EMC’09/Kyoto
23P2-3
Calculation of Radiated Electromagnetic Field from
Multi-Pair Cable by Method of Moment
Naoki Kojima 1, Masato Kawabata 2, Nobuo Kuwabara
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kojima@bussy.elcs.kyutech.ac.jp
kuwabara.nobuo@bussy.elcs.kyutech.ac.jp
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I. INTRODUCTION
The UTP cable is widely used as various LAN (Local Area
Network) cable because it is easy to handle compared with the
optical fiber. The signal speed propagating on the UTP cable
is increasing by the advancement of the telecommunication
technology [1].
The possibility of the electromagnetic field leakage from
the UTP cable increases when a high-speed signal is
transmitting on the cable. Therefore, the electromagnetic field
radiated from UTP cable has been analyzed several method
such as the four port network method [2] and the method of
moment [3].
The advantage of the four port network method is a little
computation time and few memory capacities. However, it can
not calculate the radiated field from only common mode
current [2].
The method of moment can consider the radiated electric
field from both differential and common mode current.
However, it can not consider the influence of the dielectric
material of the cable. The presented paper reported that the
influence of the dielectric material can consider inserting the
capacitance between wires. However, the calculation model
used multiple pairs has not been cleared and the model should
be studied because most of cables are constructed with the
multiple pairs.
This paper presents the calculation model of radiated
electromagnetic field from multiple pair cable. The calculation
model is created based on the model of the single twisted pair.
The twisting pitch of each pair was considered. The radiated
electromagnetic field from the UTP cable with the calculation
results to confirm the validity of the model.
II. CALCULATION MODE L OF RADIATED ELECTROMAGNETIC
FIELD FROM MULTIPLE PAIR CABLE
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Figure 1 shows the method of modeling the single pair [3].
It is difficult for the method of moment to treat dielectric
material of the cable. Therefore, the wire radius is changed
and the capacitor is inserted between wires to meet the
transmission constant of the wire model with the theoretical
value or the numerical value. The creating process if the
model is as follows
Copyright © 2009 IEICE
571
Fig. 1 Method of creating wire gird model
EMC’09/Kyoto
23P2-3
First, the dielectric material is removed from the pair as
shown subfigure (a) in Fig.2.
Second, the radius of wire is changed to meet the per-unit
length inductance of the cable with the theoretical value as
shown subfigure (b) in Fig. 2 [2]. In this modeling, the
transmission loss does not considered because the cable length
which we can model by the wire grid is limited up to several
meters, and the transmission loss can be negligible in this
length. The open short method [4] was used to obtain the perunit length inductance. The wire radius of 0.3164 mm was
obtained from the investigation for the cable shown in Fig.1.
Third, the capacitance in inserted between wires to meet the
per-unit length capacitance of the cable with the numerical
value. The value calculated based on the electro-static theory
is used as the per-unit length capacitance. Finite element
method [5] based on the two-dimensional model is used to
obtain the numerical value. The inserted conductance and
capacitance values are obtained by the following equation.
& = & )(0 ́& ZLUH (1)
Where, & )(0 is the numerical value of per-unit length
capacitance, and & ZLUH is the per-unit length capacitance
obtained by the open short method [4].The insertion
capacitance value of 1.24 u 10 pF was obtained for the
model shown in Fig. 1.
The developed wire grid model is shown in Fig. 2.The
length of segment, L, is 1.1mm and the capacitance with
wire is inserted at each segment connection point. The wire
radius of 0.32 mm is used to insert the capacitance. The
twisted pitch is determined from the measurement results for
the actual cable. In this investigation, we used 20 mm as a
long pitch and 16 mm as a short pitch.
́2
cm pitch each other. The pitch is determined from the
investigation results of the cable.
Fig.3 Calculation model of cable
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The transmission constant of the multiple pair cable is
calculated by using the open short method to confirm the
validity of the model.
The method of calculating the transmission constant is
illustrated in Fig. 4. As shown in this figure, one of the pairs,
whose length is 16 mm is selected and a voltage source with
resistance is connected one end of the pair. The input
impedance is calculated when the other end of the pair is
opened and shorted. From the impedance, the characteristic
impedance and the phase constant are calculated [4]. The both
ends of other pairs are opened as shown in Fig. 4.
NEC2 [6] was used as the calculation of the radiated
electric field.
Fig. 2 Developed wire grid model of twisted pair cable
Fig. 4 Method of calculating characteristic impedance and phase constant
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UTP cable used LAN is usually configured by four twisted
pairs. The model of the UTP cable is shown in Fig.3. The
investigation for a UTP cable shows that two pairs are twisted
long pitch, the others are twisted short pitch and, the long
pitch and short pitch pairs place at opposite angle position
each other. These four twisted pairs of cable are twisted with 8
The calculation results of the characteristic impedance and
phase constant are shown in Fig. 5. In this figure, the solid
line is the calculation results of single pair and the dotted line
with circle is the results of one of the multiple pair. The both
calculation results are well agreed. This means that the
assembly of the pairs does not influence to the transmission
characteristics.
Copyright © 2009 IEICE
572
EMC’09/Kyoto
23P2-3
100
80
ω Characteristic Impedance
60
100
Phase Constant ψ
40
single pair UTP cable
Multi-Pair UTP cable
0
0.5
1
1.5
Frequency [GHz]
20
Phase constant [rad/m]
Characteristic Impedance[:]
200
0
2
( 9LQ $) 6 21 /div
Fig. 5: Calculation result of transmission characteristics
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The wire grid model of the telecommunication equipment
is shown in Fig. 6. The telecommunication equipment is
represented by the T type network, which is constructed with
the impedances of Za, Zb, and Zc. The wire grid model is
created by the three wires. The lengths of wires between
conductors are 0.5 mm and the lengths of wire between
conductors and ground is 7 mm. Impedances are inserted at
the junction point of the segment for each wire. For the
transmitter, voltage sources are also inserted in the model in
series of Za and Zb respectively. The value of the impedances
and the sources are determined from the measurement.
E2
UTP Cable1
E1
distance between the antenna and the cable was 3 m, and the
angle toward the antenna was fixed at the position in Fig. 7.
The antenna height was changed from 1 m to 4 m above the
ground plane, and the maximum value of S21 was measured
using a network analyzer.
The height of the cable was 0.25 m and the horizontal length
was 0.5 m, so total length is1.0 m. The input voltage, Vin, at
the power divider was 0 dBm. Measured frequency range was
from 0.3 GHz to 3 GHz. The log-periodic antenna was used as
the measurement from 0.3 GHz to 1 GHz and the ridge-guide
antenna was used from 1 GHz to 3 GHz. From S21 [dB] and
the antenna factors, AF[dB/m], the insertion loss of the power
divider, Ldiv[dB], and the electric field strength E[dBPV/m] is
given by
The value of AF was used to the data presented on the
antenna manual and the value of Ldiv was used the
measurement value.
The calculation model is also shown in Fig. 3. The twisted
pairs and their termination conditions are determined
according with the measurement conditions shown in Fig. 7.
UTP Cable2
Zb
Za
0.5mm
0.25mm
Zc
7mm
Fig.7 Experiment set-up for measuring radiated electric field strength
III. EXPERIMENT
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To confirm the validity of the calculation model, the
radiated electromagnetic field was measured by the
experimental set up shown in Fig. 7. Measurement was carried
out in a semi-anechoic chamber (L=6.2m, W=7.0m, H=5.9m).
CAT-5 LAN cable with four twisted pairs was used for the
experiment. A differential mode signal was impressed to the
two pairs of the cable by the hybrid couplers, and at the other
ends of the pairs, the each wire of the pair was terminated to
the ground plane by the resistance of 50:. The same phase
signal was supplied to the hybrid couplers using power divider.
Other two pairs of the cable were opened at both ends.
The radiated electric field strength from the cable was
measured both horizontal and vertical polarization. The
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A balun has been used to generate a differential mode signal.
However, there is no balun operating more than 1 GHz.
Therefore, we used a hybrid coupler to generate the signal.
Figure 8 shows the measurement result of the impedances, Za,
Zb, and Zc.
Copyright © 2009 IEICE
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100
80
Impedance [:]
Fig.6 Wire grid model of telecommunication equipment
Za
Zb
60
40
20
Zc
0
1
2
Frequency [GHz]
3
Fig. 8 Measurement result of impedances for hybrid coupler
EMC’09/Kyoto
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As shown in Fig. 8, Zc is almost zero because the external
conductor of the output ports is connected to the ground plane
directly. Za and Zb are almost 50 :. This means that the
transmission line is terminated by the resistance of 100 :.
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The calculated and measured field strength when the
number of signal sources is changed is shown in Fig. 9. The
maximum field strength is shown in this figure. Circles in the
figure indicate the measurement results when the number of
the signal is one, triangles indicate the measurement results
when the number of signal is two, the solid lines indicate
when the calculation results the number of the signal is one,
and the dotted lines indicate when the calculation results when
the number of signal is two.
As shown in Fig. 9, the average deviation between one
source and two sources is 4.03 dB for the measurement and
6.47 dB for the calculation respectively. This means that the
average field strength increases when the number of signal
sources increases from one to two.
E-field-strength[dBǴV/m]
110
100
Measurement(two source)
Measurement(one source)
Calculation(two source)
Calculation(one source)
90
80
70
60
300
Vertical Polarizaion
1000
2000
3000
Frequency [MHz]
Fig.9 Maximum field strength when number of sources is changed
E-field-strength[dBǴV/m]
110
Measurement
Calculation(changed pitch)
Calculation(not changed pitch)
100
80
70
300
IV. CONCLUSION
The transmission speed of the systems using UTP cable
increases day by day. The study of the electromagnetic field
emitted from UTP cable is needed in the frequency rang more
than 1GHz. This paper presents the method of analysis for the
radiated electromagnetic field from multiple-pair cable by
using the method of moment.
The wire radius was modified to meet the per-unit length
inductance of the wire model with the theoretical value, and
the capacitance which was determined from the per-unit
length capacitance of the wire model and the numerical
calculation for electrostatic field, inserted between the wires.
The wire models were assembled to construct the multiple
pair cable.
The radiated electromagnetic field was measured using the
semi-anechoic chamber. The hybrid couplers and the power
divider were used to supply the differential mode signal to the
multiple pairs. The calculation results are almost agreed with
the measured one from 0.3 GHz to 3 GHz. This means that the
model proposed in this paper is effective to calculate the
radiated electromagnetic field.
Future problem is the study of the radiated electromagnetic
field dependence when the signals supply to the multiple pairs.
REFERENCES
90
60
signal is 2, the solid line indicates the calculation results when
the twisting pitch is changed at the position of pair, and the
dotted lines indicates the calculation results the twisting pitch
is not changed.
As shown in Fig. 10, the calculation results are almost
agreed with the measurement one. The average deviation
between changed pitch and not changed pitch is 1.74 dB. This
means that the difference of twisted pitch does not pay the
significant affect to the radiated field.
These results suggest that the calculation model proposed
in this paper is effective to calculate the radiated
electromagnetic field from the multiple pair cable.
Vertical Polarizarion
1000
2000
3000
Frequency [MHz]
Fig.10 Maximum field when twisted pitch is changed
The calculated and measured field strength, when the
twisting pitch is changed, is shown in Fig. 10. The maximum
field strength is shown in this figure. Circles in the figure
indicate the measurement results when the number of the
[1] IEEE802.3ab,“ Physical layer parameters and specifications for
1000Mb/s operation over 4-pair of category 5 balanced copper
cabling Type 1000Base-T ”, 1999.
[2] S. Fujiishi, N. Kuwabara, and F. Amemiya, Calculation of
radiated field from UTP Cable at high frequency using 4-port
network model, EMC Europe 2004, L02, pp.570-575,
Eindhoven, Sep. 2004
[3] H. Tamaki, N. Kuwabara, . Ishida, and M. Kawabata,
“Calculation of emitted electromagnetic field from UTP cable
by moment method form 0.3 GHz to 2 GHz,” EMC Europe
2006, OThB2-4, Barcelona, pp. 568-573, Sep. 2006
[4] T. Nango, R. Matsubara, . Murakawa, N. Kuwabara, and M
Tokuda, “Investigation of radiated electromagnetic field
characteristics of imitated equipment and its application”,
Trans. IEICE apan, vol. 86-B, no.8, pp.1629-1638, 2003
[5] URL: http://www.ansoft.com/maxwellsv/
[6] G. . Burke and A. . Poggio, “Numerical Electromagnetics
Code (NEC) - Method of Moments, Part I-III, Lawrence
Livermore Laboratory, 1981
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