure are crucial for how the magnetic field is attenuated. The complexity of these mechanisms means that shielding effectiveness is not constant, but strongly depends on the field frequency as well as the geometry and properties of the material itself Fig. 4

Fig. 4 Close-up of shielding material

Parameters Affecting the Effectiveness of Magnetic Shielding

The effectiveness of materials shielding the magnetic field depends on many factors, which can be divided into two main groups: the internal properties of the material and the physical structure of the conductive fibers. Understanding these parameters is key to consciously selecting or designing an effective magnetic shield.

Internal Properties of the Material: R', L', C'

In technical literature and engineering practice, shielding is described, among others, by three basic parameters:

• R' (linear resistance) – determines the electrical resistance of the conductors inside the material, which affects the attenuation of eddy currents generated by the alternating magnetic field.
• L' (linear inductance) – responsible for the material's ability to store energy in the magnetic field and regulates the propagation of electromagnetic waves.
• C' (linear capacitance) – related to dielectric properties and the arrangement of conductive fibers relative to each other, it affects the behavior of the electric field.

These three parameters interact, determining how the magnetic field is attenuated and how it penetrates the shielding material structure. They change with signal frequency, which further complicates analysis and requires specialized measurements.

The Importance of Fiber and Mesh Structure

In addition to electrical parameters, the physical structure of the material has a huge impact on shielding effectiveness. In the case of fibrous shielding materials, the following are key:

• Size and shape of mesh openings – the smaller the holes, the more effective the blocking of the magnetic field, especially at higher frequencies. • Arrangement and density of fibers – affects the uniformity of coverage and continuity of paths conducting eddy currents. • Conductivity of fibers – materials with higher conductivity (e.g., copper, silver) attenuate the magnetic field better, but may be more expensive or less flexible.

The structure of the material determines whether the magnetic field will penetrate mainly through the metal fibers or through the air openings between them. This dynamic relationship between the magnetic field and the physical structure explains the complexity of shielding effectiveness depending on operating conditions.

Effective shielding is not only a matter of material, but also of its structure and electrical properties. To predict the effectiveness of a shield, a comprehensive approach is necessary, taking into account all these parameters and their interrelationships.

How Does the Magnetic Field Penetrate the Shield? Mechanisms of Action

Understanding how the magnetic field penetrates the shielding material is essential for optimizing electromagnetic protection. This process is not simple, because the behavior of the field depends on many factors, including the frequency of the signal and the structure of the material itself.

Principle of magnetic field coupling (shown without skin effect)

Description of Magnetic Field Penetration through the Shield

The magnetic field interacts with the shield mainly through induction – a varying magnetic field generates eddy currents in the conductive material, which in turn create a magnetic field opposing the external field. This inductive interaction is measured by the so-called mutual inductance L12, which describes how effectively the material “passes” the magnetic field.

A linearly propagating current i1 is applied to the bottom side of the shielding material (see figure above). The magnetic flux Φ1 generated by the current (Φ1 = L12 * i1) penetrates the shielding material depending on frequency. On the top surface of the shielding material, a voltage u2 is induced (u = ω * L12 * i1).

• Φ1 = L12 * i1
• u = ω * L12 * i1

The inductance L12 links current i1 with voltage u2. The inductance L12 depends on frequency due to the skin effect. Its characteristic describes the influence of the skin effect and thus the magnetic properties of the shielding material. The voltage u2 behind the shield may cause other disturbances such as currents, magnetic, and electric fields.

A special measurement chamber is used to measure inductance L12. (Figure below) shows the configuration of this chamber. The shielding material is placed in a metal closed enclosure of the measurement chamber. On the bottom side of the shielding material, there is a 50 Ω stripline (stripline 1). The current i1 flowing through the stripline uses the shielding material as a return path. The magnetic field generated by current i1 penetrates the shielding material according to its shielding effectiveness. On the top side of the shielding material, there is a second 50 Ω stripline (stripline 2). The voltage u2 is induced in stripline 2 by the magnetic flux Φ1.

Measurement Configuration with Striplines and Measurement Chamber

The inductance L12 (L12 = -u2 / (ω * i1)) describes how much magnetic flux Φ1 can penetrate through the shielding material and induce voltage u2.

• L12 = -u2 / (ω * i1)

If no shielding material is present in the measurement chamber (see figure above), the reference inductance L12 of the measurement configuration is measured (see below). The inductance L12 remains constant over a wide frequency range. The end of the linear frequency response of the measurement chamber occurs at 1 GHz.

Frequency Response and Inductive Coupling of the Measurement Chamber without Shielding Material (i1 = const.)

During measurements (e.g., in a stripline setup as shown in the figure above), the voltage induced in the second line (u2) is an indicator of the degree of field penetration. The value of inductance L12 is calculated from the formula:

L12 = - U2 / (W i1)

where U2 is the induced voltage, W – angular frequency, and i1 – current in the first line.

Mechanisms of Magnetic Field Shielding

The voltage u2 induced by the magnetic field (see figure below) is read by stripline 2 as u2'. This voltage is slightly smaller than the voltage u2 on the surface of the shielding material, because part of the magnetic field still penetrates the space between the stripline and the shielding material. This effect is neglected later, and u2' is assumed to be identical to u2.

Derivation of Voltage u2 Using Stripline

The voltage u2 induced in the stripline depends on the magnetic shielding effectiveness of the shielding material. The corresponding inductance L12 describes the magnetic penetration of the shielding material.

Figure 5 shows the induced voltage u2 and inductance L12 for shielding material S10.

Inductive Penetration of Shielding Material S10

Conductive fibers in the metallized nonwoven fabric form closed meshes. The magnetic field is displaced from the metallic meshes as frequency increases (from 500 kHz to 200 MHz).

In the lower frequency range (below 1 MHz) the shielding material does not show any attenuation effect (see Figure 5). The induced voltage u2 and inductance L12 are equal to the reference values measured in the empty chamber.

Inductive Penetration of Shielding Material in the Lower Frequency Range without Skin Effect.

Inductive Penetration of Shielding Material with Skin Effect; Magnetic Field Penetrates through Air-filled Openings in the Material

From about 0.5 MHz the inductance of the empty chamber remains constant at -169.8 dBH (3.23 nH). Below 400 kHz the inductance appears to be increased, probably due to an increase in voltage u2 caused by the influence of the electric field of stripline 2.

First principle of inductive operation

From 0.5 MHz the skin effect becomes noticeable in the metallic parts of the shielding material (see Figure 7). The voltage u2 and inductance L12 decrease progressively (see Figure 5). The induced voltage reaches its lowest value at 200 MHz. At this point, a new principle of operation arises, which overlaps with the displacement of the field in the metal fibers (see Figure 8).

Second Principle of Inductive Operation

From 200 MHz, the voltage u2 increases linearly with a slope of 20 dB/dec, and the inductance transitions into a constant curve: -235.9 dBH (0.16 pH) (see Figure 5).

The magnetic field component F2 penetrates through the air-filled openings in the shielding material. At lower frequencies, this component of the magnetic field was weaker than the one penetrating through the metal of the shielding material. As the frequency continues to rise, the entire field is displaced from the metal of the shielding material and passes only through the air-filled openings (see Figure 8). The propagation path of the magnetic field lines stops changing with frequency increase, which causes the inductance to remain constant. The value of inductance L12 can be extrapolated for even higher frequencies.

The coupling inductance L12 of the shielding material is a material parameter that can be defined as a specific linear inductance L12' [pH/cm].

Comparison of shielding materials

Inductive penetration of the shield was measured for six shielding materials and presented in Figure 9.

Magnetic shielding properties of six shielding materials with inductive coupling

Above about 2 MHz, good shielding properties can be observed for three materials (S10, S2, and 02). For the other three materials (01, 03, and 04), the shielding effect was absent or weak up to 1.5 GHz!

The shielding effectiveness of the materials differs significantly – from ineffective to effective. The frequency ranges in which different shielding mechanisms occur shift slightly depending on the material.

• Shielding material 04: Does not exhibit a magnetic shielding effect, behaves like air (empty measurement chamber).
  
  ● Shielding material 03: Achieves magnetic field attenuation only at the level of 3 dB at 1 GHz.
• Shielding material 01: Achieves attenuation of 12 dB at 1 GHz.
• Shielding materials 02, S2, and S10: Are effective and demonstrate frequency ranges of two shielding mechanisms. In the first range (up to 200 MHz), the material acts by displacing the field through the mesh openings. In the second range (>200 MHz) the effect is defined by the size of the metallic openings in the mesh and their ohmic resistance (attenuation 40...65 dB). The structure of the shielding material determines the effect in both ranges.

Coupling inductance L12

The coupling inductance L12 of the shielding material is a parameter that describes the penetration of the magnetic field through the material. It can be normalized to the current in a 10 mm long line. Magnetic field attenuation is expressed as the difference in dB between the measurement with the shielding material and the reference measurement (without material): Attenuation = L12-material [dBH] - L12-empty [dBH]

Design conclusions

The quality of magnetic field shielding depends on the size of the mesh openings, their cross-section, and conductivity. The measurement results from Figure 9 clearly show the influence of shielding materials on the magnetic field, which is beneficial for their applications and development. When designing shielding materials, it is important to constructively influence the two inductive shielding mechanisms.

Two main mechanisms of magnetic shielding</2>

Understanding the effectiveness of magnetic shielding requires knowledge of the basic mechanisms that determine how the magnetic field is attenuated or penetrates through a given material. In the studied shielding materials, we distinguish two key effects:

I. Skin effect and field displacement in the metal

The first mechanism is the so-called skin effect. It consists in the fact that alternating current (AC) flows mainly in a thin surface layer of the conductor, called the “skin layer.” As the current frequency increases, this layer becomes thinner, which results in increased effective resistance and attenuation of the magnetic field inside the material. In practice, this means that the metallic elements of the mesh or conductive fibers in the shielding material “displace” the magnetic field outward, limiting its penetration inside. This effect is particularly strong in the frequency range from several hundred megahertz upward, when the skin depth becomes very small.

II. Penetration through air-filled openings in the material

The second mechanism is associated with the presence of holes, empty spaces, or “gaps” in the structure of the material. In the case of materials made of conductive meshes or fibers arranged in a specific way, the magnetic field can penetrate through these unshielded fragments.

This mechanism is dominant especially at lower frequencies, up to about 200 MHz, where the field penetrates mainly through the air spaces between the conductive elements.

The effectiveness of shielding here strongly depends on the size and shape of these openings and on their distribution.

The role of material structure in both mechanisms

The combination of these two phenomena determines the final effectiveness of the shielding material. Meshes with fine openings and fibers with high conductivity cause stronger attenuation of the magnetic field, especially in higher frequency ranges, where the skin effect is most effective.

On the other hand, large, irregular openings can significantly reduce shielding effectiveness, allowing the field to penetrate even at high frequencies.

How to choose the right shielding material?

The selection of material for effective magnetic field shielding is a process that requires consideration of several key factors that affect the efficiency of protection against electromagnetic interference. Understanding how the structure of the material and its electrical properties translate into the behavior of the shield under different conditions is essential to ensure the optimal performance of electronic devices.

Dependence of effectiveness on structure and frequency

The primary issue is choosing the material according to the frequency range in which the shield is intended to operate. At low frequencies (tens to hundreds of MHz), minimizing air gaps in the material is most important. Even small breaks or gaps in the conductive mesh allow magnetic fields to penetrate, significantly reducing shielding effectiveness. In this range, materials with a dense fiber structure forming an almost continuous conductive surface work best.

At higher frequency bands (hundreds of MHz to GHz), the skin effect plays a key role. Here, high conductivity of fibers and their arrangement are important—thin, well-arranged conductive fibers create a layer through which alternating current can flow with minimal losses. Materials with greater thickness and good conductivity provide higher attenuation of magnetic waves.

Importance of openings, resistance, and conductivity

Openings in the structure of the material, even if small, act as channels that allow magnetic fields to pass through. Their size and distribution determine how much of the field “leaks” through the shield. Therefore, it is important to select materials with minimal porosity or apply additional layers to fill these spaces.

The surface resistance of the material is another important parameter. Low resistance promotes the flow of shielding current and increases the effectiveness of field attenuation. In practice, this means that even small changes in the composition or structure of fibers can noticeably impact shield performance.

Conductivity should be as high as possible, which is often achieved by using metallic fibers or conductive coatings. Carbon or nickel fibers are popular solutions that combine good mechanical properties with effective shielding.

Selecting the right shielding material requires a holistic approach, taking into account the frequency range of operation, the structure of the material, its conductivity, and the presence of openings. A well-chosen material allows optimal reduction of the impact of magnetic fields, which is crucial for protecting modern electronic devices against interference.

Summary: What influences effective magnetic field shielding?

Magnetic field shielding is one of the more challenging tasks in electromagnetic engineering. As we have shown throughout the article, the effectiveness of protection against interference depends on a complex combination of material, structural, and frequency-related properties.

Factors influencing shielding effectiveness:

• Electrical properties of the material: Parameters such as surface resistance (R’), internal inductance (L’), and capacitance (C’) determine how the material reacts to a varying magnetic field. Materials with low resistance and appropriately adjusted inductance attenuate the field more effectively.
• Structure of fibers and conductive mesh: The density and arrangement of conductive fibers are of great importance. Meshes with small openings allow less magnetic field penetration, and fiber arrangement affects the directionality of shielding.
• Mechanisms of field penetration: The magnetic field can penetrate the shield through inductive penetration and through air openings. Understanding the skin effect and the role of air gaps helps design a more effective shield.
• Field frequency: Shielding effectiveness changes with signal frequency. At low frequencies, continuity of the conductive surface is key, while at high frequencies conductivity and the skin effect dominate.
• Characteristics of tested materials: Comparison of six different shielding materials showed that the best results are achieved by those with high conductivity and minimal porosity, especially in the range up to 1.5 GHz.

Magnetic shielding requires not only the selection of the right material but also an understanding of its physical and electromagnetic properties. Advanced materials with conductive fibers represent a promising alternative to traditional metal shields, offering greater flexibility and ease of use.

When designing protection systems against magnetic fields, it is worth considering all the aspects discussed to ensure maximum protection of devices in an electromagnetic environment that is becoming increasingly complex and demanding.

Sources: How Do Magnetic Fields Penetrate Shielding Materials? Characterization of Shielding Materials October 26, 2023 Gunter Langer and Amirali Taghavi