Reflection and absorption

When an electromagnetic field impinges on a conductive wall, part is reflected and part is absorbed into the wall. For that part of the wave that is reflected, the degree of reflection depends on the ratio of the impinging wave impedance to the barrier impedance. That part which is not reflected, will induce a current flow in that side of the wall, which reduces in intensity as it penetrates into the wall. The remaining current flow which reaches the far side is then reflected back into the barrier, and the surface current density results in an attenuated transmitted field. Shielding effectiveness - the ratio of impinging to transmitted field strengths - of a solid conductive barrier of infinite extent can therefore be expressed as the sum of reflection, absorption, and re-reflection losses:

SE(dB)          =   R(dB) + A(dB) + B(dB)          (1)

The re-reflection loss B is insignificant in most cases where absorption loss A is greater than 10dB. A itself depends on the barrier thickness and its skin depth (see below). At high frequencies, it becomes the dominant term. Different materials (such as steel or aluminium) will exhibit some variation in values for both skin depth and reflection loss, but these variations are rarely significant enough to dominate the choice of material for a particular shielding application.

This description assumes a thin conducting barrier of infinite extent, that is, one with no edges. It also assumes negligible interaction of the shield with the radiating source. And in order to use it, you must know the wave impedance of the source being shielded. These restrictions mean that its practical use is limited.

An alternative view is to think of the shield as a plane, folded around an enclosed volume to protect it by providing a barrier to propagating fields in either direction. A prime (but not the only) function that it performs is to provide a surface for current to flow across, so that the current sheet tends to oppose the undesired fields. This is the same as the "shorted turn" effect in transformers: the magnetic flux from an impinging field induces current in a conductor wrapped around the region of interest, which itself induces an opposite and nearly equal flux within the region. This dramatically reduces magnetic coupling to the region while at the same time dissipating power in the conductor. The effectiveness as a shielding method depends on good conductivity. A full shield provides the same effect in three dimensions, for fields impinging from any direction.

The shield also acts as a conducting surface to terminate electric fields and prevent them from propagating across the barrier. Again, its effectiveness in this aspect depends on good conductivity.

Skin depth and the skin effect

As a second effect, in a perfect shield the skin effect separates the inner and outer surface currents. The skin depth d is an expression of the electromagnetic property which tends to confine AC current flow to the surface of a conductor, becoming less as frequency, conductivity or permeability increases. The current density is attenuated ("absorbed") by 8.6dB (1/e) for each skin depth of penetration, so the absorption loss is easily expressed for a material of thickness t as

A          =          8.6·(t/δ) dB           (2)

Skin depth for a given conductive material is:

δ  =  K · 1/√(μ_r·σ_r·F)          (3)

where K = 2.6 for inches or 6.61 for cm, and μ_r is relative permeability, σ_r is relative conductivity (both = 1 for copper) and F is in Hz

A third important effect, not directly related to current flow, is that the shield provides a boundary for the termination of the electric (as opposed to magnetic) component of impinging fields. This is another way of describing the reflection loss of high impedance fields: faced with a low impedance at the boundary, the high impedance field is reflected, while a low impedance field sees a lesser discontinuity and so experiences less reflection.

Enclosure resonance

Both radiated emissions from, and RF coupling into, a screened enclosure are modified by the fact that a conductively enclosed volume also forms a resonant cavity. At the resonant frequencies the field distribution within the cavity reaches a peak, maximum current flows within the walls and hence maximum coupling occurs through the apertures of an imperfect enclosure. Consequently, shielding effectiveness degrades at the resonances.

The resonant frequencies are determined by the electromagnetic wave modes supported by the cavity. For an empty rectangular cavity, resonances occur at

F          =      150·√{(k/l)² + (m/h)² + (n/w)²} MHz            (4)

where l, h, w are enclosure dimensions in metres and k, m and n are positive integers, only one of which may be zero.

The lowest frequency shows the strongest resonance and is given by (k, m, n = 1,0,1) if l and w are the largest dimensions. Filling the cavity with for example circuit boards and wiring will detune these resonances, reducing their amplitudes and altering their frequencies, but will not remove them entirely. The graph shows the use of an analytical model to calculate the shielding effectiveness of a box of a size typical of rack-mounted enclosures, with a display window in the front. This shows that shielding effect differs depending on how far into the box the measuring point (p) is located, and it also shows that the shielding effectiveness becomes negative – i.e., the field inside the box is higher than the incident field – at the box resonances.

Ken Wyatt has created a simple demonstration of enclosure resonance in this easy-to-read article.

Try your own calculation for skin depth, based on equation (3):

And for the first few resonant frequencies of an empty oblong screened box, based on equation (4):

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