Equivalent cable harness method generalized for predicting the electromagnetic emission of twisted-wire pairs Текст научной статьи по специальности «Электротехника, электронная техника, информационные технологии»

Electrical Insulation and Cable Engineering

UDC 621.319 https://doi.Org/10.20998/2074-272X.2022.2.05

S. Bensiammar, M. Lefouili, S. Belkhelfa

Equivalent cable harness method generalized for predicting the electromagnetic emission of twisted-wire pairs

Introduction. In this paper, the equivalent cable harness method is generalized for predicting the electromagnetic emissions problems of twisted-wire pairs. The novelty of the proposed work consists in modeling of a multiconductor cable, in a simplified cable harness composed of a reduced number of equivalent conductors, each one is representing the behavior of one group of conductors of the initial cable. Purpose. This work is focused on the development and implementation of simplified simulations to study electromagnetic couplings on multiconductor cable. Methods. This method requires a four step procedure which is summarized as follows. Two different cases, of one end grounded and two ends grounded configurations can be analyzed. Results. The results had shown that the model complexity and computation time are significantly reduced, without, however, reducing the accuracy of the calculations. References 20, tables 1, figures 8.

Key words: electromagnetic emission, asymmetric digital subscriber line, crosstalk, equivalent cable harness method, multiconductor transmission line network, power loss, twisted-wire pairs.

Вступ. У цш cmammi метод е^валентного кабельного джгута узагальнюеться для прогнозування задач електромагнтного випромтювання кручених пар дротiв. Новизна запропонованог роботи полягае в моделюванш багатожильного кабелю в спрощеному джгутi проводiв, що складаеться зi зменшеног K^rnc^i еквiвслентних провiдникiв, кожен з яких репрезентуе поведтку одшег групи провiдникiв вихiдного кабелю. Мета. Робота зосереджена на розробц та реалiзацii спрощеного моделювання для до^дження електромагттних зв'язюв у багатожильних кабелях. Методи. Цей метод вимагае чотириступтчастог процедуры, яка коротко описана у cтаттi. Можна проаналiзувати два рiзнi випадки: конф^рацп iз заземленням одного ктця та заземлення двох ктщв. Результати. Результати показали, що складшсть моделi та тривалкть обчислень значно знижуються, проте без зниження точноcтi обчислень. Бiбл. 20, табл. 1, рис. 8. Ключовi слова: електромагштне випромшювання, асиметрична цифрова абонентська лЫя, перехресш перешкоди, метод еквiвалентного кабельного джгута, мережа багатопроввдних лшш передач^ втрати потужноси, кручеш пари дроив.

Introduction. For transmission signal in complex telecommunication network one of principle resources of noise that affect the signal quality is due to the crosstalk coupling. The crosstalk among twisted-wire pairs (TWPs) is commonly classified into near end crosstalk (NEXT) and far end crosstalk (FEXT) [1-4]. Furthermore, we distinguished two types of coupling crosstalk, the inductive coupling and the capacitive coupling, the dominant coupling at an arbitrary configuration is due to the termination impedance effects [5, 6].

The survey of literature shows that reducing the number of wires is not a new task. An efficient simplification technique called the «equivalent cable bundle method» (ECBM) has been proposed for modelling electromagnetic (EM) common-mode currents on complex cable bundles for telecommunications networks applications with arbitrary loads [7]. This method, allows, using the theory of Multiconductor Transmission Line Network (MTLN), to take into account the phenomena of propagation and couplings on and between all the wires of the network.

In recent years, the increase in the frequency of disturbances electromagnetic that can potentially attack the wiring network encourages the research to extend digital immunity to high frequencies. This will unfortunately comes up against the limitation in MTLN frequency.

In high frequencies, the use of three-dimensional methods, solving the Maxwell equations in space then proves to be obligatory. However, they require a fine discretization of each conductor of the beam in segments whose length is usually less than one tenth of the wavelength. The computation times then become

prohibitive as soon as the number of conductors of the beam in important.

It must therefore find simplifying hypotheses allowing the complexity to be reduced wiring harness without, however, reducing the accuracy of the calculations [8, 9]. The goal final is to generalize the feasibility of such an approach for twisted-wire pairs.

Purpose of the work is focused on the development and implementation of simplified simulations to study electromagnetic couplings on multiconductor cable.

Presentation of the equivalent cable harness method proposed of complex twisted-wire pairs. Description of the main assumption adopted in this modified procedure for a coupling problem in twisted-wire pairs cable will be detailed in this section.

The proposed geometry consists of a cable composed of twisted-wire pairs, both ends or only one end of the each pair circuit can be grounded.

Note that the twisted-wire pairs used here are connected to the ground plane. We would expect common mode current to be dominant. Therefore, the main assumption of the original ECBM is unchanged [10], we make approach that the impedance loads in such case of twisted-wire pairs can be considered such as a common mode loads and the differential loads in one end of the pairs can be neglected.

The determination of geometrical characteristics of the reduced cable is omitted here because the aim of the method is to predict crosstalk in the pairs that we are interested in his currents and voltages [11, 12].

The modified equivalent cable harness method for modeling crosstalk in frequency domain among twisted-

© S. Bensiammar, M. Lefouili, S. Belkhelfa

wire pairs requires a four-step procedure [9], which is summarized as follows.

Step I. The goal of this step is to classify the pairs of the initial cable in different groups according to their termination loads at both ends of each pair. The culprit and victim pairs are classified into two groups separately and they hold its initial characteristics (including its positions, radius, and medium). The common-mode characteristic impedance Z^ is determined by modal transformation in the MTLN formalism in order to obtain the characteristics of all the modes propagating along the cable. Furthermore, the very important condition of the eigenvector associated with the common mode in the matrix [Tx] is verified, this part is more detailed in the original ECBM [8, 10].

Then all the remaining pairs in the complete cable bundle are sorted into groups by comparing the value of the termination loads (near Z0i and far ZL) to Zmc. The conductors are installed as pairs; each two conductors for one pair are in the same group because the modal analysis is made of twisted-wire pairs configuration. We define the four groups (may be less than four) which can be determined in each configuration in Table 1.

Table 1

Classification of the pairs according to their termination loads

Termination load Group 1 Group 2 Group 3 Group 4

Near end (0) 7 < 7 ^0/ ^mc 7 < 7 0i mc 7 > 7 0i mc 7 > 7 0i mc

Far end (L) 7 < 7 ^Li ^mc 7Li > Rmc 7 < 7 ^Li ^mc 7 > 7 ^Li ^mc

//////////////////////////////////////////////////// Fig. 1. Mode common current and voltage of k conductors in the same group

To determine the inductance reduced matrix, we need two additional assumptions detailed in [9]:

1) the currents flowing along all the «k» conductors of a cable bundle are decomposed in common mode currents and a differential mode currents. The differential mode current can be neglected [5, 13, 14].

The current and the voltage of «k» conductors in the same group can be written by:

(1)

Iec = I1 +I2 + - + Ik ;

Fee = V + V2 + ... + Vk

(2)

Thus, from the telegrapher's equation on the MTLN formalism for lossless line we can obtain the inductance matrix links the currents and the voltages on each conductor on an infinitesimal segment of length:

d_

~dz

. L11 L12 ' ' L1k ' Id

£... = - J® . L21 L22 ' ' L2k .. Ic2

Vk _ _ Lk1 Lk2 ' • Lkk _ _ Ick

(3)

2) The common mode currents along all the conductors of a same group are identical:

Iec = I1 = 12 = - = Ik , (4)

where Ik is the mode common current in the k conductor.

The common-mode characteristic impedance of the harness can be obtained:

V Z

Vck = ^ = , (5)

kle

k

where Z is the common-mode characteristic impedance of each conductor in the group (Fig. 2).

Step II. The determination of the per unit length (p.u.l) parameter matrices of an equivalent cable is based on the determination of p.u. parameter matrices of the pairs from which it is consisted.

We consider a short circuit between conductors of one group of «k» conductors (Fig. 1). This assumption allows: firstly to define the group current Iec for the equivalent cable and secondly the group voltage Vec for the equivalent cable.

Conductor ]

twmi}:i№i!7-7 ittPfi»

Fig.2. Cross section view of complete and reduced cable

These assumptions may allow finding the final system matrix; we index the conductors of each group as follows:

• N1 conductors of the first group indexed 1 to x;

• N2 conductors of the second group indexed x+1 to y;

• N3 conductors of the third group indexed y+1 to z;

• N4 conductors of the fourth group indexed z+1 to N. The final system that allows finding Lred can be

obtained:

dV1 ox

= - J®

XLLi, .X

Ni

^ecl +■

y

■¡1=x+i

L

1i

-I.

X=y+1Ll

N

Iec3 +

N2 XN r

x=z+1Li

ec2

N

4

dV,

N

Ox

= - J®

XX=i Ln , , Zi=.

Ni

iz -Ii=y+1'

Ieci +■

i=x+1

Ni

Xi=y+1 LNi

Iec3 +

X

N 2

N

i=z+1 '

Iec4

1 ec2

; (6)

L

Ni

I

ec4

. (7)

N3 N4

The voltages of each conductor belonging to the same group being equal (2), the insertion of this property in previous equations leads to the following system connecting the voltages and currents of the four groups of conductors [7]:

dVe

ecl

dx

= -jm

yi=1yj=lLij T yi=1yj=.

N2

hcl +"

j=x+1Lij

NN

hc2 +

lJV2

j=y+iLij

N1N3

hci +

yi=1y j=

NL

NlN4

'ec4

(8)

d¥e

ec2

dx

= -jm

Ti=x+]Sj=lLiJ J S=x+lX,=x+lLj

NlN2

N22

Iec2 +

yy y t yy y L

/-i=x+lZ-j=y+l ''j /—i=x+l/—ij=z+llJ

N2N3

N2N4

ec4

(9)

dVe

ec3

dx

■■-jm

yz yx l yz yy L

L-ii=y+\L-ij=\ ij ¿—ii=y+iAjj=x+l i 1 -TTVt-7ecl +-\7~Tt-Iec2 +

(10)

yz yz L.. yz yN L..

L-, i=y+iA.i j=y+i ij ¿—ii=y+iL-i j=z+1 V j

+ N3 Iec3 + N3N4 Iec4

dVe

ec4

dx

= -jm

yN yx L yN yy L.

¿-,i=z+lL-i j=1 ij ¿^i=z+1^j=x+1 Li -TTTT-7ec1 +-TTT7-

hc2 +

(11)

ZN y z L yN yN l

i= z+1Z-lj=y+1 ij Z-l i= Z+1^-l j=Z+1 ij J

+ rTTT Iec3 + 772 Iec4

N

d_

dz

Jred J

Vec1

Vec2 Vec3 Vec4 L11r L21r L31r

= - jm[Lred ]•

^ce1 he2 he3 ^ce4

L

41r

L11r =

L12r L13r L14r

L22r L23r L24r

L32r L33r L34r

L42r L43r L44r

yx x 1y j=1 Lij

N2

(13)

(14)

considered as pure resistance and are not frequency dependent. There are two kinds of the termination loads, differential-mode loads and common-mode loads:

• Common-mode loads. Each load connected to the ground plane at his terminal end (Fig. 3).

Fig. 3. Equivalent termination common-mode loads

The impedance equivalent Zec for «k» conductors in the same group (Zj, Z2 .. .Zk), is:

111 1

-= — + — +... + —. (16)

Zec Z1 Z 2 Zk

• Differential-mode loads. We consider the type differential loads connected between conductors from different groups (Fig. 4). The impedance equivalent Zd12, for two conductors (1 and 2) in group 1 and two conductors (N1+1 and N1+2) in group 2, is:

1 1 1

-+—

Zd12 Z1-N1+1 Z 2-N1+2

(17)

(12)

The expression of p.u. capacitance matrix for the reduced model [Cred] can be obtained with the same reasoning in no homogenous and polar medium.

For a weakly polar medium, one can ignore the dispersion of the dielectric constant and, accordingly, the phase velocity [11]:

[Cred ] = ""2" [red ] ^ (15)

O2

where o = c/-yfeT.

So, using the assumptions and approximations set out above, the matrix inductance and capacitance with (N*N) dimension can be reduced into matrix (4*4) which coefficients exerted on and between the conductors.

Step III. The aim of this step is to determine the termination loads to be connected at both ends of the equivalent conductor. Here, all load impedances are

nfflmmnmrnfflMiMK

Fig. 4. Equivalent termination differential-mode loads

The type of differential loads connected between conductors in the same group is neglected.

Step IV. The aim of this step is to determine the section geometry (radius, coating radius, permittivity relative of coating, height, distance between harnesses), of each reduced harness using the linear parameter matrices determined at the Step II. This part is more detailed in the original ECBM [8, 10].

For modeling the twist of pairs on complete model the matrix P [1] was used, in the reduced model this matrix is evaluated to take into account only the twisted wires of the pairs which we not apply the method [1].

For the equivalent cable for each group the current and voltage are multiplied by 1 in the matrix P.

In order to determine currents and voltages in both ends of each pair, the excited pair is assumed to be a disturber and the crosstalk in an arbitrary victim pair in term of power loss (PL) is shown.

Note that the values of the power loss crosstalk (PLnext, PLfext) in decibels can be calculated as follows [15-18]:

+

(18)

(19)

(20) (21)

PLNEXTjdB - " 10log!0(| H NEXT (f )|2);

PLFEXT/dB - " 10log10( H FEXT (f )2),

where HNEXT and HFEXT are the transfer function.

The PL expression can be written as follows:

PLnext,,/dB - 10log10[(V-(X1)/V1(x1))2

PLfexti/dB - 10log10 [(V- (xl )/V (X1 ))2 where V- is the voltage in the victim wire which we want calculates his crosstalk; X\, Xl are the first and the last extremities of the line [19].

Application of the equivalent cable harness method. The mathematical model established will be used for obtaining the power loss near and far (PLNEXT and PLFEXT) in a bundle of twisted wire pairs. Twisted wire-pair is connected by two ends of each pair to the ground plane. Figure 5 illustrates the geometry used, they shows the first case of initial model of twenty-eight pairs denoted from 1 to 56, and the reduced cable of two pairs and two equivalent harness denoted ec1, ec2.

insulation is much less than the capacitive resistance œC, respectively: R << œL, G << œC [20].

wtlhiwmim mi mvmit am) wiw

Fig. 5. Complete model cable and reduced model cable twisted-wire pairs cross sectional view

All wires are further assumed to have the same radius a = 0.523 mm and polyvinyl chloride coating radius of b = 0.549 mm. The length of the wire is L = 1 km. The twisted pair consists of N = 10000 loops. The height of the first wire (numerated 8 and 10) above ground conductor is h = 20 mm, the height is very close to the reference plane, the intention in doing so is to avoid the noise produced by the loop between the receptor circuit and the reference plane.

The other conductors are located just above and next to the first wire with vertical distance of 0.127 mm for the same pair conductors and 3.17 mm for other conductors, the horizontal distance between the wires is d = 3.17 mm.

In Fig. 6 the pair one is given as an example, which is connected to the voltage source V0 at its near end through a load Z01 and adapted at its far end through a load ZL1.

The crosstalk will be studied in the frequency range from 1 kHz to 30 MHz with reference to Fig. 6 and in order to make same loads such as in XDSL systems, the loads in the pairs which we are interested are set to Z01 = ZL1= Z02 = = ZL2 = 120 Q under the condition, that for a twisted pair the active resistance R of the conductors is much less than the inductive resistance mL, and the active conductivity G of the

-Vi XL

Fig. 6. Model of two ends grounded geometry of twisted-wire pairs longitudinal view

The classification of groups is made according to the comparison with the common-mode loads determined by the modal analysis.

The pairs of the complete cable bundle sorted into four groups as follows (Fig. 5):

• group 1: pairs 1 (conductors 1-2);

• group 2: pairs 2 (conductors 3-4);

• group 3: harness 1 (conductors 5-30);

• group 4: harness 2 (conductors 31-56);

The p.u. parameter matrices [Lred] and [Cred] of the reduced harnesses cables are calculated in nH/m and pF/m for a 1 km long line respectively:

"1.02 0.88 0.25 0.25 0.25 0.19"

i^red ] =

1.02 0.25 0.24 0.24 0.19

1.02 0.88 0.13 0.17

1.02 0.13 0.17 0.36 0.16 0.34

- 0.53 -0.47 -4.13 -1.21

- 0.47 -0.52 -4.64 -0.71

43.70 -36.59 -0.64 -1.04

43.72 -0.65 -0.64

46.10 -15.20

46.17

[^red]

Next before and after applying our equivalent cable harness method the results are compared. The culprit pair is the pair one numerated (1, 2) in Fig. 5, we are interested in the voltage and current of the second pair numerated (3, 4) in Fig. 5.

The near end of conductor one (first pair (culprit pair)) is excited with a constant voltage source of 1 V.

The first pair is activated and we calculate the PL in the second pair (conductor 3). Next, we apply the method and we calculate again the PL on the second pair when the first pair is activated.

Figures 7, 8 show the power loss in the second pair (conductor 3) for NEXT and FEXT successively for the initial model and the complete model.

100 90 80 70

§• 60

K

g 50

J

& 40 30 20

105 106 frequency (Hz)

Fig. 7. PLNEXT voltage in the frequency domain on pair two

frequency (Hz)

Fig. 8. PLfext voltage in the frequency domain on pair two

For this configuration the difference between the two models is a few decibels. In the high frequency some differences are observed which are possibly due to the apparition of the transverse electric and magnetic mode. Results for this case confirm that equivalent cable harness method can be successfully applied in prediction crosstalk in a two ends grounded configuration of twisted-wire pairs cable in frequency domain.

To evaluate currents and voltages at both ends of each pair, the MTLN technique is used [5, 6] because for telecommunications networks the length of the wire is L = 1 km and greater than. For automotive applications where the lengths are too shirt (some meters) we can used three-dimensional methods, solving the Maxwell equations in space, how require a fine discretization of each conductor of the beam in segments.

Conclusion.

In this work the equivalent cable harness method was applied at different groups of pairs and voltages for a model of twisted-wire pairs in a cable bundle of telecommunication networks.

The foremost attributes of the modified method are:

• the study of crosstalk is established in the frequency domain from 1 kHz to 30 MHz where the line is electrically long and the transverse electric and magnetic mode is considered;

• the conductor, twisted wire to wire in both configurations studied which affect the terminal loads and give rise to a new approach of the equivalent loads;

• the victim and culprit pairs considered as different groups and were involved in the reduced per unit length parameter matrices.

The crosstalk NExT and FExT are simulated at an arbitrary culprit pair in term of power loss this task allows reduction of complexity and computation time for a complete cable bundle modeling and maintains a fairly good precision, the total computation time is reduced by a factor of 2.8 after equivalence of the complete model by using the method of Multiconductor Transmission Line

Network theory for cable of 28 pairs (56 conductors), which have been performed on a 2.5 GHz processor and a 4 GB RAM memory computer. Numerical simulations presented in this paper validate the efficiency and the advantages of the proposed method.

Conflict of interest. The authors declare that they have no conflicts of interest.

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Received 19.11.2021 Accepted 20.01.2022 Published 20.04.2022

Samir Bensiammar 1, M.Sc. Student, Moussa Lefouili 1, PhD, Professor, Soufiane Belkhelfa 1, M.Sc. Student, 1 Mechatronic Laboratory, University of Jijel, Algeria,

e-mail: bensiammar.samir@umc.edu.dz (Corresponding Author), lefouili_moussa@yahoo.fr, sofiankhalf@gmail.com

How to cite this article:

Bensiammar S., Lefouili M., Belkhelfa S. Equivalent cable harness method generalized for predicting the electromagnetic emission of twisted-wire pairs. Electrical Engineering & Electromechanics, 2022, no. 2, pp. 29-34. doi: https://doi.org/10.20998/2074-