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1 Jounal of Applied Reseach and Technology ISSN: Cento de Ciencias Aplicadas y Desaollo Tecnológico México Neuda, M.; Vojtech, L. Veification of Suface Conductance Model of Textile Mateials Jounal of Applied Reseach and Technology, vol. 10, núm. 4, agosto, 2012, pp Cento de Ciencias Aplicadas y Desaollo Tecnológico Distito Fedeal, México Available in: How to cite Complete issue Moe infomation about this aticle Jounal's homepage in edalyc.og Scientific Infomation System Netwok of Scientific Jounals fom Latin Ameica, the Caibbean, Spain and Potugal Non-pofit academic poject, developed unde the open access initiative

2 Veification of Suface Conductance Model of Textile Mateials M. Neuda* 1, L. Vojtech 2 1, 2 Czech Technical Univesity in Pague, FEE, Dept. of Telecommunication Engineeing Technicka 2, Pague, Czech Republic *maek.neuda@fel.cvut.cz ABSTRACT Suface conductance is one of the main paametes which descibes basic chaacteistics of specific textile mateials. These textile mateials ae used, fo example, in envionments with highe equiements on hadwae electostatic potection duing thei poduction pocess. Published measuement standadized methods ae followed by modeling methods which do not each satisfactoy esults. This pape is theefoe focused on the modeling of suface conductance of textile mateials. The esults show that the stuctue of textile mateials can be seen as seial-paallel connections of esistos. A deivation of this model is descibed. Keywods: deivation, suface conductance, textile mateial. RESUMEN La supeficie de la conductancia se encuenta dento de los paámetos pincipales de mateiales textiles específicos y descibe sus caacteísticas básicas. Estos mateiales se usan po ejemplo en situaciones donde se equiee una potección electoestática paa el hadwae duante el poceso de poducción. Los métodos de medida estándaes publicados siguen métodos modelados que no alcanzan esultados satisfactoios. Po lo tanto, este infome se enfoca en modela la supeficie de la conductancia de mateiales textiles. Los esultados muestan que la estuctua de los mateiales textiles pueden considease como conexiones de esistencias seie-paalelo. Se descibe, además, una deivación de este modelo. 1. Intoduction Suface conductance of textile mateials is often caused by coating of the textile which is composed of non-conductive fibes. This type of textiles achieves high values of suface conductance in wide fequency band and is used, fo example, in the constuction of flexible antenna stuctues. Suface conductance modeling is geneally based on the examination of conductance of uppe metal laye of oiginally non-conductive textiles. The suface esistance of these textile mateials is calculated as esistance between standadized electodes [1]. It is equivalent to 1/(t σ) [2], whee σ is the conductance of coating mateial on the textile suface with thickness t. Suface conductance modeling is geneally pefomed by 3D softwae [3], which simulates a specific model. Pesent modeling methods ae not sufficient in the case of equiements of exact modeling of textile mateials suface conductance duing thei poduction. Simplified models mainly malfunction with textiles with low suface conductance which ae poduced fom cabon, fo example. Cabon fibes ae chaacteized by electic conductivity in thei whole coss section and, theefoe, these textiles ae classified as textile mateials with conductive fibes. Resultant conductance of these fibes cannot be eplaced by suface conductance of theoetical homogeneous sheets which is used at coating mateial modeling. The eason is seen in electic conductivity, which is an indispensable component of inhomogeneity between weft and wap. Pesented models completely malfunction at equiement of modeling of textile mateials with the ability to distibute electostatic chage. The textiles ae used fo potection against undesiable effects of accumulated chages with the aid of 57 Vol. 10 No. 4, August 2012

3 Veification of Suface Conductance Model OF Textile Mateials, M. Neuda. / electostatic dischage (ESD). The eason of malfunctioning is due to the stuctue of textiles. Bigge distances in wap and weft fom athe conductive gid than homogeneous stuctues. Standad statistic and geometic models malfunction similaly. These models ae used fo a desciption of electic chaacteistics of multicomponent mateials [4]. The model of these electoconductive textile mateials, poduced fom coated non-conductive fibes and conductive fibes, can be seen fom the electical point of view as finite gid of esistos. The fibes fom the esultant stuctue of the textile. A close investigation of the stuctue shows, in a big magnification, it is a stuctue of cossed fibes which fom egula shapes in geneal. In ideal case these shapes ae squaes o ectangles with sides composed of fibes and the ai between them. Evey side of squae, special case of ectangle, epesents one esisto. These esistos ae connected togethe and fom a finite gid. The pape descibes the calculation of a egula squae finite gid of esistos, which is veified by simulation softwae. Standadized measuement methods ae used fo valuation of length esistance [5]. The model and its calculation esult fom the application of textile mateials with antistatic conductive fibes which ae used in ESD applications fo potection of electonic devices. The confimation is pefomed with espect to dimensions of standadized pobes [6] and common distance of conductive fibes in textile mateials [4, 7]. The est of the pape is oganized as follows: Section 2 descibes the deivation of a ecently published fomula of esistance of a egula esisto gid. Section 3 intoduces a veification of an equipotential line pesumption by simulation and calculation model. Finally, Section 4 pesents the conclusions. conside standad EN :2006 [1] o EN [2] which descibe a test method fo measuement of suface esistivity. A gauging fixtue of the method is composed of coaxially odeed electodes. The inne pobe diamete is 30 mm and the oute one is 63 mm in [6]. A measued sample is put between them. This setting of measuement expeiments leads to an idea to connect one pole of battey in the middle of the gid and the second one on the oute edge of the gid. The fist step of the calculation is to find and veify the fomula, descibing the ectangula stuctue of the textile mateial; theefoe, the calculation focuses on ectangula shapes of inne and oute electodes. The second step is specification of this fomula fo the cicle shape. Pevious eseach shows it is possible to calculate the esultant esistance as [] R' 1 R' 1 R' R, n 5, ),, naeodd 4 n5n1 4 n5n3 (1) whee R denotes the esultant esistance, R' epesents a length esistance of fibe fo squae dimension, and n ae connected esistos R' in the hoizontal diection. Despite the esultant fomula being published, the complete deivation is not descibed and the calculation is not veified by othe methods. The fist pat of (1), R'/, epesents paallel esistos connected between two poles of battey, o electodes. It foms a shape depicted in Fig Resistance of Gid of Resistos A calculation of the esultant esistance equies that the gid of esistos is connected to the electical cicuit. Poles of battey can be connected on both sides of the gid; howeve, it is bette to Figue 1. Gid of esistos (n=3, R'=). Jounal of Applied Reseach and Technology 579

Veification of Suface Conductance Model OF Textile Mateials, M. Neuda. / 57 54 The second pat of (1) descibes connected esistos between the electodes, o poles of batteies.

The solid line epesents esistos which ae connected in paallel between two electodes. Fo n=5, the second goup of esistos in a ow of calculation contains 16 esistos. This fact is also shown in Fig. 2.

It means paallel-connected esistos ae added up with othe paallel connected esistos as connection in seies. The eason is of couse in the same potential.

4 Veification of Suface Conductance Model OF Textile Mateials, M. Neuda. / The second pat of (1) descibes connected esistos between the electodes, o poles of batteies. The calculation uses a pesumption of connection of nodes with same potentials. Fig. 1 depicts the equipotential line fo n=3. The solid line epesents esistos which ae connected in paallel between two electodes. Fo n=5, the second goup of esistos in a ow of calculation contains 16 esistos. This fact is also shown in Fig. 2. If n is inceased, othe esistos ae added into the gid. These esistos ae only added as an addend of the cuent ones, but they ae connected in paallel with each othe. It means paallel-connected esistos ae added up with othe paallel connected esistos as connection in seies. The eason is of couse in the same potential. This pesumption is fundamental fo the coect deivation of the model and, theefoe, the following sections focus on its confimation. Equation (2) is ewitten as R whee m, {1, 2, 3, 4}. m1 R ' m (3) Equation (3) can be extended to incease n, and it leads to an extension of set of paametes m, ; theefoe, m, {N}. The elation between paamete n and m can be calculated fom: m 1, n 3 mn 2, m 2, n 5 m n3, m 3, n 7 m n 4, etc. The esultant fomula of (4) can be expessed as (4) whee x {0, 1, 2,..}. Consideing: m n 2 x (5) x 0, n 3, x 1, n 5, x 2, n 7, etc, (6) The elation between paametes x and n is calculated as Figue 2. Pesumption of points with the same potential of the textile mateial. Consideing n=3, n=5, n=7 and n=9, the esultant esistance is calculated as R' R' R' R' R (2) whee R'/ is the paallel-connected esistos fo n=3 and, accodingly, R'/16 fo n=5, R'/24 fo n=7 and R'/32 fo n=9. n 1 x 2 (7) 2 If (7) is substituted into (3), the second pat of (1) can be expessed. A value m=1 is eliminated because it is aleady expessed as the fist pat of (1). R' 1 R' 1 R' R m2m n5 n (2 x) n5 n 1 n (2 2) 2 1 R' 1 R' n5 2n n 1 4 n5n 1 2 () 50 Vol. 10 No. 4, August 2012

5 Veification of Suface Conductance Model OF Textile Mateials, M. Neuda. / The thid pat of (1) epesents the est of esistos which fom the cones of Fig. 3. It is calculated fom This simulation confims the pesumption of potential levels fo n=5. n 5 R R' R' R' R' R' R', n 7 R, n 9 R, etc (9) This dependence is used as 1 R' R' R' 1 R' R' R' 1 R' R n5 n 3 (10) Figue 3. Simulated electic cicuit fo n=5. 3. Reification of Equipotential Line Validity The confimation is pefomed with espect to ESD applications fo potection of electonic devices. It is possible to use the pobes with diametes 30 mm and 63 mm [6], which ae poduced accoding to EN [2]. Common distance of antistatic conductive fibes in weft in these textile mateials is appoximately 10 mm [4, 7]. Consideing a squae with dimensions 10 x 10 mm, inne diamete includes 3 squaes and oute 5 squaes. Seven squaes ae not consideed because all esistos between n=5 and n=7 ae not included. Theefoe, n=5 is consideed as a sufficient value fo the applications, which equie potection against undesiable effects of ESD. Equation (1) is valid if evey goup of paallel connected esistos has one connection end in one potential level and the second connection end in othe potential level. Then the esultant esistance is calculated as a pue addition. A lot of pogams exist which enable to simulate chaacteistics of electical cicuits. It is possible to use, fo example, a pogam called Oegano, GNOME application fo schematic captue and pinting of electical cicuits [9]. Fig. 3 depicts a simulated electical cicuit. It also shows a placement of voltage pobes of the same potential levels. The esults ae depicted in Fig. 4. It shows only one line of two pobes because the lines ae coveed with one anothe. The values of voltage ae, theefoe, the same. Figue 4. Voltage in chosen points of electical cicuit fo n=5. Equation (1) is also inteesting fom anothe point of view. Equipotential lines cause some esistos to be equal to zeo in the esultant esistance. These esistos ae connected by thei both ends to the same potential level. They ae placed on hoizontal and vetical lines which coss the inne electode. Simulation esults show this pesumption is confimed as well because the same voltage value is measued on both ends of these esistos; howeve, this pesumption can also be confimed o disconfimed by a calculation of the esultant esistance with the aid of electical cicuit laws. Basic ules elated to the counting of paallel- o seial-connected esistos and tansfomation delta-sta, sta-delta ae used in the simplification of cicuits. These electical laws ae used in Fig. 5, Fig. 6 and Fig. 7 fo n=5. They even depict values of individual esistos, whee R1 in the figues is equal to R' in the calculation. The Jounal of Applied Reseach and Technology 51

6 Veification of Suface Conductance Model OF Textile Mateials, M. Neuda. / value of the esultant esistance is shown in Fig. 7, scheme f), it is 5/24 R'. This fomula has to be theefoe specified. The diffeence is caused by the seial-paallel connection of esistos placed in the cone of the esistance gid. It is not simple addition of esistos. The specified deivation is obtained fom the connection, Fig. 9. Figue 5. Redawn electical cicuit and its modification by Delta-sta (D-S) tansfomation (n=5). If an electic cicuit in Fig. 6 a) and pesumption of equipotential lines ae consideed, nodes maked A1-A4 and nodes B1-B have the same potential and can be connected o disconnected as necessay. It leads to elimination of esistos placed between nodes B1-B, B2-B3, B4-B5 and B6-B7 which ae connected by thei both ends to the same potential level, Fig.. Resultant esistance is then calculated as (symbol indicates paallel connected esistos): Figue 6. Modified electical cicuit by Delta-sta (D-S) and Sta-delta (S-D) tansfomation (n=5). This esult confims the pesumption of equipotential lines fo n=5. R ' ææ R ' R ' ö R ' ö R ' æ R ' R ' ö ' ' 5 R= + çç ç ç + = + = R + R = R' çè èçç ø ø çè 4 ø (11) Consideing (1), the esult is R' 1 R' 1 R' R R' R' (12) Figue 7. Value of esultant esistance of electic cicuit is maked f) (n=5). This fomula has to be theefoe specified. The diffeence is caused by the seial-paallel connection of esistos placed in the cone of the esistance gid. It is not simple addition of esistos. The specified deivation is obtained fom the connection, Fig Vol. 10 No. 4, August 2012

7 Veification of Suface Conductance Model OF Textile Mateials, M. Neuda. / R' R' R' R' n 5 Rc R' R' R' R' R' R' n 7 Rc 16 R' R' R' R' R' R' R' R' n 9 Rc (13) This dependence is geneally ewitten as * R' R' * R' R' R' Rc Rn2, R5 4n 3 (14) Figue. Simplified electical cicuit by eliminating specific esistos. This impovement of (1) descibes esistance of the cones of the gid; howeve, it includes also esistos placed on the equipotential line which cosses the oute electode, Fig. 2. These esistos ae eliminated in the second pat of (2). The specified fomula is expessed as: R R R R R R R R n n ae odd R ' 1 ' * ' * ' ' ' n2, 5, ),,, 5 n5 n n (15) Accoding to the specified fomula (15), the esultant esistance fo n=5 can be calculated fo the veification of the electical cicuit depicted in Fig. 5 as R' R' R' R' R' R' R' R' R' 5 R 0 R' (16) Figue 9. Seies paallel connection of esistos in one cone of the gid. Resistance of all fou cones of the gid fo n=5, n=7 and n=9 is expessed as The esult (16) confims that the specified fomula fo ectangula shapes of electodes is valid. It also veifies the pesumption of equipotential lines fo n=5. Consideing the dimensions of the inne ectangula electode, it is possible to subtact n esistos R' in the hoizontal and vetical diection of the gid. Jounal of Applied Reseach and Technology 53

8 Veification of Suface Conductance Model OF Textile Mateials, M. Neuda. / Conclusions This pape focuses on the desciption of the suface conductance model which is applicable to antistatic textile mateials used in ESD applications fo the potection of electonic devices. A pesumption of equipotential lines is intoduced and veified by a simulation softwae and by the calculation of the esistance of the electic cicuit. The esults show the pesented fomula fo esistance calculation is valid fo this application. Futue wok will conside shote dimensions of conductive fibes which will decease the intensity of the electic field and chage of electicity. It will enable even integated cicuits to make contact with this textile mateial. The esulting goal of this wok is a model which consides cicle shapes of electodes of suface conductance measuement standad. This will enable to model the textile befoe its poduction. [7] Novak, M., The Model of Suface Electical Conductivity of Special Fabics, Maste Thesis, CTU in Pague, Czech epublic, [] Neuda, M. & Vojtech, L., Suface Conductance of Textile Mateials Modeling, Knowledge in Telecommunication Technologies and Optics, Decembe, 2010, p [9] Ubuntu [online] [cit ]. Package: oegano ( ubuntu ) [univese]. Available: Refeences [1] Standad BS EN :2006: Potective clothing. Electostatic popeties. Test method fo measuement of suface esistivity, Available at: PoductDetail/?pid= [2] Lilja, J. & Salonen, P., On the modeling of conductive textile mateials fo SoftWeaAntennas, Antennas and Popagation Society Intenational Symposium, 2009, pp.1-4, Chaleston, South Caolina, USA, June. [3] Li, L., AU, W. M., Wan, K. M., Wan S. H., Chung W. Y., Wong K. S., A Resistive Netwok Model fo Conductive Knitting Stitches, Textile Reseach Jounal, Vol. 0, No. 10, Novembe, 2009, p [4] Masalkova, M., Electic behavio of Textiles with Antistatic Popeties and Methods of Thei Evaluation, PhD. Thesis, Technical Univesity of Libeec, Czech Republic, 200. [5] Safaova, V. & Geg, J., Electical Conductivity Measuement of Fibes and Yans, 7th Intenational Confeence TEXSCI, 2010, Libeec, Czech epublic, Septembe. [6] Concentic Ring Pobes, Vemason, The Specialists in ESD Potection [online], 2012 [cit ], Available at: FullCatalog/TestEquipment/SufaceResistanceTestes/C oncenticringpobes/ 54 Vol. 10 No. 4, August 2012

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