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Electromagnetics Behind Shielding

Shielding an electromagnetic field is a complex and sometimes formidable task. The reasons are many, since the effectiveness of any strategy or technique aimed at the reduction of the electromagnetic field levels in a prescribed region depends largely upon the source characteristics, the shield geometry, and the involved materials. Moreover, as it often happens when common terms are adopted in a technical context, different definitions of shielding exist. In electromagnetics the shielding effectiveness (SE) is a concise parameter generally applied to quantify shielding performance. However, a variety of standards are adopted for the measurement or the assessment of the performance of a given shielding structure. Unfortunately, they all call for very specific conditions in the measurement setup. The results therefore are often useless if the source or system configurations differ even slightly. Last among the difficulties that arise in the solution of actual shielding problems are the difficulties inherent in both the solution of the boundary value problem and the description of the electromagnetic problem in mathematical form.

1.1 Definitions

To establish a common ground, we will begin with some useful definitions. An electromagnetic shield can be defined as [1]:

[A] housing, screen, or other object, usually conducting, that substantially reduces the effect of electric or magnetic fields on one side thereof, upon devices or circuits on the other side.

This definition is restrictive because it implicitly assumes the presence of a "victim." The definition is also based on the misconception that the source and observation points are in opposite positions with respect to the shield, and it includes the word "substantially" whose meaning is obscure and introduces an unacceptable level of arbitrariness.

Another definition of electromagnetic shielding even more restrictive is [2]:

[A] means of preventing two circuits from electromagnetic coupling by placing at least one of the circuits in a grounded enclosure of magnetic conductive material.

The most appropriate definition entails a broad view of the phenomenon:

[A]ny means used for the reduction of the electromagnetic field in a prescribed region.

Notice that no reference to shape, material, and grounding of the shield is necessary to define its purpose.

In general, electromagnetic shielding represents a way toward the improvement of the electromagnetic-compatibility (EMC) (defined as the capability of electronic equipment or systems to be operated in the intended electromagnetic environment at design levels of efficiency) performance of single devices, apparatus, or systems. Biological systems are included, for which it is correct to talk about health rather than EMC. Electromagnetic shielding is also used to prevent sensitive information from being intercepted, that is, to guarantee communication security.

Electromagnetic shielding is not implemented only for such purposes. Some sort of electromagnetic shielding is almost always used in electrical and electronic systems to reduce their electromagnetic emissions and to increase their electromagnetic immunity against external fields. In cases where the available methodologies for reducing the source levels of electromagnetic emission or strengthening the victim immunity are not available or are not sufficient to ensure the correct operation of devices or systems, a reduction of the coupling between the source and the victim (either present or only potentially present) is often the preferred choice.

The immunity of the victims is generally obtained by means of filters that are analogous to electromagnetic shielding with respect to conducted emissions and immunity. The main advantage of filters is that they are "local" devices. Thus, where the number of sensitive components to be protected is limited, the cost of filtering may be much lower than that of shielding. The main disadvantage of using a filter is that it is able to arrest only interferences whose characteristics (e.g., level or mode of transmission) are different from those of the device, so the correct operation in the presence of some types of interference is not guaranteed. Another serious disadvantage of the filter is its inadequacy or its low efficiency for the prevention of data detection.

In general, designing a filter is much simpler than designing a shield. The filter designer has only to consider the waveform of the interference (in terms of voltage or current) and the values of the input and output impedance [3], whereas the shield designer must include a large amount of input information and constraints, as it will be discussed throughout the book.

Any shielding analysis begins by an accurate examination of the shield geometry [4-7]. Although the identification of the coupling paths between the main space regions is often trivial, sometimes it deserves more care, especially in complex configurations. The complexity of a shield is associated with its shape, apertures, the components identified as the most susceptible, the source characteristics, and so forth. Subdividing its configuration into several subsystems (each simpler than the original one and interacting with the others in a definite way) is always a useful approach to identify critical problems and find ways to fix and improve the overall performance [5]. This approach is based on the assumption that each subsystem can be analyzed, and hence its behavior can be characterized, independently of the others components/subsystems. For instance, in the frequency domain and for a linear subsystem, for each coupling path and for each susceptible element, it is possible to investigate the transfer function relating the external source input and the victim output characteristics as , where represents the subsystem output in the absence of external-source excitation. In the presence of multilevel barriers, the transfer function may ensue from the product of the transfer functions associated with each barrier level.

The foregoing approach can be generalized for a better understanding of the shielding problem in complex configurations. However, it is often sufficient to consider only the most critical subsystems and components, on one hand, and the most important coupling paths, on the other hand, in order to solve the principal shielding problems and thus improve the overall performance [8]. The general approach is obviously suitable in a design context. A complete analysis of the relations between shielding and grounding is left to the specific literature [4, 9-11].

1.2 Notation, Symbology, and Acronyms

The abbreviations and symbols used throughout the book are briefly summarized here in order to make clear the standard we have chosen to adopt. Of course, we will warn the reader anytime an exception occurs.

Scalar quantities are shown in italic type (e.g., and , while vectors are shown in boldface (e.g., and ); dyadics are shown in boldface with an underbar (e.g., and ). A physical quantity that depends on time and space variables is indicated with a lowercase letter (e.g., for the electric field). The Fourier transform with respect to the time variable is indicated with the corresponding uppercase letter (e.g., while the Fourier transform with respect to the spatial variables is indicated by a tilde (e.g., ); when the Fourier transform with respect to both time and spatial variables is considered, the two symbologies are combined (e.g., ).

The sets of spatial variables in rectangular, cylindrical, and spherical coordinates are denoted by , , and , respectively. The boldface Latin letter is used to indicate a unit vector and a subscript is used to indicate its direction: for instance, , , and denote the unit vectors in the rectangular, cylindrical, and spherical coordinate system, respectively.

We will use the "del" notation with the suitable product type to indicate gradient (), curl () and divergence operators (); the Laplacian operator is indicated as . The imaginary unit is denoted with and the asterisk as a superscript of a complex quantity denotes its complex conjugate. The real and imaginary parts of a complex quantity are indicated by and , respectively, while the principal argument is indicated by the function . The base-10 logarithm and the natural logarithm are indicated by means of the and functions, respectively.

Finally, throughout the book, the international system of units SI is adopted, electromagnetic is abbreviated as EM, and shielding effectiveness as SE.

1.3 Macroscopic Electromagnetism and Maxwell's Equations

A complete description of the macroscopic electromagnetism is provided by Maxwell's equations whose validity is taken as a postulate. Maxwell's equations can be used either in a differential (local) form or in an integral (global) form, and there has been a long debate over which is the best representation (e.g., David Hilbert preferred the integral form whereas Arnold Sommerfeld found more suitable the differential form, from which special relativity follows more naturally [12]). When stationary media are considered, the main difference between the two representations consists in how they account for discontinuities of materials and/or sources. Basically, if one adopts the differential form, some boundary conditions at surface discontinuities must be postulated; on the...