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EXPERIMENTAL STUDY OF A COMPUTATIONAL HYBRID METHOD FOR THE RADIATED COUPLING MODELLING BETWEEN ELECTRONIC CIRCUITS AND ELECTRIC CABLE

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In this paper, a computational hybrid method (HM) is developed for calculating the radiated coupling on an electric cable due to external electromagnetic (EM) near-field (NF) perturbations. These sources of EM perturbation are placed at some mm of the cable proximity. The analytical approach for evaluating the voltage across the cable extremities in function of the NF aggression is proposed. The HM proposed is based on the combination of analytical coupling models and numerical methods or measured data associated to calculate the induced voltages on the cable. The model developed is tested and validated for different configurations of the perturbing source in the wide frequency band from 200 MHz to 2 GHz. The methodology was validated with measurements comprised of two electric cables in different positions.
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International Journal of Advances in Engineering & Technology, March 2012.
(c)IJAET ISSN: 2231-1963

EXPERIMENTAL STUDY OF A COMPUTATIONAL HYBRID
METHOD FOR THE RADIATED COUPLING MODELLING
BETWEEN ELECTRONIC CIRCUITS AND ELECTRIC CABLE
Elagiri Ramalingam Rajkumar, Blaise Ravelo, Mohamed Bensetti, Yang Liu,
Priscilla Fernandez Lopez, Fabrice Duval and Moncef Kadi
IRSEEM-EA4353 at the Graduate School of Engineering ESIGELEC,
Av. Galilee, B.P. 10024, 76801 St Etienne du Rouvray, France.






ABSTRACT
In this paper, a computational hybrid method (HM) is developed for calculating the radiated coupling on an
electric cable due to external electromagnetic (EM) near-field (NF) perturbations. These sources of EM
perturbation are placed at some mm of the cable proximity. The analytical approach for evaluating the voltage
across the cable extremities in function of the NF aggression is proposed. The HM proposed is based on the
combination of analytical coupling models and numerical methods or measured data associated to calculate the
induced voltages on the cable. The model developed is tested and validated for different configurations of the
perturbing source in the wide frequency band from 200 MHz to 2 GHz. The methodology was validated with
measurements comprised of two electric cables in different positions.

KEYWORDS: Hybrid method (HM), near-field (NF) radiation, radiated emission, NF coupling,
electromagnetic compatibility (EMC).

I.
INTRODUCTION
With the increase of the systems integration density as the modern automotive equipments, the
electromagnetic compatibility (EMC) and electromagnetic interference (EMI) can be sources of
serious problems to the electronic and electrical circuits [1-2]. Facing to these unintentional disturbing
effects, standards on the testing techniques were established to ensure the safety of the automotives
[3-6]. In addition, characterization methods of EMC and EMI prediction techniques were proposed [7-
8]. One of the most difficult situations for the treatment of the EMC/EMI influences in the automotive
systems concern the issues related to the immunity and the susceptibility of electronic circuits
especially in radiating context [9-10]. To overcome these limitations, efficient methods are required.
During the calculation of radiated coupling between electronic components and transmission lines, the
active or passive components are usually represented by network of electric and/or magnetic dipoles
[11-12]. This dipole set radiates the same EM fields as that of the any electronics
component/integrated circuit. In EM coupling on cabling systems, the knowledge of exciting source is
at least as important as modelling of cable network itself [13]. Due to the higher operating frequency
of advanced electronic embedded systems in the automobile and aeronautical industry, the study of
EMI between components and cables is an important topic of researcher. In this context, the non-
uniform external exciting source is derived from the incident EM fields in the absence of the cable
which is assumed as a transmission line (TL) displayed in Fig. 1.
1
Vol. 3, Issue 1, pp. 1-15


International Journal of Advances in Engineering & Technology, March 2012.
(c)IJAET ISSN: 2231-1963


Figure 1. Configuration considered for investigating the coupling between a TL and NF EM radiations.
This is derived analytically in [14-18]. In this model, the coupling of the incident EM field on a TL is
described by the application of a pair of per-unit-length current Is and voltage generator Vs. In the
particular case of transmission line above a ground plane, this model provides the induced voltage and
current everywhere on the line.
But till now, few studies [17-18] were performed on the investigation of the EM NF coupling
including the evanescent waves on the electric wires or cables. The existing ones are not valid for all
cases of positions between the radiating structure and the victim wires. For this reason, we propose to
experiment the HM (HM) whose the basic principle is introduced recently in [19-23]. For that, we
will start with the analytical approach illustrating the functioning of this HM and then, we validate the
concept with experimental studies. The paper will be ended by a conclusion.
II.
METHODOLOGY OF THE HYBRID METHOD PROPOSED
As argued in [19-23], the HM developed in this paper is based on the combination of the given EM-
data with the analytical modelling of the coupling voltages. As we are aimed to the computation of the
voltage values in function of the operating frequency, we employ the Taylor modelling method [14]
briefly described in the following paragraph.
2.1. Recall on the Taylor Model
For the better understanding, we consider the representation of the structure shown in Fig. 2. The
infinitesimal elements with length dy can be assumed as its RLCG electrical model with per unit
length parameters: Ru, Lu, Cu and Gu respectively expressing the resistance, inductance, capacitance
and conductance per unit length. The appendix of this paper summarizes certain characteristics of the
case of the TL formed by a cylindrical electric cable above the ground plane.

Figure 2: TL coupled with an electric field and its equivalent circuit.
We denote Vs the voltage derived from the transverse component of magnetic field in an elementary
cell of the structure shown in Fig. 2 as:
V ( j) = j h H .



(1)
s
0
y
where Hy represents the transverse component of the magnetic field and h is the height of the line. 0
is the magnetic permeability of vacuum; is the angular frequency given by
2 c / (c is the speed of
the light in the vacuum). The current Is is derived from the normal component of the incident electric
field according to the relation:
I ( j) = j C E .



(2)
s
u
z
where Cu represents the physical capacitance per unit length of the transmission line.
2
Vol. 3, Issue 1, pp. 1-15


International Journal of Advances in Engineering & Technology, March 2012.
(c)IJAET ISSN: 2231-1963

The transverse magnetic field and the normal electric field are supposed to be constant along the
height of the line, considering that the source is a far-field source. The response of conductor TLs
illuminated by an EM field has been reported by various investigators [17-18].
The model developed in [18] represents the effect of external EM NF field on a TL above a ground
plane as a function of the exciting electric and magnetic fields. This analytical model is developed in
the absence of TL and perturbation source is always placed above the TL. From the results between
the modelled and coupled voltages, it is observed that this method is capable of analyzing when the
perturbation source is placed above the line i.e. in the case of uniform field distribution. One major
constraint of this model is that, when the perturbation source is placed between the line and the
ground plane. This model is not considering the coupling between the cable and ground plane, and
also the perturbation source and ground plane and the cable. Thus it is necessary to have a model
which is capable of overcoming the above limitations. As illustrated in Fig. 3, the calculation of EM
coupling due to uniform and non-uniform EM field is presented here. The relation between the total
voltage and the current, as a function of the exciting EM field, is given by the following equations
[14]:
h
dV ( y) + j L
I ( y) = - j

H dz ,



(3)
u
0
e
y

dy
0
h
dI ( y) + j C
V ( y) = - j C

E dz ,



(4)
u
u
e
z
dy
0
where superscript "e" refers the incident field of both magnetic and electric fields. We point out that
the boundary conditions for a line terminated with impedances Z0 = Z(0) and ZL = Z(L) are given by:
V (0) = V = -Z I (0) ,




(5)
0
0
V (L) = V = -Z I (L) .



(6)
L
L
These relations represent the equivalent Taylor model on coupling and its approach allows us to
model the EM disturbance generated on the line, by a voltage source which represents the influence of
transverse magnetic field Hy(y,z) and a current source which represents the influence of the vertical
electric field Ez(y,z) distributed along this line.

Figure 3. Representation of the Taylor model.
The existing models that are based on analytical expressions calculate the induced voltage for cases
when the TL is excited by a plane wave. The numerical methods as finite element method (FEM) and
finite integral technique (FIT) require high computational resources and longer duration in simulation
and analytical methods are bound to be in transverse EM quasi-static conditions. Thus, the HM
capable of predicting and calculating the induced voltages and currents, will be the solution for
determining the induced voltages in the near-field analysis.
2.2. HM Formulation
In the calculation of radiated coupling with analytical model, normally in the calculation of E and H
field, we used to consider the total field to obtain the complete radiated field, whereas in the case of
analytical method we are not obliged to include the scattering field due to the fact that the model is
considered in the absence of the cable and also with the ground plane condition. This calculation also
incepts the image theory concept for the sake of ground plane condition. Added to that, this method is
not valid when the cable is very nearer to the perturbation source. This model is capable of analyzing
the coupling with the field is uniform and not with non uniform field. Whereas in the real time
industrial conditions, are dealt with non uniform field also and very close to the perturbation source.
3
Vol. 3, Issue 1, pp. 1-15


International Journal of Advances in Engineering & Technology, March 2012.
(c)IJAET ISSN: 2231-1963

These limitations posed by the purely analytical models lead us to find a solution to overcome the
above limitations.
In our work, we utilize the quasi-static condition while formulating the setup. Hence, the HM which is
capable of handling these situations has been illustrated in the flow analysis of Fig. 4. This solution is
limited to electrically short (L < ) and matched TLs (Z0 = ZL = ZC). Equations (3)-(4) and (5)-(6) thus
become:
e
V ( j) L = - j A H ,


(7)
s
0
y
e
I ( j) L = - j C A E ,



(8)
s
u
z
where, A = h L is the area between the centre of the line and the ground plane.,
e
E is the exciting,
z
incident transverse electric field, 0 is the magnetic permeability of vacuum,
e
H is the exciting,
y
normal incident magnetic field.
The fields
e
E and
e
H are obtained by the FEM simulations in the presence of cable and the ground
z
y
plane. This simplification is applied to an entire TL, not just an infinitesimal element dy. Thus, the
simplified equivalent circuit of a TL can be represented as in Fig. 2. In this case, the voltage induced
across the load Z0 and ZL by an exciting, EM incident field is given by:
Z L
0
V =
(V - Z I ) ,


(9)
0
s
L s
Z + Z
0
L
- Z L
0
V =
(V + Z I ) .


(10)
L
s
L s
Z + Z
0
L
As stated earlier, the HM proposed considers all the coupling phenomena: cable-dipole, dipole-ground
plane and cable-ground plane. Another advantage of this method is the incorporation of the dipole
based model in the radiated coupling calculation. From literatures, it is understood that plane wave
excitation is widely used as incident EM field illumination. The work demonstrated in [17-18] has the
limitations, when the radiating source is placed very nearer to the cable (victim).
S t a r t
D e f i n i t i o n o f s y s t e m :
C a b l e w i t h p e r t u r b a t i o n
s o u r c e t o b e i n v e s t i g a t e d
C a l c u l a t i o n o f t h e E M
f i e l d e x c i t a t i o n s E a n d H
b y t a k i n g i n t o a c c o u n t
t h e v i c t i m s y s t e m
( c a b l e + g r o u n d p l a n e )
D e t e r m i n a t i o n o f
t h e t o t a l E M f i e l d s
w i t h t h e c o n s i d e r a t i o n
o f t h e s c a t t e r i n g e f f e c t s
c a u s e d b y t h e c a b l e
C a l c u l a t i o n
o f t h e c o u p l i n g v o l t a g e s
i n d u c e d o n t h e c a b l e
e n d

Figure 4. Flow analysis of the HM proposed.
Hence, this method considers the limitation posed by the previous works and the calculation of the
mean value integration is replaced by the integral calculation of each and every mesh from the centre
point of each element of the mesh. Subsequently, equations (7) and (8) are transformed as follows:
4
Vol. 3, Issue 1, pp. 1-15


International Journal of Advances in Engineering & Technology, March 2012.
(c)IJAET ISSN: 2231-1963

V L = - j

H
y z ,



(11)
s
0
e
y
y
z
I L = - j

E
y z .



(12)
s
0
e
z
y
z
The discrete values of the meshes y
and z
are illustrated in the following section.
To verify the relevance of this theoretic approach, numerical experiments were carried out by using
the scientific tool Matlab programs.
2.3. Application Examples
As depicted in Fig. 5(a), an electric wire with radius r0 = 0.1 mm and length L = 8 mm above a ground
plane at a height of h = 2 mm is used as the target device and an elementary electric dipole placed
randomly and the ground plane and the wire is used as the radiating source. Both the terminals of the
wire are terminated with matched 221 impedance. The dipoles are excited by a current of I0 = 0.2 A
throughout the study and this is being tested with various configurations. Two different cases of the
radiating sources position (D1 and D2 are placed respectively above and below the cable) were
analyzed. The mathematical expressions of EM field radiation are indicated in [24-25].

y
D Dipo le
1
C ab le
z
)
Z
(
h
(
0
L
V(0)
D
Z
2
)
V(L)
G ro u nd p la n e
L
(a)
(b)

Figure 5. (a) Cable loaded by Z(0) = Z(L) = 221 and radiating dipoles D1 above and D2 below the ground
plane. (b) Mesh of the surface plane for calculating the coupling voltages.
Fig. 5(b) represents the illustration of the meshing in the shadowed surface for calculating the
coupling voltages. The EM field values Ez and Hy are determined by FEM simulation and substituted
equations (11)-(12) in equations (9)-(10) to obtain the coupled voltage V0 and VL.
Fig. 6(a) presents the comparisons of voltages at the extremities of the cables caused by the EM
couplings for the case of dipole D1 positioned at 1 mm above the cable. We can see that the results
obtained by the HM, the results show good accordance with each other in very wide microwave
frequency band from 0.2 GHz to 2.0 GHz. It is evident that thanks to the consideration of all coupling
effects of the system, this HM achieves better correlation in calculation of the induced voltages; with
about relative errors lower than 3 % from the results in Fig. 6(a).

5

5

4
4
)
)

(
V
3

(
V
3
0
L
V
V
HFSS
HFSS
2
2
AnalyticalTaylor
AnalyticalTaylor
Hybrid
Hybrid
1
1
0
0.5
1
1.5
2
0
0.5
1
1.5
2
Freq (GHz)
Freq (GHz)

Figure 6(a). Flow analysis of the HM proposed.
5
Vol. 3, Issue 1, pp. 1-15


International Journal of Advances in Engineering & Technology, March 2012.
(c)IJAET ISSN: 2231-1963

In complementary to the previous case, we also investigated the effectiveness of the method proposed
by placing the dipole radiating source at 1 mm below the cable as depicted in Fig. 5(a) only with the
dipole D2. Once again, as explained in Fig. 6(b), we observe that a very good agreement between the
HM results and those form the FEM full wave computation carried out with HFSS and the pure
analytical one using the Taylor formula. With these results, we assess relative errors lower than 2 %.
Hence, we understand that it is possible to investigate the perturbation source near the cable for
various frequency ranges from 200 MHz up to 2 GHz. In the calculation of induced voltages due to
perturbation source in the same plane of components and cables, this method can be used to obtain the
required electrical components.
5

5

4
4
Hybrid
Hybrid
HFSS
HFSS
3
)
AnalyTay
3
)
AnalyTay

(
V

(
V
0
L
V
V
2
2
1
1
0
0
0
0.5
1
1.5
2
0
0.5
1
1.5
2
Freq (GHz)
Freq (GHz)

Figure 6(b). Comparison results from the HM, analytical calculation and HFSS simulations by considering the
dipole element under the cable as shown in Fig. 5(a).
III.
EXPERIMENTAL INVESTIGATION: COUPLING BETWEEN TWO ELECTRIC
CABLES

To check the relevance of the HM methodology described in the previous section, experimental
analyses were performed with design of electronic structures showing the influence of NF radiations
interacting with a electric wire.
3.1. Design of the Structure Under Test (SUT)
As proof of concepts, we propose to evaluate the coupling voltages between the cables presented by
the HFSS design shown in Figs. 7. To calculate the coupling between the perturbation source and
electric wire, we use the electric wire (L = = 30mm, r = 0.4mm, h = 20mm).
As illustrated by Fig. 7(a), the source cable is kept at the reference position (-15mm, 0mm, 0.7mm) in
the x-axis with radius, r = 0.5mm and length L = 30mm. The victim is kept at (-15mm, 5mm, 20mm)
in the same x axis with the same dimensions of radius, r = 0.5mm and length L = 30mm. The
simulation rectangular box is fixed at the reference position defined by (-52mm, -52mm, 0mm) and
with the geometrical dimensions Lx = 104mm, Ly = 104mm and Lz = 30mm. To refine the mesh
precision, we included the mesh box at (-16mm, 1mm, 0mm) and = 32mm, Ly = 3mm and Lz = 22mm
with 1mm maximum length elements.

Figure 7. 3D HFSS design of the cables (a) in parallel and (b) in perpendicular configurations.
6
Vol. 3, Issue 1, pp. 1-15


International Journal of Advances in Engineering & Technology, March 2012.
(c)IJAET ISSN: 2231-1963

Fig. 7(b) describes the second case of the configuration cable with two cables in perpendicular
position. In this case, the source cable is kept at the reference position (-15mm, 0mm, 0.7mm) in the
x-axis with radius, r = 0.5mm and length L = = 30mm. The victim with the same geometrical
dimensions is kept at (-20mm, -15mm, 20mm) in the same x-axis. The simulation rectangular box is
fixed at the reference position of (-52mm,-52mm, 0mm) and Lx = 104mm, Ly = 104mm and Lz =
25mm. In this case, to refine the mesh precision we included the mesh box at (-21mm, -16mm, 0mm)
and Lx = 37 mm, Ly = 32mm and Lz = 22mm with 1mm maximum length elements. The first setup
both are in x-plane and later is having victim at the y-plane.
The simulations of the structures shown in Figs. 7 were carried over the frequency range between
0.5GHz to 3GHz and obtained the induced voltages at the terminations. In both configurations, the
power is injected at the lumped port and is kept as 1mW.
3.2. Description of the NF Test Bench Used
Fig. 8 depicts the photograph of the experimental setup which includes the fabricated devices tested
for scanning the EM NF of the IRSEEM laboratory. The radiating structure is comprised of a electric
wire placed above a electric ground plane. With the experimentation, we are aimed to the analysis of
the configuration with the following geometrical parameters: distance between the wires fixed to 30
mm, r = 0.4 mm, h1 = 20 mm, L = 30mm and w = 40mm.


Figure 8. Experimental setup of the NF scan radiated by the cable source.




(b)
(c)
(a)
Figure 9. (a) Synoptic of the experimental setup. Photographs of (b) the robot and (c) the probes used.
We considered the synoptic of the experimental setup presented in Fig. 9(a). The EM NF radiated by
the perturbation structure is detected from the electronic EM probes then recorded with a network
analyzer. The probes shown in Fig. 9(c) are fixed at the arm of the robot photographed in Fig. 9(b).
We point out that the radiating structure can be either excited by a signal synthesizer or directly with
the network analyser and then the transmission parameters are exploited to determine the value of the
radiated EM NF.
7
Vol. 3, Issue 1, pp. 1-15


International Journal of Advances in Engineering & Technology, March 2012.
(c)IJAET ISSN: 2231-1963

As argued before, this structure is considered as the source of the radiation and the second wire of
same dimension placed in arbitrary position in the proximity of this source is supposed as perturbation
source. The perturbation source is powered by the sine wave signal with input power Pin = -10dBm.
The measurement was made by using the network analyzer programmed with 201 points. Then, we
extracted the Ez and Hy fields for calculating the coupling.
For the first configuration, the victim is kept at 5mm distance from the source; the fields Ez and Hy are
extracted. Hy is extracted from -15 mm to 15 mm with the step size of 1 mm and similarly Ez is
extracted from 0 mm to 19.5 mm with the step size of 1 mm.
3.3. Calibrations Process
During the test, the lines are loaded with Z0 = 200 . The disturbing line is fed by the sine wave
voltages. Fig. 10(a) and Fig. 10(b) represent the models of the probes for scanning the EM NF
radiated by the disturbing cable. The scan was made with electronic probes and recorded with a vector
network analyzer. To increase the level of the voltage corresponding to the EM field detected, a
broadband amplifier with 15 V power supply was used.


(a)

(b)
Figure 10. Electrical models of the (a) electric and (b) magnetic probes shown in Fig. 9(c) during the NF scan.
To measure the emitted field, we use successively several sensitive probes each in a certain
constituent of the electric field component Ez and magnetic field component Hx. Probes are placed on
the arm of the robot shown in Fig. 9(b) which, commanded (ordered) by a PC, moves them over the
SUT. The PC assures the movement of the robot and makes the acquisition of the data measured by a
vector network analyzer (VNA) Agilent 50713 operating between 100 kHz and 8.5 GHz. These data
are converted in electric and magnetic fields (amplitude and phase) thanks to a grading of probes
which we present in the following paragraphs.
From the measured transmission parameter represented by the complex data S21, the extraction of the
EM fields with the probes used (presented in Fig. 9(b)) during the test was performed thanks to the
following expressions:
H
= a
V
(H ) ,



(13)
xy
H
mes
xy
xy
E = a V
(E ) ,



(14)
z
E
mes
z
z
with
H xy
a
=
,



(15)
H xy
V Hxy
Ez
a
=
,




(16)
Ez
V Ez
2
- j 2S
P
/10
21
V
= S
e
2 10 indB
Z .


(17)
mes
21
0
8
Vol. 3, Issue 1, pp. 1-15


International Journal of Advances in Engineering & Technology, March 2012.
(c)IJAET ISSN: 2231-1963

To extract the measured Ez, the procedure of measurement of the normal constituent Ez was taken into
account by deeming the equivalent model depicted in Fig. 10(a). It consists of the probe monopole
connected to the port of beginning of the amplifier. The output of the amplifier is connected to the
measuring device. In that case, the factor to be determined is b (Ez = b.Vmes). It is also calculated by
means of a circuit the theoretical brilliance of which we know (b = Ez_theoretical/V'mes).
To determine Hx, the procedure of measurement shown in Fig. 10(b) was considered. It contains the
probe curl differential connected to the ports of beginning of the hybrid coupler 180 . The output of
the coupler is connected to the amplifier as highlighted by Figs. 10. The output of this one is
connected to the measuring device. In practice, analyzing can be made by following the same
methodology as for the electric field. However in the case of probes magnetic field, it is possible to
model simply the buckle by means of discrete elements, and we are going to find the factor of the
procedure by electric simulations performed with the electronic/microwave software ADS (Advanced
Design System) from AgilentTM.
To obtain the antenna factors of the various probes, we measure fields in 2mm over the cable pictured
in Fig. 11, in 100MHz and in 3GHz (frequencies of our circuit tests) and we calculate the theoretical
radiation in 2mm. We can see that the radiating device is a cylindrical wire with radius a = 1.5 mm
placed at the height h = 2.05 mm above the ground plane.


Figure 11. Photograph of the referential device for the calibration factor validation.
The geometrical representation is shown in Fig. A.1 of Appendix A. For the theoretical reference, we
exploit the analytical expressions of the EM fields.
3.4. Experimental Results
By using the scanned EM NF, we evaluated the coupling on any wires placed at the proximity of this
radiating structure via the HM understudy. To validate the results, comparisons with the simulations
performed with HFSS were performed. So, two positions of the victim wires with the same length L =
30 mm presented with the perspective views of Figs. 7 were investigated.
Fig. 12(a) and Fig. 12(b) represent the maps of the modulus and phases of the measured EM NF from
the scan of the structures shown in Fig. 8. These results correspond to the radiation of the
experimented configuration at the operating frequency 3 GHz.
|Ez| (V/m) f=3GHz
ph(Ez) () f=3GHz

20
80

20
) 15
100
60
) 15
m
m
0

(
m 10
40

(
m 10
z
z
5
-100
20
5


-10
0
10
-10
0
10
x (mm)
x (mm)
|Hy| (A/m) f=3GHz
ph(Hy) () f=3GHz

20

20
0.2
) 15
) 15
100
m
0.15
m
0

(
m 10
0.1

(
m 10
z
z
5
0.05
5
-100


-10
0
10
-10
0
10
x (mm)
x (mm)

(a)
9
Vol. 3, Issue 1, pp. 1-15


International Journal of Advances in Engineering & Technology, March 2012.
(c)IJAET ISSN: 2231-1963

|Ez| (V/m) f=3GHz
ph(Ez) () f=3GHz

20

20
50
) 15
100
40
) 15
m
m
30
0

(
m 10

(
m 10
z
20
z
5
5
-100
10


-10
0
10
-10
0
10
y (mm)
y (mm)
|Hx| (A/m) f=3GHz
ph(Hx) () f=3GHz

20
0.1

20
) 15
0.08
) 15
100
m
0.06
m
0

(
m 10

(
m 10
z
0.04
z
5
0.02
5
-100


-10
0
10
-10
0
10
y (mm)
y (mm)

(b)
Figure 12. Maps of the measured electric and magnetic NF radiated by the SUTs
corresponding to the configurations respectively shown in Fig. 7(a) and Fig. 7(b).

This EM NF data was scanned in the vertical surface plane defined by the fictive victim cable and the
ground plane as illustrated in Fig. 5(a). To verify the relevance of the measured data, comparison with
the EM NF from the measurement and theory described in the Appendix was also carried out during
the calibration and the data processing. The profiles of Fig. 13 present the results obtained.
After the calculations with the standard scientific tool Matlab, we obtain the coupling voltages
indicated in Table 1. This later addresses the comparison of results calculated from the HM under
investigation and those computed with the full wave numerical method from HFSS with the
configuration of Fig. 7(a). Table 2 represents the comparison between the HFSS and HM developed
from 0.5 GHz to 3.0 GHz. Though the results are not in the good accordance each other, it is
inevitable that the induced voltages increase as the frequency increases.
It is worth noting that the coupling effect calculation HM developed in this paper main presents many
advantages as the flexibility with various complex structures, the wideness of the operating frequency
band and its less computation time compared to the full wave tools.
|En|, f=3GHz, z=2mm
400

Measured
Theory
300
)
/
m
200
|

(
V
n
|
E
100
0
-40
-30
-20
-10
0
10
20
30
40
x (mm)
|Ht|, f=3GHz, z=2mm
1

Measured
Theory
0.8
)
0.6
/
m
t
|

(
A
|
H
0.4
0.2
0
-40
-30
-20
-10
0
10
20
30
40
x (mm)

Figure 13. Comparison between the profiles of measured and theoretical electric and magnetic NF (Ht=Hy and
En=Ez) of the structure corresponding to the configuration of Fig. 8.
10
Vol. 3, Issue 1, pp. 1-15


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