Shielding Effect by Eddy Currents
Shielding Effect by Eddy Currents: Theoretical Foundations
Principle of Eddy Current Shielding
Professor, how does an aluminum enclosure shield a magnetic field?
Shielding by non-magnetic conductors (aluminum, copper) is achieved by counter magnetic fields generated by eddy currents. The principle differs from magnetic flux diversion using high-permeability materials (Permalloy).
Shielding effectiveness (flat plate):
$t$: plate thickness, $\delta$: skin depth. Higher frequency results in smaller $\delta$ and improved SE.
Does that mean shielding is ineffective at low frequencies?
Exactly. For a 50 Hz magnetic field, a 1 mm thick aluminum plate has $\delta \approx 12$ mm → SE ≈ 1 dB. Almost no shielding effect. High-permeability materials are required for low-frequency magnetic fields.
Summary
- Counter magnetic field by eddy currents — Shielding principle for non-magnetic conductors
- $SE \propto t/\delta$ — More effective at higher frequencies
- Low frequency — Conductor shields are ineffective. High $\mu_r$ materials are needed
The "Perfection" of a Faraday Cage — The Gap Between Shielding Theory and Reality
Theoretically, a completely closed conductor container (Faraday cage) can reduce internal electromagnetic fields to zero, but real shields inevitably have holes, slits, and joints that cause leakage. The shielding effectiveness by eddy currents is determined by the product of the shield material's conductivity, permeability, thickness, and frequency. For example, a 1 mm thick copper shield can theoretically achieve over 100 dB shielding effectiveness at 1 MHz. The role of eddy current FEM analysis is to bridge the gap between this theoretical value and measured values by modeling the effects of actual apertures and seams.
Computational Methods for Shielding Effect by Eddy Currents
Shielding Analysis with FEM
How do you evaluate the shielding effectiveness of an enclosure shield using FEM?
Calculate SE from the magnetic flux density ratio with/without the shield using frequency-domain eddy current analysis. Points to note:
- If shield thickness is less than $\delta$, at least 3 mesh layers are needed in the thickness direction
- Leakage from apertures (slits, holes) often becomes dominant
- Contact impedance at joints significantly degrades SE
How do you evaluate the effect of apertures?
If the maximum aperture dimension $l$ satisfies $l < \lambda/20$, its impact on shielding effectiveness is minor ($\lambda$: wavelength). For low-frequency magnetic fields, eddy current diversion through apertures is problematic. Apertures need to be modeled in 3D analysis.
Summary
- Calculate SE from B ratio — Comparison with/without shield
- Apertures are limiting — Leakage from slits/holes
- Joints — Contact resistance degrades SE
Numerical Calculation of Shielding Effectiveness — Choosing Between Transfer Matrix Method and FEM
There are two approaches for calculating the shielding effectiveness (SE) of electromagnetic shields: the Transfer Matrix Method (TMM) for idealized multi-layer flat plates and the Finite Element Method (FEM). TMM can quickly calculate analytically for uniform plates and is effective for preliminary design, but cannot be applied to realistic shields with holes and seams. FEM can accurately model complex shapes but has high computational cost. Therefore, a staged approach is standard in practice: "initial design of material/thickness with TMM → detailed evaluation of shape/apertures with FEM."