Shielding theory--Cabinets, cubicles and chambers

Shielding effectiveness

Shielding effectiveness is defined as the ratio of the field strength impinging on a shielding barrier to the field strength propagated away from the other side of the barrier.

It is calculated from measurements of the coupling between two antennas set at a fixed distance from each other, over a range of frequencies, both with and without the shielding in place around one of them.

This simple description belies the complexities both of real shielding effectiveness measurements, and of the variables that affect shielding performance even in an ideal geometrical situation.

One variant of classical shielding theory uses the "transmission line analogy" to describe how a shield barrier works. The impinging wave with its characteristic wave impedance is analogous to a wave propagating along a transmission line: it encounters a barrier of a different characteristic impedance, some of the wave is reflected and some is absorbed in the body of the barrier. The attenuated wave is further reflected at the far side of the barrier, and the remainder propagates into free space beyond the barrier. This process is shown conceptually and it results in the equation:

SE(dB) = SR(dB) + SA(dB) + SMR(dB)

... where S R is the total contribution from reflection at each surface.

Absorption S A is a function of frequency and material and is described in terms of skin depth through the barrier (). It is independent of the nature of the field source. SMR is negligible unless S A is low, since multiple reflections are attenuated on each pass through the barrier.

Reflection

This leaves S R, which can be given by:

Both Z 0 and Z M are frequency dependent. Z M is a function of the material but will always have a low value, for a conductive barrier. Z 0 depends on the nature of the source; we can discuss it for three extreme conditions, but real shielding problems fall somewhere within the extremes, and are rarely calculable.

Near field of an electric dipole

In this case the wave impedance Z 0 is high but falling with frequency and distance from the source. Very high reflective attenuation (>200dB) is theoretically possible at low frequencies and close to the source. This is described as S E. Near field of a magnetic dipole

Here, the wave impedance is low but increasing with frequency and distance from the source. For attenuation (SM), the reverse of the previous situation holds: less than 10dB is possible at low frequencies (e.g. 50Hz) and close to the source.

Far field, plane wave

The far field condition implies that the source is at a distance greater than X/2rt from the barrier. In this case, Z 0 is constant and the attenuation is independent of distance or frequency.

Skin depth and absorption

Reflection at the boundaries of the barrier is only one part of the story: absorption is the other. The important characteristic of the barrier material is its "skin depth". This is the distance into the material at which the current density has reduced to 1/, (0.37 or 8.7dB) due to the skin effect. For every distance 5 into the material the current density drops by 8.7dB. Put the other way, the absorption attenuation within a barrier will be 8.7dB per skin depth thickness. The skin depth is inversely proportional to ~/f and depends on the material parameters. --- the skin depths for copper, aluminum, mild steel and mu-metal.

NB figures for mu-metal derived from Telcon Metals data for 0.004" thick sheet

For a conductor with relative permeability ~r and relative conductivity o r at frequency F Hz: Skin depth 8 = 0.0661/4(F. l.lr. Or) meters

--- Skin depth for copper, aluminum and mild steel

--- Combined shielding effectiveness versus frequency

Total shielding effect

It is now possible to combine the reflective and absorptive attenuations and show the total shielding effectiveness of a conductive barrier. Some conclusions can be drawn from this:

• at low frequencies, screening a magnetic field with normal metallic barriers is difficult; because of its higher permeability, steel is more effective below 100kHz, but because of its higher resistivity, not above this frequency;
• at low frequencies, screening an electric field with normal metallic materials is very easy;
• at high frequencies, absorption ensures that normal metallic materials are effective whatever the field source;
• the thicker the barrier the greater its absorption, but this is less important for electric field shielding.

The figures of upwards of 100dB look very impressive. But it is important to appreciate that it is based on a theoretical concept which is not realized in practice: that of a uniform conducting barrier of infinite extent. Real enclosures are finite in size and , just as importantly, they have apertures and penetrations. For all applications except low frequency magnetic shielding, these are the aspects which actually determine the shielding performance.

Shielding effectiveness specifications and IEC 61000-5-7

In an attempt to systematize the description of shielding effectiveness a number of test methods have been used. The most common of these, historically, has been MIL-STD-285 (the German military standard VG 95373 part 15, and an adaptation of MIL STD 285, MIL G 83528B, are also sometimes used). This standard is useful for the characterization of screened rooms, but less so for enclosures, since it stipulates antenna separation and a few predetermined measurement frequencies. This makes it harder to apply meaningfully to small cabinet-sized items.

At the time of writing, a draft standard is in progress in the IEC which will define screening effectiveness tests and classes for enclosures. Its eventual publication target date, as IEC 61000-5-7, is spring 2000. The approach taken in this document is to make swept or stepped frequency measurements over each frequency decade for which performance data is required, of the loss between two antennas. One of these is either open (unshielded) or it is located inside the enclosure to be tested (shielded). The shielding effectiveness is then the difference between these two measurements. The frequency range covered by the standard extends from 10kHz to 40GHz, split into decade sub-ranges. To cover the whole range, different types of antenna (magnetic loops at low frequencies, dipoles at high frequencies and horns at microwave frequencies) are specified.

A systematic designation of shielding effectiveness (the EM code) similar to the IP environmental classification system operated in IEC 60529 is proposed. This will show minimum shielding performance according to the above tests in 10dB steps over the appropriate decades of frequency across which the minimum performance is maintained. Whilst this may appear to be a simplistic way of describing shielding performance, the proposed system does have the merit of allowing quick comparison between different enclosures, and could integrate easily with other evaluation techniques such as the root-sum-of-squares (RSS) method of summation of emissions from several different units. Because of the dynamic range required, shielding effectiveness tests are not trivial.

Antennas need to be small in order to fit inside the enclosure to be measured without significantly affecting their properties, but this means they are insensitive. Therefore to obtain a good dynamic range the transmitted signal must be at a high level, but this means the test must be conducted inside a screened chamber. Reflections from the chamber walls must not affect the measurement, so the chamber must be anechoic t, over the frequency range required for the test. This means that only a fully-equipped EMC test house can carry out such tests.

The effect of apertures, seams and penetrations

The implication of the previous description of a screening barrier is that it relies on current flow within the body of the shielding barrier, or, at higher frequencies, near to its surface. This current provides the mechanism for absorption losses and is also a necessary consequence of the reflected wave. Therefore, anything which interrupts this current flow will affect the shielding effectiveness.

Any discontinuity in the conductive material will interrupt the current flow.

Discontinuities are due to a number of factors:

• joints between structural members and /or panels
• large openings: windows, access doors
• small openings: ventilation holes, connectors, controls.

Any enclosure for electrical or electronic apparatus will have most or all of these features. Proper treatment of them will allow the enclosure to achieve some degree of shielding effectiveness, but it will rarely approach the theoretical values given.

Degradation of shielding effectiveness

Much academic effort has been expended in trying to quantify the general effect of apertures and discontinuities in shielding. Apart from the special case of a sphere, a simple analytical expression based on the fundamental field equations has been unobtainable, leaving us until recently with recourse either to numerical computer modeling of a particular situation, or to various empirical rules of thumb. The difficulties are compounded by the possible number of variables:

• the relative positions and distances between the field source, the shield barrier and the apertures in it, and the victim
• the frequency and source impedance of the field
• the shape, size, position and number of apertures
• the geometry of the shielding enclosure

… all of which have to be taken into account by the model, even disregarding the possible variations in the properties of the shielding material itself.

Some developments are still occurring in the formulation of the shielding problem.

Recent studies have looked at modeling an aperture in a rectangular shielded box as if it were a transmission line discontinuity, in effect extending the scope of basic shielding theory, and these show reasonable agreement with experiment. If adequate computing resources and skilled modeling staff are available, some shielding problems can be successfully modeled by numerical methods and substantial academic work has gone into improving these. Results have yet to be made available in a useable form to wider industry applications . This leaves us with some general guidelines and a few simplistic equations. The most widely quoted of these equations is SE = 20 log (X/21) OB (below resonance) where X is wavelength and ! is the maximum aperture dimension which suggests that the shielding effectiveness SE degrades proportional to frequency and inversely proportional to aperture size until the aperture size is a half wavelength, at which point shielding is zero. This has the merit of highlighting the general dependence on frequency and size of aperture: that is, the larger the aperture the greater its effect, and the higher the frequency the less is the available shielding. But as a means of predicting actual shielding effectiveness the equation is quite inaccurate, since SE also depends on the dimensions of the enclosure and the point at which SE is measured.

Work at leading universities do show good correlation with measurement, and more especially with position of the point of measurement with respect to the aperture, as well as predicting enclosure resonances. It treats the enclosure as a length of rectangular waveguide shorted at the far end, with the aperture appearing as a shorted transmission line at the entrance to the waveguide. An example result for two different positions of the measuring probe.

This section the general form of frequency dependence as predicted by equation, but by no means the same value. It also section the worsening of shielding effect as the measurement position is moved closer to the aperture; and most significantly it includes the confounding effect of the enclosure resonance.

---Shielding effectiveness degradation due to an aperture (Calculated and measured SE for 300 x 120 x 300mm rectangular enclosure with 100 x 5mm aperture

NB line referenced as "Ott's equation"

Enclosure resonance

Resonance is evidenced by the sharp worsening in SE, even leading to negative SE or enhancement of radiated coupling as the frequency approaches the first resonance of 700MHz. This is a feature of all rectangular box-type shielded enclosures.

At any frequency at which the box forms a resonant cavity, the maximum current flow occurs in the structure, and this magnifies the degrading effect of any discontinuity. For an empty box, the frequencies at which resonance occurs are given by

F = 150.~/{(k/l) 2 + (m/h) 2 + (n/w) 2} MHz

where 1, h, m are enclosure dimensions in meters and k, m and n are positive integers, only one of which may be zero The lowest resonant frequency will occur for the two larger dimensions of the box; e.g., for the 0.3 x 0.3 x 0.12m box, the lowest frequency is calculated as

F = 150.4{(1/0.3) 2 + (0/0.12) 2 + (1/0.3) 2} MHz = 707MHz

Many higher frequency resonances occur above 1GHz for this box, at the higher order modes given by further values of k, m and n. For larger enclosures, of course the resonant modes will occur well below 1GHz; for a typical 19" 37-U height rack cabinet (0.8m depth, 0.6m width, 1.8m high) the lowest frequency will be around 200MHz.

Accurately predicting the resonant frequencies of an enclosure with a typical load of internally-mounted modules is not normally feasible; the presence of the internal components and wiring detunes the resonances to a relatively unpredictable degree, although it is usual to find that the frequency is shifted downwards, and the depth of the resonant notch is reduced, sometimes substantially. The components themselves, and any significant apertures, also add their own subsidiary resonances. The best use to which equation can be put is to gain an idea of the frequency range above which screening is likely to be degraded and variable.

Multiple apertures and the shape of the aperture

The shielding degradation is principally due to the aperture's longest dimension. The theory given in includes a term for the height of the aperture but this has a second- order effect on the result. Shielding degradation over the majority of the frequency range (resonances excepted) is approximately proportional to the square of the length.

A square-shaped aperture has been found to have an identical performance to a round one of the same area. Practical enclosures will usually have several apertures, some of which may be combined into groups, as in ventilation louvers or meshes. Adding more apertures of the same size can be predicted to worsen the shielding effectiveness roughly in proportion to the number added, e.g. doubling the number will give a 6dB reduction in shielding. However, because of the impact of the maximum dimension of a given aperture, for a specified total open area- for a given ventilation air-flow, e.g. -- it is better to have more, smaller holes than fewer, larger ones. The work reported leads to the conclusion that for a constant area the shielding effectiveness improves proportional to ~/(number of holes). It was also shown that the difference between three 160 x 4mm slots and 20 12mm diameter holes was up to 30dB, the smaller holes being better over the whole frequency range. Dividing a long slot into two shorter ones increases shielding by about 6dB. Other theoretical work reported in which uses the same approach has resulted in analytical expressions for the shielding effectiveness of a perfect rectangular enclosure with a mesh or grid as one face. It is likely that the near future will see CAD application software becoming available which will implement these new theoretical approaches.

Guidelines for unavoidable apertures

Despite the advances in theory described above, proper calculation of the effect of apertures is still difficult, and it is more straightforward in engineering terms to apply a set of design rules to any enclosure with the intent of maximizing its shielding effect and minimizing its transfer impedance to internal parts. --- looks at the various techniques and hardware that are available, but the basic guidelines can be summarized here:

++ Any discontinuity (aperture or seam) should be treated with the techniques if its longest dimension is greater than a tenth of a wavelength at the maximum frequency of concern. For 1GHz, this converts to 30mm; for 200MHz, 150mm.

++ Internal placement of wiring and modules should avoid proximity to apertures and seams in the enclosure. Where compromises must be made, classify the wiring as and make a similar assessment for the noisiness or sensitivity of the modules, and keep the most critical items the furthest away from the largest apertures.

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