Electromagnetic Shielding — Faraday Cages and Skin Depth Physics

1. The Faraday Cage: Electrostatics Inside a Conductor

In 1836, Michael Faraday constructed a large cube lined with tinfoil, climbed inside, and subjected it to intense electrical discharges from an electrostatic generator. Using an electroscope, he measured zero electric field inside the enclosure — confirming experimentally what Gauss's law predicts theoretically.

The mechanism is straightforward: free electrons in any conductor redistribute themselves in response to an external electric field. Electrons migrate toward the region where the external field points inward and away from the region where it points outward. This redistribution continues until the internal field produced by the surface charges exactly cancels the external field everywhere inside the conductor material. Because the net internal field is zero, any cavity enclosed by the conductor is shielded from external fields.

Gauss's law makes this rigorous. Choose a Gaussian surface lying just inside the surface of a conductor. In electrostatic equilibrium, E = 0 everywhere inside the conducting material. Therefore the flux through the Gaussian surface is zero, and the enclosed charge is zero — all free charge resides on the outer surface of the conductor.

The surface charge density on the outer surface is related to the normal component of the electric field just outside: σ = ε₀ · E_n. The shape of the enclosure is irrelevant — any closed conducting surface, regardless of geometry, shields its interior from external electrostatic fields. This generalisation is often overlooked: the cage need not be spherical, cubic, or symmetric in any way.

2. Skin Depth: AC Fields and Eddy Currents

Static (DC) shielding is perfect for any conductor: even a thin foil provides complete shielding from static electric fields. Time-varying (AC) electromagnetic fields present a different challenge: the shield must attenuate the wave within the conducting material, and this depends on how deeply the field penetrates before being absorbed.

When a time-varying magnetic field threads through a conductor, Faraday's law induces circulating eddy currents that, by Lenz's law, oppose the change in flux. These currents dissipate energy as heat and produce a magnetic field that partially cancels the external field. The result is exponential attenuation of field amplitude with depth into the conductor.

Combining Maxwell's equations with Ohm's law (J = σE) and assuming sinusoidal fields, the penetration depth at which amplitude falls to 1/e (~37%) of its surface value is the skin depth:

For copper (σ = 5.8 × 10⁷ S/m, μ ≈ μ₀):

• At 60 Hz: δ = 8.5 mm
• At 1 MHz: δ = 0.065 mm (65 µm)
• At 10 GHz: δ = 0.00065 mm (0.65 µm)

Higher frequency, higher permeability, and higher conductivity all reduce skin depth, improving high-frequency shielding. For low-frequency magnetic shielding (power-line frequencies), high-permeability materials like mumetal (μ_r ~ 80,000) are far more effective than copper because the large μ reduces δ even at 50/60 Hz.

3. Shielding Effectiveness

Shielding effectiveness (SE) quantifies how much a shield reduces field strength. It is expressed in decibels as the ratio of the field without the shield to the field with the shield in place:

In general, the total SE of a solid conducting shell has three contributions: absorption loss A, reflection loss R, and a multiple reflection correction M:

Absorption loss represents energy dissipated as the wave travels through the shield material:

Each skin depth of material thickness adds about 8.7 dB of absorption. For a 1 mm copper sheet at 1 MHz (δ = 0.065 mm), absorption loss alone exceeds 130 dB.

Reflection loss arises because the large impedance mismatch between free space (η₀ = 377 Ω) and metal (η_m much less than 1 Ω) causes most incident energy to be reflected at the surface:

The multiple reflection correction M accounts for re-reflection between the two surfaces of the shield. For thick shields (t >> δ), M is negligible. For thin shields (t < δ), M can reduce the total SE significantly and must be included.

In practice, a 1 mm copper sheet at 1 MHz provides SE greater than 100 dB — a field attenuation factor exceeding 10⁵. This far exceeds the requirements of most civilian applications.

4. Aperture Effects and Resonance

Any opening in a shield — a ventilation slot, a seam, a cable entry, a display window — degrades shielding effectiveness. An aperture acts as a slot antenna that can both radiate energy out of and couple energy into the shielded enclosure.

The critical parameter is the relationship between aperture size and wavelength. A slot of length L resonates when L = λ/2 (half-wave resonance), at which point it radiates maximally. For slots shorter than resonance, SE is reduced by approximately:

At exact resonance (L = λ/2), shielding effectiveness drops to near zero at that frequency — the aperture effectively becomes transparent. The practical design rule is to keep the maximum aperture dimension below λ/20 for the highest frequency of concern.

When ventilation is required, engineers use honeycomb waveguide-below-cutoff panels: arrays of small circular tubes with diameter d. The cutoff frequency of each tube is:

Below cutoff, the wave is evanescent and attenuates exponentially along the tube. This provides high SE while allowing airflow.

5. MRI Rooms and the Radiofrequency Shield

Magnetic resonance imaging scanners operate by detecting tiny radio-frequency signals emitted by hydrogen nuclei precessing in a strong magnetic field. The operating frequency scales with field strength: a 1.5 T scanner operates at 64 MHz, a 3 T scanner at 128 MHz, and a 7 T scanner at 300 MHz.

This RF signal is extraordinarily weak — easily corrupted by external interference from mobile phones, FM radio, or nearby electronic equipment. To protect it, every MRI suite is enclosed in a Faraday cage: copper or aluminium panels lining the floor, all four walls, and the ceiling, forming a completely enclosed conductive shell.

Key engineering requirements include:

• Electrical continuity: every panel must be bonded to its neighbours with conductive gaskets or overlapping copper tape. A single poorly bonded joint can degrade SE by 30–40 dB.
• Filtered penetrations: every power cable, data cable, HVAC duct, water pipe, and fire-suppression pipe that crosses the shield boundary must pass through a waveguide feedthrough or LC filter that blocks RF while passing the desired function.
• Door design: the RF door uses multiple rows of beryllium-copper finger stock that compress against the frame to maintain electrical continuity when closed.
• Gradient coil shielding: a separate inner copper shield surrounds the gradient coils to reduce eddy currents in the superconducting cryostat caused by rapidly switching gradient fields.

The required SE is typically 100 dB at the operating frequency. Well-engineered RF rooms routinely achieve 80–120 dB in practice, verified by sweep testing with calibrated antennas before scanner installation.

6. Microwave Ovens: A Faraday Cage for 2.45 GHz

A domestic microwave oven operates at 2.45 GHz (λ = 12.2 cm), a frequency chosen to be in a globally allocated ISM (industrial, scientific, medical) band. Water molecules absorb strongly at this frequency due to rotational resonance, converting microwave energy to heat.

The metal cavity of the oven is a near-perfect Faraday cage — except for the door. The door must be transparent to visible light (so you can see your food) but opaque to 2.45 GHz radiation (for safety). This is achieved with a perforated metal mesh with hole diameter approximately 1 mm and spacing approximately 1.5 mm.

The physics follows directly from below-cutoff waveguide theory. For a circular aperture of radius a, the cutoff frequency is:

The mesh provides more than 40 dB of shielding at 2.45 GHz, reducing 800 W of internal power to less than 0.8 mW at the outer mesh surface — well below the 1 mW/cm² safety limit at 5 cm distance. Visible light (λ = 400–700 nm) passes freely through the same holes because the holes are enormous (by a factor of ~10,000) compared to optical wavelengths.

Inside the cavity, the microwave sets up standing wave resonant modes (TM and TE modes). The turntable rotates food through the resulting hot and cold spots, averaging the power distribution for more uniform heating.

7. EMC Testing: Anechoic and Shielded Chambers

Electromagnetic compatibility (EMC) testing verifies that electronic products neither emit excessive interference nor malfunction in the presence of external fields. Key regulatory standards include FCC Part 15 (United States), CISPR 22/32 (European CE marking), and MIL-STD-461 (military equipment).

Several shielded chamber types are used depending on the measurement required:

Fully Anechoic Room (FAR)

A shielded room lined with ferrite tiles (low-frequency absorber) and pyramidal RF absorber foam (high-frequency absorber). SE exceeds 100 dB across a wide frequency range. The absorber lining prevents reflections, creating a free-space-like measurement environment from 30 MHz upward. This is used for radiated emissions and immunity testing to commercial standards.

Semi-Anechoic Chamber

Absorber on the walls and ceiling but a conductive metal ground plane on the floor. This simulates the conditions of an Open Area Test Site (OATS) above a ground plane, and is the reference environment for many FCC and CISPR measurements. It is the most common type in commercial EMC labs.

Reverberation Chamber

A highly conductive room with all walls reflective (no absorber). A rotating stirrer creates a statistically uniform, isotropic field distribution over time. Used for radiated immunity testing: exposing equipment to statistically high field levels in all polarisations simultaneously. Much more efficient for immunity testing than anechoic chambers.

Pre-compliance testing uses compact shielded rooms with SE of 60–80 dB, allowing manufacturers to conduct in-house testing and catch problems before committing to expensive formal testing at accredited laboratories.

8. Military TEMPEST Shielding

TEMPEST is a US/NATO codename for security standards governing unintentional electromagnetic emanations from electronic equipment that could reveal classified information to a distant adversary — a threat formally known as compromising emanations.

The threat became public in 1985 when Dutch engineer Wim van Eck published a paper demonstrating that the video signal of a standard CRT monitor could be reconstructed from its electromagnetic emissions at distances exceeding 100 metres using equipment costing approximately $15. The technique, now called Van Eck phreaking, showed that classified information displayed on screen could be remotely read without any physical access to the facility.

TEMPEST specifications define shielding requirements across a very wide frequency range:

• Standard: NSTISSAM TEMPEST/1-92 specifies SE > 80 dB at frequencies from 1 kHz to 10 GHz
• Equipment on the NSA/CSS Evaluated Products List (EPL) has been certified to meet these requirements

The zone model divides space around a TEMPEST facility into concentric regions:

• Zone 0: Inspection zone — maximum 1 metre from equipment, highest SE required
• Zone 1: Shielded area — up to 20 metres, intermediate SE
• Zone 2: Controlled area — up to 100 metres, minimum SE

Modern threats have made TEMPEST more relevant than ever. Software-defined radio (SDR) receivers available for under $30 can receive and decode signals across gigahertz of bandwidth simultaneously. High-sensitivity antennas and digital signal processing allow recovery of emanations at greater distances and from more complex signals than van Eck originally demonstrated.