Screening or shielding is a process of preventing EM radiation from coupling into or leaking out of defined areas or regions. Basically, this is achie... Electromagnetic shielding - Electromagnetic modeling - Electromagnetic radiation - Inorganic materials - Metallization - Plastics - Analytical models - Calculators - Numerical models - electromagnetic coupling - electromagnetic interference - electromagnetic shielding - electromagnetic screening - shielding-effectiveness modeling - EM radiation - electromagnetic source separation - shielding materials - Electromagnetic emission - interference - noise - screening - shielding - shielding effectiveness - reflection loss - absorption loss - secondary reflections - aperture leakage - numerical simulation - FDTD - transmission line method - moment methods

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Abstract Screening or shielding is a process of preventing EM radiation from coupling into or leaking out of defined areas or regions. Basically, this is achieved by using shielding materials such as metals or metallized plastics. Shielding effectiveness (SE) is a parameter that determines the degree of isolation of a "victim" from an interfering electromagnetic source separated by any obstacle from the victim. This tutorial aims to review shielding-effectiveness modeling and simulation studies, and to supply some shielding-effectiveness calculators based on analytical and numerical models. Keywords: Electromagnetic emission; interference; noise; screening; shielding; shielding effectiveness; reflection loss; absorption loss; secondary reflections; aperture leakage; numerical simulation; FDTD; transmission line method; moment methods

1. Introduction

I

n addition to grounding and filtering, screening or shielding is an effective electromagnetic (EM) protection method. Enclosing devices and/or circuitry in a shielded enclosure is a good way to control EM emissions. Figure 2 shows a typical scenario for the definition of shielding effectiveness. Shielding effectiveness (SE) is the degree of isolation of an enclosure between an interfering EM source and a victim: SE = 20Log\O (

~~ ) = 20Log\O ( ~~ ),

(1)

where Eo (H0) and E} (H}) are the electric (magnetic) fieldstrength values, measured or calculated at the victim's position without and with the enclosure, respectively. If the enclosure is absent or fully transparent in terms of EM waves, then E} = Eo and the shielding effectiveness is 0 dB. Otherwise, positive and negative shielding effectiveness corresponds to the attenuation and amplification, respectively, of the interfering EM signal. The value of shielding effectiveness depends upon a number of factors: the interfering EM source's characteristics, such as the wave impedance, frequency, amplitude, and polarization; and the enclosure's characteristics, such as thickness, material permittivity, permeability, conductivity, etc. Among all of these, the factor related to the type of interfering EM source is usually dominant.

2. SE and Theoretical Models

victim in terms of three different EM mechanisms: through reflection on the air/conducting-material boundary, absorption, and multiple internal reflections (see Figure 3) [1]. The contribution from multiple reflections is usually negligible, so only reflection and absorption losses contribute to shielding effectiveness. The shielding effectiveness from reflection can be calculated in terms of the wave impedance, Zw' and the conductor impedance, Zs: (2)

where Ei and Et are the field strengths incident upon and transmitted through the screen, respectively. The screen's impedance is Zs = ~lOJ1/(J' Q. For the far field, the (plane) wave impedance in free space is Zw reduces to

(al

(b)

= Zo =1201l' Q.

Therefore, Equation (2)

•

EM8ouR:e·

.-

E118ouR:e

A conducting plate of infinite extent, having thickness t, provides shielding effectiveness between an interfering source and a

Figure 2. A typical scenario for the definition of shielding effectiveness.

IEEE Antennas and Propagation Magazine, Vol. 51, No.1, February 2009

211

_Zw-Z:; f.2 Z.",+Z.r

....

__1J .•. •. r:~

~

. . i1let. . . .

t~

))1..).1 (1- ftXl- f 1 )

I I

i.

Two typical examples are given in Figures 6 and 7 for a 0.01 mm thick screen with a 30 cm distant interfering source. Figures 6 and 7 belong to copper (Pr =1, u r =1) and mu-metal

I

,

;-

d

J

A short MATLAB script, prepared for shielding-effectiveness calculations according to the flowchart presented in Figure 4, is listed in Figure 5. A simple virtual shielding-effectiveness calculator tool has also been designed for this purpose. The user only needs to choose the type of shielding material, and to supply its thickness and the interfering-source distance. The virtual shieldingeffectiveness tool yields plots of the shielding effectiveness as a function of frequency for both electric and magnetic interfering sources.

Figure 3. An EM screen, and reflection and absorption losses.

SER = 20Log10

{! ~

CTr } = 168 + 10Log10 {

4 Prf

u r }. (3) Prf

However, in the near field, the type of interfering source is important. The wave impedance of electrical (i.e., dipole-like emitting) sources is Zwe = Zo (l/21td) 0., while the wave impedance of

Use [4,5] & calculate NF Reflection Loss, SER

magnetic (i.e., loop-like emitting) sources is Zwm = Zo (21td/ l) 0.. Therefore, the SER (in dB) in the near field is

(4)

for electrical sources, and for magnetic sources it is given by (5)

EM waves hardly penetrate conductors. The degree of this penetration is specified in terms of the skin (penetration) depth, 8 [m], given by

t5 _ ~ 2 -

OJUp

=

0A. Program : SE Calculator

0/0-------------------------------------------------------------

0.066

~furPr·

(6)

The shielding effectiveness (in dB) from absorption losses is then calculated from SEA

Figure 4. A flowchart for the mathematical shielding-effectiveness model.

= 20LoglO [exp(~)] =131.4t .J,urCTr/.

(7)

The total shielding effectiveness is then obtained from the addition of SER and SEA. A flowchart of a simple shielding-effectiveness

clear all; clc;format long; sigmar=O.I; mur=500; N=250; dt=input('Material thickness [mm] =? '); dt=dt/le3; d=input('\n Screen Distance [cm] =? '); d=d/le2; epsO=10/\(-9)/(36*p,j; muO=4*pi* 10/\(-7);zO=sqrt(muO/epsO); finin= 1e3; finax= 1e9; df=(finax-finin)/N; df=(finax-finin)/N; for k=1 :2*N % Frequency loop fr(k)=finin+k*df; wavel=3e8/fr(k); ifd < wavell(2*pi) % Near Field SRe=322+10*loglO(sigmar/(mur*fr(k)/\3*d/\2)); SRm=14.6+1O*logl O(fr(k)*d/\2*sigmar/mur); SA=131.4*dt*sqrt(fr(k)*sigmar*mur); else % Far Field SRf=168-10*log1O(mur*fr(k)/sigmar); SA= 131.4*dt*sqrt(fr(k)* sigmar*mur); SEf(k)=SRf+SA; end SEe(k)=SRe+SA; SEm(k)=SRm+SA; end

calculator, based on Equations (3)-(5) and (7), is given in Figure 4. After specifying the input parameters and the type of interfering source, one calculates the shielding effectiveness caused by the absorption using Equation (7). One then checks whether or not the interfering source is in the near or far-field region, and calculates the shielding effectiveness caused by the reflections according to either Equation (3) or Equations (4) and (5). Finally, the total shielding effectiveness is found by adding these two contributions.

Figure 5. A MATLAB script for shielding-effectiveness calculations.

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IEEE Antennas and Propagation Magazine, Vol. 51, No.1, February 2009

Figure 6. The sbielding-effectiveness calculator: the shielding effectiveness as a function of frequency for a 0.01 mm thick copper shield from an interfering source at a distance of 30 cm.

Figure 7. The shielding-effectiveness calculator: the shielding effectiveness as a function of frequency for a 0.01 mm thick mu-metal shield from an interfering source at a distance of 30cm.

Figure 12. A discrete PC case model and EM near-field distributions simulated with a commercial package (source: SEMCAD, Speag, Schmid & Partner Engineering AG). IEEE Antennas and Propagation Magazine, Vol. 51, No.1, February 2009

213

50-,-.-------------------.."

(Pr = 30,000, 0-r = 0.03) shields, respectively (here, 0-r is the relative conductivity with respect to copper: o-r = o-Io-ell , 5.8x 107 S/m). Plots of shielding effectiveness as a function of frequency for both electric and magnetic interfering sources are shown in the figures. As observed, electrical shielding is effective at low frequencies, whereas magnetic shielding is not. After a criti-

25

o-ell =

cal frequency,

Ie = 3x 108 /21rd,

determined from the near-

o -25

field/far-field boundary (d = Ae 121r), the effects of both electric and magnetic screening are the same.

- 50 """"""""""''''''''''''''''''''''''''''''T"'r'or-r-r-r-IJ'''TM''I-r-T...,....,..,.........-r-r''''''''''''''''I'"'"T'''''1--r-T-r-T''''''''''

Theoretically, more than several hundred dB of shielding effectiveness against electric interfering sources can be reached at low frequencies even with a shield of a few micrometers thickness, but this may be as low as 0 dB for the magnetic sources, as seen from Figures 6 and 7. Starting from low frequencies, shielding effectiveness decreases (increases) with frequency for electric (magnetic) shielding. Above certain frequencies that correspond to d = A/21r , shielding effectiveness is the same, and increases with frequency for both kinds of sources.

Figure 9. The shielding effectiveness as a function of frequency: solid line, FDTD; dashed line, TLM.

In practice, depending on the criticality of the problem under consideration, shielding effectiveness values of 30-60 dB are considered to be acceptable. In contrast, shielding-effectiveness values in the range of 70-90 dB represent quite high-quality shields. The shielding performance of a metal box with no holes or seams exceeds 100 dB, which is usually too high to measure. If the shield has holes, slots, joints, vents, windows, or other discontinuities, the shielding effectiveness can only be as good as allowed by such shielding imperfections. One rule of thumb is to find the longest dimension of these discontinuities, and to determine the frequency at which that length represents a half-wavelength. As a worst-case approximation, the shield can be assumed transparent (i.e., yielding odB shielding effectiveness) beyond that frequency.

0.5

1.0

::T~""" 201

-..:J

~-""-'-,-"',

. . . . . .~ IB - ... ····IT,·rl··.·T·I~T]··.··x 0

-1

::1

- 20 ..:

1 ..5

.

v~'~'

A,A ~

-lye: t

r:J ~-~---- . 0.2

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·,····'·TT·,··r..·... ··t'T·r·'t'. ·'··'·rrTTI··t·rr.'·.T',.··,···.·,f. · 1 ' · '

N~:;·.:. .;:~~f·~'··"l'·,·'T··'····t ... r ..lW•..'rm~N,.,.".···I···.··· ..··'···f··l···r·.,·'·r....-r'T~r'T'T

0.0

2. 5

2 ..0

Frequency [GHz]

0.4

0.6

~~:_,~~

....·v·r.···.vT··1··,···'···.···.···.····..··,···,,····.···,

0.8

1.0

Frequency [GHz]

Figure 10. Figure 9. The shielding effectiveness as a function of frequency: solid line, FDTD; dotted line, MoM. 35

3. SE and Numerical Models The theoretical shielding-effectiveness calculations presented in Section 2 may be used for rough estimations and initial considerations. Shielding-effectiveness predictions for real enclosures are extremely complex and mostly impossible to model analytically. They therefore necessitate the use of numerical models. One of the canonical structures used for numerical shielding-effectiveness predictions is a rectangular perfectly conducting enclosure with a few apertures in it (see Figure 8). The shielding effectiveness of this structure can be investigated via both the Finite-Difference Time-Domain (FDTD) and Transmission-Line Matrix (TLM)

'iii" :::!...

10

~ -15 - 4 0 -t-,.-,.--r-'1r--r-..,--,.-r--.--r~r-r-r-Jr--r-..,.....,.-,--.,.-.,--r--r--t'--r--r--r---r--r-l 1 2 3 4

35

~ 10

:::!...

~ -15 - 40 --t-~..,.......,r--r--r--r--r-,..--r-r-y--r-..,.....,r--r-.,..--r--r-.,...-,--r-...........-r--.-..-.....--T~ ::l 1 4 Frequency [GHz]

Figure 11. The shielding effectiveness as a function of frequency: solid line, single aperture on the side wall; dashed line, double aperture.

y

Panel1ype$

Figure 8. A rectangular enclosure with some apertures. 214

based numerical simulators supplied in [2], and with the Methodof-Moments (MoM) based packages like NEe2 [3]. Time-domain scattering effects may be simulated with FDTD and TLM methods with and without enclosures, and the behavior of broadband shielding effectiveness as a function of frequency can be obtained via off-line discrete Fourier transformation (DFT) techniques [2]. On the other hand, shielding-effectiveness calculations based on MoM should be repeated at each frequency. A few examples for the shielding-effectiveness simulations of this canonical enclosure are given in Figures 9-11 [2]. IEEE Antennas and Propagation Magazine, Vol. 51, No.1, February 2009

The shielding effectiveness of an enclosure, aperture, or a screen is critically dependent on the problem's parameters. Prediction of the shielding effectiveness is a very complex task that cannot be addressed using even the best EM engineering expertise. It can only be performed either by measurements or via simulations covering all frequencies of interest. An example is given in Figure 11 to show this complexity, where shielding effectiveness as a function of frequency is simulated for enclosures having single and double apertures with different polarizations. Some observations from these three figures may be listed as follows: Positive shielding effectiveness means EM isolation; odB shielding effectiveness corresponds to full transparency. However, negative shielding effectiveness means amplification! This happens in enclosures because of ringing effects in the time-domain, corresponding to resonances in the frequency domain. The peaks and nulls in the plots of shielding effectiveness as a function of frequency correspond to certain dimensions of the enclosures, aperture sizes, and the interfering sources, mutually resonating. Attention should therefore be paid to these frequencies. EM interactions in these structures are very complex, so it is almost impossible to make statements such as "as the frequency increases shielding effectiveness... ," or "as the number of apertures and holes increases shielding effectiveness ... ," etc. When available, mathematical models are best, because they are exact, or the contributions of the approximations made there are exactly known, and this helps one to understand the physics of the problem. Unfortunately, such models are limited to only a few canonical structures. The virtual tools such as those supplied in [2] are simple and may be used in education and training. However, when it comes to the simulation of realistic problems (such as the PC case shown in Figure 12), it is best to refer to commercial professional EM simulation packages. Shielding effectiveness is an important parameter, and, in practice, it is obtained only through measurements. Details of shielding effectiveness measurements can be found in several standards (see, for example [4, 5]).

4. Quiz from Last Issue A transformer's 20-wound primer carries 16A rms of sinusoidal current at 500 kHz. Up to the 40th of its harmonics are of interest in terms of undesired electromagnetic emissions. A sensitive electronic device operates close to (within 0.5 m of) this coil, and is susceptible to electric fields above 40 dBfJV/m. (Some of our readers still wonder why we mention units together with the dB. This is because we engineers like and need to mention the reference field. Here, 40 dBJlV1m means the reference field in the expression 2010g 10 (V/Vrej ) is V rej = 1 JlV/m).

IEEE Antennas and Propagation MagaZine, Vol. 51, No.1, February 2009

Do you think a shield is necessary in this scenario? If yes, how do you design this shield? If you use a 100fJm-thick copper shield, can you plot shielding effectiveness as a function of frequency for this shield in the range of 20 kHz to 500 MHz? If you shield the susceptible device, how do you handle ventilating slots, cable holes, etc.?

4.1 Answers One needs to measure the transformer's emissions at a distance of 0.5 m in order to answer this question. Instead, the required shielding effectiveness can be calculated analytically from a worst-case analysis. Assume the transformer's primer is a 20element loop array, each carrying 16Arms sinusoidal current at 500 kHz; or a single loop antenna with a 320Arms sinusoidal current. For a loop antenna with 0.1 m radius, the EM emission at 0.5 m is equal to 20 dBV/m or 140 dBJlV/m. This means a 100 dB shielding effectiveness is required at this frequency. The reflection loss from Equation (5) is calculated to be SER = 65.5 dB. Using SEA = 100 = 65.5 = 34.5 dB in Equation (7), the thickness of the copper shield is found to be t = 0.37 rom. The script given in Figure 5 can be used to compute and plot shielding effectiveness as a function of frequency for these parameters. A few tips: make slots smaller with respect to the wavelength at the maximum frequency; open multiple small apertures instead of one big aperture; use the polarization effect and open apertures one orthogonal to the other; use cable shields and filters surface mounted on the screen; ground cables entering the enclosure; locate everything as tightly as possible, etc.

5. Conclusions Enclosures are used to shield a broad range of electrical/electronic devises, as well as systems. The prediction of shielding effectiveness for screened rooms, anechoic chambers, cell phones, computers, cables, and the like is a very important task. Shields are mostly fabricated from metallic materials, the mechanical and electrical properties of which are well understood. Increasingly, the electronics and telecommunications industries are making use of plastic and conductive plastic enclosures to reduce weight and cost. The main limitations in shielding effectiveness are due to the seams, holes, and cable penetrations, which cannot be avoided.

6. References 1. C. R. Paul, Introduction to Electromagnetic Compatibility, New York, John Wiley InterScience, 2006.

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2. L. Sevgi, Complex Electromagnetic Problems and Numerical Simulation Approaches, New York, IEEE Press/John Wiley & Sons, 2003. 3. G. J. Burke and A. J. Poggio, "Numerical Electromagnetic Code - Method of Moments, Part I: Program Description, Theory," Technical Document 116, Naval Electronics System Command (ELEX 3041), July 1977. 4. IEEE STD-299 - 1997, IEEE Standard for Measuring the Effectiveness of Electromagnetic Shielding Enclosures. 5. ASTM D-4935, Measuring the Electromagnetic Shielding Effectiveness of Planar Materials. @

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