International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 3- April 2016
Analysis of Shielding Enclosure using
Numerical Electromagnetic Techniques
R.Seetharaman, R.Vandana, K.Venkata Srinath
Department of Electronics and Communication Engineering
College of Engineering, Guindy
Anna University, Chennai-600 025,INDIA
Abstract
A comprehensive study of shielding enclosures using
various CEM methods has been dealt here. The
inherent advantages and disadvantages of these
methods have compared and analysed. Various
aperture considerations have been taken into
account. The frequency is considered to be in GHz
range. Various softwares such as ADS, CST and
HFSS characteristics have been illustrated and a
further extended study using these softwares will be
done.
Widespread methods for numerical analysis of
enclosures include FDTD (Finite difference time
domain), FEM (Finite Element Method), FIM (Finite
Integration Method) etc. They are efficient at
predicting shielding effectiveness but added
computational time as well as enormous unknowns
confines their usage. Analytical techniques such as
MoM (Method of Moments) or the Boundary
Element Method (BEM) are effective in confronting
shielding quantification.
Keywords-Shielding, EMC, Apertures, Sheilding
Effectiveness
I.INTRODUCTION
Shielding is an important concern in EMC concept.
Shield is a metallic casing basically used to provide
susceptibility to interior electronics from external
fields. Shielding effectiveness (SE) [1] is defined as
the ratio of magnetic (electric) field incident on the
shield to magnetic (electric) field transmitted by
shield. A shield may not always be an enclosed
structure it will have may some perforations inside it
such as a personal computer casing. These slots act as
proficient
radiators
influencing
shielding
effectiveness.
Therefore, EMC modeling of metallic shielding
enclosures proves to be extremely byzantine due to
massive expansion in high speed electronics.
Determination and substantiation of SE becomes
relatively significant as the integrity of enclosures is
compromised by apertures, cable penetrations, power
supply cables etc. Radiation characteristics of an
enclosure can be corroborated by numerical as well
as analytical techniques. These analyses are carried
out keeping in mind that energy penetration is mainly
through apertures.
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II.METHOD OF MOMENTS
Method of Moments is a technique used to solve EM
boundary or volume integral equations particularly in
frequency domain. Most EM problems can be
modeled in terms of inhomogeneous equation of the
form[2]:
LΦ=g
(1)
Where g is a source function or excitation which is
primarily voltage or current source. MoM is a general
procedure for solving equations of the form as stated
in equation 1. Since EM sources such as voltages and
currents are primarily considered as quantities of
interest, this technique becomes prevalent in solving
radiation and scattering problems. For MoM
formulation a Perfectly Electrically conducting (PEC)
[3]-[5] cavity whose walls are thin and lossless are
considered for the experimentation. As an excitation,
a plane wave is made normally incident on one of the
faces of cavity. Varying degrees and polarizations of
angle can be encountered. Depending on the angle of
incidence this technique is subdivided into two: MoM
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International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 3- April 2016
for Normal Incidence(MNI) and MoM for slanting
angles(MOI).
A.Normal Incidence
A wave normally incident on an enclosure can be
expressed as [6]:
Internal domain fields can be quantified by dyadic
Green’s function for cavity[8].An apposite boundary
formulation[9] for finding aperture current
distributions using continuity of
tangential
component of magnetic field on the apertures can be
stated as:
×
+
×
=
×
(6)
=
(2)
k =wave number of free space=ω
where
is the incident magnetic field,
is the
scattered magnetic field, and
is the magnetic
field inside the enclosure.
=
The electric field on apertures can be illustrated as
[6]:
=
1)Galerkin’s Method
Finally using method of Galerkin [10] where the
basis functions themselves are used as the testing
functions a matrix representation[11] of MoM can
thus be obtained of the form [C][X]=[D]
sin
cos
=
cos
sin
(7)
(3)
-M×M matrix obtained from the
arithematic configuration of MoM.
[X] - M×1 column matrix which contains unspecified
modal amplitudes of the aperture fields.
[D] - M×1 column matrix depends on incident wave.
Upmn, Vpmn -unknown modal amplitudes of the
mnth mode at pth aperture, nonzero at aperture (in
general),zero otherwise;
Lr,Wr -length and width of pth aperture;
P - total number of apertures;
(xcp, ycp ) -center of p-th aperture.
Applying equivalence principle [7] for z=0 plane and
reinstating aperture fields by magnetic currents:
=
×
(4)
This has the advantage of enforcing the boundary
conditions throughout the solution domain, instead of
at discrete points.
B.Oblique incidence
Oblique incidence used in MoM involves random
angles and polarizations. Khan[12] developed this
method and further validations for statistical
investigations are being carried out in this area.
-normal vector of aperture.
The complete analysis of MoM solution can be
devised into external and internal domain. External
fields are calculated using free space Green’s
function [2]:
(r,r )=
(5)
(r,r )
+
(r,r )
+
(r,r )
III.FEKO METHOD
(r,r ),
(r,r ) and
(r,r ) correspond to
infinitesimal, elementary sources pointed in the y and
z direction,
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The advantages include the fact that MoM is fast,
conceptually simple and accurate [13]. It does not
require special boundary conditions. The infinite
ground plane assumption in Modal/MoM suggests a
restriction that the apertures be smaller than the walls
they are located on.
Varying EM complexity and electrical size offers no
single numerical method which can handle all
problems efficiently. These problems can be handled
by a single method known as field computations
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International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 3- April 2016
involving bodies of arbitrary shape (FEKO) [14]. By
offering a selection of different solvers, this tool
offers the option to choose a method that is most
suitable for a required problem. FEKO is an allinclusive computational electromagnetic (CEM)
simulation software tool. The diverse range of
modernized numerical simulations and hybridization
allows precise elucidation of Maxwell’s equation
extending the applicability to 3D configurations.
Essentially devised in frequency domain time domain
can be extracted by applying Fourier transform on
frequency domain data. FEKO is basically a Method
of Moments (MoM) code hybridized with techniques
such as Physical Optics (PO), Ray-launching
Geometric Optics (RL-GO), Uniform Theory of
Diffraction (UTD). Such an hybridization enables
solution of computationally massive problems on
small computers, full wave analysis, using
estimations whenever required to different parts of
the same model better optimization of solution and
time. This aspects of FEKO makes it vulnerable to
EMI\EMC investigations including shielding
enclosures.
Both
Electric
Shielding
effectivenness(SE)
and
Magnetic
Shielding
effectiveness(SM)for the above illustrated enclosure
having apertures can be experimented in two
scenarios: (1) A plane wave can be made incident on
the casing and fields inside enclosure are
calculated.(2)Internal components inside the casing
can be modeled as dipoles or patch source wherein
near and far field outside the cavity are computed.
Both metallic casings as well as enclosures made of
non-perfect screening materials can be investigated
here. It is predicted that Shielding effectiveness of the
order of 200 dB or more can be quantified. Since
quantification of shielding effectiveness requires a
wide band of frequency a method known as Adaptive
Frequency Sampling (AFS) is adapted to scan the
entire frequency range of interest in fewer frequency
points, still resolving all resonances and other
features of the problem. So, electrically large and
complex problems can be handled with this
simulation software. A FEKO 4.2 version is used to
model a metallic box with a slot before computing
the shielding effectiveness of the structure in a
typical EMI/EMC problem. The applications of
FEKO involve lightning, mitigation studies antenna
analysis including interpreting radiation patterns and
RFI mitigation studies.
The finite element analysis of any problem involves
basically four steps [13]:discretizing the solution
region, deriving governing equations for a typical
element, assembling of all elements in the solution
region and solving the system of equations obtained.
A. Basic development of three dimensional FEM
problem
Consider a volume V occupied by a lossy material
with constitutive paramaters є and μ surrounded by
free space characterized by parameters
and .An
EM wave from a source with angular frequency ω is
incident on the body. All the equations pertaining to
this explanation can be illustrated from [16].
The electric fields inside and outside the volume
satisfy the following vector partial differential
equations:
× ×
The finite element method is a tool for resolving
problems with partial differential equations [15]. Its
× E - ω²є E=0
(8)
×
×E-
² E=0
(9)
=ω
is wavenumber of free space
The field inside volume V can be expressed as:
F=
{
(
[(
] – μ[
-
² +
² +
² ] dV +
)dS
(10)
l and m are two orthogonal unit vectors tangential to
the surface S.
From discretization of volume V into 3d elements
fields within each element can be illustrated as:
=
(11)
IV.FINITE ELEMENT METHOD
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ability to deal with complex geometries makes it a
very prevelant technique. Since evaluation of
shielding effectiveness of a rectangular cavity is quite
tedious FEM modeling becomes quite appropriate.
(x,y,z) ;
=
(x,y,z)
n number of nodes within element
interpolation functions
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are
International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 3- April 2016
,
) represent field at ith node
Using Rayleigh –Ritz procedure and substituting eqn
(12) into (11) yields final formulations:
{ }+[
]{ }=0
{ }+
{ }+
(12)
{
}=0
(13)
denotes electric field at the nodes interior to the
surface S
denotes tangential electric field at nodes
on S and
is the tangential magnetic field at the
nodes on S.
denotes a matrix having three
dimensions.
A complete formulation using these equations cannot
be obtained and therefore hybrid procedures
combining fem with surface integral equations such
as Hybrid FEM/MoM [17] has been developed.FEM
is enable to hand easily complex geometries.
Generality of FEM makes it possible to construct
general purpose program for solving wide range of
problems. FEM has its own drawbacks. Harder to
understand, it is difficult to program than both
methods (FDTD and MoM). It requires preparing a
set of input data, which is tedious. If apertures are
present in the casing, the FEM solver requires an
―air-box‖ to correctly model the radiation
characteristics and its performance deteriorates
rapidly.
V.FDTD METHOD
FDTD plays a significant role in modeling
of microwave problems whose geometrical
dimensions are comparable to wavelength.
Application of the FDTD method is usually very
straightforward: the solution domain is typically
discretized into small rectangular or curvilinear
elements, with a ―leap frog‖ in time used to compute
the electric and magnetic fields from one another.
Considering the aspect of shielding enclosure with
apertures, a lot of work has already been done in
evaluating shielding effectiveness of electrically large
physically small casings using this CEM tool.
The loss necessary for FDTD [18] analysis
of shielding enclosures technique is introduced by
using a specific resistance at the end of the monopole
probe. S-parameters, EMI, Far field, Near fields etc.
are quantified. Modeling of fields outside enclosure
is done using equivalence theory for apertures taking
into consideration surface electric and magnetic
currents of enclosure. The FDTD method has the
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following inherent advantages and disadvantages [2]
over other modeling techniques such as Method of
Moments.
Advantages include: The algorithm does not
require formulation of integral equations, and
relatively complex scatterers can be treated without
the inversion of large matrices. It is simple to
implement
for
complicated,
inhomogeneous
conducting or dielectric structures because
constitutive parameters can be assigned to each
lattice point. The algorithm makes use of the memory
in a simple sequential order. It is much easier to
obtain frequency domain data from time domain
results than the converse. Thus, it is more convenient
to obtain frequency domain results than the converse.
The disadvantages include: Its implementation
necessitates modeling object as well as its
surroundings. Thus, the required program execution
may be excessive. Its accuracy is at least one order
worse than that of the MoM example. Since the
computational meshes are rectangular in shape, they
do not conform to scatterers with curved surfaces, as
in the case of the cylindrical or spherical boundary.
VI.PROPOSED SOFTWARES
A.Computer Simulation Technology
CST [19] offers an extensive range of features and
solvers suited to all kinds of electromagnetic (EM)
problems. It is computationally efficient and
accurate. The solver range includes: time domain,
frequency domain, integral equation, asymptotic, fast
resonant, eigenmode , static and stationary fields,
charged particles, temperature, mechanical stress, and
circuit simulation. Specifically speaking, CST PCB
STUDIO (CST PCBS) used for the simulation of
signal and power integrity and EMI/EMC on printed
circuit boards and CST DESIGN STUDIO (CST DS)
a versatile tool that facilitates 3D EM circuit cosimulation and synthesis plays a trivial role in
enclosure analysis.
B.High Frequency Structure Simulator
Ansoft High Frequency Structure Simulator[20] is a
full-wave, FEM based electromagnetic field solver
for simulating arbitrary(3D) structures such as
computing behavior of high-frequency and highspeed components. With HFSS, engineers can extract
parasitic parameters (S,Y,Z) to visualize 3D
electromagnetic fields (near – and far-field) , generate
broadband SPICE models and optimize design
performance. HFSS is widely used for the design of
on-chip embedded passives, PCB interconnects,
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International Journal of Engineering Trends and Technology (IJETT) – Volume 34 Number 3- April 2016
antennas, RF-microwave components, and highfrequency IC packages.
constructed for shielding effectiveness vs. frequency
for comparative study.
C.Advanced Design System
VIII.CONCLUSION
Advanced Design System[21] abbreviated as ADS is
the world’s leading design automation software for
RF, microwave and high speed digital application. It
versatility of solvers such as the momentum,
momentum microwave and FEM make it a high end
tool for 3D electromagnetic simulation. It offers a
powerful and easy to use interface ADS pioneers in
most commercially and successfully used industrial
tool.
The proposed paper here illustrates the comparison of
various CEM techniques used for the analysis of
shielding enclosures. These techniques can be
henceforth applied for the modeling of casings with
distinct aperture compositions. CST, HFSS and ADS
are the anticipated softwares used for 3D EM
simulation and modeling. The operation frequency is
considered in GHz range. This work will be further
extended to the aspect of PCB modeling and its
components in shielding enclosures with versatile
solvers using ADS tool.
VII.APERTURE CONSIDERATIONS
All the techniques here mentioned FDTD, MOM,
FEM and FEKO will be run for single, double and
multiple aperture cases. Low frequency as well as
high frequency analysis is encountered. Multiple
square apertures of size 1cm forming an
(1)
(2)
(3)
(4)
Fig 1. Illustrates the example of different aperture
plates to be analysed
array of approximately 250 are also considered.
Smallest to largest apertures cases are investigated.
For MNI and MOI arbitrary angles and polarizations
are taken into account. Graphical plots are to be
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