SHIELDING

Electronic devices are commonly packaged in a conducting enclosure(shield) in order to (1) prevent the electronic devices inside the shield fromradiating emissions efficiently and/or (2) prevent the electromagnetic fieldsexternal to the device from coupling efficiently to the electronics inside theshield.

(1) (2)

The effectiveness of the shield in preventing externally-directedradiation or internally-directed radiation is a function of the shield materialand thickness, along with the enclosure geometry. Ideally, the shield wouldbe a completely enclosed structure. However, the need for power andcommunication conductors to penetrate the enclosure, along with the needfor effective ventilation, will compromise the effectiveness of the shield.

The shielding effectiveness of an electromagnetic shield is typicallydefined as the ratio of a field magnitude (electric or magnetic) without theshield in place to the field magnitude with the shield in place. Thisdefinition of the shielding effectiveness is equivalent to that of insertionloss in microwave circuits where the insertion loss of a given componentis typically defined as the ratio of the signal obtained without thecomponent in the circuit to the signal obtained with the component in thecircuit.

SHIELDING EFFECTIVENESS

In order to make a straightforward comparison of the shieldingcapabilities of one material to another, the simple geometry of a planarmetallic shield of thickness t in air is considered, as shown below. Theshielding effectiveness of a given shield is actually a function of thedistance from the incident wave source (near-field sources and far-fieldsources). The source is initially assumed to be a far-field source such thatthe incident wave can be approximated by a normally-incident uniformplane wave. As the incident wave encounters interface #1at z = 0, a portionof the wave is reflected away from the interface, while the remainder of thewave is transmitted into the metal, and is attenuated as the wave travelsthrough the metal. A portion of forward wave in the metal is reflected frominterface #2 at z = t producing a reverse wave, while the remainder of thewave is transmitted into the air region (z > t). The reflection/transmissionprocess at the two interfaces produces, in theory, an infinite number ofreflected, forward, reverse and transmitted wave components.

EThe electric field shielding effectiveness (SE ) and the magnetic fieldMshielding effectiveness (SE ) in dB of the planar shield are defined by

E MFor far-field sources, SE = SE since the ratio of the electric field to themagnetic field for a uniform plane wave is constant (equal to the waveimpedance of the medium).

E MFor near-field sources, in general, SE SE given the rapid variation ofthe near fields in the vicinity of the source. Thus, the electric and magneticshielding effectiveness terms are different and vary as a function ofdistance from the source.

The shielding effectiveness of the planar shield is governed by threedistinct mechanisms involving the interaction of the incident wave with theair/conductor interfaces and the conducting medium of the shield. Thesemechanisms are:

(1) Reflection loss A portion of the incident wave is reflected from interface#1. The amplitude of the reflected wave fields are equalto those of incident wave fields multiplied by thereflection coefficient for waves moving from air into the

a-cconductor ( ).

(2) Absorption lossAll of the forward and reverse waves propagating withinthe conducting shield are significantly attenuatedaccording to the attenuation constant for the conductingshield. This attenuation of the wave corresponds to theloss of wave energy in the form of heat. The complex-valued propagation constant () within the conductingshield is given by

where is the attenuation constant and is the phaseconstant for the shield material. The amplitudes of thewaves internally reflected from interface #1 and interface#2 are proportional to the reflection coefficient for waves

c-amoving from the conductor into air ( ) given by

For good conductors, the attenuation constant can beapproximated by the inverse of the skin depth ().

The thickness of the shield relative to the skin depth(which is a function of frequency) dictates howsignificantly the wave is attenuated as it propagatesthrough the shield.

(3) Multiple reflectionsA portion of each of the forward waves within the planarshield is transmitted into the air region (z > t). Thetransmitted fields used in the SE calculations are thevector sum of the fields associated with these forwardwaves. Likewise, a portion of each of the reverse waveswithin the planar shield is transmitted into the air region(z < 0). The reverse waves transmitted out of the planarshield represent additional losses which enhance theshielding effectiveness value. Both of these transmitted waves are proportional to the transmission coefficient for

c-awaves moving from the conductor to air (T ).

The significance of the multiple reflections is related tothe thickness of the planar shield relative to the skindepth. If the shield is several skin depths thick, there issignificant attenuation as the initial wave progressesacross the shield, making the effect from multiplereflections negligible. Conversely, the effect of multiplereflections can be significant for shields that are onlyfractions of a skin depth (low frequencies).

E MAn exact solution for the shielding effectiveness (SE = SE = SE)can be obtained for the case of a far-field source assuming normalincidence. The general form of the fields associated with the separate wavecomponents are shown below.

Interface #1 Interface #2 z = 0 z = t

Applying the boundary conditions (continuous tangential electric andmagnetic fields) at interface # 1 (z = 0) gives

Applying the boundary conditions at interface # 2 (z = t) gives

Given the incident field amplitude, the preceding four equations can besolved for the four unknowns (the reflected, forward, reverse andtransmitted amplitudes). The resulting ratio of the incident field to thetransmitted field is

The shielding effectiveness of the planar shield is then

The three terms in the equation above can be identified separately as thecontributions to the shielding effectiveness from reflection loss, multiplereflections and absorption loss.

The shielding effectiveness in dB can then be written as

dB dB dBwhere R , M and A represent the contributions to the shieldingeffectiveness in dB due to reflection loss, multiple reflections andabsorption loss, respectively.

The separate terms in the shielding effectiveness expression can besimplified for typical shields made from good conductors ( o ), forwhich the following approximations are valid.

This gives

Inserting these approximations into the SE component equations gives

The terms above represent the far-field shielding effectivenesscontributions for a good conductor.

Example

Determine the shielding effectiveness in dB for a 20 mil thick sheetof copper ( = 5.8 10 S/m) at 1 MHz due to (a.) reflection loss7from the surface of the copper sheet (b.) multiple reflections withinthe copper sheet (c.) absorption loss within the copper and (d.) allthree shielding mechanisms (the total SE of the copper sheet).

(a.)

(b.)

(c.)

(d.)

NEAR-FIELD SHIELDING EFFECTIVENESS

The determination of the near-field shielding effectiveness is a muchmore difficult problem than the far-field case due to the complexity of thenear fields. However, we may approximate the near-field shielding

oeffectiveness by replacing the far-field wave impedance ( ) in the far-fieldshielding effectiveness equation by an equivalent near-field waveimpedance. The near-field wave impedance is defined using the sameequation as that used for the far-field wave impedance (the ratio of electricfield to magnetic field). The near-field source can be classified as anelectric field source or a magnetic field source as to which field componentis dominant in the near-field. An electric field source can be representedas a superposition of Hertzian dipoles (elemental electric sources) while amagnetic field source can be represented as a superposition of small loops(elemental magnetic sources). The wave impedances of these sources are

where r represents the distance from the source (see Figure 10.10, p. 738).Note that the electric field is dominant in the near field of a Hertzian dipolewhile the magnetic field is dominant in the near field of the small loop.

oThe wave impedances of both sources approach in the far-field.Inserting the respective wave impedance into the far-field shielding

effectiveness terms yields the near-field shielding effectivenesscontributions. The reflection loss and multiple reflection terms arefunctions of the wave impedance (type of source) while the absorption lossterm is not.

Electric sources

Magnetic sources

Note that the electric field source generates a high-impedance fieldin the near-field, while the magnetic field source generates a low-impedance field in the near-field. The near-fields of these sources have thefollowing variation.

The wave impedances very close to the electric field or magnetic fieldosource (assuming r n 1) can be approximated by

The magnitude of the wave impedances very close to the source in termsof wavelength are

By identifying the type of near-field source in a given application, one cantranslate the shielding results for far-field sources to the case of the near-field source. In addition to simple dipole and loop geometries, examplesof electric field and magnetic field sources include such things as sparkgaps and brush contacts (electric field sources) and transformers (magneticfield sources).

Example

Determine the shielding effectiveness in dB for a 20 mil thick sheetof copper ( = 5.8 10 S/m) at 1 MHz given (a.) an electric source7at a distance of 1 m from the shield (b.) a magnetic source at adistance of 1 m from the shield.

(a.)

Note that the multiple reflection loss and absorption loss for this near-field electric source are the same as that found for the previous far-field shielding example.

(b.)