Electronics Guide

Electromagnetic Shielding Fundamentals

Electromagnetic shielding is the practice of reducing electromagnetic field strength in a region by blocking or attenuating the field with barriers made of conductive or magnetic materials. Shields work through two primary mechanisms: reflection of electromagnetic energy at the shield surface due to impedance mismatch, and absorption of energy as it penetrates the shield material. Understanding these mechanisms at a fundamental level enables engineers to predict shielding performance, select appropriate materials, and design effective enclosures for EMC compliance.

This article presents the core physics of electromagnetic shielding, beginning with the definition of shielding effectiveness and progressing through the individual loss mechanisms. We examine how wave impedance, skin depth, and material properties combine to determine overall shield performance. The distinctions between near-field and far-field shielding, as well as between electric and magnetic field shielding, are explored in detail. By mastering these fundamentals, engineers gain the insight needed to tackle complex shielding challenges with confidence.

Shielding Effectiveness Definition

Shielding effectiveness (SE) quantifies how well a shield attenuates electromagnetic fields. It is defined as the ratio of field strength without the shield to field strength with the shield in place, typically expressed in decibels:

SE (dB) = 20 log10(E0/E1) for electric fields

SE (dB) = 20 log10(H0/H1) for magnetic fields

where E0 and H0 are the field strengths without the shield, and E1 and H1 are the field strengths with the shield present. Positive values indicate attenuation; a shielding effectiveness of 40 dB means the field is reduced by a factor of 100.

Measuring Shielding Effectiveness

Shielding effectiveness can be measured by several standardized methods:

  • Shielded room method: A source antenna is placed inside a shielded enclosure, and field strength is measured outside. The SE is determined by comparing measurements with apertures open versus sealed.
  • Coaxial transmission line method: A material sample is placed in a coaxial fixture, and the attenuation of a propagating wave through the sample is measured. This method is convenient for material characterization but does not capture enclosure effects.
  • Free-space method: The sample is placed between transmitting and receiving antennas, and attenuation is measured. This approach works well for thin, flexible materials.
  • TEM cell method: A transverse electromagnetic cell provides a controlled field environment for measuring material or enclosure shielding effectiveness.

Each method has its own frequency range, sample size requirements, and accuracy characteristics. The choice depends on the application and the type of shield being evaluated.

Practical Shielding Effectiveness Values

Different applications require different levels of shielding effectiveness:

  • 10-30 dB: Minimal shielding, adequate for reducing interference in non-critical applications
  • 30-60 dB: Good shielding, typical of commercial electronic enclosures
  • 60-90 dB: Excellent shielding, required for sensitive instrumentation and some military applications
  • 90-120 dB: Very high shielding, needed for TEMPEST requirements and extremely sensitive measurements
  • Above 120 dB: Exceptional shielding, achievable only in specialized facilities with extreme attention to detail

These values represent ideal shield performance. Real-world enclosures with seams, apertures, and cable penetrations typically achieve 20-40 dB less than the intrinsic material shielding effectiveness.

Factors Affecting Shielding Effectiveness

Overall shielding effectiveness depends on multiple factors:

  • Material properties: Conductivity and permeability determine reflection and absorption
  • Shield thickness: Thicker shields provide more absorption
  • Frequency: Different mechanisms dominate at different frequencies
  • Source type: Electric field, magnetic field, or plane wave sources have different shielding characteristics
  • Distance from source: Near-field and far-field shielding behave differently
  • Apertures and seams: Openings can dominate shielding performance at high frequencies

The total shielding effectiveness is the result of complex interactions among these factors, which we examine in detail in the following sections.

Reflection Loss Mechanisms

Reflection loss occurs at the boundary between free space (or any low-conductivity medium) and a conductive shield material. The mechanism is fundamentally the same as optical reflection: when an electromagnetic wave encounters a medium with different intrinsic impedance, part of the wave energy is reflected back toward the source.

Impedance Mismatch and Reflection

The intrinsic impedance of a medium is the ratio of electric to magnetic field strength for a propagating plane wave. For free space:

eta0 = sqrt(mu0/epsilon0) = 377 ohms

For a good conductor with conductivity sigma at angular frequency omega:

eta_s = sqrt(j*omega*mu/sigma) = (1+j) * sqrt(omega*mu/(2*sigma))

The magnitude of this impedance is very small for good conductors. For copper at 1 MHz:

|eta_copper| = sqrt(2*pi*1e6 * 4*pi*1e-7 / (2*5.8e7)) = 0.00037 ohms

This enormous mismatch between free-space impedance (377 ohms) and conductor impedance (milliohms) causes most of the incident energy to be reflected at the surface.

Reflection Coefficient Calculation

The reflection coefficient for normal incidence is:

Gamma = (eta_s - eta0)/(eta_s + eta0)

Since eta_s is much smaller than eta0 for good conductors:

Gamma is approximately equal to -1

This means nearly all the incident wave is reflected with a 180-degree phase shift. The reflection loss R in decibels is:

R (dB) = 20 log10|1/(1-Gamma)| = 20 log10|(eta0 + eta_s)/(2*eta_s)|

For good conductors where eta_s is much smaller than eta0:

R (dB) = 20 log10(eta0/(4*eta_s))

Substituting the expression for conductor impedance:

R (dB) = 168 + 10 log10(sigma/(f*mu_r))

This formula shows that reflection loss increases as conductivity increases and decreases as frequency increases. High-conductivity materials like copper and aluminum provide excellent reflection loss.

Reflection Loss for Common Materials

At 1 MHz, typical reflection losses for various materials are:

  • Copper: Approximately 168 dB for plane waves
  • Aluminum: Approximately 166 dB for plane waves
  • Steel: Approximately 140-150 dB for plane waves (depends on composition)
  • Stainless steel: Approximately 130 dB for plane waves
  • Mu-metal: Approximately 120 dB for plane waves at this frequency

These values decrease by 10 dB for each decade increase in frequency. At 1 GHz, copper provides about 138 dB of reflection loss for plane waves.

It is important to note that these high reflection loss values apply to plane waves in the far field. Near-field sources, particularly magnetic field sources, have much lower wave impedance, resulting in significantly lower reflection loss. This is why magnetic field shielding at low frequencies is particularly challenging.

Double Reflection at Entry and Exit

When an electromagnetic wave enters a shield, reflection occurs at the front surface. The transmitted portion then propagates through the shield and encounters the back surface, where another reflection occurs. The wave impedance on both sides of the shield is typically the same (free space), so the exit reflection coefficient has the same magnitude but opposite sign.

The total reflection loss includes contributions from both surfaces. For a shield with air on both sides:

R_total = R_entry + R_exit

Each boundary contributes approximately the same reflection loss when the shield is thick enough that the wave inside is significantly attenuated before reaching the second surface. For thin shields, the two reflections can interact, leading to multiple reflection effects discussed later.

Absorption Loss Calculation

Absorption loss occurs as electromagnetic energy propagates through the conductive shield material. The wave is attenuated exponentially as induced currents dissipate energy as heat. This mechanism is particularly important for thick shields and at high frequencies.

Skin Depth and Field Decay

The skin depth delta is the distance over which the electromagnetic field amplitude decays to 1/e (approximately 37%) of its surface value:

delta = sqrt(2/(omega*mu*sigma)) = sqrt(1/(pi*f*mu*sigma))

where omega is the angular frequency, mu is the permeability, and sigma is the conductivity. For copper at 1 MHz:

delta_copper = sqrt(1/(pi*1e6*4*pi*1e-7*5.8e7)) = 66 micrometers

The field amplitude at depth z into the shield is:

E(z) = E0 * exp(-z/delta)

This exponential decay is rapid. At one skin depth, the field is at 37% of surface value; at two skin depths, 13.5%; at three skin depths, 5%; at five skin depths, less than 1%.

Skin Depth for Various Materials

Skin depth varies significantly with material and frequency. The following table shows skin depth at various frequencies:

Copper (sigma = 5.8 x 10^7 S/m, mu_r = 1):

  • 60 Hz: 8.5 mm
  • 1 kHz: 2.1 mm
  • 100 kHz: 0.21 mm (210 micrometers)
  • 1 MHz: 66 micrometers
  • 100 MHz: 6.6 micrometers
  • 1 GHz: 2.1 micrometers

Aluminum (sigma = 3.8 x 10^7 S/m, mu_r = 1):

  • 1 MHz: 82 micrometers
  • 100 MHz: 8.2 micrometers
  • 1 GHz: 2.6 micrometers

Steel (sigma = 7 x 10^6 S/m, mu_r = 100-1000 typical):

  • 60 Hz: 0.3-1 mm (depending on permeability)
  • 1 kHz: 0.08-0.25 mm
  • 1 MHz: 6-19 micrometers

High-permeability materials like steel have much smaller skin depths at low frequencies, making them effective for low-frequency magnetic field shielding.

Absorption Loss Formula

The absorption loss A in decibels for a shield of thickness t is:

A (dB) = 20 log10(exp(t/delta)) = 8.686 * (t/delta)

This simplifies to:

A (dB) = 8.686 * t * sqrt(pi*f*mu*sigma)

Key observations:

  • Absorption loss is proportional to shield thickness
  • Absorption loss increases with the square root of frequency
  • Higher conductivity and permeability increase absorption
  • Each skin depth of material provides approximately 8.686 dB of absorption loss

Practical Absorption Loss Values

For a 1 mm thick copper shield:

  • At 100 kHz: approximately 41 dB (thickness is about 4.8 skin depths)
  • At 1 MHz: approximately 131 dB (thickness is about 15 skin depths)
  • At 10 MHz: approximately 415 dB (theoretical; in practice, other effects dominate)

These calculations show that absorption loss quickly becomes very large at high frequencies, even for thin shields. The practical limitation at high frequencies is not material absorption but apertures and seams that bypass the solid material.

Material Selection for Absorption

When absorption is the primary shielding mechanism (such as for thick shields or high frequencies), material selection follows these guidelines:

  • Copper and aluminum: Excellent for general-purpose high-frequency shielding due to high conductivity
  • Steel: Provides higher absorption per unit thickness at low frequencies due to high permeability, despite lower conductivity
  • Mu-metal and similar alloys: Extremely effective at low frequencies for magnetic field absorption due to very high permeability
  • Conductive composites: Provide modest absorption; useful when weight or other mechanical properties are primary concerns

Multiple Reflection Effects

When an electromagnetic wave enters a shield, reflections occur at both the entry and exit surfaces. For electrically thin shields (thickness comparable to or less than one skin depth), these reflected waves can interact constructively or destructively, modifying the overall shielding effectiveness. This phenomenon is known as the multiple reflection correction factor.

Physics of Multiple Reflections

Consider a wave entering a thin shield:

  1. Part of the incident wave is reflected at the front surface; the rest enters the shield
  2. The wave propagates through the shield with some attenuation
  3. At the back surface, part of the wave exits the shield; the rest is reflected back into the material
  4. The internally reflected wave propagates back to the front surface, where it is again partially reflected and partially transmitted
  5. This process continues, with each bounce contributing to the total transmitted and reflected fields

For electrically thick shields (many skin depths), the internal reflections are so attenuated that they become negligible. For thin shields, the multiple reflections can significantly affect performance.

Multiple Reflection Correction Factor

The multiple reflection correction factor M is typically given by:

M (dB) = 20 log10|1 - exp(-2*t/delta) * Gamma^2|

where Gamma is the reflection coefficient at the shield-air interface and t is the shield thickness. This factor is:

  • Negative for electrically thin shields: Multiple reflections reduce shielding effectiveness because internally reflected waves can constructively combine with the transmitted wave
  • Approaches zero for thick shields: When t is greater than about 2 skin depths, the correction becomes negligible

For electric field (high-impedance) sources, the multiple reflection correction is typically negative for thin shields, reducing SE by up to 10-20 dB.

For magnetic field (low-impedance) sources, the correction can be positive, actually enhancing shielding effectiveness in thin shields.

When Multiple Reflections Matter

Multiple reflection effects are significant when:

  • Shield thickness is less than approximately 1.5 skin depths
  • Low frequencies are involved where skin depth is large
  • Thin foils or coatings are used as shields
  • Conductive plastics with low conductivity create large skin depths

For most practical metal shields at frequencies above a few hundred kHz, the absorption loss is large enough that multiple reflections can be ignored. However, at low frequencies (power line, audio) or with thin conductive coatings, the correction must be included for accurate SE predictions.

Total Shielding Effectiveness

The complete expression for shielding effectiveness combines all three factors:

SE (dB) = R + A + M

where:

  • R = Reflection loss (always positive)
  • A = Absorption loss (always positive)
  • M = Multiple reflection correction (can be positive or negative)

This additive relationship in decibels corresponds to multiplication of the individual attenuation factors in linear terms. The total SE represents the combined effect of all mechanisms operating on the electromagnetic wave as it interacts with the shield.

Near-Field Versus Far-Field Shielding

The effectiveness of a shield depends strongly on whether the source is in the near field or far field. This distinction affects the wave impedance of the incident field and consequently the reflection loss at the shield surface.

Field Region Boundaries

The boundary between near-field and far-field regions occurs at approximately:

r = lambda/(2*pi) = c/(2*pi*f)

where r is the distance from the source, lambda is wavelength, and f is frequency. At 1 MHz, this boundary is about 48 meters; at 100 MHz, about 0.48 meters; at 1 GHz, about 4.8 centimeters.

In the near field, the wave impedance varies with distance and source type. In the far field, the wave impedance equals the free-space value of 377 ohms, regardless of source characteristics.

Far-Field (Plane Wave) Shielding

In the far field, the incident wave is essentially a plane wave with wave impedance of 377 ohms. The shielding effectiveness formulas presented earlier for reflection and absorption loss apply directly. Key characteristics:

  • Wave impedance is constant at 377 ohms
  • Electric and magnetic fields are in phase
  • Both field components are attenuated equally by the shield
  • Shielding effectiveness can be calculated from material properties alone

Far-field shielding is conceptually simpler because the source geometry does not affect the wave impedance.

Near-Field Electric Source Shielding

Near an electric field source (high voltage, low current, high impedance), the wave impedance is much higher than 377 ohms. For a small electric dipole at distance r:

Z_wave = (lambda/(2*pi*r)) * 377 ohms = (c/(2*pi*f*r)) * 377 ohms

At distances much closer than lambda/(2*pi), this can be thousands of ohms. The consequences for shielding:

  • High wave impedance means larger mismatch with conductive shield (low impedance)
  • Reflection loss is higher than for plane waves
  • Even thin conductive shields are effective
  • Electric fields are relatively easy to shield

This is why almost any metal enclosure, even with significant apertures, provides good shielding against nearby electric field sources.

Near-Field Magnetic Source Shielding

Near a magnetic field source (high current, low voltage, low impedance), the wave impedance is much lower than 377 ohms. For a small current loop at distance r:

Z_wave = (2*pi*r/lambda) * 377 ohms = (2*pi*f*r/c) * 377 ohms

At close distances, this can be a fraction of an ohm. The consequences for shielding:

  • Low wave impedance approaches the impedance of conductive shields
  • Reflection loss is much lower than for plane waves
  • Shielding must rely primarily on absorption
  • Low-frequency magnetic fields are the most difficult to shield

This explains why power-frequency (50/60 Hz) magnetic fields from transformers and motors are notoriously difficult to shield. The skin depth in copper at 60 Hz is about 8.5 mm, requiring impractically thick shields for significant absorption.

Transition Region Effects

Between the near field and far field, wave impedance gradually transitions between the extreme values. Accurate shielding calculations in this region require knowledge of the actual source geometry and distance.

For practical shielding design:

  • If the shield is definitely in the far field (distance much greater than lambda/(2*pi)), use plane wave formulas
  • If the shield is definitely in the near field, identify whether the source is predominantly electric or magnetic
  • In the transition region, conservative design should use the lower of electric and magnetic field SE estimates

Electric Field Shielding Theory

Electric field shielding is generally easier than magnetic field shielding because electric fields have high wave impedance that mismatches strongly with conductive shields. Understanding the mechanisms involved helps in designing effective solutions for electrostatic and quasi-static electric field problems.

Electrostatic Shielding Principles

At DC and very low frequencies, electric field shielding works through the redistribution of charge on the shield surface. When an external electric field impinges on a conductor:

  1. Free charges in the conductor redistribute to cancel the external field inside
  2. Surface charges create an opposing field that exactly cancels the applied field within the conductor
  3. The interior of the conductor (and any enclosed cavity) is field-free

This is the principle of the Faraday cage. A complete enclosure of any conductor, regardless of thickness, provides perfect electrostatic shielding. The shield does not need to be thick or particularly conductive; even a thin metal foil or wire mesh works perfectly for static fields.

Quasi-Static Electric Field Shielding

At frequencies below about 1 MHz (depending on shield size), electric field shielding remains dominated by the Faraday cage effect. The time required for charge redistribution is short compared to the field oscillation period, so the shield continuously adjusts to cancel the external field.

Key considerations for quasi-static electric field shielding:

  • Completeness: Apertures allow field penetration proportional to their size
  • Grounding: The shield must be connected to a reference to allow charge flow; isolated shields can have their potential driven by external fields
  • Conductivity: Any reasonable conductor is adequate; the charge redistribution time constant is extremely short
  • Thickness: Not critical for electric field shielding; very thin foils are effective

High-Frequency Electric Field Shielding

At higher frequencies, the wave nature of the field becomes important, and shielding effectiveness is determined by reflection and absorption mechanisms. For electric field sources in the near field, the high wave impedance results in excellent reflection loss:

R (dB) = 20 log10(Z_wave/(4*|eta_s|))

where Z_wave is the source wave impedance (much greater than 377 ohms) and eta_s is the shield impedance. This can easily exceed 200 dB for good conductors close to electric field sources.

The practical limitations for high-frequency electric field shielding are:

  • Apertures and seams that allow field leakage
  • Cable penetrations that can carry the field through the shield
  • Cavity resonances that can enhance internal fields at certain frequencies

Electric Field Shield Design Guidelines

For effective electric field shielding:

  • Ensure continuity: Make the shield as complete as possible; minimize apertures
  • Bond seams properly: Seams should have low-impedance connections at intervals much smaller than wavelength
  • Ground the shield: Connect to circuit common or earth ground to provide a charge sink
  • Filter cable penetrations: Use feedthrough capacitors or filtered connectors
  • Any conductor works: Material selection is rarely critical for electric field shielding alone

Magnetic Field Shielding Principles

Magnetic field shielding presents fundamentally different challenges than electric field shielding. Magnetic fields have low wave impedance in the near field, minimizing reflection, and static magnetic fields cannot be blocked by any conductor. Effective magnetic field shielding requires different approaches depending on frequency.

Static Magnetic Field Shielding

DC and very low-frequency magnetic fields cannot be shielded by conductors alone. Unlike electric fields, magnetic fields penetrate any conductor as if it were not there (at DC). Shielding approaches for static magnetic fields include:

Flux shunting: High-permeability materials (mu-metal, permalloy, soft iron) provide a low-reluctance path for magnetic flux. The field preferentially flows through the high-permeability material rather than through the shielded region. Effectiveness depends on:

  • Permeability of the shielding material (higher is better)
  • Cross-sectional area of the shield (thicker walls provide more flux-carrying capacity)
  • Complete enclosure (any gap allows flux to leak through)
  • Avoiding magnetic saturation (field strength must be within material limits)

Bucking coils: Active cancellation using currents in coils to create an opposing magnetic field. This approach can provide very high attenuation in a localized region but requires power and control circuitry.

Low-Frequency AC Magnetic Field Shielding

At power-line frequencies (50/60 Hz) and low audio frequencies, magnetic field shielding relies on both flux shunting and eddy current effects:

Eddy current shielding: Time-varying magnetic fields induce eddy currents in conductive materials. These currents create opposing magnetic fields that partially cancel the applied field. Effectiveness depends on:

  • Frequency (higher frequencies induce larger eddy currents)
  • Conductivity (higher conductivity allows larger currents)
  • Shield geometry (closed paths for eddy currents are essential)

At 60 Hz, the skin depth in copper is about 8.5 mm. A 1 mm copper shield provides less than 1 dB of absorption loss. For effective 60 Hz shielding:

  • Use high-permeability materials for flux shunting
  • Consider multiple nested shields
  • Accept that very high attenuation is impractical

High-Frequency Magnetic Field Shielding

As frequency increases, eddy current shielding becomes increasingly effective. At frequencies where the skin depth is small compared to the shield thickness, even good conductors provide substantial magnetic field attenuation:

  • At 100 kHz, skin depth in copper is about 0.2 mm; a 1 mm shield provides about 40 dB absorption
  • At 1 MHz, skin depth in copper is about 0.07 mm; a 0.5 mm shield provides over 60 dB absorption
  • At 10 MHz and above, even thin foils provide substantial magnetic field shielding

High-permeability materials can enhance high-frequency magnetic shielding by providing both high absorption (due to reduced skin depth) and some flux shunting effect.

Magnetic Shield Design Guidelines

For effective magnetic field shielding:

  • Identify the frequency range: Approach varies dramatically with frequency
  • For DC/low-frequency: Use high-permeability materials in complete enclosures; consider multiple layers
  • For mid-frequencies (kHz range): Combine high permeability for flux shunting with adequate thickness for eddy currents
  • For high frequencies: Any good conductor with sufficient thickness relative to skin depth works well
  • Avoid saturation: Calculate whether field strength will saturate high-permeability materials
  • Minimize gaps: Any opening in a magnetic shield allows flux leakage
  • Consider active cancellation: For extreme requirements at low frequencies, bucking coils may be the only practical solution

Wave Impedance Considerations

Wave impedance is a key concept linking electromagnetic theory to practical shielding calculations. The ratio of electric to magnetic field strength in a propagating or quasi-static field determines how effectively various materials will reflect the incoming wave.

Defining Wave Impedance

Wave impedance Z is defined as the ratio of electric field strength to magnetic field strength:

Z = E/H

For a plane wave in free space, this equals the intrinsic impedance:

Z = eta0 = sqrt(mu0/epsilon0) = 377 ohms

For waves from localized sources, the wave impedance varies with distance and source type.

Wave Impedance of Elementary Sources

Electric dipole (rod antenna, high-voltage trace):

At distance r from a small electric dipole:

Z = 377 * (1 + 1/(j*k*r) + 1/(j*k*r)^2) / (1 + 1/(j*k*r))

where k = 2*pi/lambda = omega/c. In the near field (k*r much less than 1):

Z approximately equals 377/(k*r) = lambda/(2*pi*r) * 377 ohms

This is much greater than 377 ohms at close distances.

Magnetic dipole (current loop, transformer):

At distance r from a small current loop:

Z approximately equals 377 * k * r = (2*pi*r/lambda) * 377 ohms

This is much less than 377 ohms at close distances.

Wave Impedance and Reflection Loss

Reflection loss depends on the mismatch between source wave impedance and shield impedance:

R (dB) = 20 log10(|Z_wave + eta_s|/(4*|eta_s|))

For high wave impedance (electric field sources):

  • Large mismatch with low-impedance conductor
  • High reflection loss
  • Easy to shield

For low wave impedance (magnetic field sources):

  • Small mismatch with low-impedance conductor
  • Low reflection loss
  • Difficult to shield through reflection alone

Practical Wave Impedance Values

At various frequencies and distances, wave impedance varies dramatically:

Electric dipole at 1 MHz, 1 meter distance:

lambda = 300 m, k*r = 2*pi*1/300 = 0.021

Z approximately equals 377/0.021 = 18,000 ohms

Magnetic dipole at 1 MHz, 1 meter distance:

Z approximately equals 377 * 0.021 = 7.9 ohms

Either source in far field (any distance much greater than lambda/(2*pi)):

Z = 377 ohms

These dramatic differences in wave impedance explain why electric and magnetic field shielding require different approaches at low frequencies and short distances.

Implications for Shield Design

Understanding wave impedance guides shield design decisions:

  • Mixed-source environments: Design for the worst case (typically magnetic field sources)
  • Frequency-dependent behavior: A shield adequate for far-field sources may be inadequate for near-field magnetic sources at the same frequency
  • Distance matters: Moving the shield farther from a magnetic source increases wave impedance and improves reflection loss
  • Material selection: For magnetic sources, high permeability is more valuable than high conductivity

Skin Depth Calculations

Skin depth is perhaps the most important parameter in electromagnetic shielding calculations. It determines how rapidly fields decay within a conductor and directly affects absorption loss. Accurate calculation of skin depth for various materials and frequencies is essential for shield design.

Fundamental Skin Depth Formula

The skin depth delta is given by:

delta = sqrt(2/(omega*mu*sigma)) = sqrt(rho/(pi*f*mu))

where:

  • omega = 2*pi*f is angular frequency in rad/s
  • mu = mu0 * mu_r is absolute permeability in H/m
  • sigma is conductivity in S/m
  • rho = 1/sigma is resistivity in ohm-m
  • f is frequency in Hz

This formula applies when sigma is much greater than omega*epsilon (good conductor approximation), which is valid for all metals at EMC frequencies.

Skin Depth Calculation Examples

Copper at room temperature:

sigma = 5.8 x 10^7 S/m, mu_r = 1

delta_copper = 0.066 / sqrt(f) meters (f in Hz)

delta_copper = 66.1 / sqrt(f) mm (f in MHz)

Example calculations:

  • At 1 kHz: delta = 2.1 mm
  • At 1 MHz: delta = 66 micrometers
  • At 1 GHz: delta = 2.1 micrometers

Aluminum at room temperature:

sigma = 3.8 x 10^7 S/m, mu_r = 1

delta_aluminum = 0.082 / sqrt(f) meters (f in Hz)

Steel (typical):

sigma = 6 x 10^6 S/m, mu_r = 100 (varies widely)

delta_steel = 0.0065 / sqrt(f) meters (f in Hz)

Steel has about 1/10 the skin depth of copper due to its higher permeability.

Temperature Effects on Skin Depth

Conductivity decreases with increasing temperature, affecting skin depth:

sigma(T) = sigma(20C) / (1 + alpha*(T - 20))

where alpha is the temperature coefficient (about 0.004/degC for copper and aluminum). At 100 degrees C:

  • Copper conductivity drops to about 76% of room temperature value
  • Skin depth increases by about 15%

For high-temperature applications, this conductivity reduction should be factored into shielding calculations.

Permeability Effects on Skin Depth

Magnetic materials have much smaller skin depths due to their high permeability. However, permeability is frequency-dependent and amplitude-dependent:

  • Initial permeability (low field levels) can be 1000 or more for mu-metal
  • Permeability decreases at high frequencies (typically above 100 kHz for most materials)
  • Permeability decreases as field strength approaches saturation

For accurate calculations with magnetic materials:

  1. Obtain permeability versus frequency curves from manufacturer
  2. Verify field levels are well below saturation
  3. Use the appropriate permeability value for the operating frequency and field level

Skin Depth in Composite and Coated Materials

Many practical shields use composite materials or thin conductive coatings:

Conductive coatings: Zinc or nickel plating on steel, copper plating on plastic, conductive paints

  • If coating thickness is much greater than skin depth, shielding is determined by coating properties
  • If coating thickness is comparable to skin depth, both coating and substrate contribute
  • Calculate skin depth for both materials and compare to thicknesses

Conductive composites: Carbon-filled plastics, metal-flake loaded polymers

  • Conductivity is typically 10-100 S/m (much lower than metals)
  • Skin depths can be centimeters or more at low frequencies
  • Primarily useful for high-frequency shielding applications

Using Skin Depth in Shield Design

Practical shield design guidelines based on skin depth:

  • For greater than 40 dB absorption: Shield thickness should exceed 5 skin depths
  • For greater than 20 dB absorption: Shield thickness should exceed 2.5 skin depths
  • Minimum practical thickness: At least 1 skin depth to avoid multiple reflection degradation
  • Consider frequency range: Calculate skin depth at lowest frequency of concern
  • Account for variations: Material properties and thickness tolerances affect actual performance

Practical Considerations

While the theoretical foundations provide essential insight, real-world shielding involves many practical factors that can dominate performance.

Apertures and Seams

Any opening in a shield allows electromagnetic leakage. The shielding effectiveness of an aperture is approximately:

SE_aperture (dB) = 20 log10(lambda/(2*L))

where L is the maximum dimension of the aperture. A 3 cm slot provides only 20 dB of shielding at 1 GHz (lambda = 30 cm). For high shielding effectiveness:

  • Keep apertures small compared to wavelength
  • Use waveguide-below-cutoff principles for ventilation
  • Bond seams at intervals much smaller than lambda/10

Cable Penetrations

Cables passing through shields can completely defeat shielding effectiveness by carrying interference directly through the barrier. Proper treatment requires:

  • Filtering (feedthrough capacitors, filtered connectors, ferrite chokes)
  • 360-degree shield bonding for shielded cables
  • Minimizing cable length inside the shielded volume

Material and Construction Quality

Practical shielding effectiveness depends on:

  • Material conductivity and uniformity
  • Surface treatment (corrosion can degrade contact resistance)
  • Joint design (overlap, gasketing, fastener spacing)
  • Assembly workmanship

Conclusion

Electromagnetic shielding effectiveness results from the interplay of reflection, absorption, and multiple reflection mechanisms. Reflection loss depends on the impedance mismatch between the incident wave and the shield material, varying dramatically with wave impedance and thus with source type and distance. Absorption loss depends on skin depth, which decreases with increasing frequency, conductivity, and permeability. Multiple reflection corrections become important for electrically thin shields.

Understanding the differences between near-field and far-field shielding, and between electric and magnetic field shielding, is essential for selecting appropriate materials and designing effective enclosures. Electric field shielding is relatively straightforward, relying on the Faraday cage principle and the high reflection loss from impedance mismatch. Magnetic field shielding, particularly at low frequencies, requires careful attention to material selection, shield thickness, and flux path geometry.

While these fundamental principles provide the foundation for shield design, practical implementation must account for apertures, seams, cable penetrations, and construction quality. The best theoretical shielding effectiveness means little if practical details allow leakage through uncontrolled paths. Armed with both theoretical understanding and practical awareness, engineers can design shields that meet their EMC requirements reliably and cost-effectively.

Further Reading

  • Explore shielding materials and their selection criteria for various applications
  • Study enclosure design techniques for maintaining shielding integrity
  • Investigate gasket and seam treatment methods for high-performance shields
  • Learn about aperture control and waveguide-below-cutoff ventilation panels
  • Examine cable shielding and penetration treatment best practices