lineas de trasmision

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Technical Theme Topics c d

Transmission Lines and Interconnects

Welcome to the first set of papers on traditional and emergingthemes of interest to EMC practitioners. In this issue we addressthe topic of Transmission L ines and Interconnects. These havebeen used extensively for many years and their behaviour is wellunderstood. However, as we increasingly use interconnects athigher frequencies and in ever increasing complexity of configura

tions, new issues have emerged which require a deeper understanding of the assumptions on which popular models of propaga

tion and coupling are based.

The first paper by Besnier et al examines the characterization of

propagation on wire harnesses typically found in automotive and

aerospace applications and how radiation losses may be accommodated within the relatively simple formalism of transmissionline theory, especially near wire resonances and for particularloading conditions when their impact is the greatest.

The paper by De utter considers the calculation of the RLGCparameters of multi-conductor lines typically encountered inprinted circuit boards and on-chip. Problems associated with thedefinition of voltage and current over a wide range of frequenciesand in mixed material environments (perfect electric conductors,good conductors, dielectrics and semi-conductors) are alsoaddressed in detail.

Some Limiting Aspects of Transmission LineTheory and Possible ImprovementsP B S b d c K '/ETR UMR CNRS 1 Rennes, France PSA Peugeot Citron, Vlizy-Vilacouba [email protected]

Abstract

Wiring still supports most of electric power fluxes as well as data transmission in various infrastructures and transport systems.Hopefully, transmission line theory is a very helpful approximation to estimate interference propagation among cable harnesses. Thisis definitely a useful tool for engineers, since it enables anticipating the probability of failure of equipment they are connected to.Everything has been written from the initial roots of transmission line derivation, dated from the ancient telegraphist's equationsestablished by . Heaviside back to.. . 1880! until the last developments of sophisticated and off-the-shelf transmission line solvers forcomplex arrangements of cable networks. The fact is, that these tools are so familiar to many EMC engineers that it might come withsome misunderstanding of some results. In this paper, we take a look at the root assumptions of this approximate theory and examinesome of its potential weaknesses, through simple examples. Then, we investigate the question of the possible improvement of theclassical transmission line theory (when and if required). In principle, this would require the derivation of some kind of generalized

transmission l ine theory or even the examination of the super theory of transmission lines. We rather show that a much more simplemodification of transmission line equations is possible for a better approximation of the experimental observations.

Transmission line theory (TLT): From school books to real world

School books generally describe electric cable links as theoretical (multi-conductor) transmission lines, in which straight horizontalcoated or uncoated wires are placed parallel to each other and parallel to a perfect conducting (or lossy) ground plane. To close theelectrical circuit at each end, these horizontal wires are connected to the ground plane by vertical wires that are terminated by loads,but that are not part of the theoretical (multi-conductor) transmission line model.

In practice however, this is generally not the case. Depending on the domain (aircraft, domestic, power lines, automotive, railway,

PCB etc), these theoretical models are more or less representative, either geometrically or electrically. For instance, in the automotive industry, harnesses are made of cables bundled together and routed in the vehicle wherever it is convenient (Fig. 1). Automotiveharnesses are typically non-uniform, and composed of single wires, assembled cables and twisted pairs. Some coaxial cables can

ltmat Cmpatlt Maa lm 3 Qat


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Figure 1: A typical bundle and example of the electrical archiecture of a vehicle

Signa Battery

/Zero vot conuctors

Figure 2: A typical piece of wiring system in a vehicule

also be found, but in very few numbers, mainly to connect antennas for RF applications or to shield power links of electric powertrains. Shielded harnesses, even partially, are practically never chosen because of their specific connector requirements, their overall weight and cost.

From a wiring point of view, the electrical system of a vehicle often uses the metallic car body as part of the return currents' path(Fig.2) but the equipment is generally not directly connected to the car body, leading to portions of harnesses where the returncurrents from the equipment are carried by wires in the harness (zero-volt conductors). To avoid increasing considerably the number of wires connected to the vehicle body, several equipotential conductors in a same harness are very often connected by splices at a given position within the harness. Signals and power are therefore transmitted and received by the equipment eitherbetween two wires of a same harness, between a wire and the car body, or both alternatively. Finally, parts of the harness do notrun close to the body of the vehicle (e. g. behind the dashboard), and can pass over slots and gaps (e.g. between the car body and

the engine). Therefore, the return currents are forced to deviate from beneath the harness. In such a real world context, one caneasily recognize that:

The loads (equipment) are not connected to ground at the end of the harness and the vertical wires at the end of the harness(at the equipment location) do not exist

When connected to the reference ground plane (car body), the transition of the contact wires are progressive and do not look likevertical wires

The harnesses have interleaved wires, that lead to non-uniform cross-sections that must be modeled by segmentation

The distances between the harnesses and the reference ground plane (car body) can be important compared to the wavelengthand therefore breaches the conditions of applicability of the multi-conductor transmission line theory.

Nevertheless, even with all these imperfections, multi-conductor transmission line theory remains extremely useful to model such complex harnesses in real electrical systems because it avoids having to represent the harness as a geometrical structure in the same wayas the car body (electromagnetic model), introducing multi-scale, model size and computation time issues. However, in order to produce

simulation results closer to those that can be obtained by an electromagnetic model, multi-conductor transmission line models havebeen improved in the past decade to overcome most of their drawbacks, in particular the loss of energy by radiation which will be themain focus of this article.



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Classical transmission line theory

In this section we recall directly the telegraphist's equations that bind the voltage difference between a single wire and ground and thecurrent that flows in this wire. For the sake of simplicity, this paper deals with the case of a single wire forming a transmission line overa surrounding ground. We will not provide all the theoretical details about the derivation of the corresponding equations. Readers interested in these mathematical developments should refer to original articles and well-known textbooks on this topic 4

1 Oriin of Tlrit qutionThe situation is that of a single uncoated wire of radius and length g lying at a height over an infinite ground plane. The wire is considered as a perfect electrical conductor (PEC) and is aligned with the z axis of the Cartesian coordinate system a,,y,zwhile theground plane lies in the a,y,z plane.

Complete details of the following derivation may be found in Maxwell's equations in an infinite domain surrounding the sources may besorted out in terms of the electric field vector or the magnetic field vector and equivalently in terms of scalar potential and

vector potential Given the sources in terms of current (J) and charge densities p one obtain:

2

Note that these relations are derived after having adopted an appropriate gauge relation between the scalar and vector potential (here,the L orenz gauge Therefore, the following important relationships define and

H=-\xAfo

= jwA \

3

4

The derivation of TLT equations from Maxwell's equations follows the procedure below. The excitation field gives rise to the scatteredfield s which is the exact opposite to the applied field e at the wire's surface:

Since the scattered field obeys Maxwell's equations, it satisfies (4) as well. Moreover, and are governed by (2) and (1) respectively.

Given the general solution of Eq. 1 and of Eq. 2 and introducing the continuity equation that relates and J Uw+V.J=Ol one can derivethe following coupled equations:

\ jWfou

I()go(, )d = Eh, , )

1L9 dI(). -go(z, z')dz'+c=0]WEo d

6

7

where goz,z' is the free-space Green's function that governs the radiation at the observation pointz given the source point z' Eq uations and () already look like the Telegraphist's equations (see Eq. 10 and Eq. 11 in next b-section). The scalar potential will be directlyidentified with the scattered voltage difference Vis taken as the line integral of the electric field along the x-axis. To fully recover the TLT,one has to determine the terms in the integral of Eq. and Eq. The Green's function for the case of a wire of radius at a height overa ground plane is given by:

8



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For small enough with respect to the wavelength ,(h k /2)we find the following approximate result for the integral of Eq. :

iLg j

z

' +2h 2h1(z')90(Z, z')dz' 1(z) 90(Z, z')dz' - -)1(z)

o

z

l

2

h

2 a 9

A similar result is provided for the integral in Eq. This approximation of the integral of the Green's function is the basis of the classicalTLT. Note that the integral of the Green's function is therefore approximated as a pure real number. This is equivalent to say that TLT

does not consider radiation (antenna mode). The scattered field is confined and entirely guided along the wire axis: the transverse electromagnetic (TEM) mode of propagation. Another consequence is that the intrinsic or characteristic impedance of the line is also a purereal number (Zc

v

LIC and the per-unit-ength (p.u.l.) parameters for a lossless transmission line are given by

L 2h

. d C 2Eoo -

7

n an

0- InC) .

Tlrit qution

Therefore, Maxwell's equations yield clearly to TLT if the three following conditions are met:

1. The cross-section of the wire is much smaller than its length and much smaller than the minimum significant wavelength.Namely, it is the so-called thin wire approximation. It may additionally assumed that it is much smaller than its height.

2. fwhere f is the minimum significant wavelength of involved signals.

Then, come the Telegraphist's equations for continuous waves with angular frequency C:

dVs(z)dz

jwLo1(z) E;h, , z)

d1(z)

jwCoV(z)

Approximation of Eq. 9 is in fact accepted if conditions 2 f and 3 g apply. This point will be specifically addressed in section 3.

3 Limitations of transmission line theory

The previous section infers that the current induced on the transmission line propagates along the line without giving rise to any radiation effects, i.e. without loss of energy elsewhere than in the loading impedances at the wire's ends (for a lossless transmission line).

Should a radiation effect occur, it would be associated with a loss of energy that could be related to a radiation resistance Rr This oneis defined as Pr=(Rr /2)(zo) where Pr is defined as the total radiated power and o as an arbitrary location on the wire. A trans

mission line may be therefore seen as a 1D-cavity that stores electric (line's capacitance) and magnetic energy (line's inductance) balanced by the real part of the loading impedances. If the radiation resistance accounts for a non negligible part with respect to theimpedance of the line determined by the loading resistances (at a given angular frequency), then the current predicted on the transmission line may be different from the one that would be found using a full-wave calculation.

Saying this is in some way equivalent to admit that the transmission line acts as 1 D-cavity with a (more or less) high -factor driven bythe loaded impedances. Indeed, according to the -factor definition, it is, within a period of time and in steady state, the ratio betweenthe stored energy and the power losses. In transmission line theory power losses (if any) only occur at the end-of-wire resistances andthrough Joule's effect if considered. Not accounting for the radiation resistance is therefore neglecting a loss mechanism that wouldlower the 0factor of the transmission line.

These phenomena may be highlighted thanks to a simple example that will be used throughout all this paper. This example is depicted in

Fig.3. A voltage source e is applied at the extremity z=O of a single transmission line of diameter 2 at a height over a PE infiniteground plane. The internal impedance of the source is labeledZowhereas the other extremity of the line is loaded by the impedanceZv

ltmat Cmpatlt Maa lm 3 Qat 9


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20 L

h

xz

Figure 3. A cylindrical wire of dimeter 2a and length L and excited by a localized genetor e over a PEC innie ground plane

Let's have a look at two load configurations. Load impedances are pure resistances given by Z=Z=50 in the first configuration andZ=O and Z= in the second configuration. In both cases, we extract the current crossing Z through the classical TLT and compare it with a full-wave solution provided by a method of moments (MoM) software. Throughout this paper, the contribution of Joule'slosses of the copper wires has not been taken into account neither in the modified TLT simulations nor in the MoM simulations.Thelength of the wire is =m and its height over the ground plane is =10. However, the calculation by the MoM requires that a closedcircuit exists between the end of the horizontal wire and the ground plane. For this purpose, two vertical wires each of 10cm long, areadded using the same cylindrical wire of diameter 2=1.5mm. In turn, these vertical wires are simulated in TLT by extension of the wire

length such as =+2(1.2 m) with identical characteristic impedance 6

-44

-46

-48P= -50

U

-52

-54

Transmission Line Theory

Method of Moments

/

J

5

6L

le+07 le+08Frequency (Hz)

Figure 4 Current in ZL obtained through classical TLT and MoM for configuration 1: ZO=ZL =50 Q (e=0.632 V)

For both configurations (see Fig.4 and Fig.5), we first note that there is a good agreement between MoM and TLT with a noticeableexception around resonances. Focusing now on these resonance effects, it also appears that the higher the frequency, the worse is the

comparison between the maximum magnitudes predicted by TLT (theoretically constant) and the maximum level predicted by the MoMwhich becomes lower and lower. Around resonances, the wire stores energy which is entirely lost in the load impedances by theapproximation of the classical TL However, a part of this energy is radiated, a phenomenon which is taken into account in the MoM. Inconfiguration 1, since the load impedances are 50, the part of energy they absorb is the most significant and differences between maximum at resonances between curves of Fig. 4 reach 5 dB at 500 MHz. In configuration 2, the load impedance in only . Under these circumstances, the electric losses are much smaller and the radiation losses are predominant. Resonances are much sharper, but theQ-factor of resonances obtained from the TLT is much higher than the ones obtained from the MoM calculations. This time, radiationlosses provide a noticeable difference. At 500 MHz the predicted current magnitude given by the MoM is about 40 dB less than the oneprovided by TL

A widely accepted rule of thumb states that TLT is applicable if the condition s 0 is fulfilled. This would correspond to an upper frequency of 300 MHz in this example. The above configurations show that the applicability of TLT, in its classical form may be questionable

and would probably require another condition at least around resonances. This condition concerns the relationship between the radiation resistance and the terminal loads. Fig. illustrates this point showing the near-field mapping all around the transmission line for bothload configurations. A a frequency of 130 MHz, which corresponds to the first resonance of the line, the contribution of the radiated



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electric field from the ends of the wire is clearly much more significant in the configuration Z=O andZ= (right hand side). n thecontrary, at a frequency of 200 MHz, far away from a resonance, the two near field distributions are similar in both cases.

0

-

-10

-20

Transmission Line Theory

Method of Moments

le+08Frequency (Hz)

Figure 5: Current in ZL obtained through classical tnsmission line theo and method of moments for configuration 1: ZO=Q and ZL=Q (e= V)

X EF Jud* cBVlfO.0.

a) Frequency 13 MHz

b Frequeny 2 MHz

.'x

X EF rin udtBV m)"l-

(a ) Frequency 13 MH

Fequey = 2 Mz

.z

X

Figure 6: Near field mapping of the x-component (horizontal) electric eld around the tnsmission line at 130 MHz and 200 MHz for two dferent

load congutions ZO=ZL=50 Q (e=0.632 left-hand side), ZO= Q and ZL= Q (e= right-hand side)

4. A solution to overcome this limitation

nce the TLT limitations have been recalled, we aim at discussing ways of overcoming these ones. pen literature suggests differentsolutions that range from iterative solutions 47 to the introduction of the transmission line super theory As a common feature of thesereferences and others, a key element is to obtain a rigorous solution of Eq. 9 rather than its approximate solution. As already mentioned,

this approximation resulted to the conclusion that the integral of the Green's function (Eq. 8) was the product of a pure real scalar and ofthe current distribution along the line. A rigorous calculation of this integral leads to a complex scalar. Its real part is a frequency dependent number accounting for the evolution of the and C p.u.l. parameters of the line. Its imaginary part is related to the radiation proper

ties and more specifically to the and G p.u.l. parameters. Therefore it results in a new definition of the p.u.l. parameters.

A complete mathematical analysis of the resulting p.u.l. parameters, so called RHF,LHF,CHF,GHF, was developed. These parametersmay be put into the following form :

2

3

4



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with M calculated as:

6

In these expressions, C() accounts for an adding correction factor of the rigorous solution of the integral of the Green's function (Eq.9). Its expression is given in It is highly dependent on the angular frequency. C()tends to a null value when 0 and therefore thep.u.l. parameters converge to classical ones :LHF(O)=Lo RHF(O)=O CHF(O)=C' HF(O)=O.

The existence of a radiation mode is equivalent to have RHF and HF non-null. They have been established from a reference work Note that RHF is different from the definition of the radiation resistance Rdthat accounts for current distribution along the line whereas RHF is independent from the current distribution and is a p.u.l. parameter in Q/m. The most important consequences are the resultingproperties of the propagation constant and of the characteristic impedance of the transmission line. First of all, the propagation constantis not affected by this change in the p.u.l. parameters and remains a pure imaginary number ( jw j

Wyf

o

J

o)

.

This isexplained by the balanced relationship RHFCHF+HFLHF=O. However the characteristic impedance becomescomplex and is given by:

7

Therefore, the characteristic impedance of the transmission line is split into its classical TEM mode and a radiation mode that corresponds to its imaginary part which appears as the ratio of the p.u.l. resistance to the wavenumber.

We could therefore solve the transmission line equations under this enhanced form:

d

(z)+ (RHF+jwLHF)J(z)= E(h,0, z) 8

9

However, solving this new pair of equations leads to the same solution as the classical solution for the current and voltage induced onthe line. It is due to the fact that the TEM mode and the radiation mode both propagate without losses and no modification of the boundary conditions are introduced. To account for radiation losses at the termination of the line, a possible solution is to add the imaginarypart of the characteristic impedance as loss resistances at ends of the transmission line.

Another solution consists in inserting an additional p.u.l. resistance in series with RHF. This additional p.u.l. resistance, labeled R+ isadjusted to account for the radiation losses. Therefore, the equivalent circuit for a short section of a transmission line, with respect tothe wavelength, becomes that of Fig.

IE

z

I

GHFdzl

Figure 7 Equivalent circuit of a short section of a lossless tnsmission line of length dz' wih the new deniion of p.u.l. pameters and an additional p.u.l. resistance (R+)

For small values of R+ the propagation constant may be written as:



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2

Adjusting the value of R+ consists in equating the power losses along the length of line Lg (i.e. 1-exp(2aLg)) and the inverse of theQ-factor of the transmission line given by the ratio of the imaginary part of the characteristic impedance of the transmission line to itsreal part:

2

We thus extract R+ as:

22

Therefore, a possible solution consists in using the enhanced version ofTelegraphist's equations (i.e. Eq. 18 and Eq. 19) with the additionof a p.u.l . resistance R + to account for radiation losses. The next section is dedicated to the application of this modified version of thecoupled equations of TLT to the previous examples.

5 Application of the modified version of TLT

The two examples of section 2 are now calculated with the modified version of TLT and the result is compared with the MoM simulation.

-44Modied Transmission Line Theory Method of Moments

-46

"

-48

P g -50

U

' -52

I

-54

\1 I

5

6

- L

-

le 07 le 08

Frequency (Hz)

Figure 8 Current in ZL obtained through moded TTand MoM for configution 1: ZO=ZL=50 Q (e=.632 V)

Fig.8 shows that the maximum current associated with successive resonance frequencies tends to decrease following the trend of theMoM simulation. The modified TLT involves differences of only one or two dB: for this load configuration (Zo=Z=50 ) this modified version of TLT may be considered as unnecessary, in this frequency range. An opposite conclusion may be drawn as regards to the result ofFig.9. The magnitude of current at resonances has been deeply reduced and is now much closer to the magnitude of the resonancesobtained by the MoM.

In both cases, two additional remarks may be provided. i) In the low frequency region, the response of the modified transmission line formalism is not different from the classical one since, in that case the modified p.u.l. are close to classical ones: RHF" 0 , GHF" 0 LHF

LO, CHF" CO. ii) The results from the modified transmission line theory do not exactly match those of the MoM. The main explanationfor this is the role played by the vertical wires considered only as additional sections of the transmission line in TLT. Their own radiation

properties are fully taken into account in the MoM calculation only.



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-

-10

Modified Transmission Line Theory

Method of Moments

6

0

-------

------

le+07 IN08Frequency (Hz)

Figure 9: Current in ZL obtained through classical TTand MoM for configution 1: ZO= Q and ZL=1 Q (e=1 V)

An experimental validation is provided in the configurationZo=Z=50Q. For this purpose, the uncoated wire is installed over a ground

plane and ended into a connector which is fited in the ground plane itself (see Fig.O), thus being as close as possible to the configuration whichwas simulated with the MoM method. The measurement was performed using a sine wave generator with a constant amplitude, tuned from10 MHz to 500 MHz and a spectrum analyzer. This experiment confirms the general trend about the slight reduction of the maximum current of thesuccessive resonances on the line as obseed with the MoM and as reproduced by the modified TLT formalism described in this paper.

. I .

\

j

Figure 10: Experimental test set up

-

44

-48

-50"

U -52

-54

-56

Modied Transmission Line Theory

Method of MomentsMeasurement

le+07 le+08Frequency (Hz)

,'\

,

',

gure 11: Cuent in ZL obtained fm experiment and comparison with moded TTand MoM results for conguration 1: ZO=ZL=50 Q (e=0.632 V)



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6. ConclusionTLT is commonly used to determine currents and voltages induced within cable networks and at devices' inputs. Resonances are imporant phenomenaat the origin of radiated emission or radiated immunity issues. However, although TLT provides a rather excellent way for evaluating field to cable inter

ferences, it has some weaknesses. ne of them is the accuracy of the estimation of currents and voltages specifically at resonances, depending ontransmission line boundary conditions. ne may assume this estimation is likely to be incorrect at resonances specifically for low or high values of loadimpedances (i.e. magnitude of reflexion coeficients close to 1). This is related to non negligible values of the radiation resistance that accounts forantenna mode. This parameter tends to increase with the ratio of the height of the transmission line to the wavelength. A modified version of TLT is presented in this paper, based on the calculation of the integral of the Green's function. This leads to enhanced p.u.l. parameters including per-unit-ength

resistance and conductance associated with the radiation properies of the wire. Neverheless, this leads only to the decomposition of energy in thewire into a transmission line mode and an antenna mode (imaginary par of the characteristic impedance). Therefore, this one is still not radiated. Consequently, we introduce an additional loss resistance that dissipates the corresponding radiated energy. The modified equations of TLT obtained keepthe simplicity of the classical ones and are compatible with standard solvers, since they only involve a modification of per-unit-ength parameters.Results are shown to be much closer to the MoM calculation than the classical formalism at resonances.

7 References1. C Paul, "Frequency response of multiconductor transmission lines illuminated by an electromagnetic field," IEEE Transactions on Electromagnetic Compatibility, vol.

18, no. 4, pp. 183-190, November 1976.2. A. Agrawal, H. Price, and S. Gurbaxani, "Transient response of multiconductor transmission lines excited by a nonuniform electromagnetic field," IEEE Tns. ec-

tmagnetic Compatability, vol. 8, no. 24, 1988.3. C. Paul, Analysis of multiconductor transmission lines WileyBlackwell (2d edition), 2007.

4. F. Rachidi and S. Tkachenko, Electmagnetic field interaction with transmission lines. WIT Press, 2008.5 J Nitsch, F. Gronwald, and G. Wollenberg, Radiating non-uniform tnsmission line systems and the partial element equivalent circuit method Wiley, 2009.6. P. Oegauque and A. Zeddam, "Remarks on the transmission line approach to determining the current induced aboveground cables," IEEE Transactions ectmag

netic Compatability, vol. 30, no. 1, pp. 77- 80, February 1988.7. Y Bayram and J Volakis, "A generalized MoM spice iterative technique for field coupling to long terminated lines," ectnic Letters, vol. 47, no. 3, pp. 222-223, February 2011.8. S. Chabane, P. Besnier, and M. Klingler, "Extension of the transmission line theory application with modified enhanced perunitIength parameters," Progress in

ectmagnetics Research vol. 32, pp. 229-244, September 2013.9. J Nitsc h and S Tkachenko, "Complexvalued transmission line parameters and their relation to the radiation resistance," IEEE Transactions lectromagnetic

Compatability, vol. 3, no. 3, pp. 477-487, August 2004.

8 BiographiesPhippe Besnier (M'04, SM0) received the diplome dngnieur degree fm Ecle Universitaire dngnieurs de Le (EUDIL

Le, France, in 19 and the Ph.D. degree in electnics fm the universi f Le in 1993. Fwing a ne year perid at ONER,

Meudn as an assistant scientist in the EMC divisi he was with the Labrat f Radi Ppagatin and ectnics, Universf Le, as a researcher at the Centre Natinal de la Recherche Scientifique (CNRS) fm 19 t 199 Fm 1997 t 2 Philippe

Besnier was the Directr f Centre d'Etudes et de Recherches en Ptecn ectmagntique (CERPEM): a nn-pfit rganiza

tin fr researc expeise and training in EMC, and related activities, based in Lava France. He c-funded TEKCEM in 199 a

private cmpany specialized in tu-key systems fr EMC measuremen. Back t CNRS in 2 he has been since en with e

Instute f ectnics and Telecmmunicatins f Rennes (IETR), Rennes, France. Philippe Besnier was appinted as senir

researcher at CNRS in 2013 and has been c-head f the Antennas and Micwave devices depament f IETR since 2012. His research activies are

mainly dedicated t inteerence analysis n cable haesses (including electmagnetic tplgy), reverberatin chambers, near-field pbing and

recently t the analysis f unceain ppagatin in EMC mdeling.

Mao Kngler was b in Zuric Swiean in 196. He received his Engineer degree in cmputer science fm H, Le

(France) in 198 his DEA (S.) degree in autmatics/ btics and his Ph.D. in electnics in 1989 and 1992 respectivel bth

fm the Universiy f Le. He then jined the French Nanal Institute fr ansp and Safey Research (INRETS) in Vieneuvedscq (France) as a researcher where he was in charge f e R&D acvities in EMC f gund anspatin systems. His main

_ interes were electmagnetic inteerences n PCBs, behavir f electnic cmpnents in electmagnetic envinmen,

cupling t wire stctures, test methds, and test facies. In 22, he jined PSA Peuget Citn in Vzy-Viacublay (France)

in the Develpment Divisin where he was successively in charge f the EMC design activities, the EMC/ antenna simulan

activities, and finay the EMC fu vehicle validatin activies. In 201 1, he mved t the Research Divisin where he is currently an

EMC pe and respnsible f e EMC/ antenna research activies. His main interes include EMC mdeling and simulatin f autmtive electric

pweains, mul-cnductr transmissin lines, new materials, and specific vehicle antennas.

Sofiane Chabane was b in Azazga, Algeria, in 1983. He received the Diplome Dtudes Universitaires Appliques (B.S. ) degree

in 25 and the Engineers degree in 28 bth in aenautics and fm Institut dAnautique de Ba (Saad Dahleb Universiy),

Ba (Algeria). In 200, he received the master degree (S.) in physics f cmplex natural and industrial systems (SC), fm

Universi f Rennes 1, Rennes (France). He is currently wrking tward the Ph. D. degree in elecnics and telecmmunicatins

at e Institute f ectnics and Telecmmunicatins f Rennes (IETR), INSA f Rennes, France. His current main research inter

es include electmagnetic cmpatibil and inteerence, elecmagnetic field interactin with transmissin lines, electmag

netic mdeling and simulatin. EMC

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