Shielding Effectiveness (SE) Analysis
Theory: absorption, reflection and gaps
Overview
We put the board in a metal case but still failed radiated emissions at a few hundred MHz. Doesn't enclosing it in metal block everything?
The sheet itself should block plenty. The problem is almost always the gaps — lid seams, vents, connector and cable holes. As a gap's length approaches half a wavelength, the gap acts like an antenna and lets waves through. Thinking of shielding effectiveness as material absorption, reflection and leakage through gaps makes clear what to fix.
Decomposing shielding effectiveness
$E_0$ is the field without the shield and $E_s$ with it. $A$ is absorption loss while passing through the material, $R$ is reflection loss at the surfaces, and $B$ corrects for multiple internal reflections — negligible when the sheet is much thicker than the skin depth, but negative (reducing SE) when it is thin.
Absorption loss and skin depth
Skin depth $\delta$ is the depth at which the field falls to about 37% (1/e) inside the material; it gets shallower with higher frequency, permeability and conductivity. Each skin depth of thickness attenuates about 8.7 dB.
Reflection loss
Reflection loss for a plane wave far from the source. $\mu_r$ is relative permeability and $\sigma_r$ conductivity relative to copper. For magnetic fields near the source the wave impedance is low, so reflection loss is much smaller — which is why low-frequency magnetic fields are hard to shield.
Faraday's cage
In 1836 Faraday sat inside a room lined with metal foil and confirmed that an electroscope inside did not respond even to large discharges outside. Because a conducting enclosure cancels the field inside, such a space is called a Faraday cage. But that describes static fields; for high-frequency waves the condition is that mesh openings and gaps be small compared with the wavelength. A microwave-oven window's metal mesh contains 2.45 GHz microwaves (wavelength about 12 cm) while passing light because its holes are only a few millimetres.
Worked examples
Example 1: absorption loss by material and frequency
| Material | 1 kHz: skin depth / absorption | 100 kHz | 10 MHz |
|---|---|---|---|
| Copper 0.1 mm | 2.09 mm / 0.4 dB | 0.209 mm / 4.2 dB | 0.021 mm / 41.6 dB |
| Aluminium 1 mm | 2.68 mm / 3.2 dB | 0.268 mm / 32.5 dB | 0.027 mm / 325 dB |
| Steel 1 mm (μr = 1000 assumed) | 0.209 mm / 41.6 dB | 0.021 mm / 416 dB | — |
At low frequency, thin copper and aluminium are thinner than the skin depth and absorb little. Steel's high permeability gives about 42 dB for 1 mm even at 1 kHz — though steel permeability varies greatly with frequency and field strength, so μr = 1000 is only a low-frequency guide. Above 10 MHz, any metal sheet far exceeds 100 dB, and the sheet itself effectively stops mattering.
Example 2: leakage through slots
| Slot length | 100 MHz | 300 MHz | 1 GHz |
|---|---|---|---|
| 100 mm | 23.5 dB | 14.0 dB | 3.5 dB |
| 30 mm | 34.0 dB | 24.4 dB | 14.0 dB |
| 10 mm | 43.5 dB | 34.0 dB | 23.5 dB |
The sheet gives over 100 dB, yet one 100 mm gap drops it to 3.5 dB at 1 GHz!
Right. Shielding is only as good as its weakest point. Half a wavelength at 1 GHz is 150 mm, so a 100 mm gap is nearly transparent. Cutting gap length by 10 improves SE by about 20 dB, so tighter screw spacing and conductive gaskets that break seams into short segments work well. Multiple identical gaps also hurt — about 6 dB worse for four times as many and about 20 dB for a hundred — so vents are better as deep honeycomb cells than as many shallow holes.
Analysis and design practice
Analysis cautions
- Model the gaps: an idealised box without seams and screw spacing greatly overestimates SE.
- Thin sheets as surface conditions: meshing the skin depth explodes the element count; model thin conductors with surface-impedance or thin-layer boundary conditions.
- Enclosure resonance: the box interior is a cavity resonator, and SE drops sharply at resonant frequencies.
- Cable penetrations: a cable through the shield carries noise outside like an antenna; include feedthrough filters and 360° braid bonding in the model.
Evaluation steps
- Estimate absorption and reflection by formula to confirm material and thickness.
- List gaps, vents and holes, and bound SE by the longest gap.
- Check enclosure resonances and gap effects with 3D electromagnetic analysis.
- Measure a prototype; if it differs from analysis, suspect contact at the gaps.
“The paint killed the shielding”
A prototype passed, yet production units were over 10 dB worse in radiated emissions — a common story. Investigation showed the production cases were painted right into the seams, so the lid and body were not electrically connected. Paint is an insulator, so contact happens only at the screws, and the spans between screws become long gaps. Leave seams unpainted or ensure contact with conductive gaskets. Analyses tend to assume perfect contact, so check against the production specification too.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Judging by sheet values only | Gap leakage missed | Bound SE by the longest gap |
| Thin copper for LF magnetic fields | Hardly any effect | High-μ material or thick conductor |
| Assuming perfect seam contact | SE overpredicted | Model screw spacing and contact |
| Ignoring enclosure resonance | Sudden dips at certain frequencies | Compute cavity resonances |
| Ignoring cable penetrations | Noise escapes the box | Feedthrough filters and 360° bonding |
I'd like to try skin depth and gap effects myself.
Try the skin depth calculator and skin effect simulator for skin depth, and the waveguide mode tool for the cutoff idea behind gaps and apertures. Related measures are covered in radiated emission, grounding and bonding, near-field coupling and cable crosstalk.
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