I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
ION OF ODELS FOR
IC ENERGY OSURES
V I S T E O N C O R P O R A T I O N
DEVELOPMENT AND INVESTIGATAPPROXIMATE PHENOMENOLOGICAL M
THE COUPLING OF ELECTROMAGNETTHROUGH APERTURES INTO ENCL
I. Belokour
EMC APPLICATIONS ENGINEERING
VISTEON CORPORATION
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
ation)
y)
he EM Field Coupling
ng Wall
V I S T E O N C O R P O R A T I O N
Outline
1.0 Introduction
1.1 EM Interference and Susceptibility of Electronic Systems
1.2 Problem Definition
2.0 Developement of Models in EMC
2.1 Topological Decomposition of Systems (Physical Configur
2.2 Topological Decomposition of Systems (Shielding Topolog
2.3 Modeling Techniques Used in EMC for the Estimation of t
2.4 Modeling and Simulation Validation
3.0 Some EMC Concepts Relevant to Shielding
3.1 Shielding Effectiveness
3.2 Electrically Small Apertures in an Infinitely Thin Conducti
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
EM Field
of the EM Field
ture Dimensions
binations of Apertures
ith Aperture
V I S T E O N C O R P O R A T I O N
4.0 Application of the TL Method to the Estimation of the
Penetration into an Enclosure with Aperture
4.1 Approximations Based on a TL Model
4.2 Approximations Based on a Multimode TL Model
4.3 Introduction of Losses into an Enclosure
4.4 Aperture-Enclosure Resonance Condition
5.0 Application of the FDTD Technique to the Estimation
Penetration into an Enclosure with Aperture
5.1 Shielding Effectiveness of an Enclosure with Various Aper
5.2 Shielding Effectiveness of an Enclosure with Various Com
6.0 Experimental Investigation of the SE of an Enclosure w
7.0 Conclusions
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
ms
n aircraft
ncies
al models describing
enclosures
V I S T E O N C O R P O R A T I O N
1.0 Introduction
1.1 EM Interference and Susceptibility of Electronic Syste
1.1.1 Intentional and Unintentional EM Interference
• careless people - operate their equipment during the landing of a
• terrorists - try to defeat electronics used by law-enforcement age
1.1.2 Countermeasures to EM Terrorism:
• Teaching design engineers
• Estimating and testing susceptibility levels
• Hardening electronic equipment
• Special detectors that warn about EM attacks
1.2 Problem Definition
• The analysis of available analytical and numerical techniques
• Development and investigation of approximate phenomenologic
and estimating the coupling of EM energy through apertures into
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
C
roper EMC design
V I S T E O N C O R P O R A T I O N
2.0 Development of Models in EM
Figure 1. Model development in EMC
Modeling is a primary aspect in developing a correct and p
for a new product
• describe the physical configuration of a problem
• define the electrical configuration
• develop the electrical model
Configuration
Physical
System Topology
ElectricalModel
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
s (Physical
iagram: physical
d EM field
V I S T E O N C O R P O R A T I O N
2.1 Topological Decomposition of SystemConfiguration)
Figure 2. An example of an aircraft and its EM topological dconfiguration
Cloud-to-cloud lightning
Radiate
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
lding Topology)
gram: EM shielding
tration
t injection of energy
Antenna
V I S T E O N C O R P O R A T I O N
2.2 Topological Decomposition of Systems (Shie
Figure 3. An example of an aircraft and its EM topological diatopology.
Aperture penetration Diffusive pene
Direc
Barrier S1aircraft fuselage
Exteriorvolume V0
V1 V2
V3S3
CircuitsCableShields
S2
Incident EM field
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
e Estimation of
ulation of EM field
Tx-linematrixmethod
Curve-fittingto a model
techniques
method
nsientes
Semi-empirical
re
V I S T E O N C O R P O R A T I O N
2.3 Modeling Techniques Used in EMC for ththe EM Field Coupling
Figure 4. Basic modeling techniques used in EMC for the simpenetration through finite apertures
Mathematical formulations equations
Maxwell
Analyticaltechniques
Numericaltechniques
Approximateengineering
formulas
MoM FEM FDTD
Quasi-staticapproach
Tx-line
methodmethodPower balance
method
method method
Numericaltechniques
method
Power balancemethod
approximationsAperture LF HF and tra
respons
Hybridmethod
approximations
Geometricaloptics
Apertu
Boundary conditions
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
tion
to cover other
odel:
l responses
at system resonances,
V I S T E O N C O R P O R A T I O N
2.4 Modeling and Simulation Valida
Model Validation Using Experimental Methods
• making a measurement of the same effect, then extend the model
configurations which will not be measured
Model Validation Using Non Experimental Methods
• using other validated models to validate a new model
Concepts Frequently Used to Examine the Validity of a M
• conservation of energy
• causality
• time of arrival of waveform response components
• low-frequency or high-frequency asymptotic behavior of spectra
• other known physical constraints of the solution, such as finite Q
etc.
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
hielding
ld strength of the trans-
ength in free space
V I S T E O N C O R P O R A T I O N
3.0 Some EMC Concepts Relevant to S
3.1 Shielding Effectiveness
for electric fields
and for magnetic fields
where or is the incident field strength, and or is the fiemitted wave as it emerges from the shield.
An engineering formula used for enclosures with apertures
where l is the longest dimension of the aperture and is the wavel
Se 20 Ei Et⁄log=
Sm 20 Hi Ht⁄log=
Ei Hi Et Ht
Se 20 λ2l-----log=
λ
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
ucting Wall
rture
an electric dipole
a small aperture are and are the normal Ht
V I S T E O N C O R P O R A T I O N
3.2 Electrically Small Apertures in an Infinitely Thin Cond
Figure 5. Electric and magnetic dipoles of an ape
The aperture is equivalent to a magnetic dipole and
, where the electric and magnetic polarizabilities ofgiven correspondingly by and , electric field and the tangential magnetic field, respectively.
CircularAperture
Si
an̂ a
x
y
z
P
M
M αmHt–=
P ε 0αeEn–=αe 2a
33⁄–= αm 4a
33⁄= En
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
the ground plane is
uced tangential mag-icular polarizations
transmitted wave as it mitted wave at normal
and Ensc
0=
V I S T E O N C O R P O R A T I O N
The total transmitted power for dipoles radiating in the presence of
where is the intrinsic impedance of free space, and are indnetic and normal electric dipole moments. For parallel and perpendrespectively
and
The normalized shielding effectiveness
where is the incident field strength, is the field strength of theemerges from the shield, and is the field strength of the transincidence and parallel polarization.
Pt
4πη0
3λ2------------ k
2M
2ωP
2+
=
η0 M P
Htansc
2Hi and Ensc
2Ei θisin= = Htan
sc2Hi θi
cos=
SEnor 20–Et Ei⁄
EtrefEi⁄
--------------------------
log=
Ei EtEtref
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
ation of the EM Aperture
aperture
y
x
d
V I S T E O N C O R P O R A T I O N
4.0 Application of the TL Method to the EstimField Penetration into an Enclosure with
4.1 Approximations Based on a TL Model
Figure 6. Geometry of a rectangular enclosure with
z
Incident field
Epar
Eperp
a
blw
pP
n̂
k̂
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
e with aperture
e impedance
g
V I S T E O N C O R P O R A T I O N
Figure 7. The equivalent circuit of the rectangular enclosur
The aperture is represented as a length of coplanar TL. The apertur
,
where is the aperture characteristic impedance.
A Pp d-p
l/2
l/2
Z0
V0
Zgkg Zgk
Z0S, k0
Zap j Z0s
l2a------ 0.5k0ltan=
Z0s
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
acteristic impedance
.
.
le system topology
lower frequencies
2a)2
0
V0
V I S T E O N C O R P O R A T I O N
The enclosure is represented by the shorted waveguide whose char and propagation constant are respectively
,
The electric and magnetic shielding effectiveness are given by
The TL model
• gives good predictions of the electric and magnetic SE for a simp
• does not consider higher-order TE and TM modes, i.e., limited to
• does not include the polarization of the incident EM field
Zg kg
Zg Z0 1 λ 2a⁄( )2–⁄= kg k0 1 λ ⁄(–=
Se 20 Vp V'p⁄log– 20 2Vp( ) V⁄log–= =
Sm 20 Ip Ip'⁄log– 20 2IpZ0( ) ⁄log–= =
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
rectangular enclosure
1000
tric SEnetic SE
V I S T E O N C O R P O R A T I O N
Figure 8. Electric and magnetic shielding effectiveness of an emptywith aperture
0 200 400 600 800−20
−10
0
10
20
30
40
50
60
Frequency, MHz
Se,
dB
ElecMag
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
e TL Model
sure with aperture
vely
rm0
Y
y = d
Zl
rcuit
V I S T E O N C O R P O R A T I O N
4.2 Approximations Based on a Multimod
Figure 9. The equivalent circuit of an empty rectangular enclo
The equivalent source voltage with source impedance, respecti
V0
VsZ0
Zs Zlm0 Z
y = py = 0
kgm0
Zgm0Zap
P
+- Vpm0
Zpm0
Enclosure Equivalent CiEquivalent Source Circuit
Vs V0Zap Z0 Zap+( )⁄=
Zs Z0Zap Z0 Zap+( )⁄=
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
ctric mode of
gnetic mode of
ely as
TEzm0
…,
TMxm1
V I S T E O N C O R P O R A T I O N
The waveguide characteristic impedance of the m-th transverse elepropagation and the propagation constant are given respectively as
, where
The waveguide characteristic impedance of the m-th transverse mapropagation and the propagation constant are respectively
where the cutoff wavelength and mode number are given respectiv
and
Zgm0 Z0 1 mλ 2a⁄( )2–⁄=
kgm0 k0 1 mλ 2a⁄( )2–= m 1 2 3, ,=
Zgm1 Z0 1 mλ λc⁄( )2–⁄=
kgm1 k0 1 mλ λc⁄( )2–=
λc 2a 1 a b⁄( )2+⁄= m 1 2 3 …, , ,=
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
d in the direction of the
e for the m-th mode.
s
the Tx-line, viewed in e , are given Vlm0
)]
V I S T E O N C O R P O R A T I O N
The impedance of the m-th mode at point P on the TL, viewetermination is
where is the normalized termination impedanc
The effective impedance at test location P considering i
The source impedance of the m-th mode at test location P onthe direction of the source impedance , and the equivalent voltagrespectively as
Zrm0Zl
Zrm0
Zl jZgm0 kgm0 d p–( )[ ]tan+
1 jZnm0 kgm0 d p–( )[ ]tan+-------------------------------------------------------------------------=
Znm0 Zl Zgm0⁄=
Zl 0=
Zrm0 jZgm0 kgm0 d p–( )tan=
Zlm0Zs
Zlm0
Zs jZgm0 kgm0 p( )tan+
1 jZnm0 kgm0 p( )tan+-----------------------------------------------------------=
Vlm0 Vs kgm0 p( )cos jZnm0 kgm0 p(sin+[⁄=
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
espectively
spectively
pectively as
Zlm0 Zrm0+( )⁄
0 Zrm0+ )
0
0
V I S T E O N C O R P O R A T I O N
The m-th mode voltage and the total voltage at test location P are r
,
The m-th mode current and the total current at test location P are re
,
The electric and magnetic shielding effectiveness is determined res
where in the absence of the enclosure
and
Vpm0 Vlm0Zrm0 Zlm0 Zrm0+( )⁄= Vtp Vlm0Zrm0m
∑=
Ipm0 Vlm0 Zlm0 Zrm0+( )⁄= Itp Vlm0 Zlm(⁄
m
∑=
SEe 20 Vtp Vp0⁄ log– 20 2Vtp V⁄log–= =
SEm 20 Itp Ip0⁄ log– 20 2ItpZ0 V⁄log–= =
Vp0
V0 2⁄= Ip0
V0 2Z0⁄=
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
bounded medium
6 7 8
41.4 3535.5 4031,1
50.1 3716.5 4190.8
986 0.0848 0.0744
2 …, ,2 …, ,3 …, ,
m n 0≠=
3 …, ,3 …, ,2 …, ,
m n 0≠=
V I S T E O N C O R P O R A T I O N
Higher-Order Modes
The resonant frequencies of the , modes and un
wavelengths of the rectangular enclosure with aperture
Table 1.
Mode order 1 2 3 4 5
, MHz 707.11 1118.0 1581.1 2061.6 2549.5 30
,MHz 1346.3 1600.8 1952.6 2358.5 2795.1 32
, m 0.4242 0.2683 0.1897 0.1456 0.1177 0.0
TEzm0 TM
xm1
fres( )TEmnp
1
2π µε----------------- mπ
d-------
2 nπb
------ 2 pπ
a------
2+ +=
m 0 1,=
n 0 1,=
p 1 2,=
fres( )TMmnp
1
2π µε----------------- mπ
d-------
2 nπb
------ 2 pπ
a------
2+ +=
m 1 2,=
n 1 2,=
p 0 1,=
TEm0z
TMm1x
λgm0
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
.3 m, p = 0.25 m) with mulation.
4000 4500
V I S T E O N C O R P O R A T I O N
Figure 10. The of the enclosure (a = 0.3 m, b = 0.12 m, d = 0aperture (l = 0.025 m, w = 0.005 m) obtained by TL si
0 500 1000 1500 2000 2500 3000 35000
10
20
30
40
50
60
70
80
90
100
Frequency, MHz
SE
, dB
SEe
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
.3 m, p = 0.25 m) with mulation.
000 4500
V I S T E O N C O R P O R A T I O N
Figure 11. The of the enclosure (a = 0.3 m, b = 0.12 m, d = 0aperture (l = 0.025 m, w = 0.005 m) obtained by TL si
1000 1500 2000 2500 3000 3500 4−10
0
10
20
30
40
50
60
70
80
90
Frequency, MHz
SM
, dB
SEm
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
.3 m, p = 0.25 m) with simulation.
4000 4500
V I S T E O N C O R P O R A T I O N
Figure 12. The of the enclosure (a = 0.3 m, b = 0.12 m, d = 0aperture (l = 0.025 m, w = 0.005 m) obtained by FDTD
0 500 1000 1500 2000 2500 3000 3500
0
10
20
30
40
50
60
70
80
Frequency, MHz
SE
, dB
TE10 TE20
TE30
TE40 TE50
TE60 TE70
TE80
SEe
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
suresorrection factor in
tant
ectangular enclosure
cies
porating the losses
γ
0)
0)
V I S T E O N C O R P O R A T I O N
4.3 Introduction of Losses into EncloDistributed losses can be modeled in TLs by including a complex cthe expressions for characteristic impedance and propagation cons
Characteristic impedance
Propagation constant
The effect of losses:
• mimic the loading effect of electronics
• appreciably dampen higher-order mode resonances of an empty r
thus improving the SE of the high-Q enclosure at higher frequen
• the higher-order mode resonant frequencies are lowered by incor
Zlgm0
Z0
1 mλ 2a⁄( )2–
------------------------------------------- 1 γ gm0 jγ gm–+(=
klgm0 k0 1 mλ 2a⁄( )2– 1 γ gm0 jγ gm–+(=
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
.3 m, p = 0.25 m) with ed by TL simulation
4000 4500
a=0a=0.01a=0.05a=0.1
V I S T E O N C O R P O R A T I O N
Figure 13. The of the enclosure (a = 0.3 m, b = 0.12 m, d = 0aperture (l = 0.025 m, w = 0.005 m) with incorporated losses obtain
500 1000 1500 2000 2500 3000 35000
10
20
30
40
50
60
70
80
Frequency, MHz
SE
, dB
gammgammgammgamm
SEe
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
ndition
e enclosure with aper-
V I S T E O N C O R P O R A T I O N
4.4 Aperture-Enclosure Resonance Co
The condition of the aperture-enclosure resonance is determined as
where the dominant-mode reactance
is compensated by the sum of the equivalent source reactance
and the reactance due to non-propagating higher-order modes in thture
Xs Xhm+ Xd=
Xd Im Zgm0( ), m 1==
Xs Im Zs( )=
Xhm Im Zgm0m
∑
, m 1≠=
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
m)-enclosure (a = 0.3 y TL simulation
900 1000
.1 m mbda/2
V I S T E O N C O R P O R A T I O N
Figure 14. SE degradation at the aperture (l = 0.2121 m, w = 0.005m, b = 0.12 m, d = 0.3 m, p = 0.25 m) resonance obtained b
0 100 200 300 400 500 600 700 800
−10
0
10
20
30
40
50
60
Frequency,MHz
Shi
eldi
ng e
ffect
iven
ess,
dB
0la
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
omparison of TL and
1000
Tx−lineFDTD
V I S T E O N C O R P O R A T I O N
Figure 15. SE degradation at the aperture-enclosure resonance. cFDTD simulations
0 200 400 600 800
−10
0
10
20
30
40
50
60
Frequency, MHz
SE
, dB
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
stimation of the th Aperture tational Space x 140 x 68 cells
V I S T E O N C O R P O R A T I O N
5.0 Application of the FDTD Technique to the EEM Field Penetration into an Enclosure wi
Figure 16. FDTD model geometry
zy
x
b
d
al
Pw
p
θi
Incident field
k̂
k̂
Epar
Eperp
Incidence plane
n̂
FDTD Compu 140
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
4.5 5
V I S T E O N C O R P O R A T I O N
Figure 17. Incident field
0 0.5 1 1.5 2 2.5 3 3.5 4
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1Electric Field
Time [ns]
Ele
ctric
Fie
ld [V
/m]
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
eld
0.9 1
V I S T E O N C O R P O R A T I O N
Figure 18. Fourier transform of the incident fi
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
1
2
3
4
5
6
7x 10
−4 Fourier Transform of Electric Field
Ele
ctric
Fie
ld [V
/m/M
Hz]
Frequency [GHz]
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
ot length for TL and
0.9 1
V I S T E O N C O R P O R A T I O N
Figure 19. Normalized shielding effectiveness vs. normalized slFDTD models
0.2 0.3 0.4 0.5 0.6 0.7 0.80
5
10
15
20
25
30
35
40
45
50
Normalized slot length
Nor
mal
ized
shi
eldi
ng e
ffect
iven
ess,
dB
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
idth for TL and FDTD
0.9 1
Tx−lineFDTD
V I S T E O N C O R P O R A T I O N
Figure 20. Normalized shielding effectiveness vs. normalized slot wmodels
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.80
2
4
6
8
10
12
14
Normalized slot width
Nor
mal
ized
SE
, dB
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
number of slots
9 10
FDTD Tx−line
V I S T E O N C O R P O R A T I O N
Figure 21. Normalized shielding effectiveness vs. the
2 3 4 5 6 7 80
5
10
15
20
25
No. of apertures
Nor
mal
ized
SE
, dB
SEnor
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
ormal incidence and
900 1000
FDTDTx−line
V I S T E O N C O R P O R A T I O N
Figure 22. Shielding effectiveness for FDTD and TL model at nparallel polarization.
100 200 300 400 500 600 700 800−20
−10
0
10
20
30
40
50
Frequency, MHz
Shi
eldi
ng E
ffect
iven
ess,
dB
Comparison of SE for FDTD and Tx−line model
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
Enclosure with
setup
Transmit antenna
V I S T E O N C O R P O R A T I O N
6.0 Experimental Investigation of the SE of anAperture
Figure 23. Shielding effectiveness measurement
Ground plane
E-field probe
HP8753D
Enclosure under test
Network analyzer
Port 1Port 2
z
y x
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
led empty rectangular
00 1000
closure
V I S T E O N C O R P O R A T I O N
Figure 24. Shielding effectiveness of the electromagnetically seaenclosure
300 400 500 600 700 800 90
10
20
30
40
50
60
70
Frequency, MHz
SE
, dB
Sealed en
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
rectangular enclosure
00 1000
rmentse
V I S T E O N C O R P O R A T I O N
Figure 25. Computed and measured shielding effectiveness of thewith aperture of 0.1 by 0.005 m.
300 400 500 600 700 800 9−10
0
10
20
30
40
50
60
70
Frequency, MHz
Shi
eldi
ng E
ffect
iven
ess,
dB
FDTDMeasuTx−lin
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
rectangular enclosure
00 1000
rmentse
V I S T E O N C O R P O R A T I O N
Figure 26. Computed and measured shielding effectiveness of thewith aperture of 0.05 by 0.005 m.
300 400 500 600 700 800 9−10
0
10
20
30
40
50
60
70
Frequency, MHz
Shi
eldi
ng E
ffect
iven
ess,
dB
FDTDMeasuTx−lin
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
method
iation and the number
omparing the relative
gainst some standard
age by geometrically
, it is better to have
an aperture has been
ividual as well as
considered
d to mimic the loading
V I S T E O N C O R P O R A T I O N
7.0 Conclusions• SE of a rectangular enclosure has been investigated using the TL
• an estimate of the SE depending on the slot length and width var
of slots has been developed. The developed method is good for c
shielding of different slot sizes or comparing relative shielding a
slot
• energy transfer into an enclosure may be reduced at the design st
trimming the size and the number of slots. From SE point of view
more smaller slots
• the problem of EM coupling into a rectangular enclosure through
studied based on a multimode approach. The contributions of ind
multiple higher-order modes to the SE of the enclosure have been
• losses can be easily incorporated in the TL model and may be use
effect of electronics
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
erture-enclosure
pair of aperture-
the SE
age by detuning the
pe of the aperture or
DTD models has been
V I S T E O N C O R P O R A T I O N
• EM coupling into a rectangular enclosure with aperture under ap
resonant conditions has been investigated using the TL model. A
enclosure resonances have been found which significantly reduce
• energy transfer into an enclosure may be reduced at the design st
aperture-enclosure resonances by geometrically trimming the sha
enclosure
• good agreement between the results obtained for the TL and the F
obtained
• solution time is the key advantage of the developed model.
I E E E S o u t h e a s t e r n M i c h i g a n E M C S o c i e t y
ods and Computational
n, M.D. Ganley, A.C.
tion for the Shielding
. on Electromagnetic
tiveness Estimation of
mpatibility Symposium
ode Transmission Line
ures”, 2001 IEEE EMC
702-707,
V I S T E O N C O R P O R A T I O N
References:[1] F.M. Tesche, M.V. Ianoz, and T. Karlsson, EMC Analysis Meth
Models, John Wiley & Sons, Inc., New York, 1997
[2] M.P. Robinson, T.M. Benson, C. Christopoulos, J.F. Dawso
Marvin, S.J. Porter, D.W.P. Thomas, “Analytical Formula
Effectiveness of Enclosures with Apertures,” IEEE Trans
Compatibility, vol. 40, no. 3, 1998, pp. 240-247.
[3] I. Belokour, J. LoVetri, and S. Kashyap, “Shielding Effec
Enclosures with Apertures”, 2000 IEEE Electromagnetic Co
Proceedings, pp. 855-860, 2000.
[4] I. Belokour, J. LoVetri, and S. Kashyap, “A Higher-Order M
Model of the Shielding Effectiveness of Enclosures with Apert
International Symposium Proceedings, Montreal, Quebec., pp.