EMI, EMC, and Shielding Shielding and Enclosure Design Informational

How do I calculate the shielding effectiveness of an enclosure at a given frequency?

Shielding effectiveness (SE) of an enclosure is calculated by combining three mechanisms: absorption loss (A), reflection loss (R), and a correction factor (B) for thin shields: SE = A + R + B (dB). For most practical shields at microwave frequencies: SE ≈ A + R (B is negligible for thick shields). (1) Absorption loss: A = 8.686 × t/delta (dB), where t is the shield thickness and delta is the skin depth. delta = sqrt(2/(omega × mu × sigma)) = sqrt(1/(pi × f × mu_r × mu_0 × sigma)). For copper (sigma = 5.8e7 S/m, mu_r = 1) at 1 GHz: delta = 2.09 um. For t = 0.5 mm (500 um): A = 8.686 × 500/2.09 = 2078 dB. Absorption is dominant for solid metal shields above 1 MHz. (2) Reflection loss: R = 20×log10(|eta_0/(4×eta_s)|) (dB), approximation for plane wave. eta_0 = 377 ohms (free space impedance). eta_s = sqrt(j×omega×mu / sigma) (shield surface impedance). For copper at 1 GHz: |eta_s| = 0.026 ohms. R = 20×log10(377/(4×0.026)) = 20×log10(3625) = 71 dB. (3) Aperture leakage: the actual SE of a real enclosure is limited by apertures (holes, slots, seams, cable penetrations), not by the solid metal walls. SE_aperture ≈ 20×log10(lambda/(2×d_max)), where d_max is the maximum dimension of the largest aperture. For a 1 cm slot at 10 GHz (lambda = 30 mm): SE_aperture = 20×log10(30/(2×10)) = 3.5 dB. The aperture limits the enclosure SE to 3.5 dB regardless of the wall material. The overall SE = minimum(SE_wall, SE_aperture). In practice: SE_wall > 100 dB for any solid metal wall above 1 MHz. The enclosure SE is almost always limited by the apertures.

Category: EMI, EMC, and Shielding

Updated: April 2026

Product Tie-In: Enclosures, Gaskets, Absorbers, Filters

Shielding Effectiveness Calculation

Understanding SE calculation is essential for designing enclosures that meet EMC requirements. The calculation identifies whether the shield material or the apertures are the limiting factor.

Skin Depth and Absorption

The skin depth determines how quickly the electromagnetic wave attenuates as it penetrates the shield: delta = 1/sqrt(pi × f × mu_r × mu_0 × sigma). Skin depths for common materials at selected frequencies: Copper: 1 MHz: 66 um. 100 MHz: 6.6 um. 1 GHz: 2.09 um. 10 GHz: 0.66 um. Aluminum: 1 MHz: 84 um. 1 GHz: 2.65 um. Steel (mu_r = 200): 1 MHz: 3.3 um. 1 GHz: 0.1 um. Mumetal (mu_r = 20,000): 60 Hz: 0.35 mm. 1 kHz: 0.085 mm. The absorption per skin depth is 8.686 dB (the field magnitude decreases by e^(-1) = 0.368). For a 0.5 mm copper shield at 1 GHz: number of skin depths = 0.5e-3 / 2.09e-6 = 239 skin depths. Absorption = 239 × 8.686 = 2076 dB. This is absurdly high: the solid copper wall is a nearly perfect shield. Even at 60 Hz: copper skin depth = 8.5 mm. A 0.5 mm copper wall = 0.059 skin depths. Absorption = 0.059 × 8.686 = 0.5 dB. Very poor magnetic shielding at 60 Hz. This is why mumetal is needed for low-frequency magnetic shielding.

Aperture Analysis

Real enclosures have openings that limit the SE: (1) Single aperture: SE ≈ 20×log10(lambda/(2×d)) for d < lambda/2. At d = lambda/2: SE = 0 dB (the aperture resonates and radiates efficiently). Below lambda/2: SE increases at 20 dB per decade of frequency decrease. (2) Multiple apertures: N identical apertures in a row (array): SE_array = SE_single - 10×log10(N). For 10 ventilation holes of 3 mm diameter: SE_array = SE_single - 10 dB. At 10 GHz (lambda = 30 mm, d = 3 mm): SE_single = 20×log10(30/6) = 14 dB. SE_array = 14 - 10 = 4 dB. Very poor shielding. (3) Slot (long narrow opening): a slot of length L and width W: SE ≈ 20×log10(lambda/(2×L)). The slot has much lower SE than a round hole of the same area because the slot length determines the coupling (the longest dimension is the effective aperture dimension). A 10 cm slot at 1 GHz (lambda = 300 mm): SE = 20×log10(300/(2×100)) = 3.5 dB. Very poor at 1 GHz. At 100 MHz (lambda = 3000 mm): SE = 20×log10(3000/200) = 23.5 dB. Better at lower frequencies. (4) Mitigation: waveguide-below-cutoff (WBC) panels: arrays of small tubes (honeycomb) where each tube acts as a waveguide below cutoff. The cutoff frequency of a circular tube: f_c = 1.841×c/(pi×d). For d = 3 mm: f_c = 58.6 GHz. Below 58.6 GHz: the tube attenuates the wave exponentially. The attenuation per unit length: A = 27.3/d (dB/length for d in mm). For a tube 10 mm deep: A = 27.3 × 10/3 = 91 dB at frequencies well below cutoff. This provides excellent SE while allowing airflow.

Practical SE Estimation

For a real enclosure: (1) Identify all apertures: ventilation holes, cable entry points, seam gaps, display windows, LED holes, and connector cutouts. (2) Find the largest aperture dimension (d_max). (3) Calculate SE_aperture = 20×log10(lambda/(2×d_max)). (4) If the shield material is solid metal (any metal > 0.1 mm thick): SE_wall > 80 dB at frequencies above 1 MHz. SE_wall is not the limiting factor. (5) SE_enclosure ≈ SE_aperture (limited by the largest aperture). To improve SE: reduce the maximum aperture dimension (use smaller holes, add gaskets to seams, use waveguide panels for ventilation), bond all cable shields 360° to the enclosure wall, and use conductive gaskets at all panel joints and access doors.

Shielding Effectiveness Equations

SE = A + R + B (total, dB)
δ = √(1/(πfμ₀μᵣσ)) skin depth
A = 8.686·t/δ dB (absorption)
R ≈ 20log₁₀(η₀/4η_s) dB (reflection)
SE_aperture = 20log₁₀(λ/2d) dB

Common Questions

Frequently Asked Questions

What SE do I need to pass FCC Part 15?

FCC Part 15 specifies maximum radiated emission levels, not SE directly. The required SE depends on: the internal emission level of your circuit, the test distance (3 m or 10 m), and the FCC emission limit at each frequency. Rule of thumb: if your circuit generates emissions 20-40 dB above the FCC limit (common for high-speed digital circuits with clocks > 100 MHz): you need SE > 20-40 dB at the emission frequencies. For most commercial electronics: SE > 30 dB from 30 MHz to 1 GHz provides adequate margin. At higher frequencies (1-6 GHz): SE > 20 dB is usually sufficient (emissions tend to decrease with frequency). The enclosure SE is typically verified by pre-compliance testing (measuring radiated emissions with and without the enclosure).

How do I handle cable penetrations?

Every cable entering the enclosure is a potential SE leak: (1) Unshielded cables (power, digital): use feedthrough EMI filters. A pi-filter (C-L-C) at the enclosure wall provides 40-60 dB attenuation to conducted emissions. (2) Shielded cables (coaxial, shielded data): bond the cable shield 360° to the enclosure wall using a bulkhead connector or shield clamp. A pigtail ground (grounding only the shield wire): 20-30 dB worse than 360° bonding. (3) Fiber optic cables: inherently immune to EMI (no metallic conductor). Use fiber for data connections whenever possible. (4) Power cables: use ferrite chokes (common-mode) and feedthrough capacitors (differential-mode) at the enclosure entry. (5) All penetrations should be on one face of the enclosure (to minimize the coupling paths between penetrations and sensitive circuits inside).

Does paint or anodizing affect SE?

Yes, significantly. Paint and anodizing create an insulating layer on the metal surface. This layer: (1) Does not affect the SE of the solid panel (the electromagnetic wave still penetrates the metal underneath). (2) Severely degrades the SE at seams and joints: the insulating layer prevents metal-to-metal contact between mating panels. Without metal contact: the seam acts as an open slot (SE determined by slot dimensions). Even a 10 um paint layer can reduce the seam SE from > 60 dB to < 20 dB. (3) Mitigation: mask paint and anodizing from all mating surfaces where EMI gaskets or shield contacts are needed. Use conductive paint or conductive anodize (chromate conversion) if full-surface conductivity is needed. Verify the surface resistance of coated surfaces: for good SE at seams: surface resistance < 10 milliohms/square.

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