Characterization of Shield Inhomogeneities of Multiconductor Cables
by Evaluation of Measured Transfer Impedances and Admittances
Lorenz Jung
Jan Luiken ter Haseborg
Member IEEE
Senior Member IEEE
Hamburg University of Technology
Dept. of Measurement Engineering / EMC
Harburger S&loss Strasse 20, D-2 107 1 Hamburg, Germany
Abstract: The determination of the complex transfer
impedances and transfer admittances of shielded multiconductor cables is the prerequisite for calculating disturbing
currents on the inner wires of the cable. With a measurement
procedure based on the improved triaxial measurement setups
using multiconductor transmission line theory for evaluation,
it is possible to determine individual transfer impedances and
admittances for each inner conductor of a shielded multiconductor cable over a broad frequency range [3]. This paper
shows the determination of the location and the calculation of
the area of shield inhomogeneities by the evaluation of
measured transfer impedances and admittances.
INTRODUCTION
The reliability of large control and communication systems is
a topic of increasing importance. The reliability can be
affected by disturbed signal transmission via cables.
Especially in the design stage of a system it is important to
calculate the expected disturbing currents and voltages on the
transmission wires of the cable. For this calculation the
electromagnetic interferences from the environment of the
cable have to be known. Then, with a coupling model, the
Ill
ZsrnIodz
Kdz
current on the cable shield and the voltage between cable
shield and environment have to be determined. To calculate
the interfering currents and voltages on the inner wires of the
cable, the complex transfer impedance and the complex
transfer admittance of each wire of the cable have to be
known. The measured transfer impedances and admittances
can also be used to characterize shield inhomogeneities.
MULTICOM)UCTORTRANSMISSIONLINE
THEORYPORSHIELDEDCABLES
An infmitesimally short part of a shielded multiconductor
transmission line under consideration of the conductive
environment is represented by the equivalent circuit shown in
figure 1. The equivalent circuit consists of the inner system
representing the cable shield and the inner conductors of the
cable. The outer system depends on the interaction of the
environment with the shield. The current on the cable shield
and the voltage between the cable shield and the environment
which are caused by interferences from the environment
originate from the distributed sources J&z and E&z in the
equivalent circuit of the outer system. The interaction of the
outer system with the inner system is represented by the
In+dIn
I&dz
inner system:
conductors and shield
t
IO
EFdz
Rbdz Lj-,dz
outer system:
shield and environment
Figure 1. Equivalent circuit of an infinitesimally
short part of a transmission line in interfering environment.
0-7803-5057-X/99/$10.00 © 1999 IEEE
571
distributed sources Z’TiIodz and Y’riUodz for each inner
conductor. Z’,i and Y’,i represent the complex transfer
impedance and admittance per unit length of the i-th
conductor. Z’,i is defined as the ratio of the voltage between
the inner conductor i and the cable shield and the disturbing
current on the cable shield per unit length. Y’rr is defined as
the ratio of the current on the inner conductor i and the
disturbing voltage between the cable shield and the
environment per unit length. Both Z’ri and Y’ri have to be
determined individually for each conductor by measurements.
The mathematical approach to the circuit of the inner system
shown in figure 1 is based on the telegraphers’s equation in
matrix form including the consideration of the distributed
interference sources
measure the disturbing voltage between the respective
conductor and the shield. The input impedance of the network
analyzer represents one of these terminations.
termination
N-connector
brass block
(1)
termination
5OQ
According to figure 1 [U(z)] and [I(z)] are the vectors
containing the voltages between the n inner conductors and
the shield, respectively the currents on the n conductors. The
nxn impedance matrix [Z’] and the nxn admittance matrix ryl]
are composed of the frequency-dependent complex primary
line parameters per unit length. The n elements of the vector
[Z’riIs(z)] consist of the product of the transfer impedance Z’ri
of the i-th conductor of the inner system and the current of the
outer system at the location z. The vector [Y’rrUo(z)] is
composed correspondingly.
The solution of the system of differential equations (1) [8] and
the measured propagation
constant ‘ya, characteristic
impedance r, and termination of the outer system (see figure
3) allows to calculate the voltage and current on every
location of the outer system from the voltage U,(O), so that the
voltages and currents of the inner system can be determined as
function of the primary line parameters per unit length, the
propagation constants, the complex transfer impedances and
the complex transfer admittances [5].
SETUPFORTHEMEASUREMENTOFTHE
TRANSFERIMI'EDANCES
By analogy with IEC96-1 [12], the improved setup is a biaxial
system consisting of an outer tube that forms together with the
shield of the cable under test (CUT) the outer system. The
length of the tube is, depending on the necessary frequency
range and sensitivity, 62 or 31 cm. The outer system is fed on
the near end (see figure 2). Each inner conductor of the CUT
is terminated at the near end. For proper decoupling the
termination resistors are embedded entirely in a brass block .
The diameter of this brass block is equal to the outer diameter
of the cable shield. On the far end each inner conductor is also
terminated by 50 Sz resistors. The termination resistors are not
soldered to the conductors in order to allow their removal to
572
SMB-connector
output
near end
far end
Figure 2. Improved
transfer impedances.
-2 [I(‘)]=[yr][u(z)]
- [Y+iUCJ(Z)]
.
resistors
resistors
setup for the measurement of the
In order to evaluate the measurements the equivalent circuit of
the setup has to be regarded.
1v31
r_..___._.
CUT
Ldl
WAdI ,.______________
W.ll
Figure 3. Equivalent
circuit
of the
measurement of the transfer impedances.
setup
for
the
The termination resistors are represented by the admittance
matrices [Ys] and [Y,J. The influence of the connector head is
considered by the impedance matrix [Z,,] and the admittance
matrix [Y,,]. [Z,,] represents the complex self impedances
and mutual inductances between the inner conductors and has
to be determined by short circuit measurements. [Y,,]
represents the complex self admittances and mutual
capacitances and has to be determined by open circuit
measurements.
The transfer impedance is calculated as
[zi]=[Al][[&$qp+]].
The matrices [Ai] to [As] are functions of the known electrical
and mechanical parameters of the inner and outer system and
the
teeations:
[51.
[y31,
[yd,
[YAdk
[zAd19
[z’l,
[y’l,
‘Ya and
ra
Measurement results
Figure 4 shows the measured magnitude and phase of the
transfer impedances of all conductors of a seven-conductor
cable LICY-7x0. 14mm2.
now exposed to the shield inhomogeneity
center conductor.
and also to the
Phase
(“) ,80
1
1
10
10
f (MHz)
100
Figure 6. Measured transfer impedances of four conductors
of a seven-conductor cable LICY-7x0.14mm2 with a shield
inhomogeneity in terms of a hole above conductors 2 and 7.
100
f (MHz)
Figure 4. Measured transfer impedances of all conductors
of a seven-conductor cable LICY-7x0. 14mm2.
The phases show the typical behavior that is attributed to
porpoising coupling into single braided coaxial cables [ 11[lo].
In the case of a shield inhomogeneity the coupling behavior
for the conductor which is exposed to this shield
inhomogeneity changes to aperture coupling as shown in
figure 5. For clearness the complex transfer impedances are
shown only for four conductors.
Assuming Dr’ and M,,’ as independent of a shield inhomogeneity, the contribution of the inhomogeneity to Mt,’ can
be calculated as the difference of the imaginary parts of Zr
from the measurement results in case of a shield inhomogeneity and the intact cable (e.g. shown in fig. 6 and 4).
Figure 7 shows Mr,’ calculated as:
Mr,’ = Im{ Z,‘(figure 6)- Z,‘(tigure 4) } / o
Mh’
(“Hhl,
(4)
0.1
0.01
: :I :::::
I ,I,, ----------j-----i---i--i-;t5i-~~t;I I ,I,_
0.2-----_____
~____~----~---t-:--~-i-i-i
-.-- -. r.
_:-:.
_:_
: _:_:_:_:_
___- ;I - - -I- : -;- j :4:
I
I
I
I11111
II
0
1
10
100
f(MHZ,
Figure 7. Calculated Ml according to (4).
0.001
0.0001
1
10
f (MHz)
100
Figure 5. Measured transfer impedances of four conductors
of a seven-conductor cable LICY-7x0.14mm2 with a shield
inhomogeneity in terms of a hole above conductor 2.
The complex transfer impedance of braided coaxial cables can
be expressed as [lo]
ZG = Dr’ + jW(Mr,’ - M<)
As a first approach to calculate the area of the inhomogeneity
from the measurement results, an expression of the mutual
inductance Ml2 due to aperture coupling for a circular hole
with radius r in a single conductor cable with outer diameter D
was used [2]:
M1,=4u0r3/(3n2D2)
(5)
(3)
where Dr’ is attributed to diffusion coupling and can be
neglected towards higher frequencies [4]. The mutual
inductance per unit length Mb’ describes the porpoising coupling and the mutual inductance per unit length Mt,’
characterizes aperture coupling. Mt,’ and Mb’ become dominant
at higher frequencies and are opposite in phase as expressed in
(3). The unexpected behavior of the measured phase of
conductor 2 towards higher frequencies shown in figure 5 may
be due to long line effects (see also figure 6).
If the shield inhomogeneity is increased, the change of the
coupling mechanism extends to the outer conductors that are
573
Figure 8.
Calculated area of the inhomogeneity.
Setting Ml2 = Mh and so obtaining r, the area of the inhomogeneity was calculated as shown in figure 8. It is planned
to improve the fair agreement of the calculation with the
reality by considering the eccentricity of the outer conductors.
The matrices [BJ, [Bs] and [Yv] are functions of the known
electrical and mechanical parameters of the inner and outer
system and the terminations: [Y3], p4], vAa], [Z,J, [Z’],
SETUPFORTHEMEASUREMENTOFTHE
TRANSFERADMITTANCES
In order to measure the complex transfer admittances, the
setup for the measurement of the transfer impedances has to
be modified. The setup consists of the same elements as in the
setup for the measurement of the transfer impedances except
for a different input connection to the outer system and an
open circuit between the tube and the connector head. The
similarity to the setup for the measurement of the transfer
impedance allows an easy interchange of the CUT -including
the connector head- between these two setups.
termination resistors
SMB 5021
connector head
The transfer admittance is calculated as
WI, L andra [51.
Measurement results
In the figures 11 and 12 measured transfer admittances of a
seven-conductor cable LICY-7x0.14mm2 are shown. Also in
this example individual transfer admittances with very similar
values for each conductor can be seen.
1Y’Tl (S/m)
Phase (‘)
la-l
1e-2
outer tube
le-3
7
le-4
18-5
inner conductor
I&
1e-7
le-8
bras; block
SMB-conn&tor
output
input
near end
far end
Figure 9. Improved
transfer admittances.
.--‘-“i
!..-‘~-.‘l
100
Figure 11. Measured transfer admittances of the outer
conductors of a seven-conductor cable LICY-7x0.14mm2.
near end
setup for the measurement of the
UUI
10
f (MHz)
The equivalent circuit has to be changed accordingly.
I&d1 LyAdl
ry31
1‘1’41
PTIT
:;
:
:
conductor n
l__._.___.
1
0.1
’
termination
resistors
50R
,..__..___...____
In case of a shield inhomogeneity the value of the transfer
admittance changes for the conductor near to this inhomogeneity. As example for a shield inhomogeneity a hole
was made into the shield. Fig. 12 shows the measurement
results for a 3 mm by 10 mm hole above conductor 4. It can
be seen, that the value of the transfer admittance of conductor
4 is increased.
conductor 1
k-T1
le-1
shield
t
(S/m)
Phase (“)
I
Hole above conductor 4:
I
I
f
16-Z
. ..______.
Z=O
far
end
Z,-+m
2=1
shield
*la ra
outer tube
R: termination
resistor 50 C2
0
1
U,(1)
Conductor 4
le-3
-
l-4
near
end
1e-5
IFS-6
Figure 10. Equivalent circuit of the setup for the
measurement of the transfer admittances.
1e-7
Again, the termination resistors are represented by the
admittance matrices [YJ and [YJ. The influence of the
connector head is considered by the impedance matrix [Z,,]
and the admittance matrix [Y,,] in the similar manner as in
the equivalent circuit for the measurement of the transfer
impedances.
574
18-a '
0.1
.
1
10
I
1
ICUJ
f (MHz)
Figure 12. Measured transfer admittances of the outer
conductors of a seven-conductor cable LICY-7x0.14mm2 with
a shield inhomogeneity in terms of a hole above conductor 4.
The transfer admittance of the cable without a shield
inhomogeneity (fig.1 1) under consideration of the environment is described as [9]:
Yi, =
coci
jw--,
c ’
=
jo
%E*
(7)
where C’,, is the capacitance per unit length of the (small)
apertures of the braided cable shield and C’ is the capacitance
per unit length as a primary line parameter of each inner
conductor as intrinsic cable parameters. The environment is
considered by the capacitance per unit length Cs between the
shield and in this case the outer tube of the setup. C’, can be
calculated from the measured Ta and ya of the outer system.
The calculation of the area of the inhomogeneity is based on
the additional capacitance CA of the inhomogeneity’s aperture.
With the known length of the setup 1, the measured transfer
admittance (fig. 12) in case of a shield inhomogeneity Y’rA for
each conductor can be expressed as:
Y;*
E,~ [l l] considers the aperture loading and is defined by the
known relative permittivities ai and zszof the inner and outer
system of the setup.
% = EI+E
(11)
2
Under assumption of the practical case that the geometry of
the inhomogeneity is unknown, so an elliptic integral cannot
be applied, the aperture polarizability a, of a circle with the
diameter d was chosen [6].
CX+13
(12)
Set&g
CA in eq. (9) equal to CA h eq. (lo), d can be
calculated. Figure 14 shows the so calculated area of the
&omogeneity.
H&size
(mmmz)
(c~O+C*l-l)C~
c’
.
Assuming C’,, and C’ as independent of the shield inhomogeneity, CA can be calculated from the difference of the
imaginary parts of the measurement results in case of a shield
inhomogeneity and the intact cable:
(9)
The term Im{Y’,A-Y’,o}/o
calculated from the measurement
results shown in figures 11 and 12 is shown in figure 13.
~m~a-r~o)
IO
0.1
I
10
100
f (MHz)
Figure 14. Calculated aperture area.
It can be seen, that the area of the aperture is over- or under
estimated, respectively, depending of the proximity of the
individual conductor to the aperture. The average value over
all six outer conductors matches up to approximately 20 MHZ
very well the real value of 30 mm2.
CONCLUSION
1
0.1
10
,@I
f (MHz)
Figure 13. Calculated Im{Y’r*-Y’r,,}/w
according to (9).
It can be seen that Im{Y’r*-Y’,,}/o
is almost constant over a
broad frequency range.
The capacitance of a single aperture [6] depends on the radius
of an inner conductor a,,, the inner radius of the cable shield a,
the aperture polarizability a, [6j, [l l] and the equivalent
relative permittivity seq.
c,
=-
Eo%q%
( 2naq >2
“Z-&L
’
0 a0
(10)
575
The setups for the determination of the complex transfer impedances and transfer admittances of shielded multiconductor
cables and the methods of evaluation based on transmission
line theory for shielded multiconductor cables were explained.
A more detailed description can be found in [3] and [5]. The
discussed measurement examples cover a broad frequency
range. The influence of shield inhomogeneities on the complex transfer impedances and transfer admittances has been
shown. The possibility of calculating the area of a single
shield inhomogeneity from the measurement data of both the
transfer impedances and transfer admittances has been demonstrated. Although some parameters were neglected, e.g. the
eccentricity of the outer conductors, the calculations show a
good agreement with the reality. The investigations to improve these measurement methods will go on.
REFERENCES
[l] Hoeft, L.O., Hofstra, J.S., Peel, R.J., Porpoising
Coupling in Braided Cables, 1989 International Symposium
on EMC, Nagoya, Japan, 1989, pp. 595-599.
[2] Hoeft, L.O., A Model for Predicting the Surface Transfer
Impedance of Braided Cable, 1986 IEEE Int. Symposium on
EMC, San Diego, 1986, pp. 402-404.
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Setup for the Measurement of the Complex Transfer
Impedances and Transfer Admittances of Shielded
Multiconductor Cables, 1998 IEEE Int. Symposium on EMC,
Denver, 1998, pp. 214-218.
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Shaker Verlag, Aachen 1997, Ph.D. thesis, Hamburg University of Technology, 1997
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Techniquesand ReferenceData, AFWL-TR80-402, Air Force
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[8] Paul, C. R., Analysis of Multiconductor Transmission
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[9] Tesche, F.M., Ianoz, M.V., Karlson, T., EMC Analysis
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[lo] Tyni, M., The Transfer Impedance of Coaxial Cables
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[ 121 Radio-frequency cables, General requirements and
measuring methods, International Electrotechnical Commission IEC Standard, Publication 96-1, fourth edition ,1986
576