Modeling and Measuring the Shielding Effectiveness of Carbon Fiber Composites

1 Modeling and Measu ing he Shielding E ec i eness o Ca bon Fibe Composi es Luis D. Angulo, Da id Esco Bocaneg a, Pa icia G´ omez de F ancisco, Bo ja Plaza Galla do, Da id Poya os Ma inez, Miguel R. Cabello, Sal ado G. Ga cia, Senio Membe , IEEE Abs ac —We p o ide a model able o p edic he shielding e ec i eness (SE) o ca bon ibe composi e (CFC) panels made o s acked laye s o conduc ing ibe s. This model pe mi s us o ob ain simple o mulas in which he only pa ame e s needed a e he shee squa e esis ance and he e ec i e panel hickness. These ools le us o p edic a minimum SE, which always inc eases wi h he equency and he e o e cons i u ing he wo s case, om an elec omagne ic shielding pe spec i e. Consequen ly, he measu emen o minimum SE equi emen s can be simply measu ed wi h a mic o-ohmme e using an speci ic expe imen al se up which is also desc ibed he e. Addi ionally, his me hod allows o measu e e y high SE alling a beyond he dynamic ange o he alues measu able wi h he mos commonly used s anda d, he ASTM D4935. A e desc ibing he modeling echnique and he di e en es se ups used, a c oss- alida ion be ween heo e ical and expe imen al esul s is made o ou di e en samples o CFC; wo designed o es he modeling assump ions and wo which a e ep esen a i e o he ones nowadays used in a eal ai c a . Index Te ms—ca bon ibe composi es, elec omagne ic com- pa ibili y, shielding e ec i eness, hin-laye modeling I. INTRODUCTION IN RECENT TIMES ca bon ibe composi e (CFC) panels ha e ea ned a la ge sha e as design ma e ials in many in- dus ies, which g ea ly app ecia e hei mechanical p ope ies [1]. Howe e , om an elec omagne ic compa ibili y (EMC) pe spec i e, CFCs ha e in e io capabili ies when compa ed o he me als ha hey usually eplace [2]. Fo his eason, i is con enien o adequa ely model hei elec omagne ic shielding e ec i eness (SE) in o de o ensu e an adequa e p o ec ion o he di e en sys ems in which hey a e used. E en when hei mechanical cha ac e is ics a e well-known, hei elec omagne ic beha io p esen s many sub le ies which a ise om hei ilamen a y and s ock-piled geome y. On op o his, hey pose an in insically mul i-scala p oblem when hey mus be inco po a ed in o simula ions which in ol e an en i e sys em. Such p oblem is no ye ully sol ed o aniso opic hin laye s, bu some s eps ha e been made in ha di ec ion [3], [4]. Luis D. Angulo, M. R. Cabello, and Sal ado G. Ga cia a e wi h he Uni e si y o G anada, G anada 18071, Spain. (e-mail: lmdiazangulo@ug .es) Da id Esco Bocaneg a, Pa icia G´ omez de F ancisco, Bo ja Plaza Galla do and Da id Poya os Ma inez a e wi h he Na ional Ins i u e o Ae ospace Technology (INTA), in Spain. The wo k desc ibed in his pape and he esea ch leading o hese esul s ha e been suppo ed by he Spanish MINECO and EU FEDER unde P ojec TEC2016-79214-C3-1,2,3-R (MINECO, Spain), he EU PRACE p ojec 2018184436 ESECELS, and he Alhamb a-LFT con ac wi h AIR- BUS (Spain). The heo e ical modeling o hin panels has been add essed by many au ho s in he pas . A low equencies o when he conduc ing ibe s in he panel a e e y loose, a simple impedance model can be deduced [2], [5], [6]. Howe e , o ha e loose ibe s is no he mos common si ua ion o CFCs. On he con a y, ibe s a e ypically packed e y close and he main app oach consis s on de eloping an e ec i e pe mi i i y model om he conduc ing cha ac e is ics o ibe and he ma ix ma e ial [7], [8]. These implici ly assume he exis ence o a p oximi y e ec be ween cu en s induced in he ibe s, which domina es he SE a high equencies. Al hough alid, hese app oaches equi e he use o nume ical ools which make e y di icul o ack he ob ained SE o he di e en design pa ame e s in he CFC, such as he adius and ibe conduc i i y. Addi ionally, in hese wo ks, p edic ions a e alida ed wi h nume ical simula ions p oducing e y good ma ches, bu always lacking an expe imen al con i ma ion. F om an expe imen al app oach, we can ind many wo ks measu ing CFC panels wi h a ew laye s, ypically less han ou , and SE below 100 dB [9], [10]. This is ypically accom- plished using he ASTM me hod [11] o some a ian [12]. The measu emen o highe SE has no been epo ed despi e he ac ha CFCs o 10 o 30 laye s, wi h a bi a y o ien a ions, a e ubiqui ously used in ehicles, and can a guably p esen much highe shielding. The eason o his can be a ibu ed o he lack o a dynamic ange in he ins umen s employed which is ypically abou 100 dB. These wo ks also lack a connec ion be ween he mic oscopic le el and he measu ed SE. Mo eo e , he in e p e a ion o expe imen al esul s is con ined o he i ing o an e ec i e conduc i i y, which clea ly lacks he capabili y o explaining some o he obse ed phenomena. In his con ex , he aim o his wo k is o p opose and alida e a model which allows o connec high equency (HF) p ope ies wi h hei low equency (LF) ones, he la e much easie o measu e and ha ing a much la ge dynamic ange. Wi h he help o hese models, we de ise a new me hod which can accu a ely p edic and measu e much highe SE o CFCs, going beyond he ypical equency anges, han he ones epo ed un il now. II. MODELING METHOD A CFC is usually composed o se e al laye s o s acked ibe s wi h di e en o ien a ions, ypically o ming angles o 0, 45, o 90 deg ees among each o he (Fig. 1). These ibe s can be wea ed o laid s aigh , he la e being he subjec o 2 Fig. 1. Mic oscopic image o a CFC panel cu . Elec omagne ic wa es a e assumed o illumina e he panel coming om op o bo om o he image, o ice- e sa. Laye s o ming 45 o 90 deg ees a e seen as ellipsoids o lines, espec i ely. his wo k. A non-conduc i e ma ix esin is usually used o cu e he panels, gluing he ibe s oge he . When a ha monic plane-wa e, ha ing an inciden elec ic ield ampli ude (Ei) illumina es pe pendicula ly a la panel (Fig. 2), pa o i can be e lec ed (E ), ansmi ed (E ), o abso bed. The SE can be de ined as he in e se o he ansmission coe icien , SE =1 |T|=|Ei| |E |(1) In o de o de i e an exp ession om i s geome ical and physical pa ame e s, hin panels can be concep ualized as wo- po ne wo ks. The ields on one side (E1,H1) and he o he (E2,H2) a e ela ed by E2 H2= [Φ] E1 H1= Nl Y i=1 [Φi]E1 H1(2) wi h Φand Φibeing he ansmission ma ices, o ABCD ma- ices, o he whole hin panel and o each o he s acked laye s composing i , espec i ely. Fo panels loca ed in ee-space, cha ac e ized by an in insic impedance η0, he ansmission coe icien (T) can be ob ained as [13], T=2η0 Φ11η0+ Φ12 + Φ21η2 0+ Φ22η0 (3) No e ha Eq. (1) is a scala , which is su icien o iso opic media. Howe e , as CFCs a e in insically aniso opic media, we would need o accoun o he di e en pola iza ion modes ha illumina e he ibe in a ans e sal (TE) o pa allel (TM) di ec ion. Fo his kind o aniso opic media, we can de ine an a e age SE combining he ansmission coe icien s as SEa =2 |TTM|+|TTE|(4) Please no e ha (4) does no conside in e -mode con e sions which would domina e i wo consecu i e laye s o conduc i e ibe s a e no pe pendicula ly o ien ed. Howe e , o he sake o simplici y, we do no conside hese cases in he emainde o his wo k. z y x=ξ ζ ψ ϕ ETE ETM a P Fig. 2. Geome ical cha ac e is ics o he ca bon ibe seen om he on : diame e a, and pe iod P. The ep esen a ion wi h local (ξ, ψ, ζ) and global (x, y, z)coo dina e sys ems A. Single laye o CFC As a i s app oxima ion, le us assume a CFC composed o a single laye o homogeneously dis ibu ed ibe s wi h diame e a, in ini ely la ge, and pe iodically epea ed in he plane a e a dis ance P. The ma e ial which cons i u es hem is modeled wi h a conduc i i y σ which causes hem o ha e an e ec i e pe mi i i y o ε (ω) = ε0−jσ ω(5) Fibe s a e embedded in a dielec ic ma ix o esin wi h pe - mi i i y εmwi h a o al hickness da e cu a ion. The e o e, ibe s occupy a ela i e olume space o g=πa2 4Pd (6) This mix u e o ma e ials can be homogenized using an e ec- i e media app oach [7] which simpli ies hei elec omagne ic p ope ies o εTE =εm(1 −g)−1 εTM =ε g µTE =µTM =µ0(7) when ε εm. This simpli ica ion is jus i ied when we no e ha e en a equencies as high as ∼100 GHz, he conduc i e e m (σ/ω) will domina e o e he pe mi i i y in (5) e en o conduc i i ies as low as ∼6 Ω/m. In [2] we made an s udy on se e al models a ailable and ound ha o mos cases his homogeniza ion is su icien . F om hese assump ions, we can now deduce how TE and TM modes a e ansmi ed using he concep o ansmission ma ix in oduced in (2). F om [14], [Φ] = cosh(γd)ηsinh(γd) η−1sinh(γd) cosh(γd)(8) 3 wi h γ=jω√µε and η=pµ/ε being he ma e ial’s complex p opaga ion cons an and in insic impedance, espec i ely. Being aniso opic, he CFC suppo s wo p opaga ion modes, TE and TM. Fo TE modes he e m γTEd= jk0dqεmε−1 0is negligible o he ypical hicknesses o CFC panels a equencies below se e al GHz and a pe mi i i y o a ew ε0. In consequence, (8) educes o he iden i y ma ix and om (3) we ob ain ha TTE = 1. Wi h he TM mode he si ua ion is e y di e en as γTM is domina ed by he ibe conduc i i y. This allows γTMd o be also exp essed as a unc ion o he skin dep h δ= (π µσe)−1/2wi h σe=gσ being he e ec i e conduc i i y, as γTMd= (1 + j)d δ(9) and he in insic impedance as ηTM =2 1 + j 1 σeδ(10) Subs i u ing (8) in (3) |TTM|= cosh(γTMd) + 1 2 η2 TM +η2 0 ηη0 sinh(γTMd) −1 (11) o |TTM|= (ηTM +η0)2 4ηTMη0 eγTMd−(ηTM −η0)2 4ηTMη0 e−γTMd −1 (12) Le us now explo e Eq. 12 in wo equency egimes. In he LF egime, we can pe o m a i s o de Taylo expansion as e±γTMd≃≃1±γTMd. Using (9), (10) on (12); and conside ing ha o conduc i e panels |η||η0|below equencies up o hund eds o GHz, we ob ain |TTM,LF|= η0σed 2 −1 = 1 2 η0 R −1 (13) wi h R=1 σed(14) being he DC squa e esis ance o he laye . No e also, ha eq. (13) does no depend on he equency. In he HF egime, he app oach e−γTMd≃0can be made, and (12) akes he o m |TTM,HF|= √2 8η0σeδ eγTMd −1 = 4 √2 η0 R δ ded/δ −1 (15) which is domina ed by he exponen ial e m γTMd∝ω1/2. To iden i y he egime in which one o o he app oach is mo e pe inen , we can de ine wcas he co ne equency in which e−γTMd=e−1(o equi alen ly δ=d√2) esul ing in ωc=1 µ0σed2=R µ0d(16) An in e es ing esul which de i es om his equa ion is ha he SE o a hicke panel will p esen a HF exponen ial beha io a lowe equencies, e en i i has he same squa e esis ance as a hinne panel. Summa izing, om he p e ious discussion we ha e educed he p oblem o de e mining he SE o a CFC o knowing only wo a iables, i.e. he shee esis ance Rand he hickness d. Bo h, much mo e easy o ob ain expe imen ally han he exclusi ely geome ic ones. B. CFCs wi h an a bi a y numbe o s acked laye s Le us conside a simpli ied case in which we ha e a s ack o CFC laye s as he ones desc ibed in sec ion II-A o ming angles ϕo 0 o 90 deg ees angles wi h espec o he zaxis. We es ic ou discussion o jus hese angles o he simplici y o a oiding he in e -mode e ms which would appea in Φ a e applying he Moh ans o ma ions o enso o a ions. Fo a wa e a eling pe pendicula o he CFC (xaxis) he ields a bo h sides can be desc ibed wi h a gene alized e sion o (2),     Ey,2 Hz,2 Ez,2 −Hy,2     = Nl Y i=1 [Φϕi,i] [Φϕi−90◦,i]    Ey,1 Hz,1 Ez,1 −Hy,1     (17) whe e [Φϕi,i]co esponds o he i- h laye wi h ibe o ming an angle ϕiwi h espec o he zaxis. Fo ins ance, le us assume a wa e pola ized in he ydi ec ion. This implies ha [Φ0◦]co esponds o a TM ansmission and [Φ90◦] co esponds o a TE ansmission. III. EXPERIMENTAL SETUPS A. ASTM D4935 s anda d es The ASTM S anda d D4935 [11] allows he measu emen o he SE o a plana ma e ial unde he ac ion o TEM mode elec omagne ic ields in a coaxial line. The use o his mode only allows o measu e he SE a e aged o all di ec ions, i.e. he measu emen o pu e TE o TM modes is impossible wi h his me hod. The s anda d ensu es ha he me hod is alid o e a equency ange o 30 MHz o 1.5GHz o a no mally inciden wa e. I also p o ides he dimensions o he specimen holde which is indeed an enla ged, coaxial ansmission line wi h special ape sec ions and no ched ma ching g oo es o main ain a cha ac e is ic impedance o 50 Ω h oughou he en i e leng h o he holde . Ins ead o ab ica ing an exac copy o his langed-coaxial sample holde (FCSH), we ha e de eloped an al e na i e se up based on comme cial connec o s and which has been used o his wo k. This is based on wo 3 1/8” EIA o N emale adap e s om SPINNER wi h modi ied inne connec o s (Fig. 3). The diame e s o he ou e and inne conduc o s o his adap e s a e 76.9mm and 33.4mm espec i ely, wha yields a cu -o equency o 1.73 GHz be o e o e moding, in ag eemen wi h he bounds o he s anda d. The signal gene a o and he ecei e desc ibed in he s anda d we e subs i u ed o a ec o ne wo k analyze (VNA) whose po s 1 and 2 a e di ec ly connec ed h ough coaxial cables o each o he N connec o s o he adap e s. The SE o he ma e ial unde es (MUT) agains a la TEM wa e wi h no mal incidence is hen ob ained om he measu emen o he inse ion loss (IL) in he FCSH o med by he wo adap e s connec ed o each o he . Then, he expe imen al SE is e alua ed as SE = 20 log10  S21,L S21,R  (18) whe e S21,L and S21,R a e he measu ed sca e ing pa ame e s ela ed o he elec omagne ic powe ans e ed om he VNA 4 Fig. 3. The wo 3 1/8” EIA o N emale adap e s used in his wo k as sample holde s. po 1 o he VNA po 2 when he FCSH is illed wi h he load and e e ence samples o he specimen, espec i ely. Thus, wo samples a e needed o a ce ain MUT and hey mus be iden ical in hickness o ge he bes epea abili y o SE measu emen s. The s anda d speci ies he dimensions o he e e ence and load samples o he a o emen ioned FCSH. I is wo h no ing ha he s anda d does no men ion any need o u he manipula ion o he samples so hey we e no modi ied o imp o e he elec ical con ac be ween hem and he coaxial holde , as opposed o [9]. I is impo an o men ion ha du ing he es s, he hal es o he cell a e connec ed by means o nylon sc ews, in o de o 1) minimize s ay ield coupling, 2) educe he con ac esis ance wi h he sample, and 3) imp o e he capaci i e coupling be ween he wo FCSH langes desc ibed in [12]. In o de o be su e ha he o que gi en o he sc ews is always he same, a calib a ed dynamome ic o que w ench was used. B. DC esis ance es In he ollowing se up, we aim o measu e he DC squa e esis ance (14) o he samples. This is he esis ance be ween wo opposi e sides o a squa e and i is independen o i s size. To ca y ou his es he ma e ials equi ed we e: a specimen suppo , a mic o-ohmme e , and a pneuma ic p ess (Fig. 4). The specimen suppo consis s o wo me allic holde s sepa a ed by wo polyme s uc u es ab ica ed wi h a 3D p in e . This suppo makes possible ha he cu en d i es only in one di ec ion h ough he sample ( e ically in Fig. 4). To ensu e a good con ac be ween he me allic holde s and he sample, sil e pain was used on he sides o he sample in con ac wi h he holde s, p e iously cleaned wi h isop opyl alcohol. The pain ed sample is hen placed in o he pneuma ic p ess, MEGA PRP20 model [15] wi h a nominal o ce o 20 ons in o de o wa an y enough p essu e o an adequa e ohmic con ac wi h he ibe s and epea abili y o measu emen s. To measu e he elec ical esis ance o he samples, a Kei hley 580 mic o-ohmme e [16] was used. This Fig. 4. Tes se up o DC esis ance measu emen s. The ed pa s belong o he hyd aulic p ess used o make p essu e on he specimen holded by he blue pa s. A mic o-ohmme e was used o measu e he squa e esis ance o he sample. uni is designed o esis ance measu emen equi emen s om 10 µΩ o 200 kΩ. The samples used in his se up we e 200 mm long and 200 mm wid h, while he hickness depends on he numbe o CFC laye s. IV. THEORETICAL MODEL AND EXPERIMENTAL CROSS-VALIDATION In o de o alida e he model in oduced in sec ion II and he expe imen al se ups desc ibed in III we ha e selec ed ou di e en samples o CFC. Two samples, Monolaye and Bilaye , ha e been designed and manu ac u ed wi h he aim o being as simple as possible in o de o simpli y hei modeling. A second se ies o wo samples, codenamed Red and Blue, is ep esen a i e o he CFCs used in he MILANO ai c a . The MILANO is a emo ely pilo ed ai c a sys em de eloped by INTA and cu en ly in ope a ion. All samples we e made wi h a Cy ec MTM 45-1 epoxy ma ix and HexTow IM7- 12K ca bon ibe . The pa icula numbe o laye s and he di e en o ien a ions used du ing he s acking sequence o he di e en samples is summa ized in Table I. E e y laye is made o unidi ec ional ows composed o 12000 ibe s each, wi h diame e a= 5.2µm and esis i i y σ−1 = 1.5mΩ·cm. Ha ing a ow densi y o h ee ows pe cen ime e his adds o 3.6×105 ibe s/m. A e cu a ion, each laye has a o al phys- ical hickness dp= 128 µm. Howe e , we mus dis inguish be ween he physical hickness and he e ec i e hickness,d. We de ine das he dis ance o ibe ma e ial a e sed by he wa e in which he ibe is aligned wi h he elec ic ield (TM mode). Using Eq. (14) we ob ain a p edic ed alue o R,l = 196 mΩ o each o hese laye s. The Monolaye sample is composed o a single laye as he one desc ibed p e iously. In his case, he R alue could no be measu ed wi h he DC esis ance es because being so hin and weak, he laye could no be wa an ed an a achmen o he holde wi hou being damaged. To compu e i s SE, we 5 TABLE I MEASURED SAMPLES Name S acking Sequence Laye s Monolaye 0 1 Bilaye 0/90 2 Red 45/-45/0/-45/45/90/90/45/-45/0/-45/45 12 Blue 45/-45/-45/0/45/90/45/0/-45/-45/0/45/90/45/0/45/-45/45 18 TABLE II MEASURED AND PREDICTED VALUES Name d[µm]P ed. R[mΩ] Meas. R[mΩ] P ed. SELF [dB]Meas. SELF [dB]P ed. c[GHz] Monolaye 128/0 196/∞ − 6.0 5.7±0.3 1.220 Bilaye 128 196 −59.6 57.1±0.5 1.220 Red 768 98 99.6±6.8 75.2−0.033 Blue 1152 49 46.4±0.4 78.7−0.015 Fig. 5. SE expe imen al esul s ob ained wi h he applica ion o he modi ied e sion o ASTM D4935 s anda d desc ibed in sec ion III-A. ealize ha TTE = 1 is much la ge han TTM. The e o e Eq. (4) gi es a alue o SEa = 2 = 6 dB (Table II). In Fig. 5 we obse e he expe imen al esul s o he SE o his sample and we can ealize ha a e ∼1.5GHz hey end o he p edic ed alued o 6dB. The de ia ion om he cons an alue in he ange om 0.1GHz o 1.5GHz can be a ibu ed o he aniso opic na u e o he sample. This e ec was co obo a ed by a simula ion using he HFSS so wa e [17], a comme cial Fini e Elemen Me hod nume ical sol e . Below 0.1GHz he de ia ion co esponds o he los o capaci i e coupling be ween he samples and he FCSH which makes impossible any ansmission [11], possibly mixed wi h he capaci ance s ay e ec s epo ed in [12]. The Bilaye sample combines wo laye s pe pendicula ly laid. Using (16) we ind ha non-cons an e ec s should be obse ed beyond 1.220 GHz, as he da a in Fig. 5 s a s o ain ly sugges . In his case we ind ha TTE =TTM a e calcula ing he ansmission ma ix in (17). In consequence a LF, he SE is simply SELF =2R η0 = 59.6dB (19) which g ea ly coincides wi h he measu ed alue o 57.1± 0.5dB. We can also obse e ha , again, and mainly below 0.1GHz, he ASTM s anda d ails o p o ide eliable mea- su emen s and ends o o e es ima e he SE, as men ioned in i s in oduc ion [11]. The Red and Blue samples a e made o 12 and 18 laye s, s acked pe pendicula ly wi h hei neighbo s in mos cases. The cases in which he ansi ions a e no pe pendicula would lead us o expec some in e -modal con e sions which may modi y he assump ions made in sec ion II bu which we will igno e as hey all beyond wha we can measu e in he scope o his wo k. The squa e esis ance o hese samples was measu ed using he se up desc ibed in sec ion III-B inding alues ha co obo a e he squa e esis ance p edic ions made om pu e geome ical conside a ions (Table II). The same assump ions as wi h he Bilaye case we e made o p edic SELF alues o 75.2dB and 78.7dB o he Red and Blue samples, espec i ely. Howe e , when we compu e hei co ne equencies using (16), we p edic ha his LF egime ends a 33 MHz and 15 MHz, espec i ely. This means ha abo e hose equencies we mus obse e a SE which g ows exponen ially wi h ω1/2. This is wha we obse e in he ange 6 up o 0.4GHz jus be o e he alues escape he dynamic ange o he VNA. As in he p e ious cases, he ASTM s anda d does no p o ided eliable esul s below 0.1GHz. This, oge he wi h he e y low expec ed alue o cmakes impossible o p o ide a measu emen o SELF and we a e le only wi h he heo e ical p edic ions which se an in e io limi o he samples. V. CONCLUSIONS In his wo k we ha e p o ided a model able o p edic he SE o some CFC panels ep esen a i e o he ones used in eal ai c a s (Sec. II). This modeling pe mi ed us o ob ain simple o mulas in which he only pa ame e s needed o make p edic ions a e he shee squa e esis ance and he e ec i e panel hickness; bo h easy o ob ain wi h inexpensi e equipmen . These ools le us o p edic a minimum, o wo s case, SE. This minimum alue is always a LF and always inc eases wi h he equency. In consequence, he measu emen o minimum SE equi emen s can be deduced simply wi h a mic o-ohmme e using he expe imen al se -up desc ibed in sec ion III-B. REFERENCES [1] G. G. Gu ie ez, D. Ma eos, M. R. Cabello, E. Pascual-Gil, L. D. Angulo, and S. G. Ga cia, “On he design o ai c a elec ical s uc u e ne - wo ks,” IEEE T ansac ions on Elec omagne ic Compa ibili y, ol. 58, no. 2, pp. 401 – 408, Ma ch 2016. [2] L. D. Angulo, M. R. Cabello, J. Al a ez, A. R. B e ones, and S. G. 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